Study on Financial Management

Description
Financial Management means the efficient and effective management of money (funds) in such a manner as to accomplish the objectives of the organization.

CHAPTER 2 1. As a rule of thumb, real rates of interest are calculated by subtracting the inflation rate from the nominal rate. What is the error from using this rule of thumb for calculating real rates of return in the following cases? Nominal rate (%) Inflation rate (%) Solution:
Nominal rate(%)(NR) Inflation rate(%) ( IR) Real rate by the rule of thumb(%) Correct rate(%)=(1+NR)/(1+IR)-1 Error from using the rule of thumb(%) 7 4 3 2.88 0.12 12 6 6 5.66 0.34 18 8 10 9.26 0.74 22 10 12 10.91 1.09

7 4

12 6

18 8

22 10

2.

As a rule of thumb, real rates of interest are calculated by subtracting the inflation rate from the nominal rate. What is the error from using this rule of thumb for calculating real rates of return in the following cases? Nominal rate (%) Inflation rate (%) 4 1 8 3 11 2 19 4

Solution:
Nominal rate(%)(NR) Inflation rate(%) ( IR) Real rate by the rule of thumb(%) Correct rate(%)=(1+NR)/(1+IR)-1 Error from using the rule of thumb(%) 4 1 3 2.97 0.03 8 3 5 4.85 0.15 11 2 9 8.82 0.18 19 4 15 14.42 0.58

CHAPTER 3 1. At the end of March, 20X6 the balances in the various accounts of Dhoni & Company are as follows: Rs. in million Accounts Balance Equity capital Preference capital Fixed assets (net) Reserves and surplus Cash and bank Debentures (secured) Marketable securities Term loans (secured) Receivables Short-term bank borrowing (unsecured) Inventories Trade creditors Provisions Pre-paid expenses 120 30 217 200 35 100 18 90 200 70 210 60 20 10

Required: Prepare the balance sheet of Dhoni & Company as per the format specified by the Companies Act. Solution: Balance Sheet of Dhoni & Company As on March 31, 20 X 6 Liabilities Share capital Equity Preference Reserve & surplus Assets Fixed assets 120 Net fixed assets 30 200 Investments Marketable securities Current assets, loans & advances 100 90 Pre-paid expenses Inventories 70 Receivables Cash & Bank 60 20 690 217

18

Secured loans Debentures Term loans Unsecured loans Short term bank borrowing Current liabilities & provisions Trade creditors Provisions

10 210 200 35

690

2.

At the end of March, 20X7 the balances in the various accounts of Sania Limited are as follows: Rs. in million Accounts Balance Equity capital Preference capital Fixed assets (net) Reserves and surplus Cash and bank Debentures (secured) Marketable securities Term loans (secured) Receivables Short-term bank borrowing (unsecured) Inventories Trade creditors Provisions Pre-paid expenses 250 80 380 350 100 190 30 120 420 110 310 90 70 20

Required: Prepare the balance sheet of Sania Limited as per the format specified by the Companies Act. Solution: Balance Sheet of Sania Limited as on March 31, 20 X 7 Liabilities Share capital Equity Preference Reserve & surplus Fixed assets 250 Net fixed assets 80 350 Investments Marketable securities Current assets, loans & advances 190 120 Pre-paid expenses Inventories 110 Receivables Cash & Bank 90 70 1260 380 Assets

30

Secured loans Debentures Term loans Unsecured loans Short term bank borrowing Current liabilities & provisions Trade creditors Provisions

20 310 420 100

1260

3.

The comparative balance sheets of Evergreen Company are given below: Owners' Equity and Liabilities Share capital Reserves and surplus Long-term debt Short-term bank borrowings Trade creditors Provisions Total Assets Fixed assets (net) Inventories Debtors Cash Other assets Total As on 31.3.20X6 70 40 80 80 40 10 320 120 90 60 25 25 320 (Rs. in million) As on 31.3.20X7 70 80 90 85 70 20 415 210 95 65 30 15 415

The profit and loss account of Evergreen Company for the year ending 31st March 2007 is given below: (Rs. in million) Profit & Loss Account for the Period 1.4.20X6 to 31.3.20X7 Net sales Cost of goods sold Stocks Wages and salaries Other manufacturing expenses Gross profit Operating expenses Selling, administration and general Depreciation Operating profit Non-operating surplus or deficit EBIT Interest Profit before tax Tax Profit after tax Dividends Retained earnings 750 505 290 105 110 245 135 120 15 110 (20) 90 25 65 15 50 10 40

Required:

(a) Prepare the classified cash flow statement for the period 1.4.20X6 to 31.3.20X7 (b) Develop the cash flow identity for the period 1.4.20X6 to 31.3.20X7

Solution: A. Cash flow from operating activities - Net profit before tax and extraordinary items - Adjustments for Interest paid Depreciation - Operating profit before working capital changes - Adjustments for Inventories Debtors Trade creditors Provisions Increase in other assets - Cash generated from operations Income tax paid - Cash flow before extraordinary items Extraordinary item - Net cash flow from operating activities Cash flow from investing activities - Purchase of fixed assets - Net cash flow from investing activities Cash flow from financing activities - Increase in loans - Dividends paid - Interest paid Net cash flow from financing activities Net increase in cash and cash equivalents - Cash and cash equivalents as on 31.03.20X6 - Cash and cash equivalents as on 31.03.20x7 It has been assumed that “other assets” represent “other current assets”.

85 25 15 125 (5) (5) 30 10 10 165 (15) 150 (20) 130 (105) (105)

B.

C.

15 (10) (25) (20) 5 25 30

D.

Note

(b) A.

Cash flow from assets - Operating cash flow - Net capital spending - Decrease in net working capital - Cash flow from assets Cash flow to creditors - Interest paid - Repayment of long term debt - Cash flow to creditors Cash flow to shareholders - Dividends paid - Net new equity raised - Cash flow to shareholders

90 (105) 35 20

B.

25 (15) 10

C.

10 0 10

We find that (A) i.e., Cash flow from assets = = (B) + ( C) Cash flow to creditors + Cash flow to shareholders

4.

The comparative balance sheets of Xavier Limited are given below: Owners' Equity and Liabilities Share capital Reserves and surplus Long-term debt Short-term bank borrowings Trade creditors Provisions Total Assets Fixed assets (net) Inventories Debtors Cash Other assets Total As on 31.3.20X6 20 10 30 15 10 5 90 16 44 20 5 5 90 (Rs. in million) As on 31.3.20X7 30 18 25 15 15 8 111 20 55 21 8 7 111

The profit and loss account of Xavier Limited for the year 2007 is given below: (Rs. in million) Profit & Loss Account for the Period 1.4.20X6 to 31.3.20X7 Net sales 220 Cost of goods sold Stocks Wages and salaries Other manufacturing expenses Gross profit Operating expenses Selling, administration and general Depreciation Operating profit Non-operating surplus or deficit EBIT Interest Profit before tax Tax Profit after tax Dividends Retained earnings Required: 140 90 35 15 80 40 20 5 15 1 16 4 12 2 10 2 8

(a) Prepare the classified cash flow statement for the period 1.4.20X6 to 31.3.20X7 (b) Develop the cash flow identity for the period 1.4.20X6 to 31.3.20X7

Solution : A. Cash flow from operating activities - Net profit before tax and extraordinary items - Adjustments for Interest paid Depreciation - Operating profit before working capital changes Adjustments for Inventories Debtors Trade creditors Provisions

11 4 5 20

(11) (1) 5 3

B.

Increase in other assets - Cash generated from operations Income tax paid - Cash flow before extraordinary items Extraordinary item - Net cash flow from operating activities Cash flow from investing activities - Purchase of fixed assets - Net cash flow from investing activities Cash flow from financing activities - Increase in equity - Repayment of term loans -Dividend paid - Interest paid Net cash flow from financing activities Net increase in cash and cash equivalents - Cash and cash equivalents as on 31.03.20X6 - Cash and cash equivalents as on 31.03.20x7

(2) 14 (2) 12 1 13 (9) (9)

C.

10 (5) (2) (4) (1) 3 5 8

D.

Note (b) A

It has been assumed that “other assets” represent “other current assets”.

B.

C.

Cash flow from assets - Operating cash flow - Net capital spending - Decrease in net working capital - Cash flow from assets Cash flow to creditors - Interest paid - Repayment of long term debt - Cash flow to creditors Cash flow to shareholders - Dividends paid - Net new equity raised - Cash flow to shareholders

19 (9) (9) 1 4 5 9 2 (10) (8)

We find that (A) i.e., Cash flow from assets = = (B) + ( C) Cash flow to creditors + Cash flow to shareholders

CHAPTER 4 1. Premier Company's net profit margin is 8 percent, total assets turnover ratio is 2.5 times, debt to total assets ratio is 0.6. What is the return on equity for Premier? Net profit Return on equity = Equity = Net profit x Net sales = Debt Note : Total assets = 0.6 So Total assets 0.08 x Total assets 1 2.5 x 0.4 Equity = 1- 0.6 = 0.4 = 0.5 or 50 per cent Net sales x Equity Total assets

Solution:

Hence Total assets/Equity = 1/0.4 2. The following information is given for Alpha Corporation Sales 3500 Current ratio 1.5 Acid test ratio 1.2 Current liabilities 1000 What is the inventory turnover ratio? Solution: Current liabilities x 1.5 1000 x 1.5 = 1500 Current liabilities x 1.2 1000 x 1.2 = 1200 300 3500 Inventory turnover ratio = = 11.7 300 The following information is given for Beta Corporation. Sales Current ratio Inventory turnover ratio Acid test ratio 5000 1.4 5 1.0 Current assets = = Quick assets = = Inventories =

3.

What is the level of current liabilities?

Solution: Inventory = 5000/5 = 1000 Current assets Current ratio = Current liabilities Current assets – Inventories Acid test ratio = Current Liabilities C.A - 1000 = 1.0 CL CA CL 1.4 CL 1000 0.4 = CL 4. Safari Inc. has profit before tax of Rs.90 million. If the company's times interest covered ratio is 4, what is the total interest charge? CL = 2500 CL 1000 = 1.0 1000 = 1.0 = 1.0 = 1.4

Solution: PBT = Rs.90 million PBIT Times interest covered = Interest So PBIT = 4 x Interest PBT = PBIT – interest = 4x interest- interest = 3 x interest = 90 million Therefore interest = 90/3 = Rs.30 million 5. A has profit before tax of Rs.40 million. If its times interest covered ratio is 6, what is the total interest charge? = 4

Solution: PBT = Rs. 40 million PBIT Times interest covered = Interest So PBIT = 6 x Interest PBIT – Interest = PBT = Rs.40 million 6 x Interest – Interest = Rs. 40 million 5 x Interest = Rs.40 million = 6

Hence Interest = Rs.8 million 6. McGill Inc. has profit before tax of Rs.63 million. If the company's times interest covered ratio is 8, what is the total interest charge?

Solution: PBT = Rs.63 million PBIT Times interest covered = Interest So PBIT = 8 x Interest PBIT – Interest = PBT = Rs.63 million 8 x Interest – Interest = 7 x Interest = Rs.63 million Hence Interest 7. = Rs.9 million = 8

The following data applies to a firm : Interest charges Rs.200,000 Sales Rs.6,000,000 Tax rate 40 percent Net profit margin 5 percent What is the firm's times interest covered ratio?

Solution: Sales = Rs.6,000,000 Net profit margin = 5 per cent Net profit = Rs.6,000,000 x 0.05 = 300,000 Tax rate = 40 per cent

300,000 So, Profit before tax = (1-.4) Interest charge = Rs.200,000 = Rs.500,000

So Profit before interest and taxes = Rs.700,000 Hence Times interest covered ratio = 700,000 = 3.5 200,000 8. The following data applies to a firm: Interest charges Sales Tax rate Net profit margin Rs.50,000 Rs.300,000 25 percent 3 percent

What is the firm's times interest covered ratio? Solution: Sales = Rs.300,000 Net profit margin = 3 per cent Net profit = Rs.300,000 x 0.03 = 9,000 Tax rate So, = 25 per cent 9,000 Profit before tax = (1-.25) Interest charge = Rs.50,000 62,000 = 1.24 50,000 9. The following data applies to a firm : Interest charges Sales Tax rate Net profit margin Rs.10,000,000 Rs.80,000,000 50 percent 10 percent So Profit before interest and taxes = Rs.62,000 Hence Times interest covered ratio = = Rs.12,000

What is the firm's times interest covered ratio?

Solution: Sales = Rs.80,000,000 Net profit margin = 10 per cent Net profit = Rs.80,000,000 x 0.1 = 8,000,000 Tax rate = 50 per cent 8,000,000 So, Profit before tax = = Rs.16,000,000 (1-.5) Interest charge = Rs.10,000,000 So Profit before interest and taxes = Rs.26,000,000 Hence 26,000,000 Times interest covered ratio = = 2.6 10,000,000 10. A firm's current assets and current liabilities are 25,000 and 18,000 respectively. How much additional funds can it borrow from banks for short term, without reducing the current ratio below 1.35?

Solution: CA = 25,000 CL = 18,000 Let BB stand for bank borrowing CA+BB = CL+BB 25,000+BB = 18,000+BB 1.35x 18,000 + 1.35 BB = 25,000 + BB 0.35BB = 25,000- 24,300 = 700 BB = 700/0.35 = 2,000 11. LNG’s current assets and current liabilities are 200,000 and 140,000 respectively. How much additional funds can it borrow from banks for short term, without reducing the current ratio below 1.33? 1.35 1.35

Solution: CA = 200,000 CL = 140,000 Let BB stand for bank borrowing

CA+BB = CL+BB 200,000+BB = 140,000+BB 1.33 1.33

1.33 x 140,000 + 1.33BB = 200,000 + BB 0.33 BB = 200,000- 186,200 = 13,800 BB =13,800/0.33 = 41,818 12. Navneet’s current assets and current liabilities are 10,000,000 and 7,000,000 respectively. How much additional funds can it borrow from banks for short term, without reducing the current ratio below 1.4?

Solution: CA = 10,000,000 CA+BB = CL+BB 10,000,000+BB = 7,000,000+BB 1.4 x 7,000,000 + 1.4BB = 10,000,000 + BB 0.4 BB = 10,000,000- 9,800,000 = 200,000 BB = 200,000/0.40 = 500,000 13. A firm has total annual sales (all credit) of 25,000,000 and accounts receivable of 8,000,000. How rapidly (in how many days) must accounts receivable be collected if management wants to reduce the accounts receivable to 6,000,000? 1.4 1.4 CL = 7,000,,000

Let BB stand for bank borrowing

Solution: 25,000,000 Average daily credit sales = = 68,493 365 If the accounts receivable has to be reduced to 6,000,000 the ACP must be: 6,000,000 = 87.6 days 68,493

14.

A firm has total annual sales (all credit) of 1,200,000 and accounts receivable of 500,000. How rapidly (in how many days) must accounts receivable be collected if management wants to reduce the accounts receivable to 300,000?

Solution: 1,200,000 Average daily credit sales = 365 If the accounts receivable has to be reduced to 300,000 the ACP must be: 300,000 = 91.3 days 3287.67 15. A firm has total annual sales (all credit) of 100,000,000 and accounts receivable of 20,000,000. How rapidly (in how many days) must accounts receivable be collected if management wants to reduce the accounts receivable to 15,000,000? = 3287.67

Solution: 100,000,000 Average daily credit sales = 365 If the accounts receivable has to be reduced to 15,000,000 the ACP must be: 15,000,000 = 54.8 days 273,972.6 16. The financial ratios of a firm are as follows. Current ratio Acid-test ratio Current liabilities Inventory turnover ratio What is the sales of the firm? = = = = 1.25 1.10 2000 10 = 273,972.6

Solution: Current assets = Current liabilities x Current ratio = 2000 x 1.25 =

2500

Current assets - Inventories = Current liabilities x Acid test ratio = 2000 x 1.10 = 2200 Inventories = 300 Sales = = Inventories 300 x Inventory turnover ratio x 10 = 3000

17.

The financial ratios of a firm are as follows. Current ratio = Acid-test ratio = Current liabilities = Inventory turnover ratio = What is the sales of the firm?

1.33 0.80 40,000 6

Solution: Current assets = Current liabilities x Current ratio = 40,000 x 1.33 = 53,200 Current assets - Inventories = Current liabilities x Acid test ratio = 40,000 x 0.80 = 32,000 Inventories Sales = = = 21,200 Inventories x Inventory turnover ratio 21,200 x 6 = 127,200

18.

The financial ratios of a firm are as follows. Current ratio Acid-test ratio Current liabilities Inventory turnover ratio What is the sales of the firm? = = = = 1.6 1.2 2,000,000 5

Solution:

Current assets = Current liabilities x Current ratio = 2,000,000 x 1.6 = 3,200,000 Current assets - Inventories = Current liabilities x = 2,000,000 x Inventories Sales = = = 800,000 Inventories x Inventory turnover ratio 800,000 x 5 = 4,000,000 Acid test ratio 1.2 = 2,400,000

19.

Complete the balance sheet and sales financial data: Debt/equity ratio Acid-test ratio Total assets turnover ratio Days' sales outstanding in Accounts receivable Gross profit margin Inventory turnover ratio

data (fill in the blanks) using the following = = = = = = 0.80 1.1 2 30 days 30 percent 6

Balance sheet Equity capital 80,000 Retained earnings 50,000 Short-term bank borrowings . . . . .... .... …….. Plant and equipment Inventories Accounts receivable Cash .... .... .... .... ....

Sales Cost of goods sold Solution: Debt/equity = 0.80

Equity = 80,000 + 50,000 = 130,000 So Debt = Short-term bank borrowings = 0.8 x 130,000 Hence Total assets = 130,000+104,000 = 234,000 Total assets turnover ratio = 2 So Sales = 2 x 234,000 = 468,000 Gross profit margin = 30 per cent So Cost of goods sold = 0.7 x 468,000 = 327,600 Day’s sales outstanding in accounts receivable = 30 days Sales So Accounts receivable = 360 468,000 = 360 Cost of goods sold Inventory turnover ratio = Inventory = Inventory 327,600 = 6 x 30 = 39,000 x 30 = 104,000

So Inventory = 54,600 As short-term bank borrowing is a current liability, Cash + Accounts receivable Acid-test ratio = Current liabilities Cash + 39,000 = 104 ,000 So Cash = 75,400 Plant and equipment = Total assets - Inventories – Accounts receivable – Cash = 234,000 - 54,600 - 39,000 – 75,400 = 65,000 Putting together everything we get Balance Sheet Equity capital 80,000 Retained earnings 50,000 Short-term bank borrowings 104,000 Plant & equipment Inventories Accounts receivable Cash 65,000 54,600 39,000 75,400 234,000 = 1.1

234,000 Sales Cost of goods sold 20. 468,000 327,600

Complete the balance sheet and sales data (fill in the blanks) using the following financial data: Debt/equity ratio = 0.40 Acid-test ratio = 0.9 Total assets turnover ratio = 2.5 Days' sales outstanding in Accounts receivable = 25 days Gross profit margin = 25 percent Inventory turnover ratio = 8 Balance sheet Equity capital 160,000,000 Retained earnings 30,000,000 Short-term bank borrowings . . . …… .... ....…. ……. Plant and equipment-------Inventories ……… Accounts receivable ….. . . . Cash .... ....

Sales Cost of goods sold

Solution: Debt/equity = 0.40 Equity = 160,000,000 + 30,000,000 = 190,000,000 So Debt = Short-term bank borrowings = 0.4 x 190,000,000 Hence Total assets = 190,000,000+ 76,000,000 = 266,000,000 Total assets turnover ratio = 2.5 So Sales = 2.5 x 266,000,000 = 665,000,000 Gross profit margin = 25 per cent So Cost of goods sold = 0.75 x 665,000,000 = 498,750,000 Day’s sales outstanding in accounts receivable = 25 days Sales So Accounts receivable = x 25 360 665,000,000 x 25 360 Cost of goods sold Inventory turnover ratio = Inventory So Inventory = 62,343,750 As short-term bank borrowings is a current liability, Cash + Accounts receivable Acid-test ratio = Current liability Cash + 46,180,556 = = 0.9 76,000 ,000 So Cash = 22,219,444 Plant and equipment = Total assets - Inventories – Accounts receivable – Cash = 266,000,000 - 62,343,750 - 46,180,556 – 22,219,444 = 135,256,250 Putting together everything we get Balance Sheet Equity capital Retained earnings Short-term bank borrowings 160,000,000 30,000,000 76,000,000 266,000,000 665,000,000 498,750,000 Plant & equipment 135,256,250 Inventories 62,343,750 Accounts receivable 46,180,556 Cash 22,219,444 266,000,000 = Inventory = 76,000,000

=

= 46,180,556 498,750,000 = 8

Sales Cost of goods sold

21.

Complete the balance sheet and sales data (fill in the blanks) using the following financial data: Debt/equity ratio Acid-test ratio Total assets turnover ratio Days' sales outstanding in Accounts receivable Gross profit margin Inventory turnover ratio = 1.5 = 0.3 = 1.9 = 25 days = 28 percent = 7

Balance sheet Equity capital 600,000 Retained earnings 100,000 Short-term bank borrowings . . . Plant and equipment Inventories Accounts receivable Cash .... .... .... .... ....

Sales Cost of goods sold Solution: Debt/equity = 1.5

.... . . . ….. ………

Equity = 600,000 + 100,000 = 700,000 So Debt = Short-term bank borrowings =1.5 x 700,000 Hence Total assets = 700,000+1050,000 = 1,750,000 Total assets turnover ratio = 1.9 So Sales = 1.9 x 1,750,000 = 3,325,000 Gross profit margin = 28 per cent So Cost of goods sold = 0.72 x 3,325,000 = 2,394,000 Day’s sales outstanding in accounts receivable = 25 days Sales So Accounts receivable = 360 = 3,325,000 x 25 = 230,903 360 Cost of goods sold 2,394,000 = = 7 Inventory Inventory x 25 = 1050,000

Inventory turnover ratio = So Inventory = 342,000

As short-term bank borrowings is a current liability , Cash + Accounts receivable Acid-test ratio = Current liabilities Cash + 230,903 = 1050 ,000 So Cash = 84,097 Plant and equipment = Total assets - Inventories – Accounts receivable – Cash = 1,750,000 – 342,000 – 230,903 – 84,097 = 1,093,000 Putting together everything we get Balance Sheet Equity capital 600,000 Retained earnings 100,000 Short-term bank borrowings 1050,000 Plant &equipment 1,093,000 Inventories 342,000 Accounts receivable 230,903 Cash 84,097 1,750,000 = 0.3

1,750,000 Sales Cost of goods sold 22. 3,325,000 2,394,000

Compute the financial ratios for Acme Ltd. Evaluate Acme's performance with reference to the standards. Acme Limited Balance Sheet, March 31, 20X7 Liabilities and Equity Equity capital Reserves and surplus Long-term debt Short-term bank borrowing Trade creditors Provisions Total Assets Fixed assets (net) Current assets Cash and bank Receivables Rs.110,000,000 30,000,000 45,000,000 Rs.60,000,000 45,000,000 72,000,000 40,000,000 30,000,000 15,000,000 62,000,000

Inventories Pre-paid expenses Others Total

61,000,000 10,000,000 6,000,000 262,000,000

Acme Limited Profit and Loss Account for the Year Ended March 31, 20X7 Net sales Cost of goods sold Gross profit Operating expenses Operating profit Non-operating surplus Profit before interest and tax Interest Profit before tax Tax Profit after tax Dividends Retained earnings Acme Current ratio Acid-test ratio Debt-equity ratio Times interest covered ratio Inventory turnover ratio Average collection period Total assets turnover ratio Net profit margin ratio Earning power Return on equity Solution: For purposes of ratio analysis, we may recast the balance sheet as under. Let assume that ‘Others’ in the balance sheet represents other current assets. Liabilities and Equity Equity capital Reserves and surplus Long-term debt Short-term bank borrowing Total Rs.320,000,000 204,000,000 116,000,000 50,000,000 66,000,000 4,000,000 70,000,000 12,000,000 58,000,000 20,000,000 38,000,000 4,000,000 34,000,000 Standard 1.3 0.70 2.0 4.5 5.0 45 days 1.5 8% 20 % 18 %

.60,000,000 45,000,000 72,000,000 40,000,000 217,000,000

Assets Fixed assets (net) Current assets Cash and bank 30,000,000 Receivables 45,000,000 Inventories 61,000,000 Pre-paid expenses 10,000,000 Others 6,000,000 Less: Current liabilities Trade creditors 30,000,000 Provisions 15,000,000 Net current assets Total Current assets (i) Current ratio = Current liabilities 152,000,000 = 1.8 85,000,000 (Current liabilities here includes short-term bank borrowing also) Current assets – Inventories (ii) Acid-test ratio = 91,000,000 = 1.1 = 110,000,000

152,000,000

45,000,000 107,000,000 217,000,000

= Current liabilities 85,000,000 (Current liabilities here includes short-term bank borrowing also) Long-term debt + Short-term bank borrowing

(iii) Debt-equity ratio = Equity capital + Reserves & surplus 72,000,000 + 40,000,000 = 60,000,000 + 45,000,000 Profit before interest and tax (iv) Times interest coverage ratio = Interest 70,000,000 = 12,000,000 Cost of goods sold (v) Inventory turnover period = Inventory = 61,000,000 204,000,000 = 3.34 = 5.83 = 1.1

365 (vi) Average collection period = Net sales / Accounts receivable 365 = = 51.3 days 320,000,000/45,000,000 (vii) Total assets =Equity + Total debt =( 60,000,000 + 45,000,000 ) +(72,000,000+40,000,000) = 217,000,000 Net sales 320,000,000 Total assets turnover ratio = = Total assets 217,000,000 Profit after tax (ix) Net profit margin = Net sales PBIT (x) Earning power = Total assets = 217,000,000 38,000,000 = Net worth 105,000,000 = 36.2 % 70,000,000 = 32.3 % = 320,000,000 38,000,000 = 11.9%

= 1.5

Equity earning (xi) Return on equity =

The comparison of the Acme’s ratios with the standard is given below

Current ratio Acid-test ratio Debt-equity ratio Times interest covered ratio Inventory turnover ratio Average collection period Total assets turnover ratio Net profit margin ratio Earning power Return on equity

Acme 1.8 1.1 1.1 5.8 3.3 51.3 days 1.5 11.9 % 32.3 % 36.2 %

Standard 1.3 0.7 2.0 4.5 5.0 45 days 1.5 8% 20 % 18 %

23.

Compute the financial ratios for Nainar Ltd. Evaluate Nainar's performance with reference to the standards.

Nainar Limited Balance Sheet, March 31, 20X7 Liabilities and Equity Equity capital Reserves and surplus Long-term debt Short-term bank borrowing Trade creditors Provisions Total Assets Fixed assets (net) Current assets Cash and bank Receivables Inventories Pre-paid expenses Others Total Net sales Cost of goods sold Gross profit Operating expenses Operating profit Non-operating surplus Profit before interest and tax Interest Profit before tax Tax Profit after tax Dividends Retained earnings Nainar Current ratio Acid-test ratio Debt-equity ratio Times interest covered ratio Inventory turnover ratio Average collection period Total assets turnover ratio Net profit margin ratio Earning power Return on equity Rs.100,000,000 65,000,000 140,000,000 70,000,000 24,000,000 19,000,000 418,000,000 Rs.206,000,000 25,000,000 70,000,000 85,000,000 20,000,000 12,000,000 418,000,000 Rs.740,000,000 520,000,000 220,000,000 102,000,000 118,000,000 12,000,000 130,000,000 22,000,000 108,000,000 46,000,000 62,000,000 20,000,000 42,000,000 Standard 1.7 1.0 1.4 5.5 6.0 40 days 2.0 8% 30 % 35 %

Nainar Limited Profit and Loss Account for the Year Ended March 31, 20X7

Solution: For purposes of ratio analysis, we may recast the balance sheet as under. Let assume that ‘Others’ in the balance sheet represents other current assets. Liabilities and Equity Equity capital Reserves and surplus Long-term debt Short-term bank borrowing Total Assets Fixed assets (net) Current assets Cash and bank Receivables Inventories Pre-paid expenses Others Less: Current liabilities Trade creditors Provisions Net current assets

100,000,000 65,000,000 140,000,000 70,000,000 375,000,000 206,000,000

25,000,000 70,000,000 85,000,000 20,000,000 12,000,000

212,000,000

24,000,000 19,000,000 Total

43,000,000 169,000,000 375,000,000

Current assets (i) Current ratio = Current liabilities 212,000,000 = 1.9 113,000,000 ( Current liabilities here includes short-term bank borrowing also) Current assets – Inventories (ii) Acid-test ratio = 127,000,000 = 1.1 =

= Current liabilities 113,000,000 ( Current liabilities here includes short-term bank borrowing also) Long-term debt + Short-term bank borrowing (iii) Debt-equity ratio = Equity capital + Reserves & surplus

140,000,000 + 70,000,000 = = 1.3 100,000,000 + 65,000,000 Profit before interest and tax (iv) Times interest coverage ratio = Interest 130,000,000 = 22,000,000 Cost of goods sold (v) Inventory turnover period = Inventory 365 (vi) Average collection period = Net sales / Accounts receivable 365 = = 34.5 days 740,000,000/70,000,000 (vii) Total assets = Equity + Total debt =(100,000,000 + 65,000,000 ) +(140,000,000+70,000,000) = 375,000,000 Net sales Total assets turnover ratio = Total assets Profit after tax (ix) Net profit margin = Net sales PBIT (x) Earning power = Total assets = 375,000,000 62,000,000 = Net worth 165,000,000 = 37.6 % 130,000,000 = 34.7 % = 740,000,000 = 375,000,000 62,000,000 = 8.4 % 740,000,000 = 2.0 = 85,000,000 520,000,000 = 6.1 = 5.9

Equity earning (xi) Return on equity =

The comparison of the Nainar’s ratios with the standard is given below

Nainar Current ratio Acid-test ratio Debt-equity ratio Times interest covered ratio Inventory turnover ratio Average collection period Total assets turnover ratio Net profit margin ratio Earning power Return on equity 1.9 1.1 1.3 5.9 6.1 34.5 days 2.0 8.4 % 34.7 % 37.6 %

Standard 1.7 1.0 1.4 5.5 6.0 40 days 2.0 8% 30 % 35 %

24.

The comparative balance sheets and comparative Profit and Loss accounts for Nalvar Limited, are given below: Comparative Balance Sheets, Nalvar Limited (Rs. in million) 20X3 1.6 1.0 1.4 1.3 1.1 6.4 1.2 0.3 1.8 1.8 1.3 6.4 20X4 1.6 1.6 1.5 1.5 1.3 7.5 1.4 0.3 2.1 2.2 1.5 7.5 20X5 1.8 2.4 1.8 1.7 1.5 9.2 2 0.2 2.5 2.8 1.7 9.2 20X6 1.8 2.3 1.6 1.5 1.6 8.8 1.7 0.4 2.4 2.4 1.9 8.8 20X7 2 3 1.4 1.2 1.8 9.4 2 0.3 2.5 2.8 1.8 9.4

Share capital Reserves and surplus Long-term debt Short-term bank borrowing Current liabilities Total Assets Net fixed assets Current assets Cash and bank Receivables Inventories Other assets Total

Comparative Profit and Loss Accounts, Nalvar Limited (Rs. in million)

Net sales Cost of goods sold Gross profit Operating expenses Operating profit Non-operating surplus deficit Profit before interest and tax Interest Profit before tax Tax Profit after tax

20X3 3.8 2.6 1.2 0.3 0.9 0.1 1 0.1 0.9 0.05 0.85

20X4 4.2 3.1 1.1 0.3 0.8 0.2 1 0.1 0.9 0.08 0.82

20X5 5.3 3.9 1.4 0.4 1 0.1 1.1 0.2 0.9 1 -0.1

20X6 6.5 4 2.5 0.6 1.9 0.3 2.2 0.1 2.1 1.2 0.9

20X7 7.8 4.8 3 0.6 2.4 0.3 2.7 0.1 2.6 1.2 1.4

Required: Compute the important ratios for Nalvar Limited for the years 20X3-20X7. You may assume that other assets in the balance sheet represent other current assets. • Current ratio • Debt-equity ratio • Total assets turnover ratio • Net profit margin • Earning power • Return on equity Solution: We will rearrange the balance sheets as under for ratio analysis. It is assumed that ‘Other assets’ are other current assets Liabilities and Equity 20X3 20X4 20X5 20X6 20X7 Share capital 1.6 1.6 1.8 1.8 2 Reserves and surplus 1 1.6 2.4 2.3 3 Long-term debt 1.4 1.5 1.8 1.6 1.4 Short-term bank borrowing 1.3 1.5 1.7 1.5 1.2 Total 5.3 6.2 7.7 7.2 7.6 Assets Net fixed assets 1.2 1.4 2 1.7 2 Current assets Cash and bank 0.3 0.3 0.3 0.2 0.4 Receivables 2.5 1.8 2.1 2.5 2.4

Inventories Other current assets Less: Current liabilities Other current liabilities Net current assets Total

1.8 1.3 1.1

5.2 1.1 4.1 5.3

2.2 1.5 1.3

6.1

2.8 1.7

7.2 1.5 5.7 7.7

2.4 1.9 1.6

7.1 1.6 5.5 7.2

2.8 1.8 1.8

7.4 1.8 5.6 7.6

1.3 1.5 4.8 6.2

The required ratios are as under: • • • • • • Current ratio Debt-equity ratio Total assets turnover ratio Net profit margin(%) Earning power (%) Return on equity (%) 20X3 20X4 20X5 20X6 20X7 2.2 2.2 2.3 2.3 2.5 0.9 0.8 0.8 0.5 1.0 0.7 0.7 0.7 0.9 1.0 22.4 19.5 -1.9 13.8 17.9 18.9 16.1 14.3 30.6 35.5 25.6 -2.4 22.0 28.0 32.7

26. The comparative balance sheets and comparative Profit and Loss accounts for Somani Limited, a machine tool manufacturer, are given below: Comparative Balance Sheets, Somani Limited (Rs. in million)

Share capital Reserves and surplus Long-term debt Short-term bank borrowing Current liabilities Total Assets Net fixed assets Current assets Cash and bank Receivables Inventories Other Assets Total

20X3 20X4 20X5 20X6 41 50 50 50 16 36 72 118 28 25 30 29 35 30 36 38 24 28 30 30 144 169 218 265 72 8 24 35 5 144 80 9 30 42 8 169 75 15 59 55 14 218 102 12 62 75 14 265

20X7 55 150 22 38 25 290 103 11 85 79 12 290

Comparative Profit & Loss Account of Somani Ltd (Rs. in million) 20X3 20X4 20X5 285 320 360 164 150 170 121 170 190 64 66 68 57 104 122 3 4 4 60 108 126 8 6 10 52 102 116 15 26 30 37 76 86 20X6 350 175 175 68 107 3 110 12 98 26 72 20X7 355 174 181 64 117 3 120 12 108 29 79

Net sales Cost of goods sold Gross profit Operating expenses Operating profit Non-operating surplus deficit Profit before interest and tax Interest Profit before tax Tax Profit after tax

Compute the following ratios for years 20X3-20X7: • Current ratio • Debt-equity ratio • Total assets turnover ratio • Net profit margin • Earning power • Return on equity For ratio analysis purpose, we will rearrange the balance sheet as under. It is assumed that ‘Other assets’ are other current assets 20X3 20X4 20X5 20X6 20X7 Share capital 41 50 50 50 55 Reserves and surplus 16 36 72 118 150 Long-term debt 28 25 30 29 22 Short-term bank borrowing 35 30 36 38 38 120 141 188 235 265 Total Assets Net fixed assets Current assets Cash and bank Receivables Inventories Other assets Less : Current liabilities Net current assets Total 72 8 24 35 5 24 9 30 42 8 28 80 15 59 55 14 30 75 12 62 75 14 30 102 11 85 79 163 12 30 25 133 235 103

72 24 48 120

89 28 61 141

143 30 113 188

187 25 162 265

The ratios worked out are as under: 20X3 20X4 20X5 20X6 20X7 1.5 2.2 2.4 3.0 1.2 1.1 0.6 0.5 0.4 0.3 2.4 2.3 1.9 1.5 1.3 13.0 23.8 23.9 20.6 22.3 50.0 76.6 67.0 46.8 45.3 64.9 88.4 70.5 42.9 38.5

• • • • • •

Current ratio Debt-equity ratio Total assets turnover ratio Net profit margin (%) Earning power (%) Return on equity (%)

26. The Balance sheets and Profit and Loss accounts of LKG Corporation are given below. Prepare the common size and common base financial statements Balance Sheets Shareholders’ funds Loan funds Total Fixed assets Investments Net current assets Total (Rs. in million) 20x6 20x7 256 262 156 212 412 474 322 330 15 15 75 129 412 474

Profit & Loss Accounts (Rs. in million) 20x6 20x7 623 701 475 552 148 149 105 89 22 21 83 68 41 34 42 34

Net sales Cost of goods sold Gross profit PBIT Interest PBT Tax PAT

Solution: Common Size statements: Profit and Loss Account Regular ( in Rs. million) Net sales Cost of goods sold Gross profit PBIT Interest PBT Tax PAT 20x6 623 475 148 105 22 83 41 42 20x7 701 552 149 89 21 68 34 34 Common Size(%) 20x6 100 76 24 17 4 13 7 7 20x7 100 79 21 13 3 10 5 5

Balance Sheet Regular ( in million) 20x6 20x7 Shareholders' funds Loan funds Total Fixed assets Investments Net current assets Total 27. 256 156 412 322 15 75 412 262 212 474 330 15 129 474

Common Size(%) 20x6 20x7 62 38 100 78 4 18 100 55 45 100 70 3 27 100

The Balance sheets and Profit and Loss accounts of Grand Limited are given below. Prepare the common size and common base financial statements Balance Sheet Shareholders’ fund Loan funds Total Fixed assets Investments Net current assets Total 20x6 85 125 210 127 8 75 210 20x7 85 180 265 170 10 85 265

Profit & Loss Account 20x6 Net sales 450 Cost of goods sold 320 Gross profit 130 PBIT 85 Interest 12 PBT 73 Tax 22 PAT 51 Solution: Regular (Rs. in million) 20x7 20x6 85 125 210 127 8 75 210 85 180 265 170 10 85 265

20x7 560 410 150 98 17 81 38 43

Balance Sheet Shareholders' funds Loan funds Total Fixed assets Investments Net current assets Total Profit & Loss Account Net sales Cost of goods sold Gross profit PBIT Interest PBT Tax PAT

Common Size(%) 20x6 20x7 40 60 100 60 4 36 100 32 68 100 64 4 32 100

Regular (Rs. in million) 20x6 20x7 450 560 320 410 130 150 85 98 12 17 73 81 22 38 51 43

Common Size(%) 20x6 20x7 100 100 71 73 29 27 19 18 3 3 16 14 5 7 11 8

Common base year statements Regular (Rs. in Common base year Balance Sheet million) (%) 20x6 20x7 20x6 20x7 100 Shareholders' funds 85 85 100 Loan funds 125 180 100 144 Total 210 265 100 126 Fixed assets 127 170 100 134 Investments 8 10 100 125 Net current assets 75 85 100 113 Total 210 265 100 126 Regular (Rs. in million) 20x6 20x7 450 560 320 410 130 150 85 98 12 17 73 81 22 38 51 43 Common base year (%) 20x6 20x7 100 124 100 128 100 115 100 115 100 142 100 111 100 173 100 84

Profit & Loss Account Net sales Cost of goods sold Gross profit PBIT Interest PBT Tax PAT

CHAPTER 5 1. The profit and loss account of Sasi Industires Limited for years 1 and 2 is given below: Using the percent of sales method, prepare the pro forma profit and loss account for year 3. Assume that the sales will be 3500 in year 3. If dividends are raised to 40, what amount of retained earnings can be expected for year 3? Year Net sales Cost of goods sold Gross profit Selling expenses General and administration expenses Depreciation Operating profit Non-operating surplus deficit 1 2300 1760 540 150 120 94 176 12 2 2700 2000 700 180 124 84 312 10

Earnings before interest and tax Interest Earnings before tax Tax Earnings after tax Dividends Retained earnings Solution: Year

188 30 158 56 102 35 67

322 38 284 96 188 35 153

1

2

Average percent of sales

Proforma Profit & Loss account for year 3 assuming sales of 3500 3500 2635.43 864.57 230.80 171.67 125.97 336.14 15.61 351.75 47.46 304.29 104.83 199.46 40 159.46

Net sales Cost of goods sold Gross profit Selling expenses General and administration expenses Depreciation Operating profit Non-operating surplus deficit Earnings before interest and tax Interest Earnings before tax Tax Earnings after tax Dividends(given) Retained earnings

2300 1760 540 150 120 94 176 12 188 30 158 56 102 35 67

2700 2000 700 180 124 84 312 10 322 38 284 96 188 35 153

100 75.30 24.70 6.59 4.90 3.60 9.60 0.45 10.05 1.36 8.69 3.00 5.70

2.

The profit and loss account of KG Electronics Limited for years 1 and 2 is given below: Using the percent of sales method, prepare the pro forma profit and loss account for year 3. Assume that the sales will be 26,000 in year 3. If dividends are raised to 500, what amount of retained earnings can be expected for year3 . Year Net sales Cost of goods sold Gross profit Selling expenses General and administration expenses Depreciation Operating profit Non-operating surplus deficit Earnings before interest and tax Interest Earnings before tax Tax Earnings after tax Dividends(given) Retained earnings 1 18,230 13,210 5020 820 1200 382 2618 132 2750 682 2068 780 1288 320 968 2 22,460 16100 6360 890 1210 364 3896 82 3978 890 3088 980 2108 450 1658

Solution: Year Proforma Profit & Loss account for year 3 assuming sales of 26,000 26000 18738.98 7261.02 1099.89

Net sales Cost of goods sold Gross profit Selling expenses General and administration expenses Depreciation Operating profit

1 18,230 13,210 5020 820

2 22,460 16100 6360 890

Average percent of sales 100 72.07 27.93 4.23

1200 382 2618

1210 364 3896

5.98 1.86 15.85

1556.09 483.09 4121.95

Non-operating surplus deficit Earnings before interest and tax Interest Earnings before tax Tax Earnings after tax Dividends(given) Retained earnings 3.

132 2750 682 2068 780 1288 320 968

82 3978 890 3088 980 2108 450 1658

0.54 16.40 3.85 12.55 4.32 8.23

141.59 4263.55 1001.48 3262.07 1123.46 2138.61 500 1638.61

Re-work problem 1 assuming the following budgeted amounts: General and administration expenses 135 Selling expenses 200 Interest 42 Dividends 40

Solution: Year Average percent of sales 100 75.30 24.70 Budgeted Budgeted 3.60 9.60 0.45 10.05 Budgeted 8.69 3.00 5.70 Budgeted Proforma Profit & Loss account for year 3 assuming sales of 3,500 3500 2635.43 864.57 200.00 135.00 125.97 336.14 15.61 351.75 42.00 304.29 104.83 199.46 40 159.46

Net sales Cost of goods sold Gross profit Selling expenses General and administration expenses Depreciation Operating profit Non-operating surplus deficit Earnings before interest and tax Interest Earnings before tax Tax Earnings after tax Dividends(given) Retained earnings

1 2300 1760 540 150 120 94 176 12 188 30 158 56 102 35 67

2 2,700 2000 700 180 124 84 312 10 322 38 284 96 188 35 153

4.

Re-work problem 2 assuming the following budgeted amounts: General and administration expenses 1620 Depreciation 520 Interest 120 Dividends 560

Solution: Year Average percent of sales 100 72.07 27.93 4.23 Proforma Profit & Loss account for year 3 assuming sales of 26,000 26000 18738.98 7261.02 1099.89

Net sales Cost of goods sold Gross profit Selling expenses General and administration expenses Depreciation Operating profit Non-operating surplus deficit Earnings before interest and tax Interest Earnings before tax Tax Earnings after tax Dividends(given) Retained earnings 5.

1 18,230 13,210 5020 820

2 22,460 16100 6360 890

1200 382 2618 132 2750 682 2068 780 1288 320 968

1210 364 3896 82 3978 890 3088 980 2108 450 1658

Budgeted Budgeted 15.85 0.54 16.40 Budgeted 12.55 4.32 8.23 Budgeted

1620.00 520.00 4121.95 141.59 4263.55 120.00 3262.07 1123.46 2138.61 560 1578.61

The profit and loss account and balance sheet for the years 2006 and 2007 of Radiant Corporation are as under. For the year 2008 , the following are the budgeted figures. Sales 3000 General and Administration expenses 150 Depreciation 100 Non operating surplus 80 Dividend 50

Investments 110 Pre-paid expenses 80 Unsecured bank borrowings 100 There will be no change in the levels of share capital, secured bank borrowings and miscellaneous expenditure and losses. All other figures both in the proforma profit and loss account as well as balance sheet, will change in proportion to the average its proportion to sales of that year for the past two years. It is also assumed that any extra funds needed to achieve the desired financial position for 2008 will be raised by way of debentures. Prepare the proforma financial statements for the year 2008 using the excel model given in the text. Year 2006 2300 1760 540 150 120 94 176 12 188 30 158 56 102 35 67 2007 2,700 2000 700 180 124 84 312 10 322 38 284 96 188 35 153

Net sales Cost of goods sold Gross profit Selling expenses General and administration expenses Depreciation Operating profit Non-operating surplus deficit Earnings before interest and tax Interest Earnings before tax Tax Earnings after tax Dividends(given) Retained earnings

Balance Sheets Fixed assets (net Investments Current assets, loans and advances · Cash and bank · Receivables · Inventories · Pre-paid expenses

Year 2006 2007 1460 1520 75 90

61 438 620 78

58 510 710 84

Miscellaneous expenditures losses Total Liabilities Share capital Equity Preference Reserves and surplus Secured loans Debentures Bank borrowings Unsecured loans Bank borrowings Current liabilities and provision Trade creditors Provisions Total Solution:

& 38 2770 42 3014

540 80 460 690 580 120

540 80 527 642 625 200

200 100 2770

320 80 3014

Year

Net sales Cost of goods sold Gross profit Selling expenses General and administration expenses Depreciation Operating profit Non-operating surplus deficit Earnings before interest and tax Interest on bank borrowings Interest on debentures Earnings before tax Tax

2006 2300 1760 540 150 120 94 176 50 226 77 30 119 56

2007 2,700 2000 700 180 124 84 312 70 382 82.5 27.5 272 96

Average percent of sales Projected 100.0Budgeted 75.2 24.8 6.6 Budgeted Budgeted @ Budgeted @ 3.2 @ 3.0

Before After iteration iteration Proforma Proforma profit profit and loss and loss account account for 2008 for 2008 3000.0 3000.0 2256.0 2256.0 744.0 744.0 198.0 198.0 150.0 150.0 100.0 100.0 296.0 296.0 80.0 80.0 376.0 376.0 95.7 95.7 27.5 80.6 252.8 199.7 91.2 91.2

Earnings after tax Dividends(given) Retained earnings Balance Sheets Fixed assets (net Investments Current assets, loans and advances · Cash and bank · Receivables · Inventories · Pre-paid expenses Miscellaneous expenditures & losses Total Liabilities Share capital Equity Preference Reserves and surplus Secured loans Debentures Bank borrowings Unsecured loans Bank borrowings Current liabilities and provisions Trade creditors Provisions Total 6.

119 35 28 2006 1460 75

272 35 141 2007 1520 90

@ Budgeted .@ 0.1 59.6 .Budgeted

252.8 50.0 111.6 1788.0 110.0

199.7 50.0 58.5 1788.0 110.0

61 438 620 78 38 2770

58 612 710 84 42 3116

2.4 21.0 26.6 .Budgeted No change

71.4 630.0 798.0 80.0 42.0 3519.4

71.4 630.0 798.0 80.0 42.0 3519.4

540 80 910 240 580 120 200 100 2770

540 80 1051 220 625 200 320 80 3116 10.4 3.6

No change No change @

540.0 80.0 1162.6 591.8 625.0 100.0 312.0 108.0 3519.4

540.0 80.0 1109.5 644.9 625.0 100.0 312.0 108.0 3519.4

No change Budgeted

The following information is available for ABC Limited : A/S = 0.6, S = Rs.300 million, L/S = 0.30, m = 0.08, S1 = Rs.350 million, and d = 0.5. What is the external funds requirement for the forthcoming year?

Solution: The external funds requirement of Olympus is: EFR = A*/S0 (?S) – L*/S (?S) – mS1 (r) = 0.6 x 50 – 0.3 x 50 - .08 x 350 x 0.5 = Rs.1 million

7.

The following information is available for XYZ Limited : A/S = 0.5, S = Rs.35 million, L/S = 0.20, m = 0.04, S1 = Rs.55 million, and d = 0.6. What is the external funds requirement for the forthcoming year?

Solution: The external funds requirement of Olympus is: EFR = A*/S0 (?S) – L*/S (?S) – mS1 (r) = 0.5 x 20 – 0.2 x 20 - .04 x 55 x 0.4 = Rs.5.12 million 8. The balance sheet of Vasundhara Corporation as at March 31, 2007 is shown below: Share capital 500 Fixed assets 750 Retained Earnings 120 Inventories 400 Term Loans 360 Receivables 330 Short-term Bank Borrowings 300 Cash 90 Accounts Payable 210 Provisions 80 1570 1570 The sales of the firm for the year ending on March 31, 2007 were 2,800. Its profit margin on sales was 8 percent and its dividend payout ratio was 30 percent. The tax rate was 40 percent. Vasundhara Corporation expects its sales to increase by 40 percent in the year ending March 31, 2008. The ratio of assets to sales and spontaneous current liabilities to sales would remain unchanged. Likewise the profit margin ratio, the tax rate, and the dividend payout ratio would remain unchanged. Required: a. Estimate the external funds requirement for the year 2008. b. Prepare the following statements, assuming that the external funds requirement would be raised equally from term loans and shortterm bank borrowings: (i) projected balance sheet and (ii) projected profit and loss account.

Solution: a A EFR = S 1570 = 2800 2800 S 290 1120 – 0.08 x 3920 (1-0.3) L

?S – m S1 (1-d)

= Rs.292 b. (i) Projected Income Statement for Year Ending 31st March , 2008 Sales Profits before tax Taxes Profit after tax (8% on sales) Dividends Retained earnings (ii) Projected Balance Sheet as at 31.12 2001 Liabilities Share capital Retained earnings Term loans (360+146) Short-term bank borrowings (300 + 146) Accounts payable Provisions Assets 500 340 506 446 294 112 2198 Fixed assets Inventories Receivables Cash 1050 560 462 126 3,920 523 209 314 94 220

2198

9.

The balance sheet of MGM Limited as at March 31, 2007 is shown below: Share capital 4,200 Fixed assets 8,870 Retained Earnings 2,480 Inventories 3,480 Term Loans 3,920 Receivables 2,580 Short-term Bank Borrowings 2,490 Cash 180 Accounts Payable 1,240 Provisions 780 15,110 15,110 The sales of the firm for the year ending on March 31, 2007 were 31,410. Its profit margin on sales was 7 percent and its dividend payout ratio was 50 percent. The tax rate was 34 percent. MGM Limited expects its sales to increase by 30 percent(i.e by 9,423) in the year 20X8. The ratio of assets to sales and spontaneous current liabilities to sales would remain unchanged. Likewise the profit margin ratio, the tax rate, and the dividend payout ratio would remain unchanged. Required: a. Estimate the external funds requirement for the year 2008. b. Prepare the following statements, assuming that the external funds requirement would be raised from term loans and short-term bank borrowings in the ratio 1:2 (i) projected balance sheet and (ii) projected profit and loss account.

Solution: a. EFR = A L ---- - ---S S

?S – m S1 (1-d)

15,110 = 31,410 = 2498 b.(i) -

2020 9,423 – 0.07 x 40,833 (1-0.5) 31,410

Projected Income Statement for Year Ending 31st March , 2008 Sales Profits before tax Taxes Profit after tax (7% on sales) Dividends Retained earnings 40,833 4,330 1,472 2,858 1,429 1,429

(ii) Projected Balance Sheet as at 31.3 2008 Liabilities Share capital 4,200 Retained earnings 3,909 Term loans (3920+2498x1/3) 4,753 Short-term bank borrowings 4,155 (2490 + 2498x2/3) Accounts payable 1,612 Provisions 1,014 19,643 Assets Fixed assets Inventories Receivables Cash 11,531 4,524 3,354 234

19,643

10.

The balance sheet of Ganesh Associates as at March 31, 20x7 is shown below: Share capital 6,258 Fixed assets 15,721 Retained Earnings 6,780 Inventories 5,984 Term Loans 5,320 Receivables 3,586 Short-term Bank Borrowings 4,378 Cash 254 Accounts Payable 1,873 Provisions 936 25,545 25,545 The sales of the firm for the year ending on March 31, 20x7 were 58,436. Its profit margin on sales was 10 percent and its dividend payout ratio was 45 percent. The tax rate was 33 percent. Ganesh Associates expects its sales to increase by 50 percent in the year 20X8. The ratio of assets to sales and spontaneous current liabilities to sales would remain unchanged. Likewise the profit margin ratio, the tax rate, and the dividend payout ratio would remain unchanged. Required: a. Estimate the external funds requirement for the year 20x8. b. Prepare the following statements, assuming that the external funds requirement would be raised entirely from short-term bank borrowings i) projected balance sheet and (ii) projected profit and loss account.

Solution: A L ----- - ------ ?S – m S1 (1-d) S S

EFR =

25,545 = 58,436 -

2,809 29,218– 0.10 x 87,654 (1-0.45) 58,436

= Rs.6,547 Projected Income Statement for Year Ending 31st March , 2008 Sales Profits before tax Taxes Profit after tax (10% on sales) Dividends Retained earnings 87,654 13,082 4,317 8,765 3,944 4,821

Projected Balance Sheet as at 31.3 2008 Liabilities Share capital Retained earnings Term loans Short-term bank borrowings (4378 + 6547) Accounts payable Provisions Assets Fixed assets Inventories Receivables Cash

6,258 11,601 5,320 10,925 2,809 1,404 38,317

23,581 8,976 5,379 381

38,317

11.

The following information is given for ABC Company: Assets to sales ratio = 0.80 Spontaneous liabilities to sales ratio = 0.40 Profit margin = 8 per cent Dividend payout ratio = 0.5 Previous year’s sales = 24,000 What is the maximum sales growth rate that can be financed without raising external funds?

Solution:

EFR =

A -

L -

m (1+g) (1-d)

?S S S g Given A/S= 0.8 , L/S= 0.4 , m= 0.08 , d= 0.5 and EFR = 0 we have, (0.08)(1+g)(0.5) (0.8-0.4) g 0.04(1+g) = 0.4g (0.4 -0.04)g = 0.04 or g = 0.04/0.36 = 0.1111 i.e. 11.11% 12. The following information is given for Rahul Associates.: Assets to sales ratio = 0.90 Spontaneous liabilities to sales ratio = 0.50 Profit margin = 11 per cent Dividend payout ratio = 0.7 Previous year’s sales = 45,360 What is the maximum sales growth rate that can be financed without raising external funds? =0

Solution:

EFR

A

L

m (1+g) (1-d)

= ?S S S g Given A/S= 0.9 , L/S= 0.5 , m= 0.11 , d= 0.7 and EFR = 0 we have, (0.11)(1+g)(0.3) (0.9-0.5) g 0.033(1+g) = 0.4g (0.4 -0.033)g = 0.033 or g = 0.033/0.367 = 0.0899 i.e. 8.99% 13. The following information is given for Ahuja Enterprises. Assets to sales ratio = 0.50 Spontaneous liabilities to sales ratio = 0.20 Profit margin = 6 per cent Dividend payout ratio = 0.1 Previous year’s sales = 12,000 =0

What is the maximum sales growth rate that can be financed without raising external funds? Solution:

EFR =

A -

L -

m (1+g) (1-d)

?S S S g Given A/S= 0.5 , L/S= 0.2 , m= 0.06 , d= 0.1 and EFR = 0 we have, (0.06)(1+g)(0.9) (0.5-0.2) g 0.054(1+g) = 0.3g (0.3 -0.054)g = 0.054 or g = 0.054/0.246 = 0.2195 i.e. 21.95% 14. The balance sheet of Arvind Company at the end of year 20 x 7, which is just over, is given below: Share capital 200 Fixed assets 280 Retained earnings 120 Inventories 230 Long-term borrowings 210 Receivables 210 Short-term borrowings 150 Cash 60 Trade creditors 70 Provisions 30 780 780 The sales for the year just ended were 1480. The expected sales for the year 20x8 are 1702. The profit margin is 8 percent and the dividend payout ratio is 30 percent. Required: (a) Determine the external funds requirement for Arvind for the year 20x8. (b) How should the company raise its external funds requirement, if the following restrictions apply? (i) Current ratio should not be less than 1.3. (ii) The ratio of fixed assets to long-term loans should be greater than 1.3. Assume that the company wants to tap external funds in the following order: short-term bank borrowing, long-term loans, and additional equity issue. =0

Solution:

A (a) EFR = S -

L ?S – mS1 (1-d) S

780 = 1480 = 61 (b) -

100 x 222 – (0.08) (1702) (0.3) 1480

i.

Let CA = denote Current assets CL = Current liabilities SCL = Spontaneous current liabilities STL = Short-term bank borrowings FA = Fixed assets and LTL = Long-term loans Current ratio ? 1.3 CA i.e CL CA ? 1.3 STL +SCL As at the end of 20X8, CA = 500 x 1.15 = 575 SCL = 100 x 1.15 = 115 Substituting these values, we get 1.3 (STL + 115) ? 575 or 1.3 STL ? 575? (115 x 1.3) ? 425.5 425.5 greater than or equal to 1.3 or

or STL ? 1.3 i.e STL = 327.3 ii. Ratio of fixed assets to long term loans ? 1.3 FA ? 1.3 LTL At the end of 20X8, FA = 280 x 1.15 = 322 322 ?LTL ? or LTL = 247.7 1.3 If ? STL and ? LTL denote the maximum increase in ST borrowings & LT borrowings, we have :

? STL = STL (20X8) – STL (20X7) = 327.3 – 150 = 177.3 ? LTL = LTL (20X8)- LTL (20X7) = 247.7 – 210 = 37.7 Hence, the suggested mix for raising external funds will be : Short-term borrowings 61 Long-term loans ----Additional equity issue -61 15. The balance sheet of Kamath Enterprises at the end of year 20 x 7, which is just over, is given below: Share capital 35.000 Fixed assets 37.880 Retained earnings 1,160 Inventories 25,420 Long-term borrowings 28,360 Receivables 18,540 Short-term borrowings 16,520 Cash 560 Trade creditors 380 Provisions 980 82,400 82,400 The sales for the year just ended were 162,800. The expected sales for the year 20x8 are 227,920. The profit margin is 10 percent and the dividend payout ratio is 40 percent. Required: a Determine the external funds requirement for Kamath Enterprises for the year 20x8. b How should the company raise its external funds requirement, if the following restrictions apply? (i) Current ratio should remain unchanged. (ii) The ratio of fixed assets to long-term loans should be greater than 1.5. Assume that the company wants to tap external funds in the following order: short-term bank borrowing, long-term loans, and additional equity issue.

Solution: A (a) EFR = S S L ?S – mS1 (1-d)

82,400 = 162,800 = 23,299 -

1,360 x 65,120– (0.10) (227,920) (0.4) 162,800

b (i) The current ratio will remain unchanged when the assets and liabilities rise in the same proportion. The Short term borrowing as on March 31, 2008 should therefore be = 16,520 x 1.4 = 23,128 (ii) Let FA = Fixed assets STL = Short-term loans and LTL = Long-term loans Ratio of fixed assets to long term loans ? 1.5 FA ? 1.5 LTL At the end of 20X8, FA = 37,880 x 1.4 = 53,032 53,032 ?LTL ? or LTL = 35,355 1.5 If ? STL and ? LTL denote the maximum increase in ST borrowings & LT borrowings , we have : ? STL = STL (20x8) – STL (20X7) = 23,128 – 16,520 = 6, 608 ? LTL = LTL (20X8)- LTL (20X7) = 35,355 – 28,360 = 6,995 Hence, the suggested mix for raising external funds will be: Short-term borrowings 6, 608 Long-term loans 6,995 Additional equity issue 9,696 23,299 16. The following information is available about Headstrong Limited: Sales of this year = 48,240 Projected sales increase for next year = 25 percent Profit after tax this year = 4,824 Dividend payout ratio = 40 percent Projected surplus funds available next year = 2,000 Present level of spontaneous current liabilities = 12,380 What is the level of total assets for Headstrong now?

Solution: A EFR = S S A Therefore, mS1(1-d) – L L ? S – m S1 (1-d)

?S represents surplus funds S S Given m= 0.10, S1 = 60,300, d= 0.4 , L= 12,380 S= 48,240 and surplus funds = 2,000 we have A 12,380 (0.10) x 60,300x (1-0.4) x 12,060 = 2,000 48,240 48,240 A – 12,380 = 3618-2000 = 1618 4 or A = 4 x 1618+ 12,380 = 18,852

? The total assets of Headstrong must be 18,852 17. The following information is available about Meridian Corporation: Sales of this year = 100,780 Projected sales increase for next year = 30 percent Profit after tax this year = 15,117 Dividend payout ratio = 50 percent Projected surplus funds available next year = 7,000 Present level of spontaneous current liabilities = 14,300 What is the level of total assets for Meridian now?

Solution: A EFR = S S A Therefore, mS1(1-d) – L L ? S – m S1 (1-d)

?S represents surplus funds S S Given m= 0.15 , S1 = 131,014, d= 0.5 , L= 14,300 , S= 100,780 and surplus funds = 7,000 we have A 14,300 (0.15) x 131,014x (1-0.5) x 30,234 = 7,000 100,780 100,780 (A – 14,300)x 30,234 = 9826- 7000 = 2,826 100,780 or A = 2,826 x 100,780/30,234 + 14,300 = 23,720 ? The total assets of Meridian must be 23,720

18.

Maharaja Limited has the following financial ratios: Net profit margin ratio = 8 percent Target dividend payout ratio = 40 percent Assets-to-equity ratio = 3.0 Assets-to-sales ratio = 1.8 (a) What is the rate of growth that can be sustained with internal equity? (b) If Maharaja Limited wants to achieve a 8 percent growth rate with internal equity, what change must be made in the dividend payout ratio, other ratios remaining unchanged? (c) If Maharaja Limited wants to achieve a 8 percent growth rate with internal equity, what change must be made in the assets-to-equity ratio, other ratios remaining unchanged? (d) If Maharaja Limited wants to achieve a 7 percent growth rate with internal equity, what should be the improvement in the profit margin, other ratios remaining unchanged? (e) If Maharaja Limited wants to achieve a 7 percent growth rate with internal equity, what change must occur in the assets-to-sales ratio, other ratios remaining unchanged?

Solution: m= .08 , d = 0.4 , A/E = 3.0 , A/S = 1.8 m (1-d)A/E (a) g= A/S –m(1-d)A/E .08 (1-d) x 3.0 (b) 0.08 = 1.8 - .08 (1- d ) 3.0 0.144 – 0.0192 + 0.0192 d = 0.24 – 0.24 d d( 0.24 + 0.0192) = 0.24 + 0.0192 – 0.144 = 0.1152 d = 0.4444 or 44.44 % The dividend payout ratio must be raised by 4.4 percent. 0.08 (1-0.4) x A/E 0.08 = 1.8 -.08 (1-0.4) A/E 0.144 – 0.00384 A/E = 0.048 A/E , A/E = 0.144/0.05184 =2.78 Assets to equity ratio should be reduced by 0.22 m (1-0.4) 3 (d) .07 = 1.8 – m (1-0.4) x 3 = 1.8 -.08 (1-0.4) 3.0 .08 (1-0.4) 3.0 = 8.7 per cent

(c)

0.126 -0.126m = 1.8m , m =0.126/1.926 = 6.54 % The net profit margin must be reduced from 8 per cent to 6.54 per cent .08 (1-0.4) 3 (e) .07 = A/S - .08 (1-0.4) 3 0.07 A/S – 0.01 = 0.144 , A/S = 0.154/0.07 = 2.2 The asset to sales ratio must increase from 1.8 to 2.2 19. Majestic Corporation has the following financial ratios: Net profit margin ratio = 7 percent Target dividend payout ratio = 35 percent Assets-to-equity ratio = 1.8 Assets-to-sales ratio = 1.0 (a) What is the rate of growth that can be sustained with internal equity? (b) If Majestic Corporation wants to achieve a 10 percent growth rate with internal equity, what change must be made in the dividend payout ratio, other ratios remaining unchanged? (c) If Majestic Corporation wants to achieve a 11 percent growth rate with internal equity, what change must be made in the assets-to-equity ratio, other ratios remaining unchanged? (d) If Majestic Corporation wants to achieve a 12 percent growth rate with internal equity, what should be the improvement in the profit margin, other ratios remaining unchanged? (e) If Majestic Corporation wants to achieve a 6 percent growth rate with internal equity, what change must occur in the assets-to-sales ratio, other ratios remaining unchanged?

Solution: m= .07 , d = 0.35 , A/E = 1.8 , A/S = 1.0 m (1-d)A/E (a) g= A/S –m(1-d)A/E = 1.0 -.07 (1-0.35) 1.8 .07 (1-0.0.35) 1.8 = 8.9 per cent

.07 (1-d) 1.8 (b) g= = 0.10 1.0 -.07 (1-d) 1.8 0.10 -0.0126 + 0.0126 d = 1.26 – 1.26 d d = ( 1.26 + 0.0126 – 0.10)/(1.26 + 0.0126) = 0.921 or 92.1% The dividend payout ratio must be raised from 35 % to 92.1%.

(c) .07 (1-0.0.35) A/E = 0.11 1.0 -.07 (1-0.35) A/E 0.11 – 0.005005 A/E = 0.0455 A/E A/E = 0.11/(0.0455+0.005005) = 2.2 Assets to equity ratio should be raised from 1.8 to 2.2. . (d) m (1-0.0.35) 1.8 0.12 = 1.0 -m (1-0.35) 1.8 0.12 – 0.1404 m = 1.17 m , m = 0.09 or 9 % The net profit margin should be changed from 7 percent to 9 percent. (e) .07 (1-0.0.35) 1.8 0.06 = A/S -.07 (1-0.35) 1.8 0.06 A/S – 0.0049 = 0.0819, A/S = 1.38 The assets to sales ratio should be raised from 1.0 to 1.38 CHAPTER 6 1. Calculate the value 10 years hence of a deposit of Rs.20,000 made today if the interest rate is (a) 4 percent, (b) 6 percent, (c) 8 percent, and (d) 9 percent.

Solution: Value 10 years hence of a deposit of Rs.20,000 at various interest rates is as follows: r r r r = = = = 4% 6% 8% 9% FV5 FV5 FV5 FV5 = = = = = = = = 20,000 x FVIF (4%, 10 years) 20,000 x1.480 = Rs.29,600 20,000 x FVIF (6 %, 10 years) 20,000 x 1.791 =Rs.35,820 20,000 x FVIF (8 %, 10 years) 20,000 x 2.159 =Rs.43,180 20,000 x FVIF (9 %, 10 years) 20,000 x 2.367 =Rs. 47,340

2.

Calculate the value 3 years hence of a deposit of Rs.5,800 made today if the interest rate is (a) 12 percent, (b)14 percent, (c) 15 percent, and (d) 16 percent.

Solution: Value 3 years hence of a deposit of Rs. 5,800 at various interest rates is as follows: r = 12 % FV5 14 % FV5 15 % FV5 = = = = = = = = 5,800 x FVIF (12%, 3 years) 5,800 x 1.405 =Rs.8,149 5,800 x FVIF (14%, 3 years) 5,800 x 1.482 =Rs.8,596 5,800 x FVIF (15%, 3 years) 5,800 x 1.521 =Rs.8,822 5,800 x FVIF (16%, 3 years) 5,800 x 1.561 =Rs. 9,054

r

=

r

=

r

=

16 % FV5

3.

If you deposit Rs.2,000 today at 6 percent rate of interest in how many years (roughly) will this amount grow to Rs.32,000 ? Work this problem using the rule of 72–do not use tables.

Solution: Rs.32,000 / Rs. 2,000 = 16 = 24

According to the Rule of 72 at 6 percent interest rate doubling takes place approximately in 72 / 6 = 12 years So Rs.2,000 will grow to Rs.32,000 in approximately 4 x 12 years = 48 years 4. If you deposit Rs.3,000 today at 8 percent rate of interest in how many years (roughly) will this amount grow to Rs.1,92,000 ? Work this problem using the rule of 72–do not use tables.

Solution: Rs.192,000 / Rs. 3,000 = 64 = 26 According to the Rule of 72 at 8 percent interest rate doubling takes place approximately in 72 / 8 = 9 years So Rs.3000 will grow to Rs.192,000 in approximately 6 x 9 years = 54 years

5.

A finance company offers to give Rs.20,000 after 14 years in return for Rs.5,000 deposited today. Using the rule of 69, figure out the approximate interest rate offered.

Solution: In 14 years Rs.5,000 grows to Rs.20,000 or 4 times. This is 22 times the initial deposit. Hence doubling takes place in 14 / 2 = 7 years. According to the Rule of 69, the doubling period is 0.35 + 69 / Interest rate We therefore have 0.35 + 69 / Interest rate = 7 Interest rate = 69/(7-0.35) = 10.38 % 6. Someone offers to give Rs.80,000 to you after 18 years in return for Rs.10,000 deposited today. Using the rule of 69, figure out the approximate interest rate offered.

Solution: In 18 years Rs.10,000 grows to Rs.80,000 or 8 times. This is 23 times the initial deposit. Hence doubling takes place in 18 / 3 = 6 years. According to the Rule of 69, the doubling period is 0.35 + 69 / Interest rate. We therefore have 0.35 + 69 / Interest rate = 6 Interest rate = 69/(6-0.35) = 12.21 % 7. You can save Rs.5,000 a year for 3 years, and Rs.7,000 a year for 7 years thereafter. What will these savings cumulate to at the end of 10 years, if the rate of interest is 8 percent?

Solution: Saving Rs.5000 a year for 3 years and Rs.6000 a year for 7 years thereafter is equivalent to saving Rs.5000 a year for 10 years and Rs.2000 a year for the years 4 through 10. Hence the savings will cumulate to: 5000 x FVIFA (8%, 10 years) + 2000 x FVIFA (8%, 7 years) = 5000 x 14.487 + 2000 x 8.923 = Rs.90281

8.

Krishna saves Rs.24,000 a year for 5 years, and Rs.30,000 a year for 15 years thereafter. If the rate of interest is 9 percent compounded annually, what will be the value of his savings at the end of 20 years?

Solution: Saving Rs.24,000 a year for 5 years and Rs.30,000 a year for 15 years thereafter is equivalent to saving Rs.24,000 a year for 20 years and Rs.6,000 a year for the years 6 through 20. Hence the savings will cumulate to: 24,000 x FVIFA (9%, 20 years) + 6,000 x FVIFA (9 %, 15 years) = 24,000 x 51.160 + 6, 000 x 29.361 =Rs. 1,404,006 9. You plan to go abroad for higher studies after working for the next five years and understand that an amount of Rs.2,000,000 will be needed for this purpose at that time. You have decided to accumulate this amount by investing a fixed amount at the end of each year in a safe scheme offering a rate of interest at 10 percent. What amount should you invest every year to achieve the target amount?

Solution: Let A be the annual savings. A x FVIFA (10%, 5years) A x 6.105 So, A = 2,000,000 / 6.105 10. = = = 2,000,000 2,000,000 Rs. 327,600

How much should Vijay save each year, if he wishes to purchase a flat expected to cost Rs.80 lacs after 8 years, if the investment option available to him offers a rate of interest at 9 percent? Assume that the investment is to be made in equal amounts at the end of each year.

Solution: Let A be the annual savings. A x FVIFA (9 %, 8 years) A x 11.028 = = 80,00,000 80,00,000 Rs. 7,25,426

So, A = 80,00,000 / 11.028 =

11.

A finance company advertises that it will pay a lump sum of Rs.100,000 at the end of 5 years to investors who deposit annually Rs.12,000. What interest rate is implicit in this offer?

Solution: 12,000 x FVIFA (r, 5 years) = FVIFA (r, 5 years) From the tables we find that FVIFA (24%, 5 years) FVIFA (28%, 5 years) = = 8.048 8.700 = 100,000 100,000 / 12,000 = 8.333

Using linear interpolation in the interval, we get: (8.333– 8.048) r = 24% + (8.700 – 8.048) 12. Someone promises to give you Rs.5,000,000 after 6 years in exchange for Rs.2,000,000 today. What interest rate is implicit in this offer? x 4% = 25.75%

Solution: 2,000,000 x FVIF (r, 6 years) = 5,000,000 FVIF (r, 6 years) = 5,000,000 / 2,000,000 = 2.5 From the tables we find that FVIF (16%, 6 years) = FVIF (17%, 6 years) = 2.436 2.565

Using linear interpolation in the interval, we get: (2.5 – 2.436) x 1 % r = 16% + (2.565 – 2.436) 13. At the time of his retirement, Rahul is given a choice between two alternatives: (a) an annual pension of Rs120,000 as long as he lives, and (b) a lump sum amount of Rs.1,000,000. If Rahul expects to live for 20 years and the interest rate is expected to be 10 percent throughout , which option appears more attractive = 16.5 %

Solution: The present value of an annual pension of Rs.120,000 for 20 years when r = 10% is: 120,000 x PVIFA (10%, 20 years) = 120,000 x 8.514 = Rs.1,021,680 The alternative is to receive a lumpsum of Rs 1,000,000 Rahul will be better off with the annual pension amount of Rs.120,000. 14. A leading bank has chosen you as the winner of its quiz competition and asked you to choose from one of the following alternatives for the prize: (a) Rs. 60,000 in cash immediately or (b) an annual payment of Rs. 10,000 for the next 10 years. If the interest rate you can look forward to for a safe investment is 9 percent, which option would you choose?

Solution: The present value of an annual payment of Rs.10,000 for 10 years when r = 9% is: 10,000 x PVIFA ( 9 %, 10 years) = 10,000 x 6.418 = Rs.64,180 The annual payment option would be the better alternative 15. What is the present value of an income stream which provides Rs.30,000 at the end of year one, Rs.50,000 at the end of year three , and Rs.100,000 during each of the years 4 through 10, if the discount rate is 9 percent ?

Solution: The present value of the income stream is: 30,000 x PVIF (9%, 1 year) + 50,000 x PVIF (9%, 3 years) + 100,000 x PVIFA (9 %, 7 years) x PVIF(9%, 3 years) = 30,000 x 0.917 + 50,000 x 0.772 + 100,000 x 5.033 x 0.0.772 = Rs.454,658. 16. What is the present value of an income stream which provides Rs.25,000 at the end of year one, Rs.30,000 at the end of years two and three , and Rs.40,000 during each of the years 4 through 8 if the discount rate is 15 percent ?

Solution: The present value of the income stream is: 25,000 x PVIF (15%, 1 year) + 30,000 x PVIF (15%, 2 years)

+ 30,000 x PVIF (15%, 3 years) + 40,000 x PVIFA (15 %, 5 years) x PVIF (15%, 3 years) = 25,000 x 0.870 + 30,000 x 0.756 + 30,000 x 0.658 + 40,000 x 3.352 x 0.658 = Rs.152,395. 17. What is the present value of an income stream which provides Rs.1,000 a year for the first three years and Rs.5,000 a year forever thereafter, if the discount rate is 12 percent?

Solution: The present value of the income stream is: 1,000 x PVIFA (12%, 3 years) + (5,000/ 0.12) x PVIF (12%, 3 years) = 1,000 x 2.402 + (5000/0.12) x 0.712 = Rs.32,069 18. What is the present value of an income stream which provides Rs.20,000 a year for the first 10 years and Rs.30,000 a year forever thereafter, if the discount rate is 14 percent ?

Solution: The present value of the income stream is: 20,000 x PVIFA (14%, 10 years) + (30,000/ 0.14) x PVIF (14%, 10 years) = 20,000 x 5.216 + (30,000/0.14) x 0.270 = Rs.162,177 19. Mr. Ganapathi will retire from service in five years .How much should he deposit now to earn an annual income of Rs.240,000 forever beginning from the end of 6 years from now ? The deposit earns 12 percent per year.

Solution: To earn an annual income of Rs.240,000 forever , beginning from the end of 6 years from now, if the deposit earns 12% per year a sum of Rs.240,000 / 0.12 = Rs.2,000,000 is required at the end of 5 years. The amount that must be deposited to get this sum is: Rs.2,000,000 PVIF (12%, 5 years) = Rs.2,000,000 x 0.567 = Rs. 1,134,000 20. Suppose someone offers you the following financial contract. If you deposit Rs.100,000 with him he promises to pay Rs.50,000 annually for 3 years. What interest rate would you earn on this deposit?

Solution: Rs.100,000 =- Rs.50,000 x PVIFA (r, 3 years) PVIFA (r,3 years) = 2.00 From the tables we find that: PVIFA (20 %, 3 years) PVIFA (24 %, 3 years) Using linear interpolation we get: 2.106 – 2.00 r = 20 % + ---------------2.106 – 1.981 = 23.39 % 21. If you invest Rs.600,000 with a company they offer to pay you Rs.100,000 annually for 10 years. What interest rate would you earn on this investment?

= 2.106 = 1.981

x 4%

Solution: Rs.600,000 =- Rs.100,000 x PVIFA (r, 10 years) PVIFA (r,10 years) = 6.00 From the tables we find that: PVIFA (10 %, 10 years) PVIFA (11 %, 10 years) Using linear interpolation we get: 6.145 – 6.00 r = 10 % + ---------------6.145 – 5.889 = 10.57 % 22 What is the present value of the following cash flow streams? End of year Stream X Stream Y Stream Z 1 500 750 600 2 550 700 600 3 600 650 600 4 650 600 600 5 700 550 600 6 750 500 600 --------------------------------------------------------------------------------------------The discount rate is 18 percent.

= 6.145 = 5.889

x 1%

Solution:

PV( Stream X) = 500 PV( 18%, 1yr) +550 PV( 18%, 2yrs) + 600 PV( 18%, 3yrs) + 650 PV( 18%, 4yrs) + 700 PV( 18%, 5yrs) + 750 PV( 18%, 6yrs) = 500 x 0.847 +550 x 0.718 + 600 x 0.609 + 650 x 0.516 + 700 x 0.437 + 750 x 0.370 = 2102.6 PV( Stream X) = 750 PV( 18%, 1yr) +700 PV( 18%, 2yrs) + 650 PV( 18%, 3yrs) + 600 PV( 18%, 4yrs) + 550 PV( 18%, 5yrs) + 500 PV( 18%, 6yrs) == 750 x 0.847 +700 x 0.718 + 650 x 0.609 + 600 x 0.516 + 550 x 0.437 + 500 x 0.370 = 2268.65 PV (Stream X) = 600 PVIFA (18%, 6yrs) = 600 x 3.498 = 2098.8 23. Suppose you deposit Rs.200,000 with an investment company which pays 12 percent interest with compounding done once in every two months, how much will this deposit grow to in 10 years?

Solution: FV10 = = = = Rs.200,000 [1 + (0.12 / 6)]10x6 Rs.200,000 (1.02)60 Rs.200,000 x 3.281 Rs.656,200

24.

A bank pays interest at 5 percent on US dollar deposits, compounded once in every six months. What will be the maturity value of a deposit of US dollars 15,000 for three years?

Solution: Maturity value = USD 15 ,000 [1 + (0.05 / 2)]3x2 = 15,000 (1.025)6 = 15,000 x 1.1597 = 17,395.50 25. What is the difference between the effective rate of interest and stated rate of interest in the following cases: Case A: Stated rate of interest is 8 percent and the frequency of compounding is six times a year. Case B: Stated rate of interest is 10 percent and the frequency of compounding is four times a year. Case C: Stated rate of interest is 12 percent and the frequency of compounding is twelve times a year.

Solution: A Stated rate (%) 8 B 10 4 times (1+0.10/4)4 –1 = 10.38 C 12 12 times (1 + 0.12/12)12-1 = 12.68

Frequency of compounding 6 times Effective rate (%) (1 + 0.08/6)6- 1 = 8.27 Difference between the effective rate and stated rate (%) 26.

0.27

0.38

0.68

You have a choice between Rs.200,000 now and Rs.600,000 after 8 years. Which would you choose? What does your preference indicate?

Solution: The interest rate implicit in the offer of Rs.600,000 after 8 years in lieu of Rs.200,000 now is: Rs.200,000 x FVIF (r,8 years) = Rs.600,000 Rs.600,000 FVIF (r,8 years) = = 3.000 Rs.200,000 From the tables we find that FVIF (15%, 8years) = 3.059 This means that the implied interest rate is nearly 15%. I would choose Rs.600,000 after 8 years from now because I find a return of 15% quite attractive. 27. Ravikiran deposits Rs.500,000 in a bank now. The interest rate is 9 percent and compounding is done quarterly. What will the deposit grow to after 5 years? If the inflation rate is 3 percent per year, what will be the value of the deposit after 5 years in terms of the current rupee?

Solution: FV5 = Rs.500,000 [1 + (0.09 / 4)]5x4 = Rs.500,000 (1.0225)20 = Rs.500,000 x 2.653 = Rs.780,255

If the inflation rate is 3 % per year, the value of Rs.780,255 5 years from now, in terms of the current rupees is: Rs.780,255 x PVIF (3%, 5 years) = Rs.780,255 x 0. 863 = Rs.673,360 28. A person requires Rs.100,000 at the beginning of each year from 2015 to 2019. Towards this, how much should he deposit ( in equal amounts) at the end of each year from 2007 to 2011, if the interest rate is 10 percent.

Solution: The discounted value of Rs.100,000 receivable at the beginning of each year from 2015 to 2019, evaluated as at the beginning of 2014 (or end of 2013) is: Rs.100,000 x PVIFA (10%, 5 years) = Rs.100,000 x 3.791= Rs.379,100 The discounted value of Rs.379,100 evaluated at the end of 2011 is Rs.379,100 x PVIF (10 %, 2 years) = Rs.379,100 x 0.826= Rs.313,137 If A is the amount deposited at the end of each year from 2007 to 2011 then A x FVIFA (10%, 5 years) = Rs.313,137 A x 6.105 = Rs.313,137 A = Rs.313,137/ 6.105 = Rs.51,292 29. You require Rs.250 ,000 at the beginning of each year from 2010 to 2012. How much should you deposit( in equal amounts) at the beginning of each year in 2007 and 2008 ? The interest rate is 8 percent.

Solution: The discounted value of Rs.250,000 receivable at the beginning of each year from 2010 to 2012, evaluated as at the beginning of 2009 (or end of 2008) is: Rs.250,000 x PVIFA (8 %, 3 years) = Rs.250,000 x 2.577= Rs.644,250 To have Rs. 644,250 at the end of 2008, let A be the amount that needs to be deposited at the beginning of 2007 and 2008.We then have Ax (1+0.08) x FVIFA ( 8%, 2years) = 644,250 A x 1.08 x 2.080 = 644,250 or A = 286,792

30.

What is the present value of Rs.120,000 receivable annually for 20 years if the first receipt occurs after 8 years and the discount rate is 12 percent.

Solution: The discounted value of the annuity of Rs.120,000 receivable for 20 years, evaluated as at the end of 7th year is: Rs.120,000 x PVIFA (12%, 20 years) = Rs.120,000 x 7.469 = Rs.896,290 The present value of Rs. 896,290 is: Rs. 896,290 x PVIF (12%, 7 years) = Rs. 896,290 x 0.452 = Rs.405,119 31. What is the present value of Rs.89,760 receivable annually for 10 years if the first receipt occurs after 5 years and the discount rate is 9 percent.

Solution: The discounted value of the annuity of Rs.89,760 receivable for 10 years, evaluated as at the end of 4th year is: Rs. 89,760 x PVIFA (9%, 10 years) = Rs. 89,760 x 6.418 = Rs.576,080 The present value of Rs. 576,080is: Rs. 576,080x PVIF (9%, 4 years) = Rs. 576,080x 0.708 = Rs.407,865 32. After eight years Mr.Tiwari will receive a pension of Rs.10,000 per month for 20 years. How much can Mr. Tiwari borrow now at 12 percent interest so that the borrowed amount can be paid with 40 percent of the pension amount? The interest will be accumulated till the first pension amount becomes receivable.

Solution: 40 per cent of the pension amount is 0.40 x Rs.10,000 = Rs.4,000 Assuming that the monthly interest rate corresponding to an annual interest rate of 12% is 1%, the discounted value of an annuity of Rs.4,000 receivable at the end of each month for 240 months (20 years) is: Rs.4,000 x PVIFA (1%, 240) Rs.4,000 x (1.01)240 - 1 ---------------- = Rs.363,278 .01 (1.01)240

If Mr. Tiwari borrows Rs.P today on which the monthly interest rate is 1% P x (1.01)96 = P x 2.60 = Rs. 363,278 Rs. 363,278 Rs. 363,278 ------------ = Rs.139,722 2.60

P

=

33.

After one year Mr. Khanna will receive a pension of Rs.15,000 per month for 30 years. How much can Mr. Khanna borrow now at 12 percent interest so that the borrowed amount can be paid with 25 percent of the pension amount? The interest will be accumulated till the first pension amount becomes receivable.

Solution: 25 per cent of the pension amount is 0.25 x Rs.15,000 = Rs.3,750 Assuming that the monthly interest rate corresponding to an annual interest rate of 12% is 1%, the discounted value of an annuity of Rs.3,750 receivable at the end of each month for 360 months (30 years) is: Rs.3,750 x PVIFA (1%, 360) (1.01)360 - 1 ---------------- = Rs.364,569 .01 (1.01)360

Rs.3,750 x

If Mr. Khanna borrows Rs.P today on which the monthly interest rate is 1% P x (1.01)12 = P x 1.127 = Rs. 364,569 Rs. 364,569 Rs. 364,569 ------------ = Rs.323,486 1.127

P

=

34.

You buy a car with a bank loan of Rs.525,000. An instalment of Rs.25,000 is payable to the bank for each of 30 months towards the repayment of loan with interest. What interest rate does the bank charge?

Solution: Rs.25,000 x PVIFA(r, 30 months) = Rs.525,000 PVIFA (r, 30 months) = Rs.525,000 / Rs.25,000= 21

From the tables we find that: PVIFA(3%, 30) = PVIFA (2%, 30) =

19.600 22.397

Using a linear interpolation 22.397 – 21.000 r = 2% + ---------------------22.397 – 19.600 = 2.50%

x 1%

Thus, the bank charges an interest rate of 2.50 % per month. The corresponding effective rate of interest per annum is [ (1.0250)12 – 1 ] x 100 = 34.49 % 35. You take a bank loan of Rs.174,000 repayable with interest in 18 monthly instalments of Rs.12,000 What is the effective annual interest rate charged by the bank ?

Solution: Rs.12,000 x PVIFA(r, 18 months) = Rs.174,000 PVIFA (r, 18 months) = Rs.174,000 / Rs.12,000= 14.5 From the tables we find that: PVIFA(2%, 18) = PVIFA (3%, 18) =

14.992 13.754

Using a linear interpolation 14.992 – 14.500 r = 2% + ---------------------14.992 – 13.754 = 2.397%

x 1%

Thus, the bank charges an interest rate of 2.397 % per month. The corresponding effective rate of interest per annum is [ (1.02397)12 – 1 ] x 100 = 32.88 %

36.

Metro Corporation has to retire Rs.20 million of debentures each at the end of 6, 7, and 8 years from now. How much should the firm deposit in a sinking fund account annually for 5 years, in order to meet the debenture retirement need? The net interest rate earned is 10 percent.

Solution: The discounted value of the debentures to be redeemed between 6 to 8 years evaluated at the end of the 5th year is: Rs.20 million x PVIFA (10%, 3 years) = Rs.49.74million = Rs.20 million x 2.487

If A is the annual deposit to be made in the sinking fund for the years 1 to 5, then A x FVIFA (10%, 5 years) = Rs.49.74 million A x 6.105 = Rs.49.74 million A = Rs.8,147,420 37. Ankit Limited has to retire Rs.30 million of debentures each at the end of 7, 8, 9 and 10 years from now. How much should the firm deposit in a sinking fund account annually for 5 years, in order to meet the debenture retirement need? The net interest rate earned is 12 percent.

Solution: The discounted value of the debentures to be redeemed between 7 to 10 years evaluated at the end of the 6th year is: Rs.30 million x PVIFA (12%, 4 years) = Rs.30 million x 3.037 = Rs.91.11 million If A is the annual deposit to be made in the sinking fund for the years 1 to 6, then A x FVIFA (12%, 6 years) = Rs.91.11 million A x 8.115 = Rs. 91.11 million A = Rs.11,227,357 38. Mr.Mehta receives a provident fund amount or Rs.800,000. He deposits it in a bank which pays 9 percent interest. If he plans to withdraw Rs.100,000 at the end of each year, how long can he do so ?

Solution: Let `n’ be the number of years for which a sum of Rs.100,000 can be withdrawn annually.

Rs.100,000 x PVIFA (9%, n) = Rs.800,000 PVIFA (9%, n) = Rs.800,000 / Rs.100,000 = 8 .000 From the tables we find that PVIFA (9%, 14 years) = 7.786 PVIFA (9%, 15 years) = 8.060 Using a linear interpolation we get 8.000 – 7.786 n = 14 + ----------------8.060 – 7.786 39.

x 1 = 14.78 years

Mr. Naresh wants to invest an amount of Rs. 400,000, in a finance company at an interest rate of 12 percent, with instructions to the company that the amount with interest be repaid to his son in equal instalments of Rs.100,000, for his education expenses . How long will his son get the amount ?

Solution: Let `n’ be the number of years for which a sum of Rs.100,000 can be withdrawn annually. Rs.100,000 x PVIFA (12%, n) = Rs.400,000 PVIFA (12 %, n) = Rs.400,000 / Rs.100,000 = 4 From the tables we find that PVIFA (12%, 5 years) = PVIFA (12%, 6 years) = Using a linear interpolation we get 4.000 – 3.605 n = 5 + ----------------- x 1 = 5.78 years 4.111 – 3.605 40. Your company is taking a loan of 1,000,000, carrying an interest rate of 15 percent. The loan will be amortised in five equal instalments. What fraction of the instalment at the end of second year will represent principal repayment ? 3.605 4.111

Solution: 1,000,000 Annual instalment = 3.352 = 298,329

Loan Amortisation Schedule Year 1 2 Beg. 1,000,000 851,671 Instalment 298,329 298,329 Principal Balance repayment 150,000 148,329 851,671 127,751 170,578 681,093 170,578 / 298,329 = 0.572 or 57.2% Interest

41.

Anurag Limited borrows Rs.2,000,000 at an interest rate of 12 percent. The loan is to be repaid in 5 equal annual instalments payable at the end of each of the next 5 years. Prepare the loan amortisation schedule

Solution: Equated annual installment = 2,000,000 / PVIFA(12%,5) = 2,000,000 / 3.605 = Rs.554,785

Loan Amortisation Schedule Beginning amount ------------2,000,000 1,685,215 1,332,656 937,790 495,540 Annual installment --------------554,785 554,785 554,785 554,785 554,785 Principal repaid ------------314,785 352,559 394,866 442,250 495320 Remaining balance ------------1,685,215 1,332,656 937,790 495,540 220*

Year -----1 2 3 4 5

Interest ----------240,000 202,226 159.919 112,535 59,465

(*) rounding off error 42. You want to borrow Rs.3,000,000 to buy a flat. You approach a housing company which charges 10 percent interest. You can pay Rs.400,000 per year toward loan amortisation. What should be the maturity period of the loan?

Solution: Let n be the maturity period of the loan. The value of n can be obtained from the equation. 400,000 x PVIFA(10%, n) PVIFA (10%, n) From the tables we find that PVIFA (10%,14 years) = = = 3,000,000 7.5 7.367

PVIFA (10 %, 15 years) = Using a linear interpolation we get 7.500 – 7.367 n = 14 + ----------------7.606 – 7.367 43.

7.606

x 1 = 14.56 years

You want to borrow Rs.5,000,000 to buy a flat. You approach a housing company which charges 11 percent interest. You can pay Rs.600,000 per year toward loan amortisation. What should be the maturity period of the loan?

Solution: Let n be the maturity period of the loan. The value of n can be obtained from the equation. 600,000 x PVIFA(11%, n) PVIFA (11%, n) From the tables we find that PVIFA (11%,20 years) PVIFA (11 %, 25 years) Using linear interpolation we get 8.333 – 7.963 n = 20 + ----------------8.422 – 7.963 = = = = 5,000,000 8.333 7.963 8.422

x 5 = 24.03 years

44.

You are negotiating with the government the right to mine 160,000 tons of iron ore per year for 20 years. The current price per ton of iron ore is Rs.3500 and it is expected to increase at the rate of 8 percent per year. What is the present value of the iron ore that you can mine if the discount rate is 15 percent

Solution: Expected value of iron ore mined during year 1= 160,000x3500 = Rs.560 million Expected present value of the iron ore that can be mined over the next 20 years assuming a price escalation of 8% per annum in the price per ton of iron 1 – (1 + g)n / (1 + i)n -----------------------i-g

= Rs.560 million x

= Rs.560 million x

1 – (1.08)20 / (1.15)20 0.15 – 0.08

= Rs.560 million x 10.2173 = Rs.5,721,688,000 45. You are negotiating with the government the right to mine 300,000 tons of iron ore per year for 25 years. The current price per ton of iron ore is Rs.3200 and it is expected to increase at the rate of 7 percent per year. What is the present value of the iron ore that you can mine if the discount rate is 18 percent

Solution: Expected value of iron ore mined during year 1= 300,000x3200 = Rs.960 million Expected present value of the iron ore that can be mined over the next 25 years assuming a price escalation of 7% per annum in the price per ton of iron 1 – (1 + g)n / (1 + i)n -----------------------i-g 1 – (1.07)25 / (1.18)25 0.18 – 0.07

= Rs.960 million x

= Rs.960 million x

= Rs.960 million x 8.3036 = Rs.7,971,456,000 46. As a winner of a competition, you can choose one of the following prizes: a. Rs. 800,000 now b. Rs. 2,000,000 at the end of 8 years c. Rs. 100,000 a year forever d. Rs. 130,000 per year for 12 years e. Rs. 32,000 next year and rising thereafter by 8 percent per year forever. If the interest rate is 12 percent, which prize has the highest present value?

Solution: (a) PV = Rs.800,000 (b) PV = 2,000,000PVIF12%,8yrs = 2,000,000 x 0.0.404 = Rs.808,000 (c ) PV = 100,000/r = 100,000/0.12 = Rs. 833,333 (d) PV = 130,000 PVIFA12%,12yrs = 130,000 x 6.194 = Rs.805,220

(e)

PV = C/(r-g) = 32,000/(0.12-0.08) = Rs.800,000

Option c has the highest present value viz. Rs.833,333 47. Oil India owns an oil pipeline which will generate Rs. 20 million of cash income in the coming year. It has a very long life with virtually negligible operating costs. The volume of oil shipped, however, will decline over time and, hence, cash flows will decrease by 4 percent per year. The discount rate is 15 percent. a. If the pipeline is used forever, what is the present value of its cash flows? b. If the pipeline is scrapped after 30 years, what is the present value of its cash flows? Solution: (a) PV = c/(r – g) = 20/[0.15 – (-0.04)] = Rs.105.26 million 1+g n 1 - ------1+r PV = A(1+g) ----------------r- g

(b)

= 20 x 0.96 x 5.2398 = Rs.100.604 million

48.

Petrolite owns an oil pipeline which will generate Rs. 15 million of cash income in the coming year. It has a very long life with virtually negligible operating costs. The volume of oil shipped, however, will decline over time and, hence, cash flows will decrease by 6 percent per year. The discount rate is 18 percent. a. If the pipeline is used forever, what is the present value of its cash flows? b. If the pipeline is scrapped after 10 years, what is the present value of its cash flows? Solution: (a) PV = c/(r – g) = 15/[0.18 – (-0.06)] = Rs.62.5 million 1+g n 1 - ------1+r PV = A(1+g) ----------------r- g

(b)

= 15 x 0.94 x 3.7379 = Rs.52.704 million

49.

An oil well presently produces 80,000 barrels per year. It will last for 20 years more, but the production will fall by 6 percent per year. Oil prices are expected to increase by 5 percent per year. Presently the price of oil is $80 per barrel. What is the present value of the well's production if the discount rate is 15 percent?

Solution: The growth rate in the value of oil produced, g = (1- 0.06)(1 +0.05) - 1 = - 0.013 Present value of the well’s production = 1+g n 1 - ------1+r PV = A(1+g) ----------------r- g = (80,000 x 80) x ( 1-0.013)x 1 – (0.987 / 1.15)20 0.15 + 0.013 = $ 36,930,756 MINICASE 1

1. As an investment advisor, you have been approached by a client called Vikas for your advice on investment plan. He is currently 40 years old and has Rs.600,000 in the bank. He plans to work for 20 years more and retire at the age of 60. His present salary is Rs.500,000 per year. He expects his salary to increase at the rate of 12 percent per year until his retirement. Vikas has decided to invest his bank balance and future savings in a balanced mutual fund scheme that he believes will provide a return of 9 percent per year. You agree with his assessment. Vikas seeks your help in answering several questions given below. In answering these questions, ignore the tax factor. (i) Once he retires at the age of 60, he would like to withdraw Rs.800,000 per year for his consumption needs from his investments for the following 15 years (He expects to live upto the age of 75 years). Each annual withdrawal will be made at the beginning of the year. How much should be the value of his investments when Vikas turns 60, to meet this retirement need? (ii) How much should Vikas save each year for the next 20 years to be able to withdraw Rs.800,000 per year from the beginning of the 21st year ? Assume that the savings will occur at the end of each year. (iii) Suppose Vikas wants to donate Rs.500,000 per year in the last 5 years of his life to a charitable cause. Each donation would be made at the beginning of the year. Further, he wants to bequeath Rs.1,000,000 to his son at the end of his life. How much should he have in his investment account when he reaches the age of 60 to meet this need for donation and bequeathing?

(iv) Vikas is curious to find out the present value of his lifetime salary income. For the sake of simplicity, assume that his current salary of Rs.500,000 will be paid exactly one year from now, and his salary is paid annually. What is the present value of his life time salary income, if the discount rate applicable to the same is 7 percent? Remember that Vikas expects his salary to increase at the rate of 12 percent per year until retirement. Solution: (i) This is an annuity due Value of annuity due = Value of ordinary annuity (1 + r) The value of investments when vikas turns 60 must be: 800,000 x PVIFA (9%, 15 years) x 1.09 = 800,000 x 8.060 x 1.09 = Rs.7,028,320 (ii) He must have Rs.7,092,800 at the end of the 20th year. His current capital of Rs.600,000 will grow to: Rs.600,000 x FVIF (9%, 20yrs) = 600,000 x 5.604 = Rs.3,362,400 So, what he saves in the next 15 years must cumulate to: 7,028,320 – 3,362,400 = Rs.3,665,920 A x FVIFA (9%, 20 yrs) = Rs.3,665,920 A x 51.160 = 3,665,920 A = 3,665,920/51.160 = Rs.71,656 (iii) 60 69 70 71 72 A A A 73 A 74 A 75

1,000,000 To meet his donation objective, Vikas will need an amount equal to: 500,000 x PVIFA (9%, 5years) when he turns 69. This means he will need 500,000 x PVIFA (9%, 5yrs) x PVIF (9%, 9yrs) when he turns 60. This works out to: 500,000 x 3.890 x 0.460 = Rs.894,700 To meet his bequeathing objective he will need 1,000,000 x PVIF (15%, 9yrs) when he turns 60 This works out to: 1,000,000 x 0.275 = Rs.275,000 So, his need for donation and bequeathing is: 894,700 + 275,000 = Rs.1,169,700

(iv)

1-

(1+g)n (1+r)n r–g

PVGA = A (1+g)

Where A(1+g) is the cash flow a year from now. In this case A (1+g) = Rs.500,000, g = 12%, r = 7%, and n = 20 So, (1.12)20 1(1.07)20 PVGA = 500,000 0.07 – 0.12 = Rs.14,925,065

MINICASE 2 2. As an investment advisor, you have been approached by a client called Ravi for advice on his investment plan. He is 35 years and has Rs.200, 000 in the bank. He plans to work for 25 years more and retire at the age of 60. His present salary is 500,000 per year. He expects his salary to increase at the rate of 12 percent per year until his retirement. Ravi has decided to invest his bank balance and future savings in a balanced mutual fund scheme that he believes will provide a return of 9 percent per year. You concur with his assessment. Ravi seeks your help in answering several questions given below. In answering these questions, ignore the tax factor. (i) Once he retires at the age of 60, he would like to withdraw Rs. 900,000 per year for his consumption needs for the following 20 years (His life expectancy is 80years).Each annual withdrawal will be made at the beginning of the year. How much should be the value of his investments when he turns 60, to meet his retirement need? (ii) How much should Ravi save each year for the next 25 years to be able to withdraw Rs.900, 000 per year from the beginning of the 26th year for a period of 20 years? Assume that the savings will occur at the end of each year. Remember that he already has some bank balance. (iii) Suppose Ravi wants to donate Rs.600, 000 per year in the last 4 years of his life to a charitable cause. Each donation would be made at the beginning of the year. Further he wants to bequeath Rs. 2,000,000 to his daughter at the end of his life.

How much should he have in his investment account when he reaches the age of 60 to meet this need for donation and bequeathing? (iv) Ravi wants to find out the present value of his lifetime salary income. For the sake of simplicity, assume that his current salary of Rs 500,000 will be paid exactly one year from now, and his salary is paid annually. What is the present value of his lifetime salary income, if the discount rate applicable to the same is 8 percent? Remember that Ravi expects his salary to increase at the rate of 12 percent per year until retirement. Solution: (i) 900,000 x PVIFA ( 9 %, 20 ) x 1.09 900,000 x 9.128 x 1.09 = Rs. 8,954,568 (ii) Ravi needs Rs. 8,954,568 when he reaches the age of 60. His bank balance of Rs. 200,000 will grow to : 200,000 ( 1.09 )25 = 200,000 ( 8.623 ) = Rs. 1,724,600 This means that his periodic savings must grow to : Rs. 8,954,568 - Rs. 1,724,600 = Rs. 7,229,968 His annual savings must be: 7,229,968 A = FVIFA ( 25, 9% ) = (iii) 75 76 Rs. 85,359 = 84.701 7,229,968

600 600 600 600 2000 Amount required for the charitable cause: 600,000 x PVIFA ( 9% , 4yrs ) x PVIF ( 9%, 15yrs ) = 600,000 x 3.240 x 0.275 Rs. 534,600 Amount required for bequeathing 2,000,000 x PVIF ( 9%, 20yrs ) = 2,000,000 x 0.178 = Rs.356,000

(iv) A(1+g) 0 1 ( 1 + g )n PVGA = A(1+ g) 1 ( 1 + r )n r - g ( 1.12 )25 = 500,000 1 ( 1.08 )25 0.08 - 0.12 = Rs. 18,528,922 A ( 1 + g )n n

CHAPTER 7 1. The price of a Rs.1,000 par bond carrying a coupon rate of 8 percent and maturing after 5 years is Rs.1020. (i) What is the approximate YTM? (ii) What will be the realised YTM if the reinvestment rate is 7 percent?

Solution: (i) 80 + (1000 – 1020) / 5 YTM ~ 0.6 x 1020 + 0.4 x 1000 (ii) The terminal value will be 80 x FVIFA (7%, 5yrs) + 1000 80 x 5.751 + 1000 = 1460.08 The realised YTM will be: 1460.08 1020
1/5

=

7.51%

– 1 = 7.44%

2.

The price of a Rs.1,000 par bond carrying a coupon rate of 7 percent and maturing after 5 years is Rs.1040. (i) What is the approximate YTM? (ii) What will be the realised YTM if the reinvestment rate is 6 percent?

Solution: (i) The approximate YTM is: 70 + (1000 – 1040)/5 = 0.0605 or 6.05 percent 0.6 x 1040 + 0.4 x 1000 (ii) 0 -1040 1 70 2 70 3 70 4 70 5 70 1000

The terminal value at 6 percent reinvestment rate is: 70 x FVIFA (6%, 5yrs) + 1000 70 x 5.637 + 1000 = Rs.1394.59 1394.59 1/5 Realised yield to maturity = – 1 = 6.04% 1040 3. A Rs.1000 par value bond, bearing a coupon rate of 12 percent will mature after 6 years. What is the value of the bond, if the discount rate is 16 percent?

Solution: P = 6 ? t=1 120 + (1.16)t (1.16)6 1000

= Rs.120 x PVIFA(16%, 6 years) + Rs.1000 x PVIF (16%, 6 years) = Rs.120 x 3.685 + Rs.1000 x 0.410 = Rs. 852.20

4.

A Rs.100 par value bond, bearing a coupon rate of 9 percent will mature after 4 years. What is the value of the bond, if the discount rate is 13 percent?

Solution: 4 ? t=1 9 + (1.13)t (1.13)4 100

P =

= Rs.9 x PVIFA(13%, 4 years) + Rs.100 x PVIF (13%, 4 years) = Rs.9 x 2.974 + Rs.100 x 0.613 = Rs. 88.07 5. The market value of a Rs.1,000 par value bond, carrying a coupon rate of 10 percent and maturing after 5 years, is Rs.850. What is the yield to maturity on this bond?

Solution: The yield to maturity is the value of r that satisfies the following equality. 5 100 1,000 + Rs.850 = ? t=1 (1+r) t (1+r)5 Try r = 14%. The right hand side (RHS) of the above equation is: Rs.100 x PVIFA (14%, 5 years) + Rs.1,000 x PVIF (14%, 5 years) = Rs.100 x 3.433 + Rs.1,000 x 0.519 = Rs.862.30 Try r = 15%. The right hand side (RHS) of the above equation is: Rs.100 x PVIFA (15%, 5 years) + Rs.1,000 x PVIF (15%, 5years) = Rs.100 x 3.352 + Rs.1,000 x 0.497 = Rs.832.20 Thus the value of r at which the RHS becomes equal to Rs.850 lies between 14% and 15%. Using linear interpolation in this range, we get 862.30 – 850.00 Yield to maturity = 14% + 862.30 – 832.20

x 1%

= 14.41%

6.

The market value of a Rs.100 par value bond, carrying a coupon rate of 8.5 percent and maturing after 8 years, is Rs.95. What is the yield to maturity on this bond?

Solution: The yield to maturity is the value of r that satisfies the following equality. 8 8.5 100 ? + t=1 (1+r) t (1+r)8

95 =

Try r = 10%. The right hand side (RHS) of the above equation is: 8.5 x PVIFA (10%, 8 years) + Rs.100 x PVIF (10%, 8 years) = Rs.8.5 x 5.335 + Rs.100 x 0.467 = Rs.92.05 Try r = 9%. The right hand side (RHS) of the above equation is: 8.5 x PVIFA (9 %, 8 years) + Rs.100 x PVIF (9%, 8years) = 8.5 x 5.535 + Rs.100 x 0.502 = 47.04 + 50.20 = 97.24 Thus the value of r at which the RHS becomes equal to Rs.95 lies between 9% and 10%. Using linear interpolation in this range, we get 97.24 – 95.00 97.24 – 92.05

Yield to maturity = 9 % + = 9.43 % 7.

x 1%

A Rs.1000 par value bond bears a coupon rate of 10 percent and matures after 5 years. Interest is payable semi-annually. Compute the value of the bond if the required rate of return is 18 percent.

Solution: 10 ? t=1 50 1000

P =

+ (1.09) t (1.09)10

= 50 x PVIFA (9%, 10 years) + 1000 x PVIF (9%, 10 years) = 50 x 6.418 + Rs.1000 x 0.422 = Rs. 742.90

8.

A Rs.100 par value bond bears a coupon rate of 8 percent and matures after 10 years. Interest is payable semi-annually. Compute the value of the bond if the required rate of return is 12 percent.

Solution: 20 ? t=1 4 + (1.06) t (1.06)20 100

P =

= 4 x PVIFA (6%, 20 years) + Rs.100 x PVIF (6%, 20 years) = 6 x 11.470 + Rs.100 x 0.312 = Rs.100.02 9. You are considering investing in one of the following bonds: Coupon rate Maturity Price/Rs.100 par value Bond A 11% 8 yrs Rs.80 Bond B 9% 9 yrs Rs.70 Your income tax rate is 34 percent and your capital gains tax is effectively 10 percent. Capital gains taxes are paid at the time of maturity on the difference between the purchase price and par value. What is your post-tax yield to maturity from these bonds? Solution: The post-tax interest and maturity value are calculated below: Bond A Bond B * * Post-tax interest (C ) 11(1 – 0.34) =Rs.7.26 9 (1 – 0.34) =Rs.5.94 100 [ (100 – 70)x 0.1] =Rs.97

Post-tax maturity value (M) 100 [ (100-80)x 0.1] =Rs.98 7.26 + (98-80)/8 -------------------0.6 x 80 + 0.4 x 98 10.91% 5.94 + (97 – 70)/9 ---------------------0.6x 70 + 0.4 x 97 11.06 %

The post-tax YTM, using the approximate YTM formula is calculated below Bond A : Post-tax YTM = = Bond B : Post-tax YTM = =

10.

You are considering investing in one of the following bonds: Coupon rate Bond A 12% Bond B 8% Maturity Price/Rs.1000 par value 7 yrs Rs. 930 5 yrs Rs. 860

Your income tax rate is 33 percent and your capital gains tax is effectively 10 percent. Capital gains taxes are paid at the time of maturity on the difference between the purchase price and par value. What is your post-tax yield to maturity from these bonds? Solution: The post-tax interest and maturity value are calculated below: Bond A * Post-tax interest (C) 120(1 – 0.33) =Rs.80.40 Bond B 80 (1 – 0.33) =Rs.53.6 1000 [ (1000 – 860)x 0.1] =Rs.986

*

Post-tax maturity value (M) 1000 [(1000-930) x 0.1] =Rs. 993

The post-tax YTM, using the approximate YTM formula is calculated below 80.40 + (993-930)/7 -------------------0.6 x 930 + 0.4 x 993 9.36 % 53.6 + (986 – 860)/5 ---------------------0.6x 860 + 0.4 x 986 8.66 %

Bond A :

Post-tax YTM =

=

Bond B :

Post-tax YTM =

=

11.

A company's bonds have a par value of Rs.100, mature in 5 years, and carry a coupon rate of 10 percent payable semi-annually. If the appropriate discount rate is 14 percent, what price should the bond command in the market place?

Solution: P = 10 ? t=1 5 100 + (1.07) t (1.07)10

= Rs.5 x PVIFA(7%, 10) + Rs.100 x PVIF (7%, 10) = Rs.5 x 7.024 + Rs.100 x 0.508 = Rs. 85.92 12. A company's bonds have a par value of Rs.1000, mature in 8 years, and carry a coupon rate of 14 percent payable semi-annually. If the appropriate discount rate is 12 percent, what price should the bond command in the market place?

Solution: P = 16 ? t=1 70 1000 + (1.06) t (1.06)16

= Rs.70 x PVIFA(6%, 16) + Rs.1000 x PVIF (6%, 16) = Rs.70 x 10.106 + Rs.1000 x 0.394 = Rs. 1101.42 13. The share of a certain stock paid a dividend of Rs.3.00 last year. The dividend is expected to grow at a constant rate of 8 percent in the future. The required rate of return on this stock is considered to be 15 percent. How much should this stock sell for now? Assuming that the expected growth rate and required rate of return remain the same, at what price should the stock sell 3 years hence?

Solution: Do = Rs.3.00, g = 0.08, r = 0.15 Po = D1 / (r – g) = Do (1 + g) / (r – g) = = Rs.3.00 (1.08) / (0.15 - 0.08) Rs.46.29

Assuming that the growth rate of 8% applies to market price as well, the market price at the end of the 3rd year will be: P2 = = Po x (1 + g)3 = Rs.46.29 (1.08)3 Rs. 58.31

14.

The share of a certain stock paid a dividend of Rs.10.00 last year. The dividend is expected to grow at a constant rate of 15 percent in the future. The required rate of return on this stock is considered to be 18 percent. How much should this stock sell for now? Assuming that the expected growth rate and required rate of return remain the same, at what price should the stock sell 4 years hence?

Solution: Do = Rs.10.00, g = 0.15, r = 0.18 Po = D1 / (r – g) = Do (1 + g) / (r – g) = = Rs.10.00 (1.15) / (0.18 - 0.15) Rs.383.33

Assuming that the growth rate of 15% applies to market price as well, the market price at the end of the 4th year will be: P2 15. = = Po x (1 + g)4 = Rs.383.33 (1.15)4 Rs. 669.87

The equity stock of Hansa Limited is currently selling for Rs.280 per share. The dividend expected next is Rs.10.00. The investors' required rate of return on this stock is 14 percent. Assume that the constant growth model applies to Hansa Limited. What is the expected growth rate of Hansa Limited?

Solution: Po = D1 / (r – g)

Rs.280 = Rs.10 / (0.14 – g) 0.14 –g = 10/280 = 0.0357 g = 0.14-0.0357 = 0.1043or 10.43 % 16. The equity stock of Amulya Corporation is currently selling for Rs.1200 per share. The dividend expected next is Rs.25.00. The investors' required rate of return on this stock is 12 percent. Assume that the constant growth model applies to Amulya Corporation. What is the expected growth rate of Amulya Corporation?

Solution: Po = D1 / (r – g) Rs.1200 = Rs.25 / (0.12 – g) 0.12 –g = 25/1200 = 0.0208 g = 0.12-0.0208 = 0.0992 or 9.92 %

17.

Sloppy Limited is facing gloomy prospects. The earnings and dividends are expected to decline at the rate of 5 percent. The previous dividend was Rs.2.00. If the current market price is Rs.10.00, what rate of return do investors expect from the stock of Sloppy Limited?

Solution: Po = D1/ (r – g) = Do(1+g) / (r – g) = Rs.2.00, g = -0.05, Po = Rs.10 Do So 10 = 2.00 (1- .05) / (r-(-.05)) = 1.90 / (r + .05) r +0.05 =1.90/10 = 0.19 r = 0.19 – 0.05 = 0.14 18. Mammoth Corporation is facing gloomy prospects. The earnings and dividends are expected to decline at the rate of 10 percent. The previous dividend was Rs.3.00. If the current market price is Rs.25.00, what rate of return do investors expect from the stock of Mammoth Limited?

Solution: Po = D1/ (r – g) = Do(1+g) / (r – g) Do = Rs.3.00, g = -0.10, Po = Rs.25 So 25 = 3.00 (1- .10) / (r-(-.10)) = 2.7 / (r + .10) r +0.10 =2.7/25 = 0.108 r = 0.108 – 0.10 = 0.008 or 0.8 percent 19. The current dividend on an equity share of Omega Limited is Rs.8.00 on an earnings per share of Rs. 30.00. (i) Assume that the dividend per share will grow at the rate of 20 percent per year for the next 5 years. Thereafter, the growth rate is expected to fall and stabilise at 12 percent. Investors require a return of 15 percent from Omega’s equity shares. What is the intrinsic value of Omega’s equity share? Solution:

g1 = 20 %, g2 = 12 %, n = 5 yrs , r = 15% D1 = 8 (1.20) = Rs. 9.60 1+ g1 1Po = D1 1+ r + r - g1 1.20 1 = 9.60 1.15 + 0.15 - 0.20 0.15 - 0.12 9.60 ( 1.20)4 (1.12) x ( 1.15)5 1
5 n

D1 (1 + g1)n - 1 (1 + g2 ) x r - g2

1 ( 1 + r )n

= 45.53 + 369.49 = Rs. 415.02

(ii)

Assume that the growth rate of 20 percent will decline linearly over a five year period and then stabilise at 12 percent. What is the intrinsic value of Omega’s share if the investors’ required rate of return is 15 percent?

Solution:

D0 [ ( 1 + gn) + H ( ga - gn)] P0 = r - gn 8 [ (1.12) + 2.5 ( 0.20 - 0.12 )] = 0.15 - 0.12 = 20. Rs. 352

The current dividend on an equity share of Magnum Limited is Rs.4.00. (i) Assume that Magnum’s dividend will grow at the rate of 18 percent per year for the next 5 years. Thereafter, the growth rate is expected to fall and stabilise at 10 percent. Equity investors require a return of 15 percent from Magnum’s equity shares. What is the intrinsic value of Magnum’s equity share?

Solution:

g1 = 18%, g2 = 10%, n = 5 yrs, r = 15% D1 = 4 (1.18) = Rs.4.72 1 + g1 1– 1+r P0 = D1 r – g1 1.18 11.15 = 4.72 0.15 – 0.18 = 21.62 + 100.12 = 121.74 + 0.15 – 0.10 4.72 (1.18)4 (1.10) x (1.15)5 1
5 n

D1 (1 + g1) n – 1 (1 + g2) + r – g2 x

1 (1 + r)n

(ii)

Assume now that the growth rate of 18 percent will decline linearly over a period of 4years and then stabilise at 10 percent . What is the intrinsic value per share of Magnum, if investors require a return of 15 percent ?

Solution:

(1 + gn) + H (ga – gn) P0 = D0 r – gn (1.10) + 2 (0.18 – 0.10) = 4.00 0.15 – 0.10 = Rs.100.8

21.

The current dividend on an equity share of Omex Limited is Rs. 5.00 on an earnings per share of Rs. 20.00. Assume that the dividend will grow at a rate of 18 percent for the next 4 years. Thereafter, the growth rate is expected to fall and stabilize at 12 percent. Equity investors require a return of 15 percent from Omex’s equity share. What is the intrinsic value of Omex’s equity share?

(i)

Solution: g1 = 18 %, g2 = 12 %, n = 4yrs , r = 15%

D1 = 5 (1.18) = Rs. 5.90 1+ g1 1Po = D1 1+ r + r - g1 1.18 1 = 5.90 1.15 + 0.15 - 0.18 0.15 - 0.12 5.90 ( 1.18 )3 ( 1.12 ) x ( 1.15)4 1
4 n

D1 (1 + g1)n - 1 (1 + g2 ) x r - g2

1 ( 1 + r )n

= 21.34 + 206.92

= Rs. 228.35

22.

You can buy a Rs.1000 par value bond carrying an interest rate of 10 percent (payable annually) and maturing after 5 years for Rs.970. If the re-investment rate applicable to the interest receipts from this bond is 15 percent, what will be your yield to maturity?

Solution: Terminal value of the interest proceeds = 100 x FVIFA (15%,5) = 100 x 6.742 = 674.20 Redemption value = 1,000 Terminal value of the proceeds from the bond = 1,674.20

let r be the yield to maturity. The value of r can be obtained from the equation 970 (1 + r)5 r = 1,674.20 = (1,674.20/970)1/5 -1 = 0.1153 or 11.53 %

23.

You can buy a Rs.100 par value bond carrying an interest rate of 8 percent (payable annually) and maturing after 8 years for Rs.90. If the re-investment rate applicable to the interest receipts from this bond is 10 percent, what will be your yield to maturity?

Solution: Terminal value of the interest proceeds = 8 x FVIFA (10%,8) = 8 x 11.436 = 91.49 Redemption value = 100 Terminal value of the proceeds from the bond = 191.49 let r be the yield to maturity. The value of r can be obtained from the equation 90 (1 + r)8 r = 191.49 = (191.49/90)1/8 -1 = 0.099 or 9.9 %

24.

Keerthi Limited is expected to give a dividend of Rs.5 next year and the same would grow by 12 percent per year forever. Keerthi pays out 60 percent of its earnings. The required rate of return on Keerthi’s stock is 15 percent. What is the PVGO?

Solution: Po = D1 r–g Po = 5 = Rs. 166.67 0.15-0.12 Po = E1 + PVGO r Po = 8.33 + PVGO 0.15 166.67 = 55.53 + PVGO

So, PVGO = 111.14

25.

Adinath Limited is expected to give a dividend of Rs.3 next year and the same would grow by 15 percent per year forever. Adinath pays out 30 percent of its earnings. The required rate of return on Adinath’s stock is 16 percent. What is the PVGO?

Solution: Po = D1 r–g Po = 3 = Rs. 300 0.16-0.15 Po = E1 + PVGO r Po = 10 + PVGO 0.16 300 = 62.5 + PVGO So, PVGO = 237.5 CHAPTER 8 1. You are considering purchasing the equity stock of Electra Limited. The current price per share is Rs.20. You expect the dividend a year hence to be Re.2.00. You expect the price per share of Electra stock a year hence to have the following probability distribution. Price a year hence Probability Rs.19 0.5 20 0.3 22 0.2

(a) What is the expected price per share a year hence? (b) What is the probability distribution of the rate of return on Electra 's equity stock? Solution: (a) (b) Expected price per share a year hence will be: = 0.5 x Rs.19 + 0.3 x Rs.20 + 0.2 x Rs.22 = Rs. 19.90 Probability distribution of the rate of return is Rate of return (Ri) Probability (pi) 5% 0.5 10 % 0.3 20 % 0.2

Note that the rate of return is defined as: Dividend + Terminal price -------------------------------- - 1 Initial price

2.

You are considering purchasing the equity stock of Empire Corporation. The current price per share is Rs.180. You expect the dividend a year hence to be Re.8.00. You expect the price per share of Empire Corporation stock a year hence to have the following probability distribution. Price a year hence Probability Rs.175 0.2 180 0.3 200 0.5

(a) What is the expected price per share a year hence? (b) What is the probability distribution of the rate of return on Empire Corporation 's equity stock? Solution: (a) Expected price per share a year hence will be: = 0.2 x Rs.175 + 0.3 x Rs.180 + 0.5 x Rs.200 = Rs. 189 (c) Probability distribution of the rate of return is Rate of return (Ri) Probability (pi) 3. 1.7 % 0.2 4.4 % 0.3 15.6 % 0.5

The stock of South India Corporation (SIC) performs well relative to other stocks during recessionary periods. The stock of North India Corporation ( NIC), on the other hand, does well during growth periods. Both the stocks are currently selling for Rs.100 per share. The rupee return (dividend plus price change) of these stocks for the next year would be as follows: Economic condition Low growth Stagnation 0.3 0.1 60 70 60 50

Probability Return on SIC stock Return on NIC stock

High growth 0.4 40 65

Recession 0.2 80 35

Calculate the expected return and standard deviation of: (a) (b) (c) (d) Rs.5,000 in the equity stock of SIC; Rs.5,000 in the equity stock of NIC; Rs.2,500 in the equity stock of SIC and Rs.2,500 in the equity stock of NIC; Rs.3,000 in the equity stock of SIC and Rs.2,000 in the equity of NIC. Which of the above four options would you choose? Why?

Solution: (a) For Rs.5,000, 50 shares of SIC’s stock can be acquired. The probability distribution of the return on 50 shares is Economic Condition High Growth Low Growth Stagnation Recession Expected return = = Return (Rs) 50 x 40 = 2,000 50x 60 = 3,000 50x 70 = 3,500 50x 80 = 4,000 Probability 0.4 0.3 0.1 0.2

(2,000 x 0.4) + (3,000 x 0.3) + (3,500 x 0.1) + (4,000 x 0.2) Rs.2,850

Standard deviation of the return = [(2,000 –2,850)2 x 0.4 + (3,000 –2,850)2 x 0.3 + (3,500 –2,850)2 x 0.1+ (4,000 –2,850)2 x 0.2]1/2 = Rs. 776.21 (b) For Rs.5,000, 50 shares of NIC’s stock can be acquired. The probability distribution of the return on 50 shares is: Economic condition High growth Low growth Stagnation Recession Expected return = Return (Rs) 50 x 65 = 3,250 50 x 60 = 3,000 50 x 50 = 2,500 50 x 35 = 1,750 Probability 0.4 0.3 0.1 0.2

(3,250 x 0.4) + (3,000 x 0.3) + (2,500 x 0.1) + (1,750 x 0.2) = Rs. 2,800

Standard deviation of the return = [(3,250–2,800)2 x .4 + (3,000–2,800)2 x .3 + (2,500– 2,800)2 x .1 + (1,750–2,800)2 x .2]1/2 = Rs. 567.89 (c) For Rs.2,500, 25 shares of SIC’s stock can be acquired; likewise for Rs.2,500, 25 shares of NIC’s stock can be acquired. The probability distribution of this option is: Return (Rs) Probability (25 x 40) + (25 x 65) = 2,625 0.4 (25x 60) + (25x 60) = 3,000 0.3 (25 x 70) + (25x 50) = 3,000 0.1 (25x 80) + (25 x 35) = 2,875 0.2

Expected return

Standard deviation

= (2,625 x 0.4) + (3,000 x 0.3) + (3,000x 0.1) + (2,875 x 0.2) = Rs. 2825 = [(2,625 –2825)2 x 0.4 + (3,000–2825)2 x 0.3 + (3,000–2825)2 x 0.1 + (2,875–2825)2 x 0.2 ]1/2 Rs.169.56

= d.

For Rs.3000, 30 shares of SIC’s stock can be acquired; likewise for Rs.2000, 20 shares of NIC’s stock can be acquired. The probability distribution of this option is: Return (Rs) (30x 40) + (20x 65) (30 x 60) + (20x 60) (30x 70) + (20x 50) (30x 80) + (20x 35) Expected return = = = = = = Standard deviation = = 2,500 3,000 3,100 3,100 Probability 0.4 0.3 0.1 0.2

(2,500x 0.4) + (3,000x 0.3) + (3,100x 0.1) + (3,100x 0.2) Rs.2,830 [(2,500–2,830)2 x 0.4 + (3,000–2,830)2 x 0.3 + (3,100–2,830)2 x 0.1 + (3,100–2,830)2 x 0.2]1/2 Rs.272.21

The expected return to standard deviation of various options are as follows : Expected return Standard deviation Expected / Standard Option (Rs) (Rs) return deviation a 2,850 776.21 3.67 b 2,800 567.89 4.93 c 2,825 169.56 16.66 d 2,830 272.21 10.40 Option `c’ is the most preferred option because it has the highest return to risk ratio. 4. The following table, gives the rate of return on stock of Apple Computers and on the market portfolio for five years

Year 1 2 3 4 5

Return on the stock Apple Computers (%) -13 5 15 27 10

Return Market Portfolio (%) -3 2 8 12 7

(i) What is the beta of the stock of Apple Computers? (ii) Establish the characteristic line for the stock of Apple Computers. Solution: Year 1 2 3 4 5 Sum Mean ?M2 RA -13 5 15 27 10 44 8.8 134.8 = 5-1 83.55 ?A = 33.7 (ii) Alpha = = RA – ?A RM 8.8 – (2.48 x 5.2) = - 4.1 = 2.48 = 33.7 Cov A,M = 5-1 RM -3 2 8 12 7 26 5.2 RA - RA -21.8 -3.8 6.2 18.2 1.2 RM - RM -8.2 -3.2 2.8 6.8 1.8 (RA - RA) (RM - RM) 178.76 12.16 17.36 123.76 2.16 334.2 (RM - RM)2 67.24 10.24 7.84 46.24 3.24 134.8

334.2 = 83.55

Equation of the characteristic line is RA = - 4.1 + 2.48 RM 5. The rate of return on the stock of Sigma Technologies and on the market portfolio for 6 periods has been as follows:

Period

Return on the stock of Sigma Technologies (%) 16 12 -9 32 15 18

Return on the market portfolio (%) 14 10 6 18 12 15

1 2 3 4 5 6

(i) What is the beta of the stock of Sigma Technologies.? (ii) Establish the characteristic line for the stock of Sigma Technologies Solution: (i)

Year

RA (%)

RM (%)

RA-RA

RM-RM

(RA-RA) x(RM-RM) 21.12 17.92 1585.92 496.32 237.12

(RM-RM)2

1 2 3 4 5

36 24 -20 46 50

28 20 -8 52 36

8.8 -3.2 -47.2 18.8 22.8

2.4 -5.6 -33.6 26.4 10.4

5.76 31.36 1128.96 696.96 108.16

? RA = 136 RA = 27.2 ? M2 = 1971.2 5–1 ?A =

?RM = 128 Cov A,M = RM = 25.6

2358.4 5-1

2358.4 / (5-1) ------------------1971.2 / (5-1)

=

1.196

(ii)

Alpha =

RA – ?A RM = 27.2 – (1.196 x 25.6) = -3.42 Equation of the characteristic line is RA = - 3.42 + 1.196 RM

6.

The rate of return on the stock of Omega Electronics and on the market portfolio for 6 periods has been as follows : Period Return on the stock of Omega Electronics (%) 18% 10% -5% 20% 9% 18% Return on the market portfolio (%) 15% 12% 5% 14% -2% 16%

1 2 3 4 5 6

(i)What is the beta of the stock of Omega Electronics? (ii) Establish the characteristic line for the stock of Omega Electronics. Solution:

Period R0 (%) 1 2 3 4 5 6 18 10 -5 20 9 18

RM (%) 15 12 5 14 -2 16

(R0 – R0) 6.33 -1.67 -16.67 8.33 - 2.67 6.33

(RM – RM) 5 2 -5 4 -12 6

(R0 –R0) (RM – RM) 31.65 - 3.34 83.35 33.32 32.04 37.98

(RM - RM)2 25 4 25 16 144 36 250

?R0 = 70 ?RM = 60 R0 =11.67 250 ?M =
2

?(R0-R0) (RM-RM) = 215 215

RM = 10 CovO,M = 5 = 43.0

= 50 5 43.0

?0 = 50.0 (ii)

= 0.86

Alpha = =

RO – ?A RM 11.67 – (0.86 x 10) = 3.07

Equation of the characteristic line is RA = 3.07 + 0.86 RM

7.

The risk-free return is 8 percent and the return on market portfolio is 16 percent. Stock X's beta is 1.2; its dividends and earnings are expected to grow at the constant rate of 10 percent. If the previous dividend per share of stock X was Rs.3.00, what should be the intrinsic value per share of stock X ?

Solution: The required rate of return on stock A is: RX = = = RF + ?X (RM – RF) 0.08 + 1.2 (0.16 – 0.08) 0. 176

Intrinsic value of share = D1 / (r- g) = Do (1+g) / ( r – g) Given Do = Rs.3.00, g = 0.10, r = 0.176 3.00 (1.10) Intrinsic value per share of stock X = 0.176 – 0.10 = 8. Rs. 43.42

The risk-free return is 7 percent and the return on market portfolio is 13 percent. Stock P's beta is 0.8 ; its dividends and earnings are expected to grow at the constant rate of 5 percent. If the previous dividend per share of stock P was Rs.1.00, what should be the intrinsic value per share of stock P ?

Solution: The required rate of return on stock P is: RP = = = RF + ?P (RM – RF) 0.07 + 0.8 (0.13 – 0.07) 0. 118

Intrinsic value of share = D1 / (r- g) = Do (1+g) / ( r – g) Given Do = Rs.1.00, g = 0.05, r = 0.118 1.00 (1.05) Intrinsic value per share of stock P = 0.118 – 0.05 = Rs. 15.44

9.

The risk-free return is 6 percent and the expected return on a market portfolio is 15 percent. If the required return on a stock is 18 percent, what is its beta?

Solution: The SML equation is RA = RF + ?A (RM – RF) Given RA = 18%. RF = 6%, RM = 15%, we have

0.18 = .06 + ?A (0.15 – 0.06) 0.12 i.e.?A = 0.09 Beta of stock = 1.33 10. The risk-free return is 9 percent and the expected return on a market portfolio is 12 percent. If the required return on a stock is 14 percent, what is its beta? = 1.33

Solution: The SML equation is RA = RF + ?A (RM – RF) Given RA = 14%. RF = 9%, RM = 12%, we have

0.14 = .09 + ?A (0.12 – 0.09) 0.05 i.e.?A = 0.03 Beta of stock = 1.67 = 1.67

11.

The risk-free return is 5 percent. The required return on a stock whose beta is 1.1 is 18 percent. What is the expected return on the market portfolio?

Solution: The SML equation is: RX = RF + ?X (RM – RF) We are given 0.18 = 0.05 + 1.1 (RM – 0.05) i.e., 1.1 RM = 0.185 or RM = 0.1681 Therefore return on market portfolio = 16.81 %

12.

The risk-free return is 10 percent. The required return on a stock whose beta is 0.50 is 14 percent. What is the expected return on the market portfolio?

Solution: The SML equation is: RX = RF + ?X (RM – RF) We are given 0.14 = 0.10 + 0.50 (RM – 0.10) i.e., 0.5 RM = 0.09 or RM = 0.18 Therefore return on market portfolio = 18 % 13. The required return on the market portfolio is 15 percent. The beta of stock A is 1.5. The required return on the stock is 20 percent. The expected dividend growth on stock A is 6 percent. The price per share of stock A is Rs.86. What is the expected dividend per share of stock A next year? What will be the combined effect of the following on the price per share of stock ? (a) The inflation premium increases by 3 percent. (b) The decrease in the degree of risk-aversion reduces the differential between the return on market portfolio and the risk-free return by one-fourth. (c) The expected growth rate of dividend on stock A decrease to 3 percent. (d) The beta of stock A falls to1.2

Solution: RM = 15% ?A = 1.5 RA =20 % g = 6 % Po = Rs.86

Po = D1 / (r - g) Rs.86 = D1 / (0.20 - .06) So D1 = Rs.12.04 and Do = D1 / (1+g) = 12.04 /(1.06) = Rs.11.36 RA = Rf + ?A (RM – Rf)

0.20 = Rf + 1.5 (0.15 – Rf) 0.5Rf = 0.025 So Rf = 0.05 or 5%. Original Rf RM – Rf g ?A 5% 10% 6% 1.5 Revised 8% 7.5% 3% 1.2

Revised RA = 8 % + 1.2 (7.5%) = 17 % Price per share of stock A, given the above changes is 11.36 (1.03) = Rs. 83.58 0.17 – 0.03 14. The required return on the market portfolio is 16 percent. The beta of stock A is 1.6. The required return on the stock is 22 percent. The expected dividend growth on stock A is 12 percent. The price per share of stock A is Rs.260. What is the expected dividend per share of stock A next year? What will be the combined effect of the following on the price per share of stock ? (a) The inflation premium increases by 5 percent. (b) The decrease in the degree of risk-aversion reduces the differential between the return on market portfolio and the risk-free return by one-half. (c) The expected growth rate of dividend on stock A decrease to 10 percent. (d) The beta of stock A falls to 1.1

Solution: RM = 16% ?A = 1.6 RA =22 % g = 12 % Po = Rs. 260

Po = D1 / (r - g) Rs.260 = D1 / (0.22 - .12) So D1 = Rs.26 and Do = D1 / (1+g) = 26 /(1.12) = Rs.23.21 RA = Rf + ?A (RM – Rf)

0.22 = Rf + 1.6 (0.16 – Rf) 0.6Rf = 0.036 So Rf = 0.06 or 6%. Original Rf RM – Rf g ?A 6% 10% 12 % 1.6 Revised 11% 5% 10 % 1.1

Revised RA = 11% + 1.1 (5%) = 16.5 % Price per share of stock A, given the above changes is

23.21 (1.10) = Rs. 392.78 0.165 – 0.10 CHAPTER 9 1. The returns of two assets under four possible states of nature are given below : State of nature 1 2 3 4 Probability 0.40 0.10 0.20 0.30 Return on asset 1 -6% 18% 20% 25% Return on asset 2 12% 14% 16% 20%

a. What is the standard deviation of the return on asset 1 and on asset 2? b. What is the covariance between the returns on assets 1 and 2? c. What is the coefficient of correlation between the returns on assets 1 and 2? Solution: (a) E (R1) = = E (R2) = = 0.4(-6%) + 0.1(18%) + 0.2(20%) + 0.3(25%) 10.9 % 0.4(12%) + 0.1(14%) + 0.2(16%) + 0.3(20%) 15.4 %

?(R1) = [.4(-6 –10.9)2 + 0.1 (18 –10.9)2 + 0.2 (20 –10.9)2 + 0.3 (25 –10.9)2]½ 13.98% ?(R2) = [.4(12 –15.4)2 + 0.1(14 –15.4)2 + 0.2 (16 – 15.4)2 + 0.3 (20 –15.4)2] ½ = 3.35 % (b) The covariance between the returns on assets 1 and 2 is calculated below State of nature Probability Return on asset 1 Deviation of return on asset 1 from its mean (4) -16.9% 7.1% 9.1% 14.1% Return on asset 2 Deviation of the return on asset 2 from its mean (6) -3.4% -1.4% 0.6% 4.6% Sum = Product of deviation times probability

(1) 1 2 3 4

(2) 0.4 0.1 0.2 0.3

(3) -6% 18% 20% 25%

(5) 12% 14% 16% 20%

(2)x(4)x(6) 22.98 -0.99 1.09 19.45 42.53

Thus the covariance between the returns of the two assets is 42.53. (c) The coefficient of correlation between the returns on assets 1 and 2 is: Covariance12 42.53 = = 0.91 ?1 x ?2 13.98 x 3.35 2. The returns of 4 stocks, A, B, C, and D over a period of 5 years have been as follows: 1 8% 10% 9% 10% 2 10% 6% 6% 8% 3 -6% -9% 3% 13% 4 -1% 4% 5% 7% 5 9% 11% 8% 12%

A B C D

Calculate the return on: a. b. c. d. portfolio of one stock at a time portfolios of two stocks at a time portfolios of three stocks at a time. a portfolio of all the four stocks.

Assume equiproportional investment. Solution: Expected rates of returns on equity stock A, B, C and D can be computed as follows: A: 8 + 10 – 6 -1+ 9 5 10+ 6- 9+4 + 11 5 9 + 6 + 3 + 5+ 8 5 10 + 8 + 13 + 7 + 12 5 = 4%

B:

= 4.4%

C: D:

= 6.2% = 10.0%

(a) (b)

Return on portfolio consisting of stock A

= 4%

Return on portfolio consisting of stock A and B in equal proportions = 0.5 (4) + 0.5 (4.4) = 4.2%

(c )

Return on portfolio consisting of stocks A, B and C in equal proportions = 1/3(4 ) + 1/3(4.4) + 1/3 (6.2) = 4.87% Return on portfolio consisting of stocks A, B, C and D in equal proportions = 0.25(4) + 0.25(4.4) + 0.25(6.2) +0.25(10) = 6.15%

(d)

3.

A portfolio consists of 4 securities, 1, 2, 3, and 4. The proportions of these securities are: w1=0.3, w2=0.2, w3=0.2, and w4=0.3. The standard deviations of returns on these securities (in percentage terms) are : ?1=5, ?2=6, ?3=12, and ?4=8. The correlation coefficients among security returns are: ?12=0.2, ?13=0.6, ?14=0.3, ?23=0.4, ?24=0.6, and ?34=0.5. What is the standard deviation of portfolio return?

Solution: The standard deviation of portfolio return is: ?p = [w12?12 + w22?22 + w32?32 + ?42?42 + 2 w1 w2 ?12 ?1 ?2 + 2 w1 w3 ?13 ?1 ?3 + 2 w1 w4 ?14 ?1?4 + 2 w2 w3 ?23 ?2 ?3 + 2 w2 w4 ?24 ?2 ?4 + 2 w3 w4 ?34 ?3 ?4 ]1/2 = [0.32 x 52 + 0.22 x 62 + 0.22 x 122 + 0.32 x 82 + 2 x 0.3 x 0.2 x 0.2 x 5 x 6 + 2 x 0.3 x 0.2 x 0.6 x 5 x 12 + 2 x 0.3 x 0.3 x 0.3 x 5 x 8 + 2 x 0.2 x 0.2 x 0.4 x 6 x 12 + 2 x 0.2 x 0.3 x 0.6 x 6 x 8 + 2 x 0.2 x 0.3 x 0.5 x 12 x 8]1/2 = 5.82 % 4. Assume that a group of securities has the following characteristics : (a) the standard deviation of each security is equal to ?A ; (b) covariance of returns ?AB is equal for each pair of securities in the group. What is the variance of a portfolio containing six securities which are equally weighted ?

Solution: When there are 6 securities, you have 6 variance terms and 6 x 5 = 30 covariance terms. As all variance terms are the same, all covariance terms are the same, and all securities are equally weighted, the portfolio variance is: 6wA2 ?A2 + 30 wA2 ?AB

5.

The following information is given: Expected return for the market Standard deviation of the market return Risk-free rate Correlation coefficient between stock A and the market Correlation coefficient between stock B and the market Standard deviation for stock A Standard deviation for stock B (i) What is the beta for stock A?

= 15% = 25% = 8% = 0.8 = 0.6 = 30% = 24%

Solution:

?AM = ?M2 = ?A

Cov (A,M) ?A ?M 252 = 625 Cov (A,M) 600 = ?M2 625 ; 0.8 =

Cov (A,M) ? 30 x 25 Cov (A,M) = 600

=

= 0.96

(ii) What is the expected return for stock A ? Solution: E(RA) = Rf + ?A (E (RM) - Rf) = 8% + 0.96 (7%) = 14.72%

6.

The following table gives an analyst’s expected return on two stocks for particular market returns. Market Return Aggressive Stock Defensive Stock 5% - 5% 10% 25% 45% 16% (i) What is the ratio of the beta of the aggressive stock to the beta of the defensive stock?

Solution:

45 – (-5) Beta of aggressive stock = 25 – 5 16 - 10 Beta of defensive stock = 25 – 5 Ratio = 2.5/0.30 = 8.33 (ii) If the risk-free rate is 7% and the market return is equally likely to be 5% and 25% what is the market risk premium? = 0.30 = 2.5

Solution: E (RM) = 0.5 x 5 + 0.5 x 25 = 15% Market risk premium = 15% - 7% = 8% (iii) What is the alpha of the aggressive stock? Solution: Expected return = 0.5 x –5 + 0.5 x 45 = 20% Required return as per CAPM = 7% + 2.5 (8%) = 27% Alpha = - 7% 7. The following table gives an analyst’s expected return on two stocks for particular market returns. Market Return 8% 20% Aggressive Stock 2% 32% Defensive Stock 10% 16%

(i) What is the beta of the aggressive stock? Solution: 32% - 2% Beta = 20% - 8% = 2.5

(ii)

If the risk-free rate is 6% and the market return is equally likely to be 8% and 20%, what is the market risk premium?

Solution: The expected return on the market portfolio is: 0.5 x 8% + 0.5 x 20% = 14% Since the risk-free rate is 6%, the market risk premium is 8% (iii) What is the alpha of the aggressive stock? Solution: Expected return on the aggressive stock = 0.5 x 2% + 0.5 x 32% = 17% Required return = 6% + 8 x 2.5 = 26% Alpha = 17 – 26% = – 9%

MINICASE(1) Mr. Nitin Gupta had invested Rs.8 million each in Ashok Exports and Biswas Industries and Rs. 4 million in Cinderella Fashions, only a week before his untimely demise . As per his will this portfolio of stocks were to be inherited by his wife alone . As the partition among the family members had to wait for one year as per the terms of the will, the portfolio of shares had to be maintained as they were for the time being. The will had stipulated that the job of administering the estate for the benefit of the beneficiaries and partitioning it in due course was to be done by the reputed firm of Chartered Accountants, Talwar Brothers. Meanwhile the widow of the deceased was very eager to know certain details of the securities and had asked the senior partner of Talwar Brothers to brief her in this regard. For this purpose the senior partner has asked you to prepare a detailed note to him with calculations using CAPM, to answer the following possible doubts. 1. What is the expected return and risk (standard deviation) of the portfolio? 2. What is the scope for appreciation in market price of the three stocks-are they overvalued or undervalued? You find that out the three stocks, your firm has already been tracking two viz. Ashok Exports (A) and Biswas Industries (B)-their betas being 1.7 and 0.8 respectively.

Further, you have obtained the following historical data on the returns of Cinderella Fashions(C): Period Market return (%) Return on Cinderella Fashions (%) -------------------------------------------------1 10 14 2 5 8 3 (2) (6) 4 (1) 4 5 5 10 6 8 11 7 10 15 On the future returns of the three stocks, you are able to obtain the following forecast from a reputed firm of portfolio managers. ------------------------------------------------------------------------------------------------------State of the Probability Returns ( in percentage ) Economy Treasury Ashok Biswas Cinderella Sensex Bills Exports Industries Fashions ------------------------------------------------------------------------------------------------------Recession 0.3 7 5 15 (10) (2) Normal 0.4 7 18 8 16 17 Boom 0.3 7 30 12 24 26 Required: Prepare your detailed note to the senior partner.

Solution: (1) Calculation of beta of Cinderella Fashions stock from the historical data Period 1 2 3 4 5 6 7 Return Return Rc-Rc Rm-Rm (Rm-Rm)2 (Rc-Rc) Rc ( % ) Rm ( %) x (Rm-Rm) 14 10 6 5 25 30 8 5 0 0 0 0 (6) (2) (14) (7) 49 98 4 (1) (4) (6) 36 24 10 5 2 0 0 0 11 8 3 3 9 9 15 10 7 5 25 35

?Rc=56 ?Rm=35 ? (Rm-Rm)2= 144 ? (Rc-Rc)(Rm-Rm)= 196 2 Rc= 8 Rm= 5 ?m = 144/6 =24 Cov(c,m) = 196/6= 32.7 Beta of Cinderella Fashions ?c = 32.7/24= 1.36 (2) Calculation of expected returns, standard deviations and covariances E(A) =[ 0.3x5] + [0.4x18] +[ 0.3x30] = 17.7 E(B)= [0.3x15] + [0.4x8] + [0.3x12] = 11.3 E(C)= [0.3x(-)10] + [0.4x16] +[0.3x24] = 10.6 E(M)= [0.3x(-)2]+ [0.4x17] + [0.3x26] = 14 ?A = [ 0.3(5-17.7)2 +0.4(18-17.7)2+0.3(30-17.7)2 ]1/2 = [48.4 + 0.1+45.4]1/2 = 9.7 ?B = [0.3(15-11.3)2 + 0.4(8-11.3)2 +0.3(12-11.3)2]1/2 = [ 4.11 +4.36+ 0.15]1/2 =2.94 ?c = [0.3(-10-10.6)2+0.4(16-10.6)2 + 0.3(24-10.6)2]1/2 = [ 127.31 +11.66+53.87]1/2 = 13.89 ?M = [0.3(-2-14)2 +0.4(17-14)2+0.3(26-14)2]1/2 = [ 76.8 +3.6 +43.2]1/2 = 11.1 Calculation of covariances between the stocks State of the Prob- RA-RA RB-RB RC-RC Economy ability (1) (2) (3) (4) (5) Recession 0.3 -12.7 3.7 -20.6 Normal 0.4 0.3 -3.3 5.4 Boom 0.3 12.3 0.7 13.4 ?A,B =

(2)x(3) x (4)

(2)x(4)x(5)

(2)x(3)x(5)

-14.1 -22.9 -0.1 -7.1 2.6 2.8 -11.6 ?B,C= -27.2

78.5 0.6 49.4 ?A,C= 128.5

Expected return and standard deviation of the portfolio E(P) = (0.4x17.7) + (0.4x11.3) +(0.2x10.6)= 13.7 ?p = [ wA2 ?A2 + wB2 ?B2 + wC2 ?C2 + 2 wAwB ?A,B +2 wBwC ?B,C +2 wAwC ?A,C]1/2 = [ 15.1+ 1.4 +7.7-3.7-4.4+ 20.6]1/2 = 6.1 ( 3) Determining overpricing and underpricing using CAPM ?A =1.7 ?B =0.8 ?C = 1.36 E(RM) = 14 Rf =7%

SML = 7 + (14 -7)xBeta = 7 + 7 x Beta Required return on Ashok Exports = 7 + (7 x 1.7) = 18.9 % Required return on Biswas Industries = 7 + (7 x 0.8 ) = 12.6 % Required return on Cinderella Fashions = 7 + (7 x 1.36 ) =16.5 % As the expected return of 17.7 % on Ashok Exports is slightly less than the required return of 18.9 %, its expected return can be expected to go up to the fair return indicated by CAPM and for this to happen its market price should come down. So it is slightly overvalued. In the case of Biswas Industries stock, as the expected return of 11.3% is again slightly less than the required return of 12.6 %, its expected return can be expected to go up and for this to happen its market price should come down. So it is also slightly overvalued. In the case of Cinderella Fashions the expected return is 10.6 % against the required return of 16.5 %. So it is considerably overvalued.

MINICASE(2) Seth Ratanlal, who was widower and issueless, had left his substantial wealth as legacy to his nephew and niece through a will. Detailed instructions had been left on how the estate should be shared between the two , once both of them attained the age of majority. A week before his demise he had taken a fancy to the capital market and had invested a sizeable amount in equity shares, specifically, Rs.6 million in Arihant Pharma, Rs.4.8 million in Best Industries and Rs. 1.2 million in Century Limited. As the partition among the siblings had to wait for at least one more year as the girl was still a minor, the portfolio of shares had to be maintained as they were for the time being. The will had entrusted the job of administering the estate for the benefit of the beneficiaries and partitioning in due course to the reputed firm of Chartered Accountants, Karaniwala and Karaniwala. Meanwhile the young beneficiaries were very eager to know certain details of the securities and had asked the senior partner of the firm to brief them in this regard. For this purpose the senior partner has asked you to prepare a detailed note to him with calculations using CAPM, to answer the following possible doubts. 1. What is the expected return and risk (standard deviation) of the portfolio? 2. What is the scope for appreciation in market price of the three stocks-are they overvalued or undervalued? You find that out the three stocks, your firm has already been tracking two viz. Arihant Pharma (A) and Best Industries (B)-their betas being 1.2 and 0.8 respectively. Further, you have obtained the following historical data on the returns of Century Limited(C): Period Market return (%) Return on Century Limited (%) -------------------------------------------------1 8 10 2 (6) 8 3 12 25 4 10 (8) 5 9 14 6 9 11 On the future returns of the three stocks, you are able to obtain the following forecast from a reputed firm of portfolio managers. ------------------------------------------------------------------------------------------------------State of the Probability Returns ( in percentage ) on Economy Treasury Arihant Best Century Nifty Bills Pharma Industries Limited ------------------------------------------------------------------------------------------------------Recession 0.2 6 (10) (8) 15 (8) Normal 0.4 6 18 12 6 15 Boom 0.4 6 30 20 (10) 25

Prepare your report.

Solution: (3) Calculation of beta of Century Limited stock from the historical data Period 1 2 3 4 5 6 Return Return Rc-Rc Rm-Rm (Rm-Rm)2 (Rc-Rc) Rc ( % ) Rm ( %) x (Rm-Rm) 10 8 0 1 1 0 8 (6) (2) (13) 169 26 25 12 15 5 25 75 (8) 10 (18) 3 9 (54) 14 9 4 2 4 8 11 9 1 2 4 2

?Rc=60 ?Rm=42 ? (Rm-Rm)2=212 ? (Rc-Rc)(Rm-Rm)=57 Rc=10 Rm=7 ?m2 = 212/5 =42.4 Cov(c,m) = 57/5=11.4 Beta of Century Limited ?c = 11.4/42.4 = 0.3 (4) Calculation of expected returns, standard deviations and covariances E(A) =[ 0.2x(-)10] + [0.4x18] +[ 0.4x30] = -2+7.2+12=17.2 E(B)= [0.2x(-)8] + [0.4x12] + [0.4x20] = -1.6 +4.8+8 = 11.2 E(C)= [0.2x15] + [0.4x6] +[0.4x(-) 10] = 3+2.4- 4 = 1.4 E(M)= [0.2x(-)8]+ [0.4x15] + [0.4x25] = -1.6+6.0 +10=14.4 ?A = [ 0.2(-10-17.2)2 +0.4(18-17.2)2+0.4(30-17.2)2 ]1/2 = [148 + 0.3+65.5]1/2 = 14.6 ?B = [0.2(-8-11.2)2 + 0.4(12-11.2)2 +0.4(20-11.2)2]1/2 = [ 73.7 +0.3+31.0]1/2 =10.2 ?c = [0.2(15-1.4)2+0.4(6-1.4)2 + 0.4(-10-1.4)2]1/2 = [ 37 +8.5+52]1/2 = 9.9 ?M = [0.2(-8-14.4)2 +0.4(15-14.4)2+0.4(25-14.4)2]1/2 = [ 100.4 +0.1 +44.9]1/2 = 12.1 Calculation of covariances between the stocks State of the Prob- RA-RA RB-RB RC-RC (2)x(3)x(4) (2)x(4)x(5) (2)x(3)x(5) Economy ability (1) (2) (3) (4) (5) Recession 0.2 (27.2) (19.2) 13.6 104.4 (52.2) (74.0) Normal 0.4 0.8 0.8 4.6 0.3 1.5 1.5 Boom 0.4 12.8 8.8 (11.4) 45.1 (40.1) (58.4) ?A,B =149.8 ?B,C=(90.8) ?A,C= (130.9) Expected return and standard deviations of the portfolio

E(P) = (0.5x17.2) + (0.4x11.2) +(0.1x1.4)=8.6+4.5+0.1=13.2% ?p = [ wA2 ?A2 + wB2 ?B2 + wC2 ?C2 + 2 wAwB ?A,B +2 wBwC ?B,C +2 wAwC ?A,C]1/2 = [ 53.3 + 16.6 +1.0 + 59.9-7.3-13.1]1/2 = 10.5

( 3) Determining overpricing and underpricing using CAPM ?A =1.2 ?B =0.8 ?C = 0.3

E(RM) = 14.4 Rf =6%

SML = 6 + (14.4 -6)xBeta = 6 + 8.4 x Beta Required return on Arihant Pharma = 6 + (8.44 x 1.2 ) = 16.1% Required return on Best Industries = 6 + (8.44 x 0.8 ) = 12.7% Required return on Century Limited= 6 + (8.44 x 0.3 ) = 8.5% As the expected return of 17.2 % on Arihant Pharma is slightly more than the required return of 16.1 %, its expected return can be expected to come down to the fair return indicated by CAPM and for this to happen its market price should go up. So it is slightly undervalued. In the case of Best Industries stock, as the expected return is slightly less than the required return of 12.7%, its expected return can be expected to go up and for this to happen its market price should go down. So it is slightly undervalued. Century Limited can be considered as overvalued as its required return is far in excess of the expected return which is likely to drive the market

CHAPTER 10 1. A stock is currently selling for Rs.80. In a year’s time it can rise by 50 percent or fall by 20 percent. The exercise price of a call option is Rs.90. (i) What is the value of the call option if the risk-free rate is 10 percent? Use the option-equivalent method.

Solution:

S0 = Rs.80 E = Rs.90 ?= Cu – Cd = (u – d) S u Cd – d Cu B= (u – d) R = 0.7 x 80 30 – 0

u = 1.5 r = 0.10 30 = 56

d = 0.8 R = 1.10

1.5 x 0 – 0.8 x 30 = - 31.17 0.7 x 1.10

C = ?S + B 30 = x 80 – 31.17 56 = 11.69

(ii) What is the value of the call option if the risk-free rate is 6 percent? Use the risk-neutral method. Solution:

[P x 50%] + [(1 – P) x – 20%] = 6% 50 P + 20 P = 26 ? P = 0.37 Expected future value of a call 0.37 x 30 + 0.63 x 0 = Rs.11.10 Rs.11.10 Current value = 1.06 = Rs.10.47

2.

An equity share is currently selling for Rs 100. In a year’s time it can rise by 30 percent or fall by 10 percent. The exercise price of call option on this share is Rs.110. (i) What is the value of the call option if the risk – free rate is 7 percent ? Use the option – equivalent method.

Solution:

S0 = 100, = Cu – Cd ( u – d) S0 uCd – dCu ( u – d) R S+B

E = 110, =

u = 1.3, =

d = 0.9, 20 40 = 0.5

R = 1.07

20 – 0 0.4 x 100

B C

= =

= =

1.3 x 0 – 0.9 x 20 0.4 x 1.07 0.5 x 100 - 42.06

= =

- 42.06

7.94

(ii) What is the value of the call option if the risk-free rate is 6 percent? Use the risk – neutral method. Solution:

P x 30% + (1-P) x -10% = 6% 30P + 10P - 10 = 6 == P = 0.4

Expected future value of call 0.4 x 20 + 0.6 x 0 = Rs. 8.00

Current value =

8 1.06

=

Rs. 7.55

3.

An equity share is currently selling for Rs.60. In a year’s time, it can rise by 50 percent or fall by 10 percent. The exercise price of a call option on this share is Rs.70. a. What is the value of the call option if the risk-free rate is 8 percent? Use the option-equivalent method.

Solution:

S0 = Rs. 60, E = Rs. 70, u = 1.5, d = 0.9, R = 1.08
?

Cu - Cd = (u - d ) So u Cd - d Cu =

20 - 0 = (0.6) 60

20 36

1.5 x 0 - 0.9 x 20 = = - 27.78 0.6 x 1.08 = Rs. 5.55

B

= (u - d) R

C

=

? S + B = 20 / 36 x 60 - 27.78

b. What is the value of the call option, if the risk-free rate is 6 percent? Use the risk-neutral method.
Solution:

P x 50 % + ( 1 – P ) x -10% = 6 % 50 P + 10P - 10 = 6 P = 0.27

Expected future value of call 0.27 x 20 + 0.73 x 0 = 5.4 5.4 Current value = 1.06 4. The following information is available for a call option: Time to expiration (months) Risk free rate Exercise price Stock price Call price 3 8% Rs.60 Rs.70 Rs.14 Rs. 5.09

What is the value of a put option if the time to expiration is 3 months, risk free rate is 8%, exercise price is Rs.60 and the stock price is Rs.70 ?
Hint : Use put-call parity theorem

Solution:

According to put-call parity theorem
P0 = C0 + E - S0 ert

= 14 +

60 e .08 x .25 -

-

70

= 14 + 60 1.0202

70 = Rs.2.812

5.

Consider the following data for a certain share: Price of the stock now = S0 = Rs.80 Exercise price = E = Rs.90 Standard deviation of continuously compounded annual return = ? = 0.3 Expiration period of the call option = 3 months Risk-free interest rate per annum = 8 percent (i) What is the value of the call option? Use the normal distribution table and resort to linear interpolation.

Solution:

S0 = Rs. 80, E = Rs. 90, r = 0.08, ? = 0.3 , t = 0.25 E Co = So N (d1) So ln E d1 =
??t

ert

N (d2)
?2

+

r + 2

t

0.09 - 0.1178 + ( 0.08 + 2 = 0.3 ? 0.25 d2 = d1 - ? ? t N (d1) = N (- 0.577) = - 0.577 - 0.3 ? 0.25 = - 0.727 = - 0.577 ) 0.25

N ( - 0.600) = 0.2743 N (- 0.550 ) = 0.2912 N ( -0.577) = 0.2743 +( 0.023 / 0.050) [0.2912 – 0.2743] = 0.2821

N(d2) = N ( - 0.727)

Co

N (- 0.750) = 0.2264 N (- 0.700) = 0.2420 N (- 0.727) = 0.2264 +(0 .023 /.050) [.2420 - .2264] = 0.2336 90 = 80 x 0.2821 x 0.2336 e 0.08 x 0.25 = 22.5 7 - 20.61 = Rs. 1.96

(ii) What is the value of a put option
Solution:

E Po = Co - So + e rt 90 = 1.96 - 80 + e
0.08 x 0.25

= Rs. 10.18

6.

Consider the following data for a certain share. Current Price = S0 = Rs. 80 Exercise Price = E = Rs. 90 Standard deviation of continuously compounded annual return = ? = 0.5 Expiration period of the call option = 3 months Risk – free interest rate per annum = 6 percent (i) What is the value of the call option? Use the normal distribution table given at the end of this booklet and resort to linear interpolation.
Solution:

S0 = Rs. 80 r = 0.06, ? = 0.5, C0 d1 = S0N(d1) - E N (d2) ert = ln S0 r + ?2 t E + 2 =
?

E = Rs. 90 t = 0.25

-0.1178 + 0.06 + 0.25 0.25 2 0.5 = - 0.2862 0.25

t

d2

= d1 – ?

t

= - 0.2862 - 0.5 0.25 = - 0.5362

N(d1) = N ( - 0.2862)

N(d2) =

C0

= = =

N (-0.30) = 0.3821 N (-0.25) = 0.4013 N (-0.2862) = 0.3821 + 0.0138 [ 0.4013 – 0.3821] 0.05 = 0.3874 N( - 0.5362) N (-0.55) = 0.2912 N (-0.50) = 0.3085 N( - 0.5362) = 0.2912 + 0.0138 [ 0.3085 – 0.2912] 0.05 = 0.2960 80 x 0.3874 90 x 2960 .06 x 0.25 30.99 - 26.24 Rs. 4.75

(ii) What is the value of a put option?
Solution:

P0 = C0 – S0 + E ert = 4.75 - 80 + e = Rs. 13.41
7.

90
.06 x 0.25

Consider the following data for a certain stock: Price of the stock now = S0 = Rs.150 Exercise price = E = Rs.140 Standard deviation of continuously compounded annual return = ? = 0.30 Expiration period of the call option = 3 months Risk-free interest rate per annum = 6 percent (i) What is the value of the call option? Use normal distribution table and resort to linear interpolation?

Solution:

C0 = S0 N(d1) –
ln (S0/E) + (r + ?2/2) t

E ert

N(d2) S0 = Rs.150, E = Rs.140, r = 0.06,
? = 0.3, t = 0.25

d1 =

?? t 0.069 + (0.06 + 0.09/2) 0.25

= d2 = d1 - ?? t 0.3?0.25 = 0.485

= 0.635

N (d1) = N (0.635) = 0.7373 N (d2) = N (0.485) = 0.6861

N (0.60) = 1 – 0.2743 = 0.7257 N (0.65) = 1 – 0.2578 = 0.7422 .035 N (0.635) = 0.7257 + (.7422 –.7257) .05 = 0.7373 140 N (0.45) = 1 – 0.3264 = 0.6736 C0 = 150 x 0.7373 – x 0.6861 N (0.50) = 1 – 0.3085 = 0.6915 e.06 x 0.25 .035 N (0.485) = 0.6736 + (.6915 – 0.6736) .05 =110.60 – 94.62 = Rs.15.98 = 0.6861

(ii) What is the value of the put option?
Solution:

E P0 = C0 – S0 + ert 140 = 15.98 – 150 + e.06 x . 25 = Rs.3.90

8.

Lakshmi Limited has a current value of 8000. The face value of its outstanding bonds is 6000. These are 1 year discount bonds with an obligation of 6000 in year 1. The risk-free interest rate is 8 percent and the variance of the continuously compounded rate of return on the firm’s assets is 16 percent. What is the present value of Lakshmi Limited’s equity, S0, and debt, B0?

Solution: So

= =

Vo N(d1) – B1 e –rt N (d2)

8000 N (d1) – 6000 e – 0.08 N(d2)
ln (8000 / 6000) + (0.08 x 1) + (0.16/2) ---------------------------------------------? 0.16 x ? 1 ln (1.333) + 0.16

d1

=

= 0.4 = (0.2874+0.16)/0.4 = 1.1185

N(d1) = N (1.1185) From the tables N(1.10) = 1-0.1357 = 0.8643 N(1.15) = 1- 0.1251= 0.8749 By linear extrapolation N(1.1185) = 0.8643 +(1.1185-1.10)(0.8749-0.8643)/0.05 = 0.8643 + 0.003922 = 0.8682

d2

= =

1.1185 0.7185
N (0.7185)

0.4

N (d2) =

From the tables N(0.70) = 1-0. 2420= 0.7580 N(0.75) = 1 – 0.2264 = 0.7736 By linear interpolation N(0.7185) = 0.7580+ (0.7185-0.70)(0.7736-0.7580)/0.05 = 0.7580+0.005772 = 0.7638 So
B0

= = = =

8000 x 0.8682 – (6000 x 0.9231 x 0.7638) 2715 V0 – S0 8000 – 2715 = 5285

MINICASE

On majoring in finance you have got selected as the finance manager in Navin Exports, a firm owned by Navin Sharma a dynamic young technocrat. The firm has been registering spectacular growth in recent years. With a view to broad base its investments, the firm had applied for the shares of Universal Industries a month back during its IPO and got allotment of 5000 shares thereof. . Recently Mr. Sharma had attended a seminar on capital markets organised by a leading bank and had decided to try his hand in the derivatives market . So, the very next day you joined the firm, he has called you for a meeting to get a better understanding of the options market and to know the implications of some of the strategies he has heard about. For this he has placed before you the following chart of the option quotes of Universal Industries and requested you to advise him on his following doubts, based on the figures in the chart. Universal Industries Option Quotes. (All amounts are in rupees) Stock Price :350 Calls Puts Strike Price Jan Feb March Jan Feb 300 50 55 - * 320 36 40 43 3 5 340 18 20 21 8 11 360 6 9 16 18 21 380 4 5 6 43 * A blank means no quotation is available

March 7 23 -

1. List out the options which are out-of-the-money. 2. What are the relative pros and cons (i.e. risk and reward) of selling a call against the 5000 shares held, using (i)Feb/380 calls versus (ii) March 320/ calls ? 3. Show how to calculate the maximum profit, maximum loss and break-even associated with the strategy of simultaneously buying say March/340 call while selling March/ 360 call? 4. What are the implications for the firm, if for instance, it simultaneously writes March 360 call and buys March 320/put? 5. What should be value of the March/360 call as per the Black-Scholes Model? Assume that t=3 months, risk-free rate is 8 percent and the standard deviation is 0.40 6. What should be the value of the March/360 put if the put-call parity is working?
Solution:

1) 2)

Calls with strike prices 360 and 380 are out –of –the- money. (i) If the firm sells Feb/380 call on 5000 shares, it will earn a call premium of Rs.25,000 now. The risk however is that the firm will forfeit the gains that it would have enjoyed if the share price rises above Rs. 380. (ii) If the firm sells March 320 calls on 5000 shares, it will earn a call premium of Rs.215,000 now. It should however be prepared to forfeit the gains if the share price remains above Rs.320. Let s be the stock price, p1 and p2 the call premia for March/ 340 and March/ 360 calls respectively. When s is greater than 360, both the calls will be exercised and the profit will be { s-340-p1} – { s-360- p2 } = Rs. 15 The maximum loss will be the initial investment , i.e. p1-p2 = Rs.5 The break even will occur when the gain on purchased call equals the net premium paid i.e. s-340 = p1 – p2 =5 Therefore s= Rs. 345 If the stock price goes below Rs.320, the firm can execute the put option and ensure that its portfolio value does not go below Rs. 320 per share. However, if stock price goes above Rs. 380, the call will be exercised and the stocks in the portfolio will have to be delivered/ sold to meet the obligation, thus limiting the upper value of the portfolio to Rs. 380 per share. So long as the share price hovers between R. 320 and Rs. 380, the firm will lose Rs. 1 (net premium received) per pair of call and put.

3)

4)

5) S0 = 350 ln 360 d1 = E =360 t =0.25 r = 0.07 ? =0.40 350 + 0.07 + 2 0.40 x ? 0.25 (0.40)2 x 0.25

= ( -0.0282 + 0.0375) / 0.2 = 0. 0465 d2 = 0.0465 -0.40 ?¯ 0.25¯ ¯ = -0.1535 Using normal distribution table N (0.00) = 1- 0.5000 = 0.5000 N (0.05) = 1 – 0.4801 = 0.5199 Therefore N( 0.0465) = 0.5000 + (0.0465/0.0500) x (0.5199 – 0.5000) = 0.5185 N ( - 0.20) = 0.4207 N ( -0.15) = 0.4404 Therefore N ( -0.1535) = 0.4207 + ( 0.0465/0.0500) x(0.4404 – 0.4207) = 0.4390 E / ert = 360 / e0.07 x 0. 25 = 360 / 1. 01765 = 353.75 C0 = 350 x 0.5185 – 353.75 x 0.4390 = 181.480 – 155.30 = Rs. 26.18 6) If put- call parity is working, we have P0 = C0 – S0 + E/ert Value of the March/360 put = 26.18 -350 + 353.75 = Rs.29.93

CHAPTER 11

1.

Matrix Associates is evaluating a project whose expected cash flows are as follows:
Year 0 1 2 3 4 Cash flow (Rs. in million) (23) 6 8 9 7

The cost of capital for Matrix Associates is 14 percent. (i) What is the NPV of the project?

Solution:

6 8 9 7 NPV = -23 + -------- + --------- + -------- + --------(1.14) ( 1.14)2 ( 1.14)3 ( 1.14)4 = -23 + 5.263 + 6.156 + 6.075 + 4.145 = -1.361

(ii) What is the IRR of the project?
Solution:

When the discount rate is 14 %, the NPV is -1.361 Trying a lower rate of 12% 6 8 9 7 NPV = -23 + -------- + -------- + -------- + --------(1.12) (1.12)2 (1.12)3 (1.12)4 = -23 + 5.357 + 6.378 + 6.406 + 4.449 = -0.41 Trying a still lower rate of 11% 6 8 9 NPV = -23 + -------- + -------- + -------(1.11) (1.11)2 (1.11)3

7 + ------(1.11)4

= -23 + 5.405 + 6.493 + 6.581+ 4.611 = 0.09 By linear interpolation we get 0.09 IRR = 11 + ------------------ = 11.18% (0.41 + 0.09)

(iii) What is the NPV* of the project if the reinvestment rate is 18 percent?
Solution:

Terminal value = 6(1.18)3 + 8(1.18)2 + 9(1.18) + 7 = 38.617 NPV* = 38.617 / (1.14)4- 23 = -0.136

(iv) What is the MIRR of the project if the reinvestment rate is 18 percent?
Solution:

23 (1+MIRR)4 = 38.617 (1+MIRR)4 = 38.617 / 23 = 1.679 MIRR = (1.679)1/4 – 1 = 13.83% 2. Sigma Corporation is evaluating a project whose expected cash flows are as follows:
Year 0 1 2 3 4 Cash flow (Rs.in million) - 16.0 3.2 4.5 7.0 8.4

The cost of capital for Sigma Corporation is 12 percent . (i) What is the NPV of the project?
Solution:

NPV

=

-16.0

+

3.2 (1.12)

+

4.5 (1.12)2

+

7.0 (1.12)3

+

8.4 (1.12)4

2.8576 + 3.5865 = 0.7705

+ 4.984

+ 5.3424

(ii) What is the IRR of the project?
Solution:

NPV

At 12% discount rate NPV is 0.7705 Try 13% = -16 + 3.2 (0.885) + 4.5 (0.783) = -16 + 2.832 + 3.5235 = 0.3557

+ 7 (0.693) + 4.851

+ 8.4 (0.613) + 5.1492

Try 14% NPV = -16 + 3.2 (0.877) + 4.5 (0.769) + 7 (0.675) = -16 + 2.8064 + 3.4605 + 4.725 = -0.0353 As this is very nearly zero, the IRR of the project is 14 %

+ 8.4 (0.592) + 4.9728

(iii) What is the NPV * of the project if the reinvestment rate is 16%?
Solution:

Terminal Value = = = = NPV* = 3.2 (1.16)3 3.2 (1.561) 4.9952 27.5722 27.5722 (1.12)4 (iv) What is the IRR* if the reinvestment rate is 16%?
Solution:

+ + +

4.5 (1.16)2 4.5 (1.346) 6.057

+

7 (1.16)1

+ + 8.4 + 8.4

8.4

+ 7 (1.16) + 8.12

- 16

= 1.5359

16 ( 1 + 1RR*)4 ( 1 + 1RR*)4 1RR*

= =

27.5722 27.5722 16 = 1.7233

= (1.7233) 1/4 -1 = 1.1457 - 1 = 14.57 %

3.

Dumas Company is evaluating a project whose expected cash flows are as follows:
Year Cash flow 0 - Rs.700,000 1 Rs.150,000 2 Rs.200,000 3 Rs.300,000 4 Rs.350,000 The cost of capital for Dumas Company is 12 percent

(i) What is the NPV of the project?

Solution:

- 700,000 150,000 200,000 300,000 350,000

1.000 0.893 0.797 0.712 0.636

-700,000 133,950 159,400 213,600 222,600 29,550

(ii)
Solution:

150,000 200,000 300,000 350,000

13% PVIF 0.885 0.783 0.693 0.613

14% PV 132,750 156,600 207,900 214,550 711,800 PVIF 0.877 0.769 0.675 0.592 PV 131,550 153,800 202,500 207,200 695,050

711,800 - 700,000 IRR = 13 % + 711,800 - 695,050 x 1% = 13.70%

(iii) What is the NPV * of the project if the reinvestment rate is 15% ?
Solution:

Terminal value = 150,000 (1.15)3 + 200,000 (1.15)2 + 300,000 ( 1.15)1 + 350,000 = 150,000 (1.521) + 200,000 (1.322) + 300,000 (1.150) + 350,000 = 228,150 + 264,400 + 345,000 + 350,000 = 1,187,550 1,187,550 NPV * = (1.12)4 = 54,709 - 700,000

(iv)

What is the IRR* if the reinvestment rate is 15%?

Solution:

700,000 ( 1 + IRR*)4 (1 + IRR*)4 IRR*

= 1,187,550 = 1,187,550 / 700,000 = 1.6965 = (1.6965)¼ - 1 = 1.1413 - 1 = 14.13%

4.

You are evaluating a project whose expected cash flows are as follows:
Year 0 1 2 3 4 Cash flow -1,000,000 200,000 300,000 400,000 500,000

What is the NPV of the project (in '000s) if the discount rate is 10 percent for year 1 and rises thereafter by 2 percent every year?
Solution:

200 PVB = (1.10) + +

300 + (1.10) (1.12) 500

400 (1.10) (1.12) (1.14)

(1.10) (1.12) (1.14) (1.16) = 181.82 + 243.51 + 284.80 + 306.90 = 1017.03 ; NPV = 1,017,030 – 1,000,000 = 17,030

5.

The cash flows associated with an investment are given below: Year Cash flow 0 Rs.(850,000) 1 120,000 2 450,000 360,000 3 4 210,000 5 130,000

Calculate the benefit cost ratio of this investment, if the discount rate is 12 percent.
Solution:

PV of benefits (PVB) =120,000x PVIF (12,1)+450,000x PVIF (12,2) +360,000x PVIF (12,3)+210,000x PVIF (12,4) +130,000x PVIF (12,5) =107,160+358,650+256,320+133,560+73,710 = Rs. 929,400(A) Investment = 850,000 = 929,400/850,000 = 1.09 (B)

Benefit cost ratio (A/B) 6.

The cash flows associated with an investment are given below:

Year 0 1 2 3 4 5

Cash flow Rs.(260,000) 85,420 103,240 128,430 92,480 78,350

Calculate the benefit cost ratio of this investment, if the discount rate is 18 percent.
Solution:

PV of benefits (PVB) =85,420xPVIF (18,1)+ 103,240x PVIF (18,2) +128,430xPVIF (18,3)+ 92,480x PVIF (18,4) +78,350xPVIF (18,5) =72,351+74,126+78,214+47,720+34,239 = Rs. 306,650(A) Investment = 260,000 = 306,650/260,000 = 1.18 (B)

Benefit cost ratio(A/B)

7.

Your company is considering two mutually exclusive projects, A and B. Project A involves an outlay of Rs.250 million which will generate an expected cash inflow of Rs.60 million per year for 8 years. Project B calls for an outlay of Rs.100 million which will produce an expected cash inflow of Rs.25 million per year for 8 years. The company's cost of capital is 14 percent. a. Calculate the NPV and IRR of each project b. What is the NPV and IRR of the differential project (the project that reflects the difference between Project B and Project A)

Solution:

(a)

Project A

NPV at a cost of capital of 14% = - 250 + 60 x PVIFA (14,8) = Rs.-250+ 60x 4.639 = Rs.28.34 million IRR (r ) can be obtained by solving the following equation for r. 60 x PVIFA (r,8) = 250 PVIFA (r,8) =4.17 From tables we see that when: r =17 %, r = 18%, RHS = 4.207 RHS = 4.078

By extrapolation, r =17 + (4.207-4.17)/(4.207-4.078) = 17.29 % Project B NPV at a cost of capital of 14% = - 100 + 25 x PVIFA (14,8) = Rs.15.98 million IRR (r') can be obtained by solving the equation 25 x PVIFA (r',8) = 100 PVIFA (r’,8) =4 From tables we see that when: r’ =18 %, RHS = 4.078 r’ = 19%, RHS = 3.954 By extrapolation, r’ =18 + (4.078-4)/(4.078- 3.954) = 18.63 %

(b)

Difference in capital outlays between projects A and B is Rs.150 million Difference in net annual cash flow between projects A and B is Rs.35 million. NPV of the differential project at 14% = -150 + 35 x PVIFA (14,8) = Rs.12.37 million IRR (r'’) can be obtained by solving the equation 35 x PVIFA (r'’,8) = 150 PVIFA (r’’,8) = 4.286 From tables we see that when: r’’ =16 %, RHS = 4.344 r’’ = 17%, RHS = 4.207 By extrapolation, r’’ =16 + (4.344-4.286)/(4.344- 4.207) = 16.42 %

8.

Your company is considering two projects, M and N. Each of which requires an initial outlay of Rs.240 million. The expected cash inflows from these projects are:
Year 1 2 3 4 Project M 85 120 180 100 Project N 100 110 120 90

a. What is the payback period for each of the projects? b. What is the discounted payback period for each of the projects if the cost of capital is 15 percent? c. If the two projects are independent and the cost of capital is 15 percent, which project(s) should the firm invest in? d. If the two projects are mutually exclusive and the cost of capital is 12 percent, which project should the firm invest in? e. If the two projects are mutually exclusive and the cost of capital is 20 percent, which project should the firm invest in? f. If the cost of capital is 13 percent, what is the modified IRR of each project?
Solution:

Project M The pay back period of the project lies between 2 and 3 years. Interpolating in this range we get an approximate pay back period of 2.19 years. Project N The pay back period lies between 2 and 3 years. Interpolating in this range we get an approximate pay back period of 2.25 years. (b)

Cost of capital

=

Project M 15 % p.a

Year Cash flow PV of cash flow Cumulative PV of cash flow 1 85 73.91 73.91 2 120 90.74 164.65 3 180 118.35 283 4 100 Discounted pay back period (DPB) lies between 2 and 3 years. Interpolating in this range we get an approximate DPB of 2.64 years. Project N Cost of capital = 15 % p.a

Year Cash flow PV of cash flow Cumulative PV of cash flow 1 100 86.96 86.96 2 110 83.18 170.14 3 120 78.90 249.04 4 90 Discounted pay back period (DPB) lies between 2 and 3 years. Interpolating in this range we get an approximate DPB of 2.89 years. (c ) Project M Cost of capital NPV

= =

= = Project N Cost of capital NPV

15% per annum - 240 + 85 x PVIF (15,1) + 120 x PVIF (15,2) + 180 x PVIF (15,3) + 100 x PVIF (15,4) - 240 + 85 x 0.870+120 x 0.756 + 180 x0.658 + 100 x 0.572 Rs. 100.31million

= 12% per annum = - 240 + 100 x PVIF (15,1) + 110 x PVIF (15,2) + 120 x PVIF (15,3) + 90 x PVIF (15,4) =- 240 + 100 x0.870+ 110 x 0.756 + 120 x 0.658 + 90 x 0.572 = Rs. 60.6 million

Since the two projects are independent and the NPV of each project is positive,

both the projects can be accepted. This assumes that there is no capital constraint. (d) Project M Cost of capital NPV Project N Cost of capital NPV

= 12% per annum = Rs.123.23 million

= 10% per annum = Rs.79.59 million

Since the two projects are mutually exclusive, we need to choose the project with the higher NPV i.e., choose project M.
NOTE: The MIRR can also be used as a criterion of merit for choosing between the two projects because their initial outlays are equal.

(e) Cost of capital = NPV = Project N Cost of capital: NPV =

Project M 15% per annum 66.56 million

15% per annum Rs.32.57 million

Again the two projects are mutually exclusive. So we choose the project with the higher NPV, i.e., choose project M.

(f)

Project M Terminal value of the cash inflows: 579.27 MIRR of the project is given by the equation 240 (1 + MIRR)4 = 579.27 i.e., MIRR = 24.64 %

Project N Terminal value of the cash inflows: 510.35 MIRR of the project is given by the equation 240 ( 1+ MIRR)4 = 510.35 i.e., MIRR = 20.76 %

9.

If an equipment costs Rs.350,000 and lasts 6 years, what should be the minimum annual cash inflow before it is worthwhile to purchase the equipment ? Assume that the cost of capital is 12 percent

Solution:

Let NCF be the minimum constant annual net cash flow that justifies the purchase of the given equipment. The value of NCF can be obtained from the equation NCF x PVIFA (12,6) NCF = = = 350,000 350,000 / 4.111 85,137

10.

If an equipment costs Rs.2.000,000 and lasts 8 years, what should be the minimum annual cash inflow before it is worthwhile to purchase the equipment ? Assume that the cost of capital is 14 percent

Solution: Let NCF be the minimum constant annual net cash flow that justifies the purchase of the given equipment. The value of NCF can be obtained from the equation

NCF x PVIFA (14,8) NCF

= = =

2,000,000 2,000,000 / 4.639 431,127

11.

How much can be paid for a machine which brings in an annual cash inflow of Rs.50,000 for 8 years ? Assume that the discount rate is 15 percent.

Solution:

Define I as the initial investment that is justified in relation to a net annual cash inflow of Rs.50,000 for 8 years at a discount rate of 15% per annum. The value of I can be obtained from the following equation 50,000 x PVIFA (15,8) i.e., I 12. = I = 50,000 x 4.487 = Rs. 224,350

How much can be paid for a machine which brings in an annual cash inflow of Rs.600,000 for 12 years ? Assume that the discount rate is 16 percent.

Solution:

Define I as the initial investment that is justified in relation to a net annual cash inflow of Rs.600,000 for 12 years at a discount rate of 16% per annum. The value of I can be obtained from the following equation 600,000 x PVIFA (16 ,12) i.e., I
I = = 600,000 x 5.197 = Rs. 3,118,200

CHAPTER 12 MINICASE 1

Metaland is a major manufacturer of light commercial vehicles. It has a very strong R&D centre which has developed very successful models in the last fifteen years. However, two models developed by it in the last few years have not done well and were prematurely withdrawn from the market. The engineers at its R&D centre have recently developed a prototype for a new light commercial vehicle that would have a capacity of 4 tons. After a lengthy discussion, the board of directors of Metaland decided to carefully evaluate the financial worthwhileness of manufacturing this model which they have labeled Meta 4. You have been recently hired as the executive assistant to Vijay Mathur, Managing Director of Metaland. Vijay Mathur has entrusted you with the task of evaluating the project. Meta 4 would be produced in the existing factory which has enough space for one more product. Meta 4 will require plant and machinery that will cost Rs.400 million. You can assume that the outlay on plant and machinery will be incurred over a period of one year. For the sake of simplicity assume that 50 percent will be incurred right in the beginning and the balance 50 percent will be incurred after 1 year. The plant will commence operation after one year. Meta 4 project will require Rs.200 million toward gross working capital. You can assume that gross working capital investment will occur after 1 year. The proposed scheme of financing is as follows : Rs.200 million of equity, Rs.200 million of term loan, Rs.100 million of working capital advance, and Rs.100 million of trade credit. Equity will come right in the beginning by way of retained earnings. Term loan and working capital advance will be raised at the end of year 1. The term loan is repayable in 8 equal semi-annual instalments of Rs.25 million each. The first instalment will be due after 18 months of raising the term loan. The interest rate on the term loan will be 14 percent. The levels of working capital advance and trade credit will remain at Rs.100 million each, till they are paid back or retired at the end of 5 years, after the project commences, which is the expected life of the project. Working capital advance will carry an interest rate of 12 percent.

Meta 4 project is expected to generate a revenue of Rs.750 million per year. The operating costs (excluding depreciation and taxes) are expected to be Rs.525 million per year. For tax purposes, the depreciation rate on fixed assets will be 25 percent as per the written down value method. Assume that there is no other tax benefit. The net salvage value of plant and machinery is expected to be Rs.100 million at the end of the project life. Recovery of working capital will be at book value. The income tax rate is expected to be 30 percent. Vijay Mathur wants you to estimate the cash flows from three different points of view: a. Cash flows from the point of all investors (which is also called the explicit cost funds point of view). b. Cash flows from the point of equity investors.
Solution: Cash Flows from the Point of all Investors Item

0

1

2

3

4

5

6

1. Plant and equipment (200) (200) 2. Net working capital (100) 3. Revenue 4. Operating costs 5. Depreciation 6. Profit before tax 7. Profit after tax (0.7 x 6) 8. Net salvage value of plant and equipment 9. Recovery of net working capital 10. Initial investment (200) (300) 11. Operating cash flow (7 + 5) 12. Terminal cash inflow 13. Net cash flow (200) (300)

750 525 100 125 87.5

750 525 75 150 105

750 525 56.3 168.7 118.1

750 525 42.2 182.8 128.0

750 525 31.6 193.4 135.4 100

100

187.5

180

174.4

170.2

167 200

187.5

180

174.4

170.2

367

Cash Flows from the Point of Equity Investors Item

0

1

2

3

4

5

6

1. Equity funds (200) 2. Revenues 3. Operating costs 4. Depreciation 5. Interest on working capital 6. Interest on term loan 7. Profit before tax 8. Profit after tax 9. Net salvage value of plant & equipment 10. Recovery of working capital 11. Repayment of term loans 12. Repayment of working capital advance 13. Retirement of trade credit 14. Initial investment (1) 15. Operating cash inflows (8 + 4) 16. Liquidation & retirement cash flows (9 + 10 – 13 – 14 – 15) 17. Net cash flow (200)

750 525 100 12 28 85 59.5

750 525 75 12 26.3 111.7 78.2

750 525 56.3 12 19.3 137.4 96.2

750 525 42.2 12 12.3 158.5 111

750 525 31.6 12 5.3 176.1 123.3 100 200

50

50

50

50

100 100

159.5

153.2

152.5

153.2

154.9

(50)

(50)

(50)

50

(200)

-

159.5

103.2

102.5

103.2

204.9

MINICASE 2

Max Drugs Limited is a leader in the bulk drug industry. It manufactures a range of bulk drugs, technically called APIs (active pharmaceutical ingredients). Max is considering a new bulk drug called MBD-9. You have recently joined Max as a finance officer and you report to Prakash Singh, Vice President (Finance), who coordinates the capital budgeting activity. You have been asked to develop the financials for MBD-9. After discussing with marketing, technical, and other personnel, you have gathered the following information. The MBD-9 project has an economic life of 5 years. It would generate a revenue of Rs.50 million in year1 which will rise by Rs.10 million per year for the following two years. Thereafter, revenues will decline by Rs.10 million per year for the remaining two years. Operating costs (costs before depreciation, interest, and taxes) will be 60 percent of revenues. MBD-9 is expected to erode the revenues of an existing bulk drug. Due to this erosion there will be a loss of Rs.4 million per year by way of contribution margin for 5 years. While there may be some other impacts as well, they may be ignored in the present analysis. MBD-9 will require an outlay of Rs.40 million in plant and machinery right in the beginning. The same will be financed by equity and term loan in equal proportions. The term loan will carry an interest of 8 percent per annum and will be repayable in 4 equal annual instalments, the first instalment falling due at the end of year 1. For tax purposes, the depreciation rate will be 15 percent as per the written down value method. The net salvage value of plant and machinery after 5 years is expected to be Rs.20 million. The net working capital requirement will be 20 percent of revenues. Assume that the investment in net working capital will be made right in the beginning of each year and the same will be fully financed by working capital advance carrying an interest rate of 10 percent per annum. At the end of 5 years the working capital is expected to be liquidated at par. The effective tax rate is 30% Required 1. Estimate the net cash flows relating to explicit cost funds (investor claims) over the 5-year period. 2. Estimate the net cash flows relating to equity over the 5-year period.

Solution:

Net Cash Flows Relating to Explicit Cost Funds

1. Fixed assets 2. Net working capital 3. Revenues 4. Operating costs 5. Loss of contribution margin 6. Depreciation 7. Profit before tax 8. Tax 9. Profit after tax 10. Net salvage value of fixed assets 11. Recovery of working capital 12. Initial outlay & working capital 13. Operating cash flow (9 + 6) 14. Terminal cash inflow (10 + 11) 15. Net cash flow :

0 (40.0) (10.0)

1 (2.0) 50.0 30.0 4.0 6.0 10.0 3.0 7.0

2 (2.0) 60.0 36.0 4.0 5.1 14.9 4.47 10.43

3 2.0 70.0 42.0 4.0 4.34 19.66 5.90 13.76

(Rs.in million) 4 5 2.0 60.0 36.0 4.0 3.68 16.32 4.90 11.42 50.0 30.0 4.0 3.13 12.87 3.86 9.01 20.0 10.0

(50.0)

(2.0) 13.0

(2.0) 15.53

2.0 18.10

2.0 15.1 12.14 30.00

(50.0)

11.0

13.53

20.10

17.1

42.14

1. Equity funds 2. Revenues

Net Cash Flows Relating to Equity(Rs.in million) 0 1 2 3 (20.0) 50.0 60.0 70.0

4 60.0 36.0 4.0 3.68 1.20 0.4 14.72 4.42 10.30

5 50.0 30.0 4.0 3.13 1.00 11.87 3.56 8.31 20.0 10.0

3. Operating costs 4. Loss of contribution margin 5. Depreciation 6. Interest on working capital advance 7. Interest on term loan 8. Profit before tax 9. Tax 10. Profit after tax 11. Net salvage value of fixed assets 12. Net salvage value of current assets 13. Repayment of term loan 14. Repayment of working capital advance 15. Initial investment (1) (20.0) 16. Operating cash flows (10 + 5) 17. Liquidation & retirement cash flows (11 + 12 – 13 – 14) 18. Net cash flow (20.0) (15+16+17)

30.0 4.0 6.0 1.0 1.6 7.4 2.22 5.18

36.0 4.0 5.1 1.2 1.2 12.5 3.75 8.75

42.0 4.0 4.34 1.40 0.8 17.46 5.24 12.22

5.0

5.0

5.0

5.0

10.0

11.18 (5.0) 6.18

13.85 (5.0) 8.85

16.56 (5.0) 11.56

13.98 (5.0) 8.98

11.44 20.0 31.44

MINICASE 3

Medipharm, a pharmaceutical company, is considering the manufacture of a new antibiotic preparation, M-cin, for which the following information has been gathered.
•

M-cin is expected to have a product life cycle of five years and thereafter it would be withdrawn from the market. The sales from this preparation are expected to be as follows:
Year 1 2 3 4 5 Sales ( Rs in million) 50 100 150 100 50

•

•

•

•

•

The capital equipment required for manufacturing M-cin will cost Rs.80 million and it will be depreciated at the rate of 25 percent per year as per the WDV method for tax purposes. The expected net salvage value of the capital equipment after 5 years is Rs.20 million. The net working capital requirement for the project is expected to be 25 percent of sales. The net working capital will be adjusted at the beginning of the year in relation to the expected sales for the year. For example, the net working capital at the beginning of year 1 (i.e at the end year 0) will be Rs.12.5 million, that is 25 percent of the expected revenue of Rs.50.0 million for year 1. The accountant of the firm has provided the following cost estimates for M-cin : Raw material cost : 40 percent of sales Variable labour cost : 10 percent of sales Fixed annual operating: Rs.4 million and maintenance cost Overhead allocation : 10 percent of sales (excluding depreciation maintenance, and interest) While the project is charged an overhead allocation , it is not likely to have any effect on overhead expenses as such. The manufacture of M-cin would use some of the common facilities of the firm. The use of these facilities will necessitate reducing the production of other pharmaceutical preparations of the firm. This will mean a reduction of Rs.10 million of contribution margin from those preparations. The tax rate applicable for this project is 30 percent. (a) Estimate the post-tax incremental cash flows of the project viewed from the point of all investors(which is also called the explicit cost funds point of view). (b) To calculate the cash flows from the point of equity investors, what additional information would you need ?

Solution:

Item 1. Fixed assets 2. Net working capital level 3. Investment in net working capital 4. Sales 5. Raw material cost 6. Variable labour cost 7. Fixed annual operating cost 8. Depreciation 9. Loss of contribution margin 10. Profit before tax 11. Profit after tax 12. NSV of fixed assets 13. Recovery of NWC at the end 14. Initial investment in fixed assets 15. ? Inv. In NWC 16. Cash flow from operation (11+8) 17. Terminal cash flow (12+13) Net Cash Flow

Cash Flows from the Point of All Investors 0 1 2

3

4

5

(80) 12.5 (12.5) 25.0 (12.5) 50.00 20.00 5.00 4.00 20.00 10.00 ( 9.00) (6.30) 37.5 (12.5) 100.00 40.00 10.00 4.00 15.00 10.00 21.00 14.70 25.0 12.5 150.00 60.00 15.00 4.00 11.25 10.00 49.75 34.83 12.5 12.5 100.00 40.00 10.00 4.00 8.44 10.00 27.56 19.29 – – 50.00 20.00 5.00 4.00 6.33 10.00 4.67 3.27 20.00 12.5

(80) (12.5)

(12.5) 13.7

(12.5) 29.70

12.5 46.08

12.5 27.73 9.60 32.5

(92.5)

1.20

17.20

58.58

40.23

42.10

b. The additional information needed for calculating the cash flow from the point of view of equity investors are: • Equity funds committed to the project • Interest cost on all borrowings • Repayment /retirement schedule of all borrowings and trade creditors • Net salvage value of all current assets • Preference dividend and redemption of preference capital

MINICASE 4

Zesna Auto Ltd is considering the manufacture of a new bike, Gale, for which the following information has been gathered. Gale is expected to have a product life cycle of five years after which it will be withdrawn from the market. The sales from this product is expected to be as follows: Year 1 Sales (Rs. in million) 700 • 2 3 850 1100 4 1000 5 800

•

•

•

The capital equipment required for manufacturing Gale costs Rs.600 million and it will be depreciated at the rate of 25 percent per year as per the WDV method for tax purposes. The expected net salvage value after 5 years is Rs.100 million. The working capital requirement for the project is expected to be 10% of sales. Working capital level will be adjusted at the beginning of the year in relation to the sales for the year. At the end of five years, working capital is expected to be liquidated at par, barring an estimated loss of Rs.5 million on account of bad debt, which of course, will be tax-deductible expense. The accountant of the firm has provided the following estimates for the cost of Gale. Raw material cost : 40 percent of sales Variable manufacturing cost : 20 percent of sales Fixed annual operating and : Rs.2.5 million maintenance costs Variable selling expenses : 15 percent of sales The tax rate for the firm is 30 percent.

Required: (a) Estimate the post-tax incremental cash flows for the project to manufacture Gale. (b) What is the NPV of the project if the cost of capital is 18 percent?

Solution:

Cash flows for the Gale Project

Year 1. Capital equipment 2. Level of working capital 3. Revenues 4. Raw material cost 5. Variable manufacturing cost 6. Operating and maintenance cost 7. Variable selling expenses 8. Depreciation 9. Bad debt loss 10.Profit before tax 11.Tax 12.Profit after tax 13.Net Salvage Value of Capital Equipment 14.Recovery of Working Capital 15.Initial Investment 16.Operating cash flow (12+8+9) 17. Terminal cash flow (13 + 14) 18. Working Capital investment 19. Net cash flow (15 + 16 + 17 + 18) 150.70 (b) NPV = - 670 + (1.18) = +

0 600 70

1 85 700 280 140 2.5 105 150 22.5 6.8 15.7

2 110 850 340 170 2.5 127.5 112.5 97.5 29.25 68.25

3 100 1100 440 220 2.5 165 84.4 188.1 56.4 131.7

(Rs. in million) 4 5 80 1000 400 200 2.5 150 63.3 184.2 55.3 128.9 800 320 160 2.5 120 47.5 5 145.0 43.5 101.5 100 75

(600) 165.70 (70) (670) 155.75 + (1.18)2 (1.18)3 (15) 150.7 180.75 (25) 155.75 226.1 + (1.18)4 216.1 10 226.1 212.2 + (1.18)5 192.2 20 212.2 329 329 154.0 175

- 670 + 127.71 + 111.86 + 137.61 + 109.45 + 143.81

= -39.56

MINICASE 5

Phoenix Pharma is considering the manufacture of a new drug, Torrexin, for which the following information has been gathered
•

Torrexin is expected to have a product life cycle of five years after which it will be withdrawn from the market. The sales from this drug are expected to be as follows: Year 1 Sales ( Rs in million) 100 2 150 3 200 4 150 5 100

•

•

•

The capital equipment required for manufacturing Torrexin is 120 million and it will be depreciated at the rate of 25 percent per year as per the WDV method for tax purposes. The expected net salvage value after 5 years is Rs.30 million The working capital requirement for the project is expected to be 20 percent of sales. Working capital level will be adjusted at the beginning of the year in relation to the sales for the year. At the end of five years, working capital is expected to be liquidated at par, barring an estimated loss of Rs.5 million on account of bad debt which, of course, will be tax-deductible expense The accountant of the firm has provided the following estimates for the cost of Torrexin Raw material cost : 40 percent of sales Variable manufacturing : 10 percent of sales cost Fixed annual operating and : Rs.8 million maintenance costs Variable selling expenses : 10 percent of sales The tax rate for the firm is 30 percent

•

Required :

(a) Estimate the post-tax incremental cash flows for the project to manufacture Torrexin (b) What is the NPV of the project if the cost of capital is 15 percent?

Solution:

(a) 0 1. Capital equipment 2. Level of working capital (ending) 3. Revenues 4. Raw material cost 5. Variable mfrg cost 6. Fixed annual operating and maintenance costs 7. Variable selling expenses 8. Bad debt loss 9. Depreciation 10. Profit before tax 11. Tax 12. Profit after tax 13. Net salvage value of capital equipment 14. Recovery of working capital 15. Initial investment 16. Operating cash flow (12 + 8 + 9) 17. ? Working capital 18. Terminal cash flow (13+14) 19. Net cash flow (15 + 16 + 17 + 18) 21.4 (b) NPV = - 140 + (1.15) + (1.15)2 33.1 + (1.15)3 65.5 + (1.15)4 (140) 21.4 33.1 65.5 50.2 (120) 31.4 20 10 43.1 10 55.5 (10) 40.2 (10) 45.0 71.7 26.7 (120) 20 30 100 40 10 8 10 30 2 0.6 1.4 40 150 60 15 8 15 22.5 29.5 8.9 20.6 30 200 80 20 8 20 16.9 55.1 16.5 38.6 20 150 60 15 8 15 12.7 39.3 11.8 27.5 100 40 10 8 10 5 9.5 17.5 5.3 12.2 30.0 15.0 1 2 3 4 5

50.2 +

71.7 (1.15)5

= - 140 + 18.6 + 25.0 + 43.1 + 28.7 + 35.6 = Rs 11.0 million

MINICASE 6

Malabar Corporation is determining the cash flow for a project involving replacement of an old machine by a new machine. The old machine bought a few years ago has a book value of Rs.1,200,000 and it can be sold to realise a post tax salvage value of Rs.800,000. It has a remaining life of four years after which its net salvage value is expected to be Rs.500,000. It is being depreciated annually at a rate of 20 percent the WDV method. The working capital associated with this machine is Rs.700,000. The new machine costs Rs.5,000,000. It is expected to fetch a net salvage value of Rs.2,500,000 after four years. The depreciation rate applicable to it is 20 percent under the WDV method. The new machine is expected to bring a saving of Rs.800,000 annually in manufacturing costs (other than depreciation).The incremental working capital associated with the new machine is Rs.200,000. The tax rate applicable to the firm is 34 percent. (a) Estimate the cash flow associated with the replacement project. (b) What is the NPV of the replacement project if the cost of capital is 15 percent?
Solution:

(a)

A. i. ii. iii iv.

Initial outlay (Time 0) Cost of new machine Salvage value of old machine Incremental working capital requirement Total net investment (=i – ii + iii) Rs. 5,000,000 800,000 200,000 4,900,000

B.

Operating cash flow (years 1 through 4)
Year 1 2 3 4

i. Post-tax savings in manufacturing costs 528,000 ii. Incremental depreciation iii. Tax shield on incremental dep. iv. Operating cash flow ( i + iii)

528,000

528,000

528,000

760,000

608,000

486,400

389,120

258,400

206,720

165,376

132,301

786,400

734,720

693,376

660,301

C.

Terminal cash flow (year 4) i. ii. iii. iv. Salvage value of new machine Salvage value of old machine Recovery of incremental working capital Terminal cash flow ( i – ii + iii) Rs. 2,500,000 500,000 200,000 2,200,000

D.
Year NCF

Net cash flows associated with the replacement project (in Rs)
0 (4,900,000) 1 786,400 2 734,720 3 693,376 4 2,860,301

(b)

NPV of the replacement project = - 4,900,000 + 786,400 x PVIF (15,1) + 734,720 x PVIF (15,2) + 693,376 x PVIF (15,3) + 2,860,301 x PVIF (15,4) = - Rs.1,568,050

MINICASE 7

Sangeeta Enterprises is determining the cash flow for a project involving replacement of an old machine by a new machine. The old machine bought a few years ago has a book value of Rs.2,800,000 and it can be sold to realise a post tax salvage value of Rs.2,200,000. It has a remaining life of five years after which its net salvage value is expected to be Rs.900,000. It is being depreciated annually at a rate of 30 percent the WDV method. The working capital associated with this machine is Rs.1.000,000. The new machine costs Rs.8,000,000. It is expected to fetch a net salvage value of Rs.3,500,000 after five years. The depreciation rate applicable to it is 25 percent under the WDV method. The new machine is expected to bring a saving of Rs.1,000,000 annually in manufacturing costs (other than depreciation).The incremental working capital associated with the new machine is Rs.600,000. The tax rate applicable to the firm is 33 percent. (a) Estimate the cash flow associated with the replacement project. (b) What is the NPV of the replacement project if the cost of capital is 14 percent?
Solution:

(a)

A. i. ii. iii iv.

Initial outlay (Time 0) Cost of new machine Salvage value of old machine Incremental working capital requirement Total net investment (=i – ii + iii) Rs. 8,000,000 2,200,000 600,000 6,400,000

E.
Year

Operating cash flow (years 1 through 4)
1 2 3 4 5

i. Post-tax savings in manufacturing costs ii. Depreciation on new machine iii. Depreciation on old machine iv.Incremental dereciation v.Tax shield on incremental dep. iv. Operating cash flow( i +v)

1,000,000 2,000,000 840,000 1,160,000 382,800 1,382,800

1,000,000 1,500,000 588,000 912,000 300,960 1,300,960

1,000,000 1,125,000 411,600 713,400 235,422 1,235,422

1,000,000 1,000,000 843,750 288,120 555,630 183,358 632,813 201,684 431,129 142,273

1,183,358 1,142,273

F.

Terminal cash flow (year 5) i. ii. iii. iv. Salvage value of new machine Salvage value of old machine Recovery of incremental working capital Terminal cash flow ( i – ii + iii) Rs. 3,500,000 900,000 600,000 3,200,000

G.
Year

Net cash flows associated with the replacement project (in Rs)
0 1 2 3 4 5

NCF (c)

(6,400,000)

1,382,800

1,300,960 1,235,422

1,183,358

4,342,273

NPV of the replacement project (6,400,000)+ 1,382,800x PVIF (14,1)+ 1,300,960x PVIF (14,2) + 1,235,422x PVIF (14,3)+ 1,183,358x PVIF (14,4) +4,342,273x PVIF (14,5) = - Rs.398,749

8.

A machine costs Rs.250,000 and is subject to a depreciation rate of 24 percent under the WDV method. What is the present value of the tax savings on account of depreciation for a period of 5 years if the tax rate is 34 percent and the discount rate is 16 percent?

Solution:

Tax shield (savings) on depreciation (in Rs) Depreciation Tax shield Year charge (DC) =0.34 x DC 1 2 3 4 5 60,000 45,600 34,656 26,339 20,017 20,400 15,504 11,783 8,955 6,806

PV of tax shield @ 16% p.a.

17,586 11,522 7,549 4,946 3,240 ---------44,843 ----------

Present value of the tax savings on account of depreciation = Rs.44,843

9.

A machine costs Rs.680,000 and is subject to a depreciation rate of 27 percent under the WDV method. What is the present value of the tax savings on account of depreciation for a period of 4 years if the tax rate is 36 percent and the discount rate is 18 percent?

Solution:

Tax shield (savings) on depreciation (in Rs) Depreciation Tax shield Year charge (DC) =0.36 x DC 1 2 3 4 183,600 134,028 97,840 71,423 66,096 48,250 35,222 25,712

PV of tax shield @ 18% p.a.

56,014 34,652 21,437 13,262 ---------125,365 ---------Present value of the tax savings on account of depreciation = Rs.125,365
CHAPTER 13

1.

A project requires an investment of 500,000. The unit selling price is 70 and the unit variable cost is 35. Fixed costs other than depreciation will be 280,000 per year. Depreciation will be 80,000 per year for tax purposes. The life of the project is 5 years. The effective tax rate is 33 percent. The cost of capital is 14 percent. What is the financial break-even point?

Solution:

= 0.5 of sales (S) = 0.5 of sales (S) = 280,000 = 80,000 = 0.5 S – 280,000 – 80,000 = 0.5 S – 360,000 = (0.5 S – 360,000) (1-0.33) + 80,000 = 0.335 S - 161,200 PV of cash flow = (0.335 S -161,200) PVIFA (14%, 5) = (0.335 S -161,200) x 3.433 Equating this with the initial investment, we get (0.335 S -161,200) x 3.433 = 500,000 (0.335 S -161,200) = 145,645.21 S = 915,955.85

Variable cost Contribution Fixed cost Depreciation Pre-tax profit Cash flow

2.

A project requires an investment of 800,000. The unit selling price is 50 and the unit variable cost is 25. Fixed costs other than depreciation will be 250,000 per year. Depreciation will be 85,000 per year for tax purposes. The life of the project is 6 years. The effective tax rate is 20 percent. The cost of capital is 12 percent. What is the financial break-even Point?

Solution:

Variable cost Contribution margin Fixed costs Depreciation Pre-tax profit Cash flow

= 50 percent of sales (S) = 50 percent of sales (S) = 250,000 = 85,000 = (0.5S – 250,000 – 85,000) = (0.5S – 335,000) 0.8 + 85,000 = 0.4S - 183,000 Present value of cash flows is (0.4S – 183,000) x 4.111 Equating this with the initial investment of 800,000 we get 1.6444 S – 752313 = 800,000 S = 943999.6 3. A project requires an investment of 500,000. The unit selling price is 70 and the unit variable cost is 35. Fixed costs other than depreciation will be 280,000 per year. Depreciation will be 80,000 per year for tax purposes. The life of the project is 5 years. The effective tax rate is 33 percent. The cost of capital is 14 percent. What is the financial break-even point?

Solution:

= 0.5 of sales (S) = 0.5 of sales (S) = 280,000 = 80,000 = 0.5 S – 280,000 – 80,000 = 0.5 S – 360,000 = (0.5 S – 360,000) (1-0.33) + 80,000 = 0.335 S - 161,200 PV of cash flow = (0.335 S -161,200) PVIFA (14%, 5) = (0.335 S -161,200) x 3.433 Equating this with the initial investment, we get (0.335 S -161,200) x 3.433 = 500,000 (0.335 S -161,200) = 145,645.21 S = 915,955.85

Variable cost Contribution Fixed cost Depreciation Pre-tax profit Cash flow

4.

You are the financial manager of Navneet Limited. Navneet is planning to set up a factory at Aurangabad. Your project staff has developed the following cash flow forecast for the factory.
Cash Flow Forecast for Navneet’s factory Rs. in million Years 1 - 10

Year 0

Investment (500) Sales Variable costs (60% of sales) Fixed costs Depreciation (assumed at 10% of investment per annum) Pre-tax profit Tax ( at a rate assumed at 30 % of pre-tax profit) Profit after tax Cash flow from operations Net cash flow

400 240 60 50 50 15 35 85 85

What is the NPV of the project? Assume that the cost of capital is 15 percent. The range of values that the underlying variables can take is shown below: Underlying Variable Pessimistic Expected Optimistic Investment 400 500 700 (Rs. in million) Sales (Rs. in million) 250 400 650 Variable cost as a percent 70 60 55 of sales Fixed costs (Rs. in million) 65 60 50 Cost of capital (%) 18 15 12 a. Calculate the effect of variations in the values of the underlying variables on NPV. b. Calculate the accounting break-even point.
Solution:

Expected Scenario 1. Investment 2. Sales Variable costs as a pecentage of sales 3. Variable costs 4. Fixed costs 5. Depreciation(assumed at 10% of investment per annum) 500 400 60 240 60 50

Optimistic Scenario 400 650 55 357.5 50 40

Pessimistic Scenario 700 250 70 175 65 70

6. Pre-tax profit 7. Tax( at a rate assumed at 30 % of pre-tax profit) 8. Profit after tax 9. Annual cash flow from operations 10. Net present value

50 15 35 85 -73.40

202.5 60.75 141.75 181.75 626.93

-60 -18 -42 28 -574.17

Assumptions: (1)

(2)

(3)

The useful life is assumed to be 10 years under all three scenarios. It is also assumed that the salvage value of the investment after ten years is zero. The investment is assumed to be depreciated at 10% per annum; and it is also assumed that this method and rate of depreciation are acceptable to the IT (income tax) authorities. It is assumed that only loss on this project can be offset against the taxable profit on other projects of the company; and thus the company can claim a tax shield on the loss in the same year.

(b)

Accounting break even point (under ‘expected’ scenario) Fixed costs + depreciation = Rs. 110 million Contribution margin ratio = 160 / 400 = 0.4 Break even level of sales = 110 / 0.4 = Rs.275 million

5.

You are the financial manager of Magnum Corporation. Magnum is planning to set up a Machine Tools plant at Chennai. Your project staff has developed the following cash flow forecast for the project.
Cash Flow Forecast for Navneet’s factory Rs. in million Years 1 - 8

Year 0

Investment (1000) Sales Variable costs (70% of sales) Fixed costs Depreciation (assumed at 10% of investment per annum) Pre-tax profit Tax (at a rate assumed at 33 % of pre-tax profit) Profit after tax Cash flow from operations Net cash flow

800 560 90 100 50 16.5 33.5 133.5 133.5

What is the NPV of the project ? Assume that the cost of capital is 14 percent. The range of values that the underlying variables can take is shown below:
Underlying Variable Pessimistic Investment 1300 (Rs. in million) Sales (Rs. in million) 650 Variable cost as a percent 75 of sales Fixed costs (Rs. in million) 95 Cost of capital (%) 16 Expected 1000 Optimistic 800

800 70 90 14

1000 60 80 13

(a) Calculate the effect of variations in the values of the underlying variables on NPV. (b) Calculate the accounting break-even point.
Solution:

Expected Optimistic Pessimistic Scenario Scenario Scenario 1. Investment 2. Sales Variable costs as a percentage of sales 3. Variable costs 4. Fixed costs 5. Depreciation(assumed at 10% of investment per annum) 6. Pre-tax profit 7. Tax( at a rate assumed at 33 % of pre-tax profit) 8. Profit after tax 9. Annual cash flow from operations 10. Net present value Assumptions: (1) 1000 800 70 560 90 100 50 16.5 33.5 133.5 -380.71 800 1000 60 600 80 80 240 79.2 160.8 240.8 355.54 1300 650 75 487.5 95 130 -62.5 -20.625 -41.875 88.125 -917.22

(2)

The useful life is assumed to be 8 years under all three scenarios. It is also assumed that the salvage value of the investment after eight years is zero. The investment is assumed to be depreciated at 10% per annum; and it is also assumed that this method and rate of depreciation are acceptable to the IT (income tax) authorities.

(3)

It is assumed that only loss on this project can be offset against the taxable profit on other projects of the company; and thus the company can claim a tax shield on the loss in the same year.

(b)

Accounting break even point (under ‘expected’ scenario)

Fixed costs + depreciation Contribution margin ratio Break even level of sales 6.

= Rs. 190 million = 0.3 = 190 / 0.3 = Rs.633.33 million

Rakesh Limited is considering the risk characteristics of a certain project. The firm has identified that the following factors, with their respective expected values, have a bearing on the NPV of this project. Initial investment Rs.50,000 Cost of capital 12% Quantity manufactured and sold annually 2,800 Price per unit Rs.50 Variable cost per unit Rs.28 Fixed costs Rs.8,000 Depreciation Rs.5,000 Tax rate 35% Life of the project 6 years Net salvage value Nil Assume that the following underlying variables can take the values as shown below:
Underlying variable Quantity manufactured and sold Price per unit Variable cost per unit Pessimistic 2,000 Rs.35 Rs.35 Optimistic 3,500 Rs.60 Rs.20

a. Calculate the sensitivity of net present value to variations in (a) quantity manufactured and sold, (b) price per unit, and (c) variable cost per unit.

Solution:

Sensitivity of net present value to quantity manufactured and sold

Expected Pessimistic Optimistic Quantity manufactured and sold annually Initial investment Sales revenue Variable costs Fixed costs Depreciation Profit before tax Tax Profit after tax Net cash flow

2,800 50,000 140,000 78,400 8,000 5,000 48,600 17,010 31,590 36,590
100,436

2000 50,000 100,000 56,000 8,000 5,000 31,000 10,850 20,150 25,150 53,402

3500 50,000 175,000 98,000 8,000 5,000 64,000 22,400 41,600 46,600 141,592

NPV at a cost of capital of 12 % and useful life of 6 years

Sensitivity of net present value to price per unit

Price per unit Initial investment Sales revenue Variable costs Fixed costs Depreciation Profit before tax Tax Profit after tax Net cash flow NPV at a cost of capital of 12 % and useful life of 6 years

Expected Pessimistic Optimistic 50 35 60 50,000 50,000 50,000 140,000 98,000 168,000 78,400 78,400 78,400 8,000 8,000 8,000 5,000 5,000 5,000 48,600 6,600 76,600 17,010 2,310 26,810 31,590 4,290 49,790 36,590 9,290 54,790 100,436 -11,805 175,264

Sensitivity of net present value to variable cost per unit.
Expected Pessimistic Optimistic 28 35 20 50,000 50,000 50,000 140,000 140,000 140,000 78,400 98,000 56,000 8,000 8,000 8,000 5,000 5,000 5,000 48,600 29,000 71,000 17,010 10,150 24,850 31,590 18,850 46,150 36,590 23,850 51,150 100,436 48,057 160,298

Variable cost per unit Initial investment Sales revenue Variable costs Fixed costs Depreciation Profit before tax Tax Profit after tax Net cash flow NPV at a cost of capital of 12 % and useful life of 6 years 7.

A project involving an outlay of Rs.15 million has the following benefits associated with it.
Year 1 Cash Flow (Rs. in mln) 7 8 9 Year 2 Prob. Cash Flow (Rs. in mln) 0.3 6 0.5 8 0.2 10 Year 3 Prob. Cash Flow (Rs. in mln) 0.5 5 0.2 7 0.3 9

Prob.

0.4 0.3 0.3

Assume that the cash flows are independent. Calculate the expected net present value and the standard deviation of net present value assuming that i = 12 percent.
Solution:

Define At as the random variable denoting net cash flow in year t.
A1 A2

= = = = = = = =

7 x 0.3 + 8 x 0.5 + 9 x 0.2 7.9 6 x 0.5 + 8 x 0.2 + 10 x 0.3 7.6 5 x 0.4 + 7 x 0.3 + 9 x 0.3 6.8 7.9 / 1.12 +7.6 / (1.12)2 + 6.8 / (1.12)3 – 15 Rs.2.95 million

A3

NPV

?12 ?22 ?32

= 0.3x( 7-7.9)2 + 0.5(8-7.9)2 + 0.2(9-7.9)2 = 0.49 = 0.5(6-7.6)2+0.2(8-7.6)2+0.3(10-7.6)2 = 3.04 = 0.4(5-6.8)2+0.3(7-6.8)2+0.3(9-6.8)2 = 2.76
?12 ?22 ?32

?2 NPV =

+ (1.12)
2

+ (1.12)
4

(1.12)6

= 0.49/(1.12)2 + 3.04/(1.12)4 + 2.76/(1.12)6 = 3.72 ? (NPV) = Rs.1.93 million 8. A project involving an outlay of Rs.25 million has the following benefits associated with it.
Year 1 Cash Flow (Rs. in mln) 10 12 13 Year 2 Prob. Cash Flow (Rs. in mln) 0.2 9 0.5 11 0.3 12 Year 3 Prob. Cash Flow (Rs. in mln) 0.6 12 0.2 13 0.2 14

Prob.

0.5 0.4 0.1

Assume that the cash flows are independent. Calculate the expected net present value and the standard deviation of net present value assuming that i = 15 percent.
Solution:

Define At as the random variable denoting net cash flow in year t.
A1 A2 A3

= = = =

10 x 0.2 + 12 x 0.5 + 13 x 0.3= 11.9 9 x 0.6 + 11 x 0.2 + 12 x 0.2 = 10 12 x 0.5 + 13 x 0.4 + 14 x 0.1= 12.6 11.9 / 1.15 +10 / (1.15)2 + 12.6 / (1.15)3 – 25 = Rs.1.19 million

NPV
?12 ?22 ?32

= 0.2x( 10-11.9)2 + 0.5(12-11.9)2 + 0.3(13-11.9)2 = 1.09 = 0.6(9-10)2+0.2(11-10)2+0.2(12-10)2 = 1.6 = 0.5(12-12.6)2+0.4(13-12.6)2+0.1(14-12.6)2 = 0.44 ?12 ?22 ?32 ?2 NPV = + + 2 4 (1.12) (1.12) (1.12)6

= 1.09/(1.15)2 + 1.6/(1.15)4 + 0.44/(1.15)6 = 1.93 ? (NPV) = Rs.1.39million 9. Mohan is considering an investment which requires a current outlay of Rs.25,000. The expected value and standard deviation of cash flows are:
Year 1 2 3 4 Expected Value Rs.25,000 15,000 14,000 10,000 Standard Deviation Rs.3,000 4,000 4,000 2,000

The cash flows are perfectly correlated. Calculate the expected net present value and standard deviation of net present value of this investment, if the risk-free interest rate is 7 percent.
Solution:

Expected NPV 4 At = ? - 25,000 t=1 (1.07)t = 25,000/(1.07) + 15,000 / (1.07)2 + 14,000 / (1.07)3 + 10,000 / (1.07)4 – 25,000 = 30,523 Standard deviation of NPV ?t

4 ? t=1 (1.07)t = = 10.

3,000 / (1.07) + 4,000 / (1.07)2 + 4,000 / (1.07)3 + 2,000 / (1.07)4 11,088.48

Boldman is considering an investment which requires a current outlay of Rs.100,000. The expected value and standard deviation of cash flows are:
Year 1 2 3 4 Expected Value Rs.40,000 55,000 34,000 20,000 Standard Deviation Rs.8,000 10,000 7,000 9,000

The cash flows are perfectly correlated. Calculate the expected net present value and standard deviation of net present value of this investment, if the risk-free interest rate is 10 percent.

Solution:

Expected NPV 4 At = ? - 100,000 t=1 (1.1)t = 40,000/(1.1) + 55,000 / (1.1)2 + 34,000 / (1.1)3 + 20,000 / (1.1)4 – 100,000 = 21,023 Standard deviation of NPV ?t

4 ? t=1 (1.1)t = = 11.

8,000 / (1.1) + 10,000 / (1.1)2 + 7,000 / (1.1)3 + 9,000 / (1.1)4 26,944

Dinesh Associates is considering an investment project which has an estimated life of four years. The cost of project is 400,000 and the possible cash flows are given below:
Year 2 Cash Flow Prob. Year 3 Cash Flow Prob. Year 4 Cash Flow Prob.

Year 1 Cash Flow Prob.

110,000 120,000 130,000

0.3 0.4 0.3

120,000 130,000 140,000

0.5 0.3 0.2

130,000 140,000 150,000

0.2 0.3 0.5

110,000 120,000 130,000

0.4 0.4 0.2

The cash flows of various years are independent and the risk-free discount rate (post-tax) is 8 percent. (a) (b) (c)
Solution: (a)

What is the expected NPV ? If the NPV is approximately normally distributed, what is the probability that the NPV will be zero or less ? What is the probability that the profitability index will be greater than 1.1 ?

Expected NPV 4 At = ? - 400,000 …. (1) t=1 (1.08)t A1 = 110,000 x 0.3 + 120,000 x 0.4 + 130,000 x 0.3 = 120,000 A2 = 120,000 x 0.5 + 130,000 x 0.3 + 140,000 x 0.2 = 127,000 A3 = 130,000 x 0.2 + 140,000 x 0.3 + 150,000 x 0.5 = 143,000 A4 = 110,000 x 0.4 + 120,000 x 0.4 + 130,000 x 0.2 = 118,000

Substituting these values in (1) we get Expected NPV = NPV =120,000 / (1.08)+ 127,000 / (1.08)2 + 143,000 / (1.08)3 + 118,000 / (1.08)4 - 400,000 = 20,245 (b) The variance of NPV is given by the expression 4 ?2t ?2 (NPV) = ? …….. (2) t=1 (1.08)2t ?12= [(110,000–120,000)2x0.3+(120,000–120,000)2 x0.4 = +(130,000 –120,000)2 x 0.3] = 60,000,000 2 ?2 = [(120,000 –127,000)2 x 0.5 + (130,000 –127,000)2 x 0.3 + (140,000 –127,000)2 x 0.2]= 61,000,000 2 ?3 = [(130,000 –143,000)2 x 0.2 + (140,000 –143,000)2 x 0.3 + (150,000 –143,000)2 x 0.5] = 61,000,000 2 ?4 = [(110,000 –118,000)2 x 0.4 + (120,000 –118,000)2 x 0.4 + (130,000 –118,000)2 x 0.2]= 56,000,000 Substituting these values in (2) we get ?2 (NPV) =60,000,000/ (1.08)2 + 61,000,000/ (1.08)4 + 61,000,000/ (1.08)6 + 56,000,000/ (1.08)8 = 164,972,555 ? NPV = 164,972,555= Rs.12,844
NPV – NPV 0 - NPV

Prob (NPV < 0) = Prob.
? NPV 0 – 20,245 = Prob Z < 12,844

<
? NPV

= Prob (Z < - 1.58) From the normal distribution tables, we have, when Z = -1.60, the probability = 0.0548 when Z = -1.55, the probability =0.0606 Extrapolating, we get Prob (Z < - 1.58) = 0.0548 +(1.60-1.58)(0.0606 – 0.0548)/0.05 = 0.0548 + 0.00232 = 0.0571 So the probability of NPV being negative is 5.71 % (c) Prob (P1 > 1.1) Prob (PV / I > 1.1) Prob (NPV / I > 0.1)

Prob. (NPV > 0.1 x 400,000) Prob (NPV > 40,000) Prob (NPV > 40,000)= Prob (Z > (40,000- 20,245 )/ 12,844) = Prob (Z > - 1.54) From the normal distribution tables, we have, when Z =1.55, the probability = 1 – 0.0606 =0.9394 when Z = 1.50, the probability = 1 – 0.0668 = 0.9332 Extrapolating, we get Prob (Z > - 1.54) = 0.9332 +(1.54-1.50)(0.9394 – 0.9332)/0.05 = 0.9332 + 0.00496 = 0.9382 So the probability of P1 > 1.1 is 93.82% 12. The expected cash flows of a project are given below:
Year Cash Flow 0 Rs. (50,000) 1 10,000 2 30,000 3 20,000 4 20,000 5 10 ,000 The certainty equivalent factor behaves as per the following equation : ?t = 1 – 0.08t

Calculate the net present value of the project if the risk-free rate of return is 8 percent
Solution:
Certainty Equivalent Factor: ?t =1 - 0.08t Certainty Equivalent value Discount Factor at 8%

Year

Cash Flow

Present Value

0 1 2 3 4 5

-50000 10000 30000 20000 20000 10000

1 0.92 0.84 0.76 0.68 0.6

-50000 9200 25200 15200 13600 6000

1 0.925926 0.857339 0.793832 0.73503 0.680583 NPV =

-50000 8519 21605 12066 9996 4083 6270

CHAPTER 14

1

The latest balance sheet of ARN Limited is given below
Liabilities Assets

Equity capital Preference capital Reserves & Surplus Debentures Working capital loan Current liabilities & Provisions

3500 Fixed assets 200 Investments 5200 Current assets, loans & advances 2600 2500 1500 15500

11000 800 3700

15500

The target capital structure of ARN has 60 percent equity, 5 percent preference, and 35 percent debt. ARN’s preference capital has a post-tax cost of 7 percent. ARN’s debentures consist of Rs.100 par, 8 percent coupon payable annually, with a residual maturity of 3 years. The market price of these debentures is Rs.103. Working capital loan carries an interest rate of 11 percent. ARN’s equity stock is currently selling for Rs.102 per share. Its last dividend was Rs.3.00 per share and the dividend per share is expected to grow at a rate of 14 percent per year in future. ARN’s equity beta is 1.5, the risk-free rate is 6 percent, and the market risk premium is 8 percent. ARN’s tax rate is 33 percent (i) What is ARN’s average pre-tax cost of debt? (Use the approximate yield formula)
Solution:

8 + (100-103) / 3 7 Pre-tax cost of debenture = ---------------------------- = -------- = (0.4 x 100) + (0.6 x 103) 101.8 Pre-tax cost of working capital loan = 11% 2600 2500 Average pre-tax cost of debt = -------- x 6.88 + -------- x 11 = 8.90 % 5100 5100

6.88%

(ii)

What is ARN’s cost of equity using the constant growth dividend discount model?

Solution:

3.42 D0 ( 1+g) rE = ------------- + g = ------- + 0.14 = 17.35 % 102 P0 (iii) What is ARN’s post tax weighted average cost of capital? Use the CAPM to estimate the cost of equity and employ the weights in the target capital structure.
Solution:

rE = 6 + 1.5 x 8 = 18% rA = 0.60 x 18 + 0.05 x 7 + 0.35 x 8.90 (1-0.33) = 13.24% 2. The latest balance sheet of MM Limited is given below
Liabilities Assets

Equity capital Preference capital Reserves & Surplus Debentures Working capital loan Current liabilities & Provisions

3200 300 6800 2100 2000 1700 16100

Fixed 10500 Investments 1100 Current assets, 4500

assets

loans

&

advances

16100 The target capital structure of MM has 65 percent equity, 5 percent preference, and 30 percent debt. MM’s preference capital has a post-tax cost of 8 percent. MM’s debentures consist of Rs.100 par, 9 percent coupon payable annually, with a residual maturity of 4 years. The market price of these debentures is Rs.105. Working capital loan carries an interest rate of 10 percent. MM’s equity stock is currently selling for Rs.90 per share. Its last dividend was Rs.2.00 per share and the dividend per share is expected to grow at a rate of 12 percent per year in future. MM’s equity beta is 1.05, the risk-free rate is 7 percent, and the market risk premium is 6 percent. MM’s tax rate is 30 percent (i) What is MM’s average pre-tax cost of debt? (Use the approximate yield formula)

Solution:

Pre-tax cost of debenture 9 + (100 – 105) / 4 0.6 x 105 + 0.4 x 100 Pre-tax cost of working capital loan = 10% Average pre-tax cost of debt 2100 7.52% 4100 = 3.85 + 4.88 = 8.73 % + 10% 4100 2000 = 7.52%

(ii) What is MM’s cost of equity using the constant growth dividend discount model ?
Solution:

rE

= =

D0 (1+g) P0 14.49 %

+g

=

2 (1.12) 90

+

0.12

(iii) What is MM’s post tax weighted average cost of capital? Use the CAPM to estimate the cost of equity and employ the weights in the target capital structure.
Solution:

rE rA

= = = =

7 + 1.05 (6) 0.65 x 13.3 8.645 11.664

= + +

13.30% 0.05 x 8 0.4

+ +

0.3 x 8.73 2.619

3.

The latest balance sheet of Phoenix Limited is given below
Liabilities Assets

Equity capital Preference capital Reserves & Surplus Debentures Current liabilities & Provisions

1500 200 2000 1800 1000 6500

Fixed assets Investments Current assets, loans & advances

4000 1000 1500

6500

The target capital structure of Phoenix has 70 percent equity, 5 percent preference, and 25 percent debt. Phoenix’s preference capital has a post-tax cost of 9 percent. Phoenix’s debentures consist of Rs.100 par, 8 percent coupon payable annually, with a residual maturity of 5 years. The market price of these debentures is Rs.105. Phoenix’s equity stock is currently selling at Rs.125 per share. Its last dividend was Rs.3.00 per share and the dividend per share is expected to grow at a rate of 12 percent per year in future. Phoenix’s equity beta is 0.9, the risk-free rate is 7 percent, and the market risk premium is 7 percent. Phoenix’s tax rate is 30 percent (i) What is Phoenix’s pre-tax cost of debt? (Use the approximate yield formula)

Solution:

8 +

(100 – 105) / 5 = 6.80%

0.6 x 105 + 0.4 x 100 (ii) What is Phoenix’ cost of equity using the constant growth dividend discount model?

Solution:

D0 (1 + g ) rE = P0 + g =

3 ( 1.12 ) + 0.12 = 14.69% 125

(iii) What is Phoenix’s post tax weighted average cost of capital? Use the CAPM to estimate the cost of equity and employ the weights in the target capital structure.
Solution:

rA 4.

rE = 7 + 0.9 ( 7 ) = 13.3% = 0.70 x 13.3 + 0.05 x 9 + 0.25 x 6.80 ( 1 - 0.3 ) = 9.31 + 0.45 + 1.19 = 10.95 %

Nishant Limited’s WACC is 14 percent and its tax rate is 33 percent. Nishant’s pre-tax cost of debt is 12 percent and its debt-equity ratio is 2:1. The risk-free rate is 8 percent and the market risk premium is 6 percent. What is the beta of Nishant’s equity?

Solution:

Given: 2/3 x 12% x (1 – 0.33) + 1/3 x r = 14% where r is the cost of equity capital. Therefore r= (14-5.36)x 3 = 25.92 % Using the SML equation we get: 8% + 6% x ? = 25.92 % Solving this equation we get ? = 2.99 5. Astute Corporation’s WACC is 11 percent and its tax rate is 36 percent. Astute’s pre-tax cost of debt is 10 percent and its debt-equity ratio is 1.5:1. The risk-free rate is 7 percent and the market risk premium is 8 percent. What is the beta of Astute’s equity?

Solution:

Given: (1.5/2.5) x 10% x (1 – 0.36) + (1/2.5) x r = 11 % where r is the cost of equity capital. Therefore r= (11-3.84) x 2.5 = 17.9 % Using the SML equation we get: 7% + 8% x ? = 17.9% Solving this equation we get ? = 1.36 6. North Star Limited has 30 million equity shares outstanding. The book value per share is Rs.60 and the market price per share is Rs.180. North Star has two debenture issues outstanding. The first issue has a face value of Rs.400 million, 13 percent coupon, and sells for 95 percent of its face value. It will mature in 6 years. The second issue has a face value of Rs.300 million, 12 percent coupon, and sells for 108 percent of its face value. It will mature in 7 years. North Star also has a bank loan of Rs.300 million on which the interest rate is 14 percent. What are North Star’s capital structure weights on a book value basis and on a market value basis?
Solution:

The book value and market values of the different sources of finance are provided in the following table. The book value weights and the market value weights are provided within parenthesis in the table.

(Rs. in million) Source Book value Equity 1800 (0.64) Debentures – first series 400 (0.14) Debentures – second series 300 (0.11) Bank loan 300 (0.11) Total 2800 (1.00) Market value 5400 (0.84) 380 (0.06) 324 (0.05) 300 (0.05) 6404 (1.00)

7.

Jaihind Corporation has 100 million equity shares outstanding. The book value per share is Rs.100 and the market price per share is Rs.680. Jaihind has a debenture issue outstanding with a face value of Rs.800 million. The coupon rate for a debenture is 13 percent coupon, and it sells for 85 percent of its face value. It will mature in 4 years. Jaihind also has a bank loan of Rs.600 million on which the interest rate is 11 percent. What are Jaihind’s capital structure weights on a book value basis and on a market value basis?

Solution:

The book value and market values of the different sources of finance are provided in the following table. The book value weights and the market value weights are provided within parenthesis in the table. (Rs. in million)
Source Equity Debentures Bank loan Total Book value 10,000 (0.88) 800 (0.07) 600 (0.05) 11,400 (1.00) Market value 68,000 (0.98) 680(0.01) 600 (0.01) 69,280 (1.00)

8.

Friends Associates manufactures industrial solvents. Its debt-equity ratio is 5:3 Its WACC is 13 percent and its tax rate is 34 percent. a. If Friends Associate’s cost of equity is 22 percent, what is its pre-tax cost of debt? b. If Friends Associates can issue debt at an interest rate of 10 percent, what is its cost of equity?

Solution:

(a)

Given: rD x (1 – 0.34) x (5/8) + 22% x (3/8) = 13 % rD = (13 -8.25)/0.4125 = 11.5% where rD represents the pre-tax cost of debt.

9.

Pioneer Limited’s capital structure in terms of market value is: Debt Rs.30 million Equity Rs.90 million The company plans to maintain this market-value capital structure. The company has a plan to invest Rs.16 million next year. This will be financed as follows: Retained earnings Additional equity Debt Rs.6 million Rs.6 million Rs.4 million

The company’s equity stock presently sells for Rs.40 per share. The next dividend expected is Rs.6.00. The expected rate of dividend growth is 6 percent. Additional equity can be issued at Rs.35 per share (net). The interest rate applicable to additional debt would be as follows: First Rs.3 million Next Rs.1 million Required: (a) At what amounts of new capital will there be breaks in the marginal cost of capital schedule? (b) What will be the marginal cost of capital in the interval between each of the breaks?
Solution:

12 percent 14 percent

The tax rate for the firm is 33 percent.

Cost of equity = D1/P0 + g = 6.00 / 40 + 0.06 = 21 % (a) The first chunk of financing will comprise of Rs.6 million of retained earnings and 3 millions of fresh equity costing 21 percent and Rs.3 million of debt costing 12 (1-.33) = 8.04 per cent The second chunk of financing will comprise of Rs.3 million of additional equity costing 21 per cent and Rs.1million of debt costing 14(1-.33) = 9.38 per cent The marginal cost of capital in the first chunk will be : 9/12 x 21% + 3/12 x 8.04 % = 17.76 % The marginal cost of capital in the second chunk will be : 3/4 x 21% + 1/4 x 9.38 % = 18.1 % Note : We have assumed that (i) The net realisation per share will be Rs.35, after floatation costs, and (ii) The planned investment of Rs.16 million is inclusive of floatation costs

10.

Mahaveer Cotspin’s capital structure in terms of market value is: Debt Equity Rs.50 million Rs.75 million

The company plans to maintain this market-value capital structure. The company has a plan to invest Rs.15 million next year. This will be financed as follows: Retained earnings Additional equity Debt Rs.4.5 million Rs.4.5 million Rs.6 million

The company’s equity stock presently sells for Rs.20 per share. The next dividend expected is Rs.4.00. The expected rate of dividend growth is 10 percent. Additional equity can be issued at Rs.18 per share (net). The interest rate applicable to additional debt would be as follows: First Rs.4 million Next Rs.2 million Required: (a) (b)
Solution:

14 percent 15 percent

The tax rate for the firm is 34 percent. At what amounts of new capital will there be breaks in the marginal cost of capital schedule? What will be the marginal cost of capital in the interval between each of the breaks?

Cost of equity = = =

D1/P0 + g 4.00 / 20 + 0.10 30 %

(b) The first chunk of financing will comprise of Rs.4.5 million of retained earnings and 1.5 millions of fresh equity costing 30 percent and Rs.4 million of debt costing 14 (1-.34) = 9.24 per cent The second chunk of financing will comprise of Rs.3 million of additional equity costing 30 per cent and Rs.2million of debt costing 15(1-.34) = 9.90 per cent The marginal cost of capital in the first chunk will be : 6/10 x 30% + 4/10 x 9.24 % = 21.7 % The marginal cost of capital in the second chunk will be : 6/10 x 30% + 4/10 x 9.90 % = 21.96 % Note : We have assumed that (i) The net realisation per share will be Rs.18, after floatation costs, and (ii) The planned investment of Rs.15 million is inclusive of floatation costs

11.

Modern Limited has the following book value capital structure: Equity capital (25 million shares, Rs.10 par) Preference capital, 10 percent (800,000 shares, Rs.100 par) Retained earnings Debentures 14 percent (2,000,000 debentures, Rs.100 par) Term loans, 14 percent Rs.250 million Rs. 80 million Rs. 50 million Rs.200 million Rs. 220 million Rs.800 million

The next expected dividend per share is Rs.3.00. The dividend per share is expected to grow at the rate of 10 percent. The market price per share is Rs.260. Preference stock, redeemable after 8 years, is currently selling for Rs.90 per share. Debentures, redeemable after 5 years, are selling for Rs.105 per debenture. The tax rate for the company is 34 percent. (a) Calculate the average cost of capital using (i) book value proportions, and (ii) market value proportions (b) Define the marginal cost of capital schedule for the firm if it raises Rs.280 million next year, given the following information: (i) (ii) (iii) (iv) the amount will be raised from equity and term loans in equal proportions the firm expects to retain Rs.40 million earnings next year; the additional issue of equity stock will fetch a net price per share of Rs.250. the debt capital raised by way of term loans will cost 12 percent for the first Rs.100 million and 13 percent for the next Rs.40 million.

Solution:

(a) (i) The cost of equity and retained earnings rE = D1/PO + g = 3.0 / 260 + 0.10 = 11.15 % The cost of preference capital, using the approximate formula, is: 10 + (100-90)/8
rP

= 0.6 x 90 + 0.4 x 100

= 11.97 %

The pre-tax cost of debentures, using the approximate formula, is : 14 + (100-105)/5
rD

= 0.6x105 + 0.4x100

= 12.62 %

The post-tax cost of debentures is 12.62 (1-tax rate) = 12.62 (1 – 0.34) = 8.33% The post-tax cost of term loans is 14 (1-tax rate) = 14 (1 – 0.34) = 9.24 % The average cost of capital using book value proportions is calculated below :
Source of capital Component Cost (1) 11.15% 11.97% 11.15% 8.33 % 9.24 % Book value Rs. in million (2) 250 80 50 200 220 Book value proportion (3) 0.31 0.10 0.06 0.25 0.28 Product of (1) & (3)

Equity capital Preference capital Retained earnings Debentures Term loans

3.46 1.20 0.67 2.08 2.59 10.0 %

800

Average cost of capital

(ii)

The average cost of capital using market value proportions is calculated below:
Source of capital Component cost (1) Market value Market value Product of proportion Rs. in million (2) (3) (1) & (3)

Equity capital and retained earnings Preference capital Debentures Term loans

11.15% 11.97% 8.33% 9.24%

6,500 72 210 220 7,002

0.93 0.01 0.03 0.03 Average cost of capital

10.37 0.12 0.25 0.28 11.02 %

(b) The Rs.280 million to be raised will consist of the following: Retained earnings Rs.40 million Additional equity Rs. 100 million Debt Rs. 140 million The first batch will consist of Rs. 40 million each of retained earnings and debt costing 11.15 percent and 12(1-0.34)= 7.92 percent respectively. The second batch will consist of Rs. 60 million each of additional equity and debt at 11.15 percent and 7.92 percent respectively. The third chunk will consist of Rs.40 million each of additional equity and debt costing 11.15 percent and 13(1-0.34) = 8.58 percent respectively. The marginal cost of capital in the chunks will be as under First batch : (0.5x11.15 ) + (0.5 x 7.92) Second batch : (0.5x11.15 ) + (0.5 x 7.92) Third batch : (0.5x11.15 ) + (0.5 x 8.58) = = = 9.54 % 9.54 % 9.87%

The marginal cost of capital schedule for the firm will be as under. Range of total financing (Rs. in million) 0 - 200 201-280 Weighted marginal cost of capital (%) 9.54 9.87

Here it is assumed that the Rs.280 million to be raised is inclusive of floatation costs. 12. Madhu Corporation has the following book value capital structure: Equity capital (30 million shares, Rs.10 par) Preference capital, 15 percent (1,000,000 shares, Rs.100 par) Retained earnings Debentures 11 percent (2,500,000 debentures, Rs.100 par) Term loans, 13 percent Rs.300 million Rs. 100 million Rs. 100 million Rs .250 million Rs. 300 million Rs.1050 million The next expected dividend per share is Rs.4.00. The dividend per share is expected to grow at the rate of 15 percent. The market price per share is Rs.80. Preference stock, redeemable after 6 years, is currently selling for Rs.110 per share. Debentures, redeemable after 6 years, are selling for Rs.102 per debenture. The tax rate for the company is 35 percent. (a) Calculate the average cost of capital using (i) book value proportions, and (ii) market value proportions

(b) Define the marginal cost of capital schedule for the firm if it raises Rs.450 million next year, given the following information: (i) the amount will be raised from equity and term loans in the proportion 2:1. (ii) the firm expects to retain Rs.80 million earnings next year; (iii) the additional issue of equity stock will fetch a net price per share of Rs.75. (iv) the debt capital raised by way of term loans will cost 11percent for the first (v) Rs.100 million and 12 percent for amounts thereafter.
Solution:

(a) (i) The cost of equity and retained earnings
rE

= D1/PO + g = 4.0 / 80 + 0.15 = 20 % 15 + (100-110)/6

The cost of preference capital, using the approximate formula, is :
rP

= 0.6 x 110 + 0.4 x 100

= 12.58 %

The pre-tax cost of debentures, using the approximate formula, is : 11 + (100-102)/6
rD

= 0.6x102 + 0.4x100

= 10.54 %

The post-tax cost of debentures is 10.54 (1-tax rate) = 10.54 (1 – 0.35) = 6.85 % The post-tax cost of term loans is 13 (1-tax rate) = 13 (1 – 0.35) = 8.45 %

The average cost of capital using book value proportions is calculated below:
Source of capital Component Cost (1) Book value Book value Rs. in million proportion (2) (3) Product of (1) & (3)

Equity capital Preference capital Retained earnings Debentures Term loans

20.00% 12.58 % 20.00% 6.85 % 8.45%

300 100 100 250 300 1050

0.29 0.09 0.09 0.24 0.29

5.8 1.13 1.80 1.64 2.45

Average cost 12.82 % of capital

(ii) The average cost of capital using market value proportions is calculated below :

Source of capital

Component cost (1)

Market value Market value Product of proportion Rs. in million (2) (3) (1) & (3)

Equity capital and retained earnings Preference capital Debentures Term loans

20.00% 12.58% 6.85% 8.45%

2400 110 255 300 3065

0.78 0.04 0.08 0.10 Average cost of capital

15.60 0. 50 0. 55 0. 85 17.50 %

(b)

The Rs.450 million to be raised will consist of the following: Retained earnings Rs.80 million Additional equity Rs. 220 million Debt Rs. 150 million The first batch will consist of Rs. 80 million of retained earnings and Rs.40 million of debt costing 20 percent and 11(1-0.35) = 7.15 percent respectively. The second batch will consist of Rs. 120 million of additional equity and Rs. 60 million of debt at 20 percent 7.15 percent respectively. The third chunk will consist of Rs.100 million of additional equity and Rs.50 million of debt costing 20 percent and 12(1-0.35) = 7.8 percent respectively.

The marginal cost of capital in the chunks will be as under First batch : (2/3)x20 + (1/3) x 7.15 = 15.72 % Second batch : (2/3)x20 + (1/3) x 7.15 = 15.72 % Third batch : (2/3)x 20 + (1/3) x7.8 = 15.93% The marginal cost of capital schedule for the firm will be as under. Range of total financing (Rs. in million) 0 - 300 301-450 Weighted marginal cost of capital (%) 15.72 15.93

Here it is assumed that the Rs.450 million to be raised is inclusive of floatation costs. 13. Imperial Industries is currently at its target debt-equity ratio of 0.8 : 1. It is considering a proposal to expand capacity which is expected to cost Rs.600 million and generate after-tax cash flows of Rs.150 million per year for the next 10 years. The tax rate for the firm is 35 percent. Ganesh, the CFO of the company, has considered two financing options : (i) Issue of equity stock. The required return on the company’s new equity is 25 percent and the issuance cost will be 10 percent. (ii) Issue of debentures at a yield of 14 percent. The issuance cost will be 2 percent. a. What is the WACC for Imperial Industries? b. What is Imperial Industries’s weighted average floatation cost? c. What is the NPV of the proposal after taking into account the floatation costs?
Solution:

(a)

WACC

= =

4/9 x 14% x (1 – 0.35) + 5/9 x 25% 17.93%

(b)

Weighted average floatation cost = 4/9 x 2% + 5/9 x 10% = 6.44 %

(c)

NPV of the proposal after taking into account the floatation costs = = 150 x PVIFA (17.93%, 10) – 600 / (1 - 0.0644) 675.79 – 641.30 = Rs. 34.49million

14.

Pan India Limited is currently at its target debt-equity ratio of 1.5 : 1. It is considering a proposal to expand capacity which is expected to cost Rs.1000 million and generate after-tax cash flows of Rs.200 million per year for the next 12 years. The tax rate for the firm is 33 percent. Ravikiran, the CFO of the company, has considered two financing options : (i) Issue of equity stock. The required return on the company’s new equity is 19 percent and the issuance cost will be 11 percent. (ii) Issue of debentures at a yield of 12 percent. The issuance cost will be 1.5 percent. a. What is the WACC for Pan India? b. What is Pan India’s weighted average floatation cost? c. What is the NPV of the proposal after taking into account the floatation costs?

Solution:

(a)

WACC

= =

(3/5) x 12% x (1 – 0.33) + (2/5) x 19% 12.42%

(b)

Weighted average floatation cost = 3/5 x 1.5 % + 2/5 x 11% = 5.3 %

(c)

NPV of the proposal after taking into account the floatation costs = = 200 x PVIFA (12.42%, 12) – 1000 / (1 - 0.0533) 1215.13 – 1056.30= Rs. 158.83million

15.

Jawahar Associates, an all-equity firm, is evaluating the following projects:
Project Beta ExpectedReturn (%) 12 14 18 24

A B C D

0.4 0.8 1.3 1.8

The risk-fee rate is 8 percent and the expected market premium is 7 percent. Jawahar’s cost of capital is 16 percent. Which projects would be accepted or rejected incorrectly on the basis of the firm’s cost of capital as a hurdle rate?

Solution:

Project

Beta

Required return based on SML equation (%)

Expected return (%)

A B C D

0.4 0.8 1.3 1.8

10.8 13.6 17.1 20.6

12 14 18 24

Given a hurdle rate of 16% (the firm’s cost of capital), projects A and B would have been rejected because the expected returns on these projects are below 16%. Projects C and D would be accepted because the expected returns on these projects exceed 16%. An appropriate basis for accepting or rejecting the projects would be to compare the expected rate of return and the required rate of return for each project. Based on this comparison, we find that all the four projects need to be rejected. 16. Aryan Limited, an all-equity firm, is evaluating the following projects:
Project No. Beta ExpectedReturn (%) 14 16 18 25

1 2 3 4

0.9 1.1 1.2 1.7

The risk-fee rate is 7 percent and the expected market premium is 9 percent. Aryan’s cost of capital is 15 percent. Which projects would be accepted or rejected incorrectly on the basis of the firm’s cost of capital as a hurdle rate?
Solution:

Project

Beta

Required return based on SML equation (%) 15.1 16.9 17.8 22.3

Expected return (%)

1 2 3 4

0.9 1.1 1.2 1.7

14 16 18 25

Given a hurdle rate of 15% (the firm’s cost of capital), project 1 would have been rejected because the expected returns on this project is below 15%. Projects 2, 3

and 4 would be accepted because the expected returns on these projects exceed 15%. An appropriate basis for accepting or rejecting the projects would be to compare the expected rate of return and the required rate of return for each project. Based on this comparison, we find that all the four projects need to be rejected.

CHAPTER 15

1.

Plastic emulsion for a building costs Rs.600,000 and has a life of 8 years. Distemper painting costs Rs.250,000 and has a life of 4 years. How does the UAE of plastic emulsion painting compare with that of distemper painting if the cost of capital is 15 percent? Solution: EAC (Plastic Emulsion)

= = =

600000 / PVIFA (15%,8) 600000 / 4.487 Rs.133,720 250000 / PVIFA (15%,4) 250000 / 2.855 Rs.87,566

EAC (Distemper Painting) = = =

Since EAC of distemper painting is less than that of plastic emulsion, it is the preferred alternative. 2. The initial outlay on a security system would be Rs.2,000,000. The operating costs are expected to be as follows:
Year 1 2 3 4 5 Operating Costs (in Rs.) 500,000 720,000 860,000 530,000 400,000

The estimated salvage value at the end of five years is Rs.600,000. What is the UAE if the cost of capital is 12 percent?

Solution:

PV of the net costs associated with the security system = 2 000 000 + 500 000 x PVIF (12%,1) + 720 000 x PVIF (12%,2) + 860 000 x PVIF (12%,3) + 530 000 x PVIF (12%,4) + 400 000 x PVIF (12%,5) - 600 000 x PVIF (12%,5) 2 000 000 + 500 000 x 0.893 + 720 000 x0.797 + 860 000 x 0.712 + 530 000 x 0.636 + 400 000 x 0.567 - 600 000 x 0.567 = 3,856,340

=

EAC of the security system = = 3. 3856340 / PVIFA (12%, 5) 3856340/ 3.605 = 1,069,720

The initial outlay for an internal transportation system would be Rs.900,000. The operating costs are expected to be as follows:
Year Operating Costs (in Rs.) 1 100,000 2 182,000 3 290,000 4 240,000 5 140,000 The estimated salvage value at the end of five years is Rs.100,000. What is the UAE if the cost of capital is 16 percent?

Solution:

PV of the net costs associated with the internal transportation system = 900 000 + 100 000 x PVIF (16%,1) + 182 000 x PVIF (16%,2) + 290 000 x PVIF (16%,3) + 240 000 x PVIF (16%,4) + 140 000 x PVIF (16%,5) - 100 000 x PVIF (16%,5) 900 000 + 100 000 x 0.862 + 182 000 x0.743 + 290 000 x 0.641 + 240 000 x 0.552 + 140 000 x 0.476 - 100 000 x 0.476 = 1,458,836

=

EAC of the internal transportation system = = 1,458,836/ PVIFA (16%,5) 1,458,836/ 3.274 = 445,582

4.

Hansen Electricals is evaluating a capital project requiring an outlay of Rs.1900 million. It is expected to generate a net cash inflow of Rs.600 million per year for 5 years. The opportunity cost of capital is 18 percent. Hansen Electricals can raise a term loan of Rs.800 million for the project, carrying an interest rate of 8 percent per year payable annually. The principal amount will be repayable in 4 equal annual instalments, the first instalment falling due at the end of the second year. The balance amount required for the project can be raised by issuing external equity. The issue cost is expected to be 10 percent. The effective tax rate for the company is 30 percent (i) What is the base case NPV?

Solution:

The base case NAV = -1900 = -1900 = -23.8 (ii) + 600 x PVIFA + 600 x 3.127 (18%, 5 yrs)

What is the adjusted NPV if the adjustment is made only for the issue cost of external equity?

Solution:

1100 = 1222.2 1 – 0.10 Issue cost = Rs. 122.2 million Adjusted NPV considering only the issue cost = -23.8 - 122.2 = - 146.0 million

(iii)
Solution:

What is the present value of the tax shield?

Year 1 2 3 4 5

Debt outstanding at beginning 800 800 600 400 200

Interest 64 64 48 32 16

Tax shield 19.2 19.2 14.4 9.6 4.8

PV @ 8% discount rate 0.926 0.857 0.794 0.735 0.681

PV 17.78 16.45 11.43 7.06 3.27 55.99

5.

Alok Appliances is evaluating a capital project requiring an outlay of Rs.1500 million. It is expected to generate a net cash inflow of Rs.400 million per year for 6 years. The opportunity cost of capital is 16 percent. Alok Appliances can raise a term loan of Rs.900 million for the project, carrying an interest rate of 10 percent per year payable annually. The principal amount will be repayable in 5 equal annual instalments, the first instalment falling due at the end of the first year. The balance amount required for the project can be raised by issuing external equity. The issue cost is expected to be 9 percent. The effective tax rate for Alok Appliances is 33 percent. (i) What is the base case NPV?

Solution:

Base case NPV = -1500 + 400 PVIFA (16%, 6) = -1500 + 400 x 3.685 = -26 (ii) What is the adjusted NPV if the adjustment is made only for the issue cost of external equity?

Solution:

600 / (1-0.09) = 659.34 Additional equity to be raised = 59.34 Adjusted NPV for issue cost = -26 -59.34 = -85.34

(iii)
Solution:

What is the present value of the tax shield?

Year

Debt outstanding Interest Tax shield PVIF@ 10% PV of tax shield at the beginning ------------------------------------------------------------------------------------------------1 900 90 29.70 0.909 27.00 2 720 72 23.76 0.826 19.63 3 540 54 17.82 0.751 13.38 4 360 36 11.88 0.683 8.11 5 180 18 5.94 0.621 3.69 -------71.81

6.

Mitra Chemicals is evaluating a capital project requiring an outlay of Rs.1800 million. It is expected to generate a net cash inflow of Rs.500 million per year for 6 years. The opportunity cost of capital is 15 percent. Mitra Chemicals can raise a term loan of Rs.800 million for the project. The term loan will carry an interest of 9 percent per year payable annually. The principal amount will be repayable in 4 equal annual instalments, the first instalment falling due at the end of the second year. The balance amount required for the project can be raised by issuing external equity. The issue cost is expected to be 7 percent. The effective tax rate for the company is 30 percent (i) What is the base case NPV?

Solution:

-1800 + 500 x PVIFA ( 15 %, 6 yrs) = - 1800 + 500 x 3.784 = - 92 (ii)
Solution:

What is the adjusted NPV if the adjustment is made only for the issue cost of external equity?

1,000 = 1075 .3 1 – 0.07 Issue cost = Rs.75.3 million Adjusted NPV considering only the issue cost = - 92 – 75.3 = - 167.3 million (iii) What is the present value of the tax shield?
Solution:

Year 1 2 3 4 5

Debt outstanding at beginning 800 800 600 400 200

Interest

Tax shield

72 72 54 36 18

21.6 21.6 16.2 10.8 5.4

PV @ 9 % discount rate 0.917 0.842 0.772 0.708 0.650

PV

19.81 18.19 12.51 7.65 3.51 61.67

CHAPTER 18

1.

Bearings Limited received a subscription for 390,000 shares as against 500,000 shares that were offered and fully underwritten. The underwritten commitments of 5 underwriters P, Q, R, S, and T are as under:
Underwriting commitment 90,000 P Q 80,000 R 100,000 S 130,000 T 100,000 Shares procured 70,000

70,000 85,000 115,000 120,000

Determine the liability of each underwriter.
Solution: Underwriting commitment P Q R S Shares procured Excess/ shortfall Credit Net shortfall

90,000 80,000 100,000 130,000 100,000

70,000 70,000 85,000 115,000 120,000

(20,000) (10,000) (15,000) (15,000) 20,000

4500 4000 5000 6500

(15,500) (6,000) (10,000) ( 8,500)

T

2.

Welcome Industries received a subscription for 850,000 shares as against 1,000,000 shares that were offered and fully underwritten. The underwritten commitments of 4 underwriters M, N , O and P are as under:
Underwriting commitment 200,000 M N 300,000 O 400,000 P 100,000 Shares procured 160,000

220,000 345,000 125,000

Determine the liability of each underwriter.

Solution: Underwriting commitment M N O P Shares procured Excess/ shortfall Credit Net shortfall

200,000 300,000 400,000 100,000

160,000 220,000 345,000 125,000

(40,000) (80,000) (55,000) 25,000

5556 8333 11111

(34,444) (71,667) (43,889)

3.

The equity stock of Paramount Corporation is selling for Rs.240 per share. The firm is planning to issue rights shares in the ratio of one right share for every existing four shares: (a) (b) (c) What is the theoretical value of a right if the subscription price is Rs.220? What is the ex-rights value per share if the subscription price is Rs.210? What is the theoretical value per share when the stock goes ex-rights, if the subscription price is Rs.240? Rs.200?
Po = Rs.240 N=4

Solution:

a.

The theoretical value of a right if the subscription price is Rs.220
Po – S

240 – 220 = = Rs.4 4+1 4 x 240 + 210 = = Rs.234 4+1 4 x 240 + 240 = Rs.240 4+1 4 x 240 + 100 = Rs.212 4+1

N+1 NPo + S N+1

b. The ex-rights value per share if the subscription price is Rs.210

c.

The theoretical value per share, ex-rights, if the subscription price is Rs.240? 100?

4.

The equity stock of Parakram Limited is selling for Rs.860 per share. The firm is planning to issue rights shares in the ratio of one right share for every existing three shares: (a) (b) (c) What is the theoretical value of a right if the subscription price is Rs.800 ? What is the ex-rights value per share if the subscription price is Rs.820 ? What is the theoretical value per share when the stock goes ex-rights, if the subscription price is Rs.860? Rs.700?
Po = Rs.860 N=3

Solution:

a.

The theoretical value of a right if the subscription price is Rs.800
Po – S

860 – 800 = = Rs.15 3+1 3 x 860 + 820 = = Rs.850 3+1 3 x 860 + 860 = Rs.860 3+1 3x 860 + 700 = Rs.820 3+1

N+1 NPo + S N+1

b. The ex-rights value per share if the subscription price is Rs.820

c. The theoretical value per share, ex-rights, if the subscription price is Rs.860? 700?

CHAPTER 19

1.

Advaith Corporation has a net operating income of Rs.50 million. Advaith employs Rs.200 million of debt capital carrying 12 percent interest charge. The equity capitalisation rate applicable to Advaith is 14 percent. What is the market value of Advaith under the net income method? Assume there is no tax.

Solution:

Net operating income (O) Interest on debt (I) Equity earnings (P) Cost of equity (rE) Cost of debt (rD) Market value of equity (E) Market value of debt (D) Market value of the firm (V)

: : : : : : : :

Rs.50 million Rs.24 million Rs.26 million 14 % 12 % Rs.26 million/0.14 =Rs.185.7 million Rs.24 million/0.12 =Rs.200 million Rs.385.7 million

2.

Kanishk Limited has a net operating income of Rs.100 million. Kanishk employs Rs.800 million of debt capital carrying 10 percent interest charge. The equity capitalisation rate applicable to Kanishk is 13 percent. What is the market value of Kanishk under the net income method? Assume there is no tax.

Solution:

Net operating income (O) Interest on debt (I) Equity earnings (P) Cost of equity (rE) Cost of debt (rD) Market value of equity (E) Market value of debt (D) Market value of the firm (V) 3.

: : : : : : : :

Rs.100 million Rs.80 million Rs.20 million 13 % 10 % Rs.20 million/0.13 =Rs.153.8 million Rs.80 million/0.10 =Rs.800 million Rs.953.8 million

The following information is available for two firms, Anil Corporation and Sunil Corporation. Anil Sunil Net operating income Interest on debt Cost of equity Cost of debt Rs.3,200,000 Nil 16 % 12 % Rs.3,200,000 480,000 16% 12 %

Calculate the market value of equity, market value of debt, and market value of the firm for Anil Corporation and Sunil Corporation. (a) (b) What is the average cost of capital for each of the firms? What happens to the average cost of capital of Anil Corporation if it employs Rs.50 million of debt to finance a project that yields an operating income of Rs.5 million? What happens to the average cost of capital of Sunil Corporation if it sells Rs.4 million of additional equity (at par) to retire Rs.4 million of outstanding debt?

(c)

In answering the above questions assume that the net income approach applies and there are no taxes.
Solution:

Anil Market value of equity Market value of debt Market value of the firm 3,200,000/0.16 = Rs.20 million 0 Rs.20million

Sunil 3,200,000/0.16 = Rs.20 million 480,000/0.12 =Rs.4 million 24 million

(a)

Average cost of capital for Anil Corporation 20 x 16% + 20 20 0 x 12% = 16 %

Average cost of capital for Sunil Corporation 20 x 16% + 24 (b) 24 4 x 12% = 15.33 %

If Anil Corporation employs Rs.50 million of debt to finance a project that yields Rs.5 million net operating income, its financials will be as follows. Net operating income Interest on debt Equity earnings Cost of equity Cost of debt Market value of equity Market value of debt Market value of the firm Average cost of capital 13.75 16% 63.75 x 63.75 50 + 12% x = 12.86 % Rs.8,200,000 Rs.6,000,000 Rs.2,200,000 16% 12% Rs.13.75million Rs.50 million Rs.63.75 million

(c)

If Sunil Corporation sells Rs.4 million of additional equity to retire Rs.4 million of debt , it will become an all-equity company. So its average cost of capital will simply be equal to its cost of equity, which is 16%.

4.

The management of Janata Company, subscribing to the net operating income approach, believes that its cost of debt and overall cost of capital will remain at 7 percent and 14 percent, respectively. If the equity shareholders of the firm demand a return of 25 percent, what should be the proportion of debt and equity in the firm’s capital structure? Assume that there are no taxes.

Solution: rE = rA + (rA-rD)D/E 25 = 14 + (14-7) D/E So, D/E = 1.57

5.

The management of Lavanya Corporation, subscribing to the net operating income approach, believes that its cost of debt and overall cost of capital will remain at 10 percent and 16 percent, respectively. If the equity shareholders of the firm demand a return of 22 percent, what should be the proportion of debt and equity in the firm’s capital structure? Assume that there are no taxes.

Solution: rE = rA + (rA-rD)D/E 22 = 16 + (16-10) D/E So D/E = 1.0

6.

The management of a firm believes that the cost of equity and debt for different proportions of equity and debt in the capital structure are as follows
Proportion of Equity Proportion of Debt Cost of Equity, rE% Cost of Debt, rD%

1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

15.0 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0

7.0 7.5 8.0 8.5 9.0 9.5 10.0 11.0 12.0 14.0

What is the optimal capital structure of the firm?
Solution: E D+E D D+E rE (%) rD (%) rA = E rE + D+E D rD D+E

1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

15.0 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0

7.0 7.5 8.0 8.5 9.0 9.5 10.0 11.0 12.0 14.0

15.0 15.15 14.8 14.45 14.10 13.75 13.40 13.40 13.50 14.60

The debt ratios 0.60 or 0.70 minimises the WACC . The optimal ratio is 0.60 as the firm’s financial flexibility in that case is more. 7. The following information is available on Vidyut Corporation. Net operating income Tax rate Debt capital Interest rate on debt capital Capitalisation rate applicable to debt-free Firm in the risk class to which Vidyut Corporation belongs = 14 percent What should be the value of Vidyut Corporation .according to Modigliani and Miller?
Solution:

= Rs.100 million = 35 percent = Rs.250 million = Rs.12 percent

The value of Vidyut Corporation.according to Modigliani and Miller hypothesis is Expected operating income = Discount rate applicable to the risk class to which Vidyut Corporation.belongs 0.14 100 = Rs.714 million

8.

The following information is available on Magnificent Corporation. Net operating income Tax rate Debt capital Interest rate on debt capital Capitalisation rate applicable to debt-free Firm in the risk class to which Magnificent Corporation. belongs = 15 percent What should be the value of Magnificent Corporation, according to Modigliani and Miller? = Rs.80 million = 33 percent = Rs.150 million = Rs.14 percent

Solution:

The value of Magnificent Corporation, according to Modigliani and Miller hypothesis is Expected operating income 80 = = Rs.533 million Discount rate applicable to the 0.15 risk class to which Magnificent Corporation..belongs 9. If tc = 30%, tpe = 10%, and tpd = 20%, what is the tax advantage of a rupee of debt?

Solution:

(1-tc) (1 – tpc) 1(1 - tpd) = 1-

(1-0.3) (1-0.10)

(1 – 0.20) = 0.21 or 21 paise

10.

If tc = 35%, tpe = 10%, and tpd = 25 %, what is the tax advantage of a rupee of debt?

Solution:

(1-tc) (1 – tpc) 1(1 - tpd) = 1-

(1-0.35) (1-0.10)

(1 – 0.25) = 0.22 or 22 paise

CHAPTER 20

1.

The profit and loss account for the year 1 (the year that has just ended) and the balance sheet at the end of year 1 for Red Rock Limited are as follows.
Profit and Loss Account Balance Sheet

Sales PBIT

Rs.in crore 520 86

Sources of Funds Rs. in crore Shareholders’ Funds 300 Paid up capital : 60 (Equity shares of par value Rs.10) Reserves and Surplus: 240 Loan Funds Application of Funds Net fixed assets Net current assets

Interest PBT Tax (tc = 30%) PAT Dividends (Rs. 3 per share) Retained Earnings (i)

16 70 21 49 18 31

200 500 350 150

What should have been the ROI of Red Rock Limited for it to meet its target ROE of 20 percent? Note that the pre-tax cost of debt is 8 percent.

Solution:

[ ROI + ( ROI - r) D / E ] ( 1 - tc ) [ ROI + ( ROI - 8 ) 2 / 3 ] ( 1 - 0.3) ROI

= = =

20% 20% 20 .34%.

(ii)

Red Rock Limited requires Rs. 200 crore of external financing for which it is considering two alternatives: Alternative A : Issue of 1.6 crore equity shares of Rs 10 par at Rs. 125 each. Alternative B : Issue of Rs.200 crore of debentures carrying 8 percent interest rate. What is the EPS-EBIT indifference point?

Solution:

( EBIT – 16) ( 1 – 0.3 ) EPSA = 7.6 ( EBIT - 32 ) ( 1 - 0.3 ) EPSB = 6 Equating EPSA and EPSB gives EBIT = Rs. 92 crore. 2. The profit and loss account for year 1 (the year which has just ended) and the balance sheet at the end of year 1 for Glendale are as follows:
Balance Sheet Sources of Funds • Shareholders’ Funds Profit and Loss Account Rs in crore Sales 500 PBIT 80 Interest 10

Rs. in crore 260

Paid up capital : 60 (Equity shares of Rs.10 par) Reserves & surplus : 200 • Loan Funds
Application of Funds • Net Fixed Assets • Net Current Assets

100 360 250 110 360

PBT Tax (tc=30%) PAT Dividends (Rs.3 per share) Retained earnings

70 21 49 18 31

(i)

What should have been the ROI of Glendale Company to meet a target ROE of 25 percent? Note that the pre-tax cost of debt is 10 percent

Solution:

[ROI + (ROI – r) D/E] (1 – tc) = 25% [ROI + (ROI – .10) 0.385] (1 – 0.3) = 25% ? ROI = 28.57% (ii) Glendale Company requires Rs.50 crore of external financing for which it is considering two alternatives: Alternative A : Issue of 0.4 crore shares at Rs.125 each. Alternative B : Issue of Rs.50 crore of debentures carrying 10 percent interest rate.

What is the EPS-EBIT indifference point?
Solution:

(EBIT – 10) (1 – 0.3) EPSA = 6.4 (EBIT – 15) (1 – 0.3) EPSB = 6 Equating EPSA and EPSB gives 0.7 EBIT – 7 = 6.4
? EBIT = Rs.90 crore

0.7 EBIT – 10.5 6.0

3.

A company’s present capital structure contains 4,000,000 equity shares and 100,000 preference shares. The firm’s current EBIT is Rs.25 million. Preference shares carry a dividend of Rs.3 per share. The earnings per share is Rs.4. The firm is planning to raise Rs.40 million of external financing. Two financing alternatives are being considered: (i) issuing 4,000,000 equity shares for Rs.10 each, (ii) issuing debentures for Rs.40 million carrying 12 percent interest. Required (a) Compute the EPS-EBIT indifference point. (b) Define the alternative which maximises EPS for various levels of EBIT.

Solution:

Currently No. of shares = 4,000,000 EBIT = Rs 25 million Interest = 0 Preference dividend = Rs.3 x 100,000 = Rs.0.3 million EPS = Rs.4
(EBIT – Interest) (1-t) – Preference dividend EPS =

(a)

No. of shares (25,000,000 – 0 ) (1-t) – 300,000 4 = 4,000,000 Hence t = 0.348 or 34.8 per cent The EPS under the two financing plans is :
Financing Plan A : Issue of 4,000,000 shares

(EBIT - 0 ) ( 1 – 0.348) - 300,000
EPSA =

8,000,000
Financing Plan B : Issue of Rs.10 million debentures carrying 15 per cent interest

(EBIT – 4,800,000) (1-0.348) – 300,000
EPSB =

4,000,000 The EPS – EBIT indifference point can be obtained by equating EPSA and EPSB (EBIT – 0 ) (1 – 0.348) – 300,000 = 8,000,000 (EBIT – 4,800,000) (1 – 0.348) – 300,000 4,000,000

0.652 EBIT -300,000 =2(0.652 EBIT-3,129,600 -300,000) 0.652 EBIT = 6,559,200 or EBIT = 10,060,123 (b) As long as EBIT is less than Rs.10,060,123 equity financing maximises EPS. When EBIT exceeds Rs. 10,060,123 debt financing maximises EPS.

4.

BGM Limited’s present capital structure consists of 20 million equity shares of Rs.10 each. It requires Rs.60 million of external financing. It is considering two alternatives: Alternative 1 : Issue of 3 million equity shares of Rs.10 par at Rs.15 each and 1.5 million preference shares of Rs.10 par, carrying a dividend rate of 10 percent. Alternative 2 : Issue of 2 million equity shares of Rs.10 par at Rs.15 each and debentures for Rs.30 million carrying an interest rate of 11 percent

The company’s tax rate is 35 percent? What is the EPS-PBIT indifference point?
Solution:

Alternative 1 EPS = ( PBIT – 0) (1 – 0.35) – 1.5 23

Alternative 2 EPS = ( PBIT – 3.3) (1 – 0.35) 22 0.65 PBIT – 2.145 22 = 14.95 PBIT – 49.335 = 16.335 = 25.13 =

0.65 PBIT – 1.5 23 14.3 PBIT – 33 0.65 PBIT PBIT 5.

Keerthinath Corporation presently has two million outstanding equity shares (Rs.10 par) selling at Rs.11 per share and no outstanding debt . It needs Rs.8 million of additional funds which can be raised in two ways: (a) (b) issue of 0.8 million equity shares at Rs.10 per share, issue of debt capital carrying 14 percent interest.

The expected earnings before interest and taxes after the new funds are raised will be Rs.6 million per year with a standard deviation of Rs.2 million. Keerthinath Corporation’s tax rate is 35 percent. What is the probability that the debt alternative is better than the equity alternative with respect to earnings per share

Solution:

Plan A : Issue 0.8 million equity shares at Rs. 10 per share. Plan B : Issue Rs.8 million of debt carrying interest rate of 14 per cent. (EBIT – 0 ) (1 – 0.35)
EPSA EPSB

= 2,800,000 (EBIT – 1,120,000) (1 – 0.35) = 2,000,000

Equating EPSA and EPSB, we get (EBIT – 0 ) (1 – 0.35) = 2,800,000 2,000,000 (EBIT – 1,120,000) (1 – 0.35)

1.82 EBIT -2.0384 = 1.3 EBIT or EBIT = 3.92million Thus the debt alternative is better than the equity alternative when EBIT > 3.92 million
EBIT – EBIT

3.92 – 6.000 > 2.000

Prob(EBIT>3,920,000) = Prob
? EBIT

= Prob [z > - 1.04] From the tables we have

when z = -1.00, the probability is = 1-0.1587 = 0.8413 when z = -1.05, the probability is = 1-0.1469 = 0.8531 By extrapolation we have Prob [z > - 2.08] = 0.8413 + (1.04 -1)(0.8531 -0.8413)/0.05 = 0.8507 or 85.07 percent. 6. Innovation Limited presently has 10 million outstanding equity shares (Rs.10 par) selling at Rs.11 per share and no outstanding debt. It needs Rs.60 million of additional funds which can be raised in two ways: (a) (b) issue of 6 million equity shares at Rs.10 per share, issue of debt capital carrying 11 percent interest.

The expected earnings before interest and taxes after the new funds are raised will be Rs.16 million per year with a standard deviation of Rs.8 million. Innovation Limited tax rate is 33 percent. What is the probability that the debt alternative is better than the equity alternative with respect to earnings per share.
Solution:

Plan A : Issue 6 million equity shares at Rs. 10 per share. Plan B : Issue Rs.60 million of debt carrying interest rate of 11 per cent. (EBIT – 0 ) (1 – 0.33)
EPSA EPSB

= 16,000,000 (EBIT – 6,600,000) (1 – 0.33) = 10,000,000

Equating EPSA and EPSB , we get (EBIT – 0 ) (1 – 0.33) = 16,000,000 10,000,000 (EBIT – 6,600,000) (1 – 0.33)

10.72 EBIT -70.752 = 6.7 EBIT or EBIT = 17.6 million Thus the debt alternative is better than the equity alternative when EBIT > 17.6 million
EBIT – EBIT

Prob(EBIT>17,600,000) = Prob

? EBIT

17.6 – 16.0 > 8

= Prob [z > 0.2] = 0.4207 or 42.07 % 7. Hurricane Transport has an average cost of 10 percent for debt financing. The financial leverage ratio is 0.8 and the ROI is 15 percent. What is the ROE for the company, if its tax rate is 40 percent?

Solution: ROE = [15 + (15 – 10 ) 0.8 ] (1 – 0.4) = 11.4 %

8.

Nanda Enterprises has a target ROE of 20 percent. The financial leverage ratio for the firm is 0.6 and its tax rate is 33 percent. What ROI should the company plan to earn? The cost of debt is 14 percent.

Solution:

20 = [ ROI + ( ROI – 14 ) 0.6 ] ( 1 – 0.33) = 0.67 ROI +0.402 ROI – 5.628 1.072 ROI = 25.628 ROI = 23.91 % 9. The following information is available about Excalibur Limited. Depreciation EBIT Interest on debt Tax rate Loan repayment instalment Rs.5 million Rs.35 million Rs.7 million 35 percent Rs.4.0 million

Required: (a) Calculate the interest coverage ratio. (b) Calculate the cash flow coverage ratio.
Solution:

EBIT a. Interest coverage ratio = Interest on debt 35 = 7 = 5.0
EBIT + Depreciation

b.

Cash flow coverage ratio = Loan repayment instalment Int.on debt + (1 – Tax rate) = 35 + 5 = 3.04 7 + 4/0.65

10.

The following information is available about Notting Hill Corporation. Depreciation EBIT Interest on debt Rs.30 million Rs.125 million Rs.52 million

Tax rate Loan repayment instalment

33 percent Rs.20.0 million

Required: (a) Calculate the interest coverage ratio. (b) Calculate the cash flow coverage ratio.
Solution:

EBIT a. Interest coverage ratio = Interest on debt 125 = = b. Cash flow coverage ratio = Loan repayment instalment Int.on debt + (1 – Tax rate) = 125 + 30 = 1.89 52 + 20/0.67 11. The following projections are available for Aristocrats Limited: Rs. in million Year 1 Year 2 Year 3 Year 4 Year 5 Profit after tax -3.0 13.0 24.00 28.00 25.00 Depreciation 15.0 11.25 8.43 6.33 4.75 Interest on term loan 14.00 14.00 14.0 11.20 8.4 Term loan repayment 20.00 20.00 20.00 instalment Required: Calculate the debt service coverage ratio.
Solution:

52 2.40
EBIT + Depreciation

The debt service coverage ratio for Aristocrats Limited is given by: 5 ? ( PAT i + Depi + Inti) i=1 DSCR = 5 ? (Inti + LRIi) i=1

=

87.00 + 45.76 + 61.6 61.6 + 60 194.36 121.6 1.60

= = 12.

The following projections are available for Oscar Corporation. Rs. in million Year 1 Year 2 Year 3 Year 4 Year 5 Profit after tax -4.0 -1.0 35.00 80.00 100.00 Depreciation 200 160 128 102.4 81.92 Interest on term loan 91.00 91.00 78.0 65.0 52.0 Term loan repayment 100.00 100.00 100.00 100.00 instalment Required: Calculate the debt service coverage ratio.

Solution:

The debt service coverage ratio for Oscar Corporation is given by : 5 ? ( PAT i + Depi + Inti) i=1 DSCR = 5 ? (Inti + LRIi) i=1 = 210 + 672.32 + 377 377 + 400 = = 13. 1259.32 777 1.62

Jaisurya Associates is embarking on an expansion plan requiring an outlay of Rs.800 million. The management of the firm is convinced that debt is a cheaper source of finance and is confident that it can raise the entire amount by debt finance (perpetual) at a rate of 12 percent. However, there is some apprehension about the firm’s ability to meet interest burden during a recessionary year. The management feels that in a recessionary year, the net cash flows of the company, not taking into account the interest burden on the new debt, would have an expected value of Rs.200 million with a standard deviation of Rs.80 million. Required: (a) What is the probability of cash inadequacy during a recessionary year , if the entire Rs.800 million are raised as debt finance?

(b) If the management is prepared to accept only a 4 percent chance of cash inadequacy, what proportion of Rs.800 million requirement should be raised as debt finance?
Solution:

(a)

If the entire outlay of Rs. 800 million is raised by way of debt carrying 12 per cent interest, the interest burden will be Rs. 96 million.

Considering the interest burden the net cash flows of the firm during a recessionary year will have an expected value of Rs. 104 million (Rs.200 million - Rs. 96 million ) and a standard deviation of Rs. 80 million . Since the net cash flow (X) is distributed normally X – 104 80 has a standard normal deviation Cash flow inadequacy means that X is less than 0. Prob(X<0) = Prob (z<- 1.3) = 0.0968 (b) Since µ = Rs.200 million, ?= Rs.80 million , and the Z value corresponding to the risk tolerance limit of 4 per cent is –1.75 , the cash available from the operations to service the debt is equal to X which is defined as : X – 200 = - 1.75 80 X = Rs.60 million Given 15 per cent interest rate, the debt that be serviced is 60 = Rs. 500 million 0.12 14. Medicon Limited is embarking on an expansion plan requiring an outlay of Rs.600 million. The management of the firm is convinced that debt is a cheaper source of finance and is confident that it can raise the entire amount by debt finance (perpetual) at a rate of 10 percent. However, there is some apprehension about the firm’s ability to meet interest burden during a recessionary year. The management feels that in a recessionary year, the net cash flows of the company, not taking into account the interest burden on the new debt, would have an expected value of Rs.150 million with a standard deviation of Rs.45 million.

Required: (a) What is the probability of cash inadequacy during a recessionary year, if the entire Rs.600 million are raised as debt finance? (b) If the management is prepared to accept only a 1 percent chance of cash inadequacy, what proportion of Rs.600 million requirement should be raised as debt finance ? Solution: (a) If the entire outlay of Rs. 600 million is raised by way of debt carrying 10 per cent interest, the interest burden will be Rs. 60 million. Considering the interest burden, the net cash flows of the firm during a recessionary year will have an expected value of Rs. 90 million (Rs.150 million - Rs. 60 million ) and a standard deviation of Rs. 45 million . Since the net cash flow (X) is distributed normally X – 90 45 has a standard normal deviation Cash flow inadequacy means that X is less than 0. Prob(X<0) = Prob (z<- 2.0) = 0.0228 (c) Since µ = Rs.150 million, ?= Rs.45 million , and the Z value corresponding to the risk tolerance limit of 1 per cent is –2.30 (approximately) , the cash available from the operations to service the debt is equal to X which is defined as :
X – 150

= - 2.30 45
X = Rs.46.5 million

Given 10 per cent interest rate, the debt than be serviced is 46.5 = Rs. 465 million 0.10
CHAPTER 21

1.

The following data is available for Newton Limited: Earnings per share = Rs.6.00 Rate of return = 18 percent

Cost of capital = 15 percent (a) If Walter’s valuation formula holds, what will be the price per share when the dividend payout ratio is 30 percent? 40 percent? (b) If Gordon's basic valuation formula holds, what will be the price per share when the dividend payout is 30 percent, 40 percent?
Solution:

(a)

Payout ratio

Price per share

6(0.3)+6(0.7) x 0.18 0.3 0.15 = Rs. 45.60 0.15 6(0.40)+6(0.6) 0.40 0.15 (b) Dividend payout ratio 30 % 40% 2. Price as per Gordon model P0 =E1(1-b)/(k-br) = 6 x 0.70/(0.15 - 0.70x 0.18) = 6 x 0.60/(0.15 - 0.60x 0.18) =Rs. 175 =Rs.85.7 0.18 0.15 = Rs. 44.80

The stocks of firms A and B are considered to be equally risky. Investors expect the share of firm A – the firm which does not plan to pay dividend -- to be worth Rs 100 next year. From the share of firm B, too, investors expect a pay off of Rs 100 – Rs 10 by way of dividend and Rs 90 by way of share price a year from now. Dividends are taxed at 25 percent and capital gains at 12 percent. What will be the current price of the shares of A and B, if each of them offers an expected posttax rate of 18 percent? Assume that the radical position applies

Solution: • • • • • • •

Next year’s price Dividend Current price Capital appreciation Post-tax capital appreciation Post-tax dividend income Total return

• Current price (obtained by solving the preceding equation)

A 100 0 A (100-A) 0.88(100-A) 0 0.88 (100-A) A = 18% A = Rs.83.02

B 90 10 B (90-B) 0.88 (90-B) 0.75 x 10 0.88 (90-B) + 7.5 B =18% B = Rs.81.79

3.

The stocks of firms M and N are considered to be equally risky. Investors expect the share of firm M – the firm which does not plan to pay dividend -- to be worth Rs 180 next year. From the share of firm N, too, investors expect a pay off of Rs 180 – Rs 20 by way of dividend and Rs 160 by way of share price a year from now. Dividends are taxed at 20 percent and capital gains at 10 percent. What will be the current price of the shares of M and N, if each of them offers an expected post-tax rate of 20 percent? Assume that the radical position applies

Solution: • • • • • • •

Next year’s price Dividend Current price Capital appreciation Post-tax capital appreciation Post-tax dividend income Total return

• Current price (obtained by solving the preceding equation)

M 180 0 M (180-M) 0.9(180-M) 0 0.9 (180-M) M = 20 % M= Rs.147.27

N 160 20 N (160-N) 0.9 (160-N) 0.8 x 20 0.9 (160-N) + 16 N =20 % N= Rs.145.45

4.

Assume that investors expect a payoff of Rs.305.2 a year from now from one share of Suman Company: Rs. 5.2 by way of dividend and Rs. 300 by way of share price. If dividend is taxed at 10 percent and capital appreciation is taxed at 20 percent, what will be the current price of Suman Company’s share if investors expect a post-tax return of 14 percent?

Solution:

Let the current price of the share be = Price one year hence Capital appreciation Dividend Post tax capital appreciation Post tax dividend income Total return =

P = = = = = 300 (300 – P) 5.2 0.9 (300 – P) 0.8 (5.2) 0.14

0.9 (300 – P) + 4.16 =

P 270 – 0.9P + 4.16 = 0.14P 1.04P = 274.16 P = Rs. 263.62

CHAPTER 22

1.

Handsome Apparels expects that its net income and capital expenditures over the next four years will be as follows:
Year 1 2 3 4 Net Income (Rs.) 40,000 60,000 25,000 34,000 Capital Expenditures (Rs.) 12,000 10,000 6,000 7,000

The company has 10,000 outstanding shares currently on which it pays a dividend of two rupees per share. The debt- equity target of the firm is 1:1 Required: (a) What will be the dividend per share if the company follows a pure residual policy? (b) What external financing is required if the company plans to raise dividends by 15 percent every 2 years? (c) What will be the dividend per share and external financing requirement if the company follows a policy of a constant 50 percent payout ratio?
Solution:

a. Under a pure residual dividend policy, the dividend per share over the 4 year period will be as follows:

DPS Under Pure Residual Dividend Policy
(in Rs.) Year 1 2 3 4

Earnings Capital expenditure Equity investment Pure residual dividends Dividends per share

40,000 12,000 6,000 34,000 3.4

60,000 10,000 5,000 55,000 5.5

25,000 6,000 3,000 22,000 2.2

34,000 7,000 3,500 30,500 3.05

b. The external financing required over the 4 year period (under the assumption that the company plans to raise dividends by 15 percents every two years) is given below : Required Level of External Financing
(in Rs.) Year 1 2 3 4

A. B. C. D. E. F.

Net income Targeted DPS Total dividends Retained earnings(A-C) Capital expenditure

40,000 2.00 20,000 20,000 12,000

60,000 2.30 23,000 37,000 10,000

25,000 2.30 23,000 2,000 6,000

34,000 2.65 26,500 7,500 7,000

External financing requirement 0 (E-D)if E > D or 0 otherwise

0

4,000

0

c. Given that the company follows a constant 50 per cent payout ratio, the dividend per share and external financing requirement over the 4 year period are given below

Dividend Per Share and External Financing Requirement (in Rs.) Year 1 2 3 4

A. Net income B. Dividends C. Retained earnings

40,000 20,000 20,000

60,000 30,000 30,000

25,000 12,500 12,500

34,000 17,000 17,000

D. Capital expenditure

12,000

10,000

6,000

7,000

E. External financing (D-C)if D>C, or 0 otherwise F. Dividends per share

0

0

0

0

2.00

3.00

1.25

1.70

2.

Young Turk Associates expects that its net income and capital expenditures over the next five years will be as follows:
Year 1 2 3 4 5 Net Income (Rs.) 70,000 40,000 85,000 38,000 105,000 Capital Expenditures (Rs.) 25,000 50,000 4,000 57,000 14,000

The company has 20,000 outstanding shares currently on which it pays a dividend of two rupees per share. The debt- equity target of the firm is 3:2 Required: a. What will be the dividend per share if the company follows a pure residual policy? b. What external financing is required if the company plans to raise dividends by 20 percent every 3 years? c. What will be the dividend per share and external financing requirement if the company follows a policy of a constant 60 percent payout ratio?

Solution:

a. Under a pure residual dividend policy, the dividend per share over the 4 year period will be as follows:
DPS Under Pure Residual Dividend Policy Year Earnings Capital expenditure ( in Rs.) 1 2 3 4 5 70,000 40,000 85,000 38,000 105,000 25,000 50,000 4,000 57,000 14,000

Equity investment Pure residual dividends

10,000 20,000 60,000 20,000

1,600 83,400

22,800 5,600 15,200 99,400

Dividends per share 3.0

1.0

4.17

0.76

4.97

b.

The external financing required over the 5 year period (under the assumption that the company plans to raise dividends by 20 percents every three years) is given below: Required Level of External Financing
(in Rs.) Year 1 2 3 4 5

A. B. C. D. E. F.

Net income Targeted DPS Total dividends Retained earnings(A-C) Capital expenditure

70,000 40,000 2.00 40,000 30,000 25,000 2.00 0 50,000 50,000

85,000 38,000 2.40 2.40

105,000 2.40

40,000 48,000 48,000 48,000 37,000 -10,000 57,000 4,000 57,000 14,000 0 67,000 0

External financing requirement 0 (E-D)if E > D or 0 otherwise

c. Given that the company follows a constant 60 per cent payout ratio, the dividend per share and external financing requirement over the 5 year period are given below

Dividend Per Share and External Financing Requirement
(in Rs.) Year 1 2 3 4

A. Net income B. Dividends C. Retained earnings D. Capital expenditure F. External financing (D-C)if D>C, or 0 otherwise F. Dividends per share

70,000 42,000 28,000 25,000 0 2.1

40,000 24,000 16,000 50,000 34,000 1.2

85,000 51,000 34,000 4,000 0 2.55

38,000 105,000 22,800 63,000 15,200 42,000 57,000 14,000 41,800 1.14 0 3.15

3.

The dividend per share of a firm for the current year is Rs.4. What will be the expected dividend per share of a firm for next year, if the expected EPS for that year is Rs.20 and the target payout ratio is 30% and adjustment rate is 0.6? Assume that the Lintner model applies.

Solution:

Dt

= c. r. EPS1 + (1 – c) Dt – 1 = (0.6 x 0.3 x 20) + (0.4) x 4 = Rs.5.2

Dt = c.r.EPS1 + ( 1 – c ) Dt – 1 = =
CHAPTER 23

( 0.8 x 0.35 x 8 ) + ( 1 – 0.8 ) x 2.5 2.24 + 0.50 = 2.74

1.

Primtech Limited has a Rs.2,000 million 11 percent (coupon rate) bond issue outstanding which has 4 years of residual maturity. The bonds were issued four years ago at par for Rs.2,000 million and Primtech incurred floatation costs of Rs.48 million which are being amortised for tax purposes at the rate of Rs.6 million per year. If the bonds are called, the amortised portion of the floatation costs (Rs.24.0 million) can be deducted for tax purposes. Primtech’s tax rate is 30 percent. Primtech can call the bonds for Rs.2100 million. Assume that the call premium of Rs.100 million can be treated as a tax-deductible expense.

Primetech has been advised by its merchant bankers that the firm can issue Rs.2,000 million of new bonds at an interest rate of 9 percent and use the proceeds for refunding the old bonds. The new issue will have a maturity of 4 years and involve a floatation cost of Rs.40 million, which can be amortised in 4 equal instalments for tax purposes. (i)
Solution:

What will be the initial outlay?

(a) Cost of calling the old bonds Face value Call premium (b) Net proceeds of the new issue Gross proceeds - Issue cost

Rs.2000 million 100 million 2100 million Rs.2000 million 40 million 1960 million Rs. 37.2 million

(c) Tax savings on tax-deductible expenses

Tax rate [Call premium + Unamortised issue costs on old bonds] 0.30 [100 + 24] (d) Initial outlay: (a) – (b) – (c) Rs.102.8 million

(ii)
Solution:

What will be the annual net cash savings?

(a)

Annual net cash outflow on old bonds Interest expense - Tax savings on interest expense and amortisation of issue expenses 0.3 (220 + 6)

220 67.8 152.2

(b)

Annual net cash outflow on new bonds Interest expense - Tax saving on interest expense and amortisation of issue expenses : 0.3 (180 + 10 )

180 57 123.0 29.2

(c)

Annual net cash savings: (a) – (b)

(iii) What is the NPV of refunding the bond?
Solution:

Present value of annual net cash savings: 29.2 x PVIFA (0.063, 4 yrs) = 29.2 x 3.441 = 100.48 - Initial outlay = 102.80 - 2.32

0.09 (1- 0.3) = 0.063 PVIFA (0.063, 4 yrs) 1 – [1/(1.063)]4 = = 3.441 0.063

2.

Sanofi Limited has a Rs.1200 million, 11 percent (coupon rate) bond issue outstanding which has 4 years residual maturity. The bonds were issued 4 years ago at par for Rs.1200 million and Sanofi incurred floatation costs of Rs.30 million which are being amortised for tax purposes at the rate of Rs.3.75 million per year. If the bonds are called, the unamortised portion of the floatation costs (Rs.15.0 million) can be deducted for tax purposes. Sanofi’s tax rate is 30 percent. Sanofi can call the bonds for Rs.1266 million. Assume that the call premium of Rs.66 million can be treated as a tax-deductible expense. Sanofi has been advised by its merchant bankers that due to fall in interest rates, the firm can issue Rs.1200 million of new bonds at an interest rate of 8 percent and use the proceeds for refunding of old bonds. The new issue will have a maturity of 4 years and involve a floatation cost of Rs. 24 million, which can be amortised in 4 equal annual instalments for tax purposes. (i) What will be the initial outlay?

Solution:

(a) Cost of calling the old bonds Face Value Call premium (b) Net proceeds of the new issue Gross Proceeds - Issue costs (c) Tax savings on tax-deductible expenses Tax rate [Call premium + Unamortised issue costs on old bonds] 0.30 [ 66 + 15 ] (d) Initial outlay: ( a ) – ( b ) – ( c )

Rs. 1200 million 66 million 1266 million Rs. 1200 million 24 million Rs. 1176 million 24.3 million

= Rs. 65.7 million

(ii)
Solution:

What will be the annual net cash savings?

( a ) Annual net cash outflow on old bonds Interest expense - Tax savings on interest expense and amortisation of issue expenses 0.30 ( 132 + 3.75) =

132.000 40.725 91.275

( b ) Annual net cash outflow on new bonds Interest expense - Tax saving on interest expense and amortisation of issue expenses 0.30 (96 + 6)

96.000 30.600 65.400

( c ) Annual net cash savings ( a ) – ( b ) million (iii) What is the NPV of refunding the bond?
Solution:

25.875

Present value of annual net cash savings:

rd ( 1 – t ) = .08 ( 1 - .30) = .056
4 1 1 - -----------( 1.056 ) = -------------------------.056 = 3.4971

= 25.875 x 3.4971 = 90.487 million - Initial outlay = -65.7 million = 24.787 million PVIFA 4.55% 6 yrs

3.

Synex Limited has a Rs.1000 million, 10 percent (coupon rate) bond issue outstanding which has 5 years residual maturity. The bonds were issued 3 years ago at par for Rs.1000 million and Synex incurred floatation costs of Rs.24 million which are being amortised for tax purposes at the rate of Rs.3.0 million per year. If the bonds are called, the unamortised portion of the floatation costs (Rs.15.0 million) can be deducted for tax purposes. Synex’s tax rate is 35 percent. Synex can call the bonds for Rs.1060 million. Assume that the call premium of Rs.60 million can be treated as a tax-deductible expense.

Synex has been advised by its merchant bankers that due to fall in interest rates the firm can issue Rs.1000 million of new debt at an interest rate of 7 percent and use the proceeds for refunding of old bonds. The new issue will have a maturity of 5 years and involve a floatation cost of Rs. 20 million, which can be amortised in 5 equal annual installments for tax purposes. (i)
Solution:

What will be the initial outlay?

(a) Cost of calling the old bonds Face value Call premium (b) Net proceeds of the new issue Gross proceeds - Issue cost (c) Tax savings on tax-deductible expenses

Rs.1000 million 60 million 1060 million Rs.1000 million 20 million 980 million Rs.26.25 million

Tax rate [Call premium + Unamortised issue costs on old bonds] 0.35 [60 + 15] (d) Initial outlay: (a) – (b) – (c) Rs.53.75 million

(ii)
Solution:

What will be the annual net cash savings?

(a) Annual net cash outflow on old bonds Interest expense - Tax savings on interest expense and amortisation of issue expenses 0.35 ( 100 + 3) (b) Annual net cash outflow on new bonds Interest expense - Tax saving on interest expense and amortisation of issue expenses : 0.35 ( 70 + 4 )

100 36.05 63.95 70 25.9 44.1 19.85

(c) Annual net cash savings : (a) – (b)

Present value of annual net cash savings: 0.07 ( 1- 0.35) = 0.0455 19.85 x PVIFA (0.0455, 5 yrs) 1 1.0455 PVIFA = 0.0455
5

= 4.384

(iii) What is the NPV of refunding the bond?
Solution:

= 19.85 x 4.384 - Initial outlay Rs.33.27 million. 4.

= =

87.02 53.75 33.27

Consider the following data for government securities:
Face value Rs. 100,000 Rs. 100,000 Rs. 100,000 Interest rate 0 7% 7% Maturity (years) 1 2 3 Current price 95,000 99,500 99,200

What is the forward rate for year 3(r3)?
Solution:

100,000 = 95,000 (1 + r1) 7,000 99,500 = (1.0526) 7,000 99,200 = (1.0526) r3 = 7.37 % + (1.0526) (1.0948) + (1.0526) (1 + r2) 7,000 + (1.0526) (1.0948) (1+r3) 107,000 107,000 r2 = 9.48 % r1 = 5.26 %

5.

Consider the following data for government securities:
Face value 100,000 100,000 100,000 Interest rate (%) 0 6% 7% Maturity (years) 1 2 3 Current price 94,250 99,500 100,500

What is the forward rate for year 3(r3)?
Solution:

100,000 (1+r1) 99,500 100,500 = =

= 94,250

> r1

=

6.10% > r2 = 6.46%

6000 (1.0610) 7,000 (1.061) r3

+ +

106000 (1.061) (1+r2)

7,000 + (1.061) (1.0646) 8.01%

107,000 (1.061) (1.0646) (1+r3)

=

6.

Consider the following data for government securities:
Face value 100,000 100,000 100,000 Interest rate 6% 7% Maturity (years) 1 2 3 Current price 94,800 99,500 100,500

What is the forward rate for year 3(r3)?
Solution:

100,000 = (1 + r1) 6,000 99500 = (1.0549) 7000 100500 = (1.0549)
? r = 8.01%

94,800 ? r1 = 5.49%

106,000 + (1.0549) (1 + r2) 7000 107000 + (1.0549) (1.0711) (1 + r3)
? r2 = 7.11%

+ (1.0549) (1.0711)

7.

Consider three bonds, A, B and C Bond A Face value Coupon (interest rate) payable annually Years to maturity Redemption value Current market price 12 percent 5 1,000 Rs.900 1,000

Bond B

Bond C

1,000 13 percent 6 1,000 Rs.850

100 14 percent 7 100 92

What are the (a) yields to maturity (use the approximate formula) (b) durations, and (c) volatilities of these bonds?
Solution:

a) Yield to maturity of bond A, using the approximate formula, is 120 + (1000 – 900)/5 = ------------------------= 14.89 % 0.4x1000 + 0.6x900 Yield to maturity of bond B, using the approximate formula, is 130 + (1000 – 850)/6 = ----------------------------= 17.03 % 0.4x1000 + 0.6x850 Yield to maturity of bond C, using the approximate formula, is 14 + (100 – 92)/7 = -------------------------= 15.91 % 0.4x100 + 0.6x92 (b) Solution: Duration of bond A is calculated as under:

Year Cash flow 1 120 2 120 3 120 4 120 5 1120 Sum =

Present value at Proportion of the Proportion of the 14.89 percent bond's value bond's value x time 104.45 0.116 0.116 90.91 0.101 0.201 79.13 0.088 0.263 68.87 0.076 0.305 559.51 0.620 3.099 902.87 Duration = 3.98 years

Duration of bond B is calculated as under: Present value at Proportion of the Proportion of the bond's 17.03 percent bond's value value x time 111.08 0.130 0.130 94.92 0.111 0.222 81.11 0.095 0.284 69.30 0.081 0.324 59.22 0.069 0.346 439.84 0.514 3.085 855.47 Duration= 4.39 years

Year 1 2 3 4 5 6

Cash flow 130 130 130 130 130 1130 Sum =

Duration of bond C is calculated as under: Present value at Proportion of the Proportion of the Cash flow 15.91 percent bond's value bond's value x time 14 12.08 0.131 0.131 14 10.42 0.113 0.226 14 8.99 0.097 0.292 14 7.76 0.084 0.336 14 6.69 0.073 0.363 14 5.77 0.063 0.375 114 40.56 0.440 3.077 Sum = 92.27 Duration= 4.8 years

Year 1 2 3 4 5 6 7 c)

Volatility of bond A 3.984 = 3.47 1.1489 CHAPTER 24

Volatility of bond B 4.391 = 3.75 1.1703

Volatility of bond C 4.8 = 4.14 1.1591

1.

Optex Limited has decided to go for an equipment costing Rs. 60 million. Optex is considering two alternatives: (i) leasing the equipment, and (ii) borrowing and purchasing the equipment. GT capital is willing to lease the equipment to Optex for an annual lease rental of Rs.16 million for 5 years, the lease rental being payable in arrears. There is a management fees of Rs.1 million payable on signing the lease contract. The tax relevant depreciation rate on the equipment is 25 percent as per the WDV method. The net salvage value of the equipment after five years is expected to be Rs.14 million. Optex has an effective tax rate of 30 percent and its post- tax cost of debt is 7 percent. What is the net advantage of leasing (NAL) for Optex?

Solution:

1. 2. 3.

Cost of plant Management fee Tax shield on Management fee 4. Depreciation 5. Loss of depreciation tax shield 6. Lease payment 7. Tax shield on lease payment 8. Loss of salvage value 9. Cash flow of lease (1) + (2) + (3) + (5) + (6) + (7) + (8) 10. Present value factors 11. Present value Of (9) NAL of leasing

0 +60.00 -1.00 0.30

1

2

3

4

Rs. in million 5

15.000 -4.500

11.250 -3.375

8.438 -2.531

6.328 -1.898

4.746 -1.424

-16.000 4.800

-16.000 4.800

-16.000 4.800

-16.000 4.800

-16.000 4.800 -14.000

+59.3

-15.700

-14.575

-13.731

-13.098

-26.624

1.000 +59.3 59.3

0.935 -14.680 -14.680

0.873 -12.724

0.816 -11.204

0.763 -9.994 -9.994

0.713 -18.983 -18.983

-12.724 -11.204 = -8.285

2.

Prajay Limited has decided to go for a pollution control equipment costing Rs. 50 million. Prajay is considering two alternatives: (i) leasing the equipment, and (ii) borrowing and purchasing the equipment. GE capital is willing to lease the equipment to Prajay for an annual lease rental of Rs.13.2 million for 5 years, the lease rental being payable in arrears. There is a management fees of Rs. 1 million payable on signing the lease contract. The tax relevant depreciation rate on the equipment is 25 percent as per the WDV method. The net salvage value of the equipment after five years is expected to be Rs.10.5 million. Prajay has an effective tax rate of 35 percent and its post- tax cost of debt is 6 percent. What is the net advantage of leasing (NAL) for Prajay?

Solution:

Cost of plant Management fee 3. Tax shield on Management fee 4. Depreciation 5. Loss of depreciation tax shield 6. Lease payment 7. Tax shield on lease payment 8. Loss of salvage value 9. Cash flow of lease (1) + (2) + (3) + (5) + (6) + (7) + (8) 10. Present value of factor 11. Present value of (9) NAL of leasing = -6.241

1. 2.

0 +50.000 -1.000 0.350

1

2

3

4

5

12.500 -4.375

9.375 -3.281

7.031 -2.461

5.273 -1.846

3.955 -1.384

-13.200 4.620

-13.200 4.620

-13.200 4.620

-13.200 4.620

-13.200 4.620 -10.500

+49.350

-12.955

-11.861

-11.041

-10.426

-20.464

1.000 +49.350 49.350

0.943 -12.217 -12.217

0.890 -10.556 -10.556

0.840 -9.274 -9.274

0.792 -8.257 -8.257

0.747 -15.287 -15.287

3.

Sanjeev Limited has decided to go for an air conditioning plant costing Rs. 40 million. Sanjeev Limited is considering two alternatives: (i) leasing the plant, and (ii) borrowing and purchasing the plant. GM capital is willing to lease the plant to Sanjeev Limited for an annual lease rental of Rs.10.8 million for 5 years, the lease rental being payable in arrears. The tax relevant depreciation rate on the plant is 25 percent as per the WDV method. The net salvage value of the plant after five years is expected to be Rs.8.5 million. Sanjeev Limited has an effective tax rate of 35 percent and its post- tax cost of debt is 7 percent. What is the net advantage of leasing (NAL) for Sanjeev Limited?

Solution:

1.Cost of plant 2.Depreciation 3.Loss of depreciation tax shield 4.Lease payment 5.Tax shield on lease payment 6.Loss of salvage value 7.Cash flow of lease (1) +(3) + (4) + (5) + (6) 8. Present value factor 9.Present value of (7) NAL of Leasing

0 +40000

1 10.000 -3.500

2 7.500 -2.625

3 5.625 -1.969

4 4.219 -1.477

5 3.164 -1.107

-10.800 3.780

-10.800 3.780

-10.800 3.780

-10.800 3.780

-10.800 3.780 -8.500

+40.000 1.000 40.000 40.000

-10.520 0.935 -9.836 -9.836 = -3.929

-9.645 0.873 -8.420 -8.420

-8.989 0.816 -7.335 -7.335

-8.497 0.763 -6.483 -6.483

-16.627 0.713 -11.855 -11.855

4.

Shiva Industries requires an asset costing Rs.3 million. Genuine Finance offers a hire-purchase proposal for a period of 3 years at a flat interest of 14 per cent. Genuine also gives a lease proposal wherein the lease rental would be Rs.320 per Rs.1,000 per year for the first 5 years (primary period) and Rs.30,000 per year for the next 5 years (secondary period). Thereafter, the asset would revert to Genuine. The depreciation rate on the asset is 25 per cent (WDV) and its net salvage value after 10 years would be Rs.350,000. Shiva has a tax rate of 35 percent and its post-tax cost of debt is 9 percent. Should Shiva choose the hire-purchase or the leasing option?

Solution:

Under the hire purchase proposal the total interest payment is 3,000,000 x 0.14 x 3 = Rs. 1,260,000 The interest payment of Rs. . 1,260,000 is allocated over the 3 years period using the sum of the years digits method as follows:

Year

Interest allocation

366 1 666 222 2 666 78 3 666 The annual hire purchase installments will be: Rs.3,000,000 + Rs. . 1,260,000 = Rs.1,420,000 3 The annual hire purchase installments would be split as follows
Year 1 2 3 Hire purchase installment Interest Rs. 1,420,000 Rs. 692,432 Rs. 1,420,000 Rs. 420,000 Rs. 1,420,000 Rs. 147,568 Principal repayment Rs.727,568 Rs. 1,000,000 Rs. 1,272,432

x Rs. . 1,260,000 = Rs.692,432

x Rs. . 1,260,000 = Rs.420,000

x Rs. . 1,260,000 = Rs.147,568

The lease rental will be as follows: Rs. 960,000 per year for the first 5 years Rs. 30,000 per year for the next 5 years The cash flows of the leasing and hire purchase options are shown below
Year Leasing - LRt (1-tc) Hire Purchase -It(1-tc) -PRt

Dt(tc)

NSVt

-It(1-tc)-PRt+ Dt(tc)+NSVt -915,149 -1,076,125 -1,220,695 110,742 83,057 62,293 46,719 35,040 26,280 369,710

1 -960,000(1-.35)=-624,000 -692,432 (1-.35) -727,568 750,000(0.35) 2 -960,000(1-.35)=-624,000 -420,000 (1-.35) -1,000,000 562,500(0.35) 3 -960,000(1-.35)=-624,000 -147,568 (1-.35) -1,272,432 421,875(0.35) 4 -960,000(1-.35)=-624,000 316,406(0.35) 5 -960,000(1-.35)=-624,000 237,305(0.35) 6 - 30,000(1-.35)= - 19,500 177,979(0.35) 7 - 30,000(1-.35)= - 19,500 133,484(0.35) 8 - 30,000(1-.35)= - 19,500 100,113(0.35) 9 - 30,000(1-.35)= - 19,500 75,085(0.35) 10 - 30,000(1-.35)= - 19,500 56,314(0.35) 350,000

Present value of the leasing option 5 624,000 = -? t=1 (1.09)t
?

10 ? t=6

19,500 (1.09)t

= -624,000 PVIFA(9%,5yrs) - 19,500 PVIFA(9%,5yrs) PVIF(9%,5yrs) = -624,000 x 3.890 - 19,500 x 3.890 x 0.650 = -2,427,360 – 49,306 = -2,476,666 Present value of the hire purchase option = -915,149/(1.09) – 1,076,125/(1.09)2 -1,220,695/(1.09)3+110,742/(1.09)4 +83,057/(1.09)5 + 62,293/(1.09)6 + 46,719/(1.09)7 + 35,040/(1.09)8 + 26,280/(1.09)9+ 369,710/(1.09)10 = - 2,306,951 Since the hire purchase option costs less than the leasing option, Shiva should choose the hire purchase option .
CHAPTER 25

1.

Consider the following data: • Number of shares outstanding : 80 million • Current stock price : Rs 60 • Ratio of warrants issued to the number of outstanding shares : 0.05 • Exercise price : Rs 30 • Time to expiration of warrant : 3 years • Annual standard deviation of stock price changes : 0.40 • Interest rate : 12 percent What is the value of a warrant? Ignore the complication arising from dividends and/or dilution.

Solution: l (S/E) + (r + ?2 /2) t d1

= = =

= d2 = = = N(d1) =

??t ln (60 / 30) + [0.12 + (0.4)2/2]3 0.4(3)1/2 0.6931 + 0.6 0.6928 1.8665 d1 - ? ? t 1.8665 – 0.6928 1.1737 N (1.8665).

From the tables we have N(1.85)= 1- 0.0322= 0.9678 and N(1.90)= 1- 0.0287= 0.9713 By linear extrapolation, we get N(1.8665) = 0.9678 + (1.8665 – 1.8500)(0.9713-0.9678)/0.05 = 0.9678 + 0.001155 = 0.9690 N(d2) = N(1.1737) From the tables we have N(1.15) = 1- 0.1251 = 0.8749 N(1.20) = 1- 0.1151 = 0.8849 By linear extrapolation, we get N(1.1737) = 0.8749 + (1.1737 – 1.1500)(0.8849 – 0.8749)/0.05 = 0.8749 + 0.00474 = 0.8796 E/ert = 30/1.4333 = 20.93 C = So N(d1) – E. e-rt. N(d2) = 60 x 0.9690 – 20.93 x 0.8796= 39.73 Value of the warrant is Rs. 39.73. 2. Vishal Enterprises has just issued warrants. The following data is available: • Number of shares outstanding = 60 million • Current stock price = Rs 70 • Ratio of warrants issued to the number of outstanding shares = 8 percent • Exercise price = Rs 40 • Time to expiration of warrants = 4 years • Annual standard deviation of stock price changes = 30 percent • Interest rate = 10 percent What is the value of a warrant?

Solution: l (S/E) + (r + ?2 /2) t d1

= = = = = = =
??t ln (70 / 40) + [0.10 + (0.3)2/2]4 0.3(4)1/2 0.5596 + 0.5800 0.6 1.8993 d1 - ? ? t 1.8993 – 0.6 1.2993

d2

N(d1) =

N (1.8993) , which is very nearly equal to N(1.90)

From the tables we have N(1.90)= 1- 0.0287= 0.9713 N(d2) = N(1.2993), which is very nearly equal to N(1.30) From the tables we have N(1.30) = 1- 0.0968 = 0.9032 E/ert = 40/1.4918 = 26.81 C = So N(d1) – E. e-rt. N(d2) = 70 x 0.9713 – 26.81 x 0.9032= 43.78 Value of the warrant is Rs. 43.78. 3. Shivalik Combines issues a partly convertible debenture for Rs 900, carrying an interest rate of 12 percent. Rs 300 will get compulsorily converted into two equity shares of Shivalik Combines a year from now. The expected price per share of Shivalik Combines’s equity a year from now would be Rs 200. The nonconvertible portion will be redeemed in three equal installments of Rs 200 each at the end of years 4, 5 and 6 respectively. The tax rate for Shivalik is 35 percent and the net price per share Shivalik would realise for the equity after a year would be Rs 180. (a) What is the value of convertible debenture? Assume that the investors’ required rate of return on the debt component and the equity component are 12 percent and 16 percent respectively. What is the post-tax cost of the convertible debenture to Shivalik ?

(b)
Solution:

(a)

No. of shares after conversion in one year = 2 Value of the shares at the price of Rs.200 = 2 x 200 = Rs.400 PV of the convertible portion at the required rate of 16% = 400/1.16 = Rs.344.82

Payments that would be received from the debenture portion: Year 1 2 3 4 5 6 Payments PVIF12%,t PV 108 0.893 96.44 72 0.797 57.38 72 0.712 51.26 272 0.636 172.99 248 0.567 140.62 224 0.507 113.57 Total= 632.26

Value of the convertible debenture = 344.82 + 632.26 = Rs. 977.08 (b) The cash flow for Shivalik is worked out as under: Year 0 1 2 3 4 5 6 Cash flow =-360-108*(1-0.35) =-72*(1-0.35) =-72*(1-0.35) =-200-72*(1-0.35) =-200-48*(1-0.35) =-200-24*(1-0.35) 900 -430 -47 -47 -247 -232 -216

The post-tax cost of the convertible debenture to Shivalik is the IRR of the above cash flow stream. Let us try a discount rate of 10 %. The PV of the cash flow will then be = 900 – 430/(1.1) -47/(1.1)2 - 47/(1.1)3 -247/(1.1)4-232/(1.1)5-216/(1.1)6 = 0.25 which is very near to zero. So the post –tax cost of the convertible debenture to Shivalik is 10% 4. Brilliant Limited issues a partly convertible debenture for 1000, carrying an interest rate of 10 percent. 360 will get compulsorily converted into two equity shares of Brilliant Limited a year from now. The expected price per share of Brilliant Limited’s equity a year from now would be Rs 300. The non-convertible portion will be redeemed in four equal installments of Rs 160 each at the end of years 3, 4, 5 and 6 respectively. The tax rate for Brilliant is 33 percent and the net price per share Brilliant would realise for the equity after a year would be Rs 220. (a) What is the value of convertible debenture? Assume that the investors’ required rate of return on the debt component and the equity component are 13 percent and 18 percent respectively. (b) What is the post-tax cost of the convertible debenture to Brilliant?
Solution:

(a)

No. of shares after conversion in one year = 2 Value of the shares at the price of Rs.300 = 2 x 300 = Rs.600 PV of the convertible portion at the required rate of 18% = 600/1.18 = Rs.508.47 Payments that would be received from the debenture portion:

Year 1 2 3 4 5 6

Payments PVIF13%,t PV 100 0.885 88.5 64 0.783 50.11 224 0.693 155.23 208 0.613 127.50 192 0.543 104.26 176 0.480 84.48 Total= 610.08

Value of the convertible debenture = 508.47 + 610.08 = Rs. 1118.55 (b) The cash flow for Brilliant is worked out as under: Year 0 1 2 3 4 5 6 Cash flow =-440-100*(1-0.33) =-64*(1-0.33) =-160-64*(1-0.33) =-160-48*(1-0.33) =-160-32*(1-0.33) =-160-16*(1-0.33) 1000 -361.80 -42.88 -202.88 -192.16 -181.4 -170.72

The post-tax cost of the convertible debenture to Brilliant is the IRR of the above cash flow stream. Let us try a discount rate of 4 %. The PV of the cash flow will then be = 1000 – 361.8/(1.04) -42.88/(1.04)2 – 202.88/(1.04)3 -192.16/(1.04)4181.4/(1.04)5-170.72/(1.04)6 = -16.17 Trying a discount rate of 5 %. The PV of the cash flow will then be = 1000 – 361.8/ (1.05) -42.88/(1.05)2 – 202.88/(1.05)3 -192.16/(1.05)4181.4/(1.05)5-170.72/(1.05)6 = 13.66 By extrapolation, we have the IRR = 4 + 16.17/(16.17 + 13.66) = 4.54 % So the post –tax cost of the convertible debenture to Brilliant is 4.54 %

CHAPTER 26

1.

The following information is available for NCEP Limited.
Profit and Loss Account Data Balance Sheet Data Beginning of 20X6 End of 20X6

Sales Cost of goods sold

6000 4000

Inventory Accounts receivable Accounts payable

800 500 290

820 490 205

What is the duration of the cash cycle?
Solution:

(800 + 820) / 2 Inventory Period = 4000 / 365 (500 + 490) / 2 Accounts receivable = period = 30.11 6000 / 365 (290 + 205) / 2 Accounts payable = 4000 / 365 Cash cycle = 81.44 days = 22.58 = 73.91

2.

The following information is available for ABC Limited.
Profit and Loss Account Data Balance Sheet Data Beginning of 20X5 End of 20X5

Sales Cost of goods sold

3000 1800

Inventory Accounts receivable Accounts payable

300 180 85

310 170 95

What is the duration of the cash cycle?

Solution:

Inventory Period Accounts receivable period Accounts payable Cash Cycle

= = = =

(300+310) / 2 1800/365 (180 + 170)/2 3000/365 (85 + 95) / 2 1800/365 64.9 days

= = =

61.87 21.30 18.25

3.

The following annual figures relate to Sugarcolt Limited. Sales (at two months' credit) Materials consumed (suppliers extend two months credit) Wages paid (monthly in arrear) Manufacturing expenses outstanding at the end of the year (Cash expenses are paid one month in arrear) Total administrative expenses, paid as incurred Sales promotion expenses, paid quarterly in advance
Rs. 6,000,000 1,600,000 1,300,000 140,000

440,000 200,000

The company sells its products on gross profit of 20 percent counting depreciation as part of the cost of production. It keeps one month's stock each of raw materials and finished goods, and a cash balance of Rs.200,000. Assuming a 25 % safety margin, work out the working capital requirements of the company on cash cost basis. Ignore work-in-process.
Solution:

1.

Sales Less : Gross profit (20 per cent) Total manufacturing cost Less : Materials 1,600,000 Wages 1,300,000 Manufacturing expenses 2. Cash manufacturing expenses (140,000 x 12) 3. Depreciation : (1) – (2) 4. Total cash cost Total manufacturing cost Less: Depreciation Cash manufacturing cost Add: Administration and sales promotion expenses

Rs. 6,000,000 1,200,000 4,800,000 2,900,000 1,900,000 1,680,000 220,000 4,800,000 220,000 4,580,000 640,000 5,220,000

A : Current Assets

Rs.

Total cash cost Debtors 12 Material cost Raw material stock Finished goods stock Prepaid sales promotion expenses Cash balance x 1 12 Cash manufacturing cost = x 2 =

5,220,000 x 12 1,600,000 x 12 4,580,000 x1= x 12 200,000 x3= x 3= 12 = 200,000 50,000 1= 381,667 1= 133,333 2= 870,000

12 Sales promotion expenses 12 A predetermined amount A : Current Assets

= 1,635,000

B : Current Liabilities

Rs.

Material cost Sundry creditors 12 Manufacturing expenses outstanding Wages outstanding x 2=

1,600,000 x 12 = = 140,000 108,333 515,000 2 = 266,667

One month’s cash manufacturing expenses One month’s wages

B : Current liabilities

Working capital (A – B) Add 25 % safety margin Working capital required

1,120,000 280,000 1,400,000

4.

The following annual figures relate to Universal Limited.
Rs. 8,000,000 2,000,000 1,600,000 100,000

Sales (at three months' credit) Materials consumed (suppliers extend one months credit) Wages paid (monthly in arrear) Manufacturing expenses outstanding at the end of the year

(Cash expenses are paid one month in arrear) Total administrative expenses, paid as incurred Sales promotion expenses, paid quarterly in arrears

500,000 400,000

The company sells its products on gross profit of 30 percent counting depreciation as part of the cost of production. It keeps two months’ stock each of raw materials and finished goods, and a cash balance of Rs.300,000. Assuming a 20 % safety margin, work out the working capital requirements of the company on cash cost basis. Ignore work-in-process.
Solution:

1.

Sales Less : Gross profit (30 per cent) Total manufacturing cost Less : Materials 2,000,000 Wages 1,600,000 Manufacturing expenses

Rs. 8,000,000 2,400,000 5,600,000 3,600,000 2,000,000 1,200,000 800,000 5,600,000 800,000 4,800,000 500,000 5,300,000

2. Cash manufacturing expenses (100,000 x 12) 3. Depreciation : (1) – (2) 5. Total cash cost Total manufacturing cost Less: Depreciation Cash manufacturing cost Add: Administration expenses

A : Current Assets

Rs.

Total cash cost Debtors 12 Material cost Raw material stock Finished goods stock x 2 12 Cash manufacturing cost = x 3 =

5,300,000 x 12 2,000,000 x 12 4,800,000 x2= x 12 2= 800,000 2= 333,333 3= 1,325,000

12

Cash balance

A predetermined amount A : Current Assets
B : Current Liabilities

= =

300,000 2,758,333
Rs.

Material cost Sundry creditors 12 Manufacturing expenses outstanding Wages outstanding Sales Promotion expenses x 1=

2,000,000 x 12 = = = 100,000 133,333 100,000 ------------500,000 1 = 166,667

One month’s cash manufacturing expenses One month’s wages Three months’ expenses

B : Current liabilities

Working capital (A – B) Add 20 % safety margin Working capital required
CHAPTER 27

2,258,333 451,667 2,710,000

1.

You have been asked to prepare a cash budget for the next quarter, January through March, for Sharmilee Exports. They have provided you with the following information: a. Sales are expected to be: Rs.300,000 in January, Rs.260,000 in February, and Rs.350,000 in March. All sales will be in cash. b. The estimated purchases are: Rs.240,000 in January, Rs.220,000 in February, and Rs.250,000 in March. Payments for purchases will be made after a lag of one month. Outstanding on account of purchases in December last are Rs.210,000. c. The rent per month is Rs.8,000 and the partners’ personal withdrawal per month is Rs.12,000. d. Salaries and other expenses, payable in cash, are expected to be: Rs.15,000 in January, Rs.15,000 in February, and Rs.16,000 in March. e. They plan to buy two computers worth Rs.50,000 on cash payment in March. f. The cash balance at present is Rs.12,000. Their target cash balance, however, is Rs.20,000. What will be surplus/ deficit of cash in relation to their target cash balance?

Solution:

The projected cash inflows and outflows for the quarter, January through March, is shown below .
Month December (Rs.) January (Rs.) February (Rs.) March (Rs.)

Inflows : Sales collection Outflows : Purchases Payment to sundry creditors Rent Drawings Salaries & other expenses Purchase of computers Total outflows(2to6)

300,000

260,000

350,000

210,000

240,000 210,000 8,000 12,000 15,000

220,000 240,000 8,000 12,000 15,000

250,000 220,000 8,000 12,000 16,000 50,000 306,000

245,000

275,000

Given an opening cash balance of Rs.12,000 and a target cash balance of Rs.20,000, the surplus/deficit in relation to the target cash balance is worked out below :
January (Rs.) February (Rs.) March (Rs.)

1. Opening balance 2. Inflows 3. Outflows 4. Net cash flow (2 - 3) 5. Cumulative net cash flow 6. Opening balance + Cumulative net cash flow 7. Minimum cash balance required 8. Surplus/(Deficit)

12,000 300,000 245,000 55,000 55,000 67,000 20,000 47,000

260,000 275,000 ( 15,000) 40,000 52,000 20,000 32,000

350,000 306,000 44,000 84,000 96,000 20,000 76,000

2.

You have been asked to prepare a cash budget for the next quarter, January through March, for Jahanara Fashions. They have provided you with the following information: a. Sales are expected to be: Rs.400,000 in January, Rs.400,000 in February, and Rs.600,000 in March. All sales will be in cash. b. The estimated purchases are: Rs.380,000 in January, Rs360,000 in February, and Rs.450,000 in March. Payments for purchases will be made after a lag of one month. Outstanding on account of purchases in December last are Rs.350,000.

c. d. e. f.

The rent per month is Rs.10,000 and the partners’ personal withdrawal per month is Rs.25,000. Salaries and other expenses, payable in cash, are expected to be: Rs.25,000 in January, Rs.20,000 in February, and Rs.30,000 in March. They plan to buy furniture worth Rs.40,000 on cash payment in January.. The cash balance at present is Rs.6,000. Their target cash balance, however, is Rs.15,000. What will be surplus/ deficit of cash in relation to their target cash balance?

Solution:

The projected cash inflows and outflows for the quarter, January through March, is shown below .
Month December (Rs.) January (Rs.) February (Rs.) March (Rs.)

Inflows : Sales collection Outflows : Purchases Payment to sundry creditors Rent Drawings Salaries & other expenses Purchase of furniture Total outflows (2to6)

400,000

400,000

600,000

350,000

380,000 350,000 10,000 25,000 25,000 40,000 450,000

360,000 380,000 10,000 25,000 20,000

450,000 360,000 10,000 25,000 30,000

435,000

425,000

Given an opening cash balance of Rs.6,000 and a target cash balance of Rs.15,000, the surplus/deficit in relation to the target cash balance is worked out below : January February March (Rs.) (Rs.) (Rs.) 1. Opening balance 2. Inflows 3. Outflows 4. Net cash flow (2 - 3) 5. Cumulative net cash flow 6. Opening balance + Cumulative net cash flow 7. Minimum cash balance required 8. Surplus/(Deficit) 6,000 400,000 450,000 (50,000) (50,000) (44,000) 15,000 ( 59,000)

400,000 435,000 (35,000) ( 85,000) (79,000) 15,000 (94,000)

600,000 425,000 175,000 90,000 96,000 15,000 81,000

3.

Smartlink Corporation issues cheques of Rs.10,000 daily and it takes 6 days for its cheques to be cleared. Smartlink Corporation receives cheques of Rs.30,000 daily and it takes 4 days for these cheques to be realised. Assume that there is a balance of Rs.80,000 to begin with; show the balance in the book of the firm and the books of the bank. What will be the balance in the steady state situation? Solution: The balances in the books of Smartlink Corporation and the books of the bank are shown below: (Rs)
1 2 3 4 5 6 7 8

Books of Smartlink Corporation: Opening Balance Add: Cheque received Less: Cheque issued Closing Balance Books of the Bank: Opening Balance Add: Cheques realised Less: Cheques debited Closing Balance 80,000 80,000 80,000 80,000 110,000 140,000 80,000 80,000 80,000 80,000 80,000 30,000 110,000 30,000 140,000 30,000 10,000 160,000 160,000 30,000 10,000 180,000 80,000 30,000 10,000 100,000 100,000 30,000 10,000 120,000 120,000 30,000 10,000 140,000 140,000 30,000 10000 160,000 160,000 30,000 10,000 180,000 180,000 30,000 10,000 200,000 200,000 30,000 10,000 220,000 220,000 30,000 10,000 240,000

From day 7 we find that the balance as per the bank’s books is less than the balance as per Smartlink Corporation’s books by a constant sum of Rs.60,000. Hence in the steady situation Smartlink Corporation has a negative net float of Rs.60,000. 4. Shahanshah Limited issues cheques of Rs.50,000 daily and it takes 5 days for its cheques to be cleared. Shahanshah Limited receives cheques of Rs.80,000 daily and it takes 3 days for these cheques to be realised. Assume that there is a balance of Rs.100,000 to begin with; show the balance in the book of the firm and the books of the bank. What will be the balance in the steady state situation?

Solution:

The balances in the books of Shahanshah Limited and the books of the bank are shown below:

(Rs) Books of Shahanshah Limited

Opening Balance Add: Cheque received Less: Cheque issued Closing Balance

100,000 130,000 160,000 190,000 220,000 250,000 280,000 80,000 80,000 80,000 80,000 80,000 80,000 80,000 50,000 50,000 50,000 50,000 50,000 50,000 50,000 130,000 160,000 190,000 220,000 250,000 280,000 310,000
Books of the Bank:

Opening Balance Add: Cheques realised Less: Cheques debited Closing Balance

100,000 100,000 100,000 100,000 180,000 260,000 290,000 80,000 80,000 80,000 80,000 50,000 50,000 100,000 100,000 100,000 180,000 260,000 290,000 320,000

From day 6 we find that the balance as per the bank’s books is more than the balance as per Shahanshah Limited’s books by a constant sum of Rs.10,000. Hence in the steady situation Shahanshah Limited has a positive net float of Rs.10,000. 5. Sourav International requires Rs. 150 million in cash for meeting its transaction needs over the next two months, its planning horizon for liquidity decisions. It currently has the amount in the form of marketable securities that earn 9 percent annual yield. The cash payments will be made evenly over the two months planning period. The conversion of marketable securities into cash entails a fixed cost of Rs. 6,000 per transaction. What is the optimal conversion size as per Baumol model?

Solution:

T= 150,000,000 I = 0.09/6 = 0.015 According to the Baumol model: 2bt ----I

b = 6,000

C=

=

2 x 6,000 x 150,000,000 --------------------------------- = Rs. 10,954,451 0.015

6.

Vishal Exports requires Rs.90 million in cash for meeting its transaction needs over the next three months, its planning horizon for liquidity decisions. Vishal Exports currently has the amount in the form of marketable securities. The cash payments will be made evenly over the three months planning period. Vishal Exports earns 8 percent annual yield on its marketable securities. The conversion of marketable securities into cash entails a fixed cost of Rs.4,500 per transaction. What is the optimal conversion size as per the Baumol model ?

Solution:

T = 90,000,000

I = 0.08/4 = 0.02

b = 4,500

According to the Baumol model: 2bT --------I 2 x 4500 x 90,000,000 = -------------------------------0.02

c

=

=

Rs. 6363961.03

7.

Topnotch Corporation requires Rs.45 million in cash for meeting its transaction needs over the next six months, its planning horizon for liquidity decisions. Topnotch currently has the amount in the form of marketable securities. The cash payments will be made evenly over the six month planning period. Topnotch earns 6 percent annual yield on its marketable securities. The conversion of marketable securities into cash entails a fixed cost of Rs.1,500 per transaction. What is the optimal conversion size as per the Baumol model ?

Solution:

T = 45,000,000 I=

0.06 = 0.03 2

b = 1,500

According to the Baumol model: 2bT C = I = Rs.2,121,320 = 0.03 2 x 1500 x 45,000,000

8. Ajit Associates expects its cash flows to behave in a random manner, as assumed by the Miller and Orr model .The following information has been gathered. • Annual yield on marketable securities = 9 percent • The fixed cost of effecting a marketable securities transaction = Rs.2,800 • The standard deviation of the change in daily cash balance = Rs.19,000 • Minimum cash balance required to be maintained as per management policy = Rs.2,500,000 What are the ‘return point’ and ‘upper control point’?

Solution:

I = 0.09/360 = 0.00025 3b?2 3 ------- + LL = 4I 3 x 2,800 x 19,000 x 19,000 3 ----------------------------------- + 2,500,000 4 x 0.00025

RP =

= Rs. 2,644,742 UL = 3 RP -2 LL = 3 x 2,644,742 – 2 x 2,500,000 = Rs. 2,934,226

9.

Hanson Corporation expects its cash flows to behave in a random manner, as assumed by the Miller and Orr model. The following information has been gathered. Annual yield on marketable securities = 8 percent • The fixed cost of effecting a marketable securities transaction = Rs. 1700 • The standard deviation of the change in daily cash balance = Rs.27,000 • The management wants to maintain a minimum cash balance of Rs.3,500,000 What are the ‘return point’ and ‘upper control point’?

Solution:

I = 0.08 / 360

= 0.000222 3 x 1700 x 27,000 x 27,000 = 3 ---------------------------------- + 3,500,000 4 x 0.000222 = 3,661,174

RP

=

3b? 2 3 -------UI

+ LL

UL =

3RP – 2LL = 3 x 3,661,174 - 2 x 3,500,000 = Rs. 3,983,522

10.

Premier Limited expects its cash flows to behave in a random manner, as assumed by the Miller and Orr model. The following information has been gathered. • Annual yield on marketable securities = 5 percent • The fixed cost of effecting a marketable securities transaction = Rs. 800 • The standard deviation of the change in daily cash balance = Rs.12,000 • The management wants to maintain a minimum cash balance of Rs.1,500,000 What are the ‘return point’ and ‘upper control point’?

Solution:

I = 0.05/360 = 0.000139 3b?2 RP = 3 4I 3 x 800 x 12,000 x 12,000 = 3 4 x 0.000139 UL = 3 RP – 2LL = 1,756,029 + 1,500,000 = 1,585,343 + LL

CHAPTER 27

1.

Rakesh Enterprises currently provides 30 days credit to its customers. Its present sales are Rs. 200 million .Its cost of capital is 12 percent and the ratio of variable costs to sales is 0.80 Rakesh Enterprises are considering extending the credit period to 45 days which is likely to push sales up by Rs.60 million. The bad debt proportion on additional sales would be 15 percent. The tax rate is 33 percent. What will be the effect of lengthening the credit period on the residual income of the firm?

Solution: ?RI = [ ?S(1-V) –?Sbn](1-t) – k?I ?I = (ACPN – ACP0){ S0/360} + V(ACPN) ?S/360 = (45-30) x (200,000,000/360) + 0.80 x 45 x ( 60,000,000/360) = 14,333,333 ?RI = (60,000,000 x 0.20 - 60,000,000 x 0.15)(0.67) -0.12 x 14,333,333 = 290,000

2.

Phoenix Limited currently provides 30 days of credit to its customers. Its present level of sales is Rs.150 million. The firm’s cost of capital is 14 percent and the ratio of variable costs to sales is 0.70. Phoenix is considering extending its credit period to 60 days. Such an extension is likely to push sales up by Rs.12 million. The bad debt proportion on the additional sales would be 6 percent. The tax rate for Phoenix is 30 percent. What will be the effect of lengthening the credit period on the residual income of Phoenix Limited? Assume 360 days to a year.

Solution:

[12,000,000 x 0.30 – 12,000,000 x 0.06] (1 – 0.3) 150,000,000 - 0.14 (60 – 30) x 360 = 2,016,000 – 1,946,000 = 70,000 + 0.70 x 60 x 360 12,000,000

3.

Acme Limited provides 30 days of credit to its customers. Its present level of sales is Rs.300 million. The firm’s cost of capital is 12 percent and the ratio of variable costs to sales is 0.75. Acme is considering extending its credit period to 45 days. Such an extension is likely to push sales up by Rs.25 million. The bad debt proportion on the additional sales would be 8 percent. The tax rate for Acme is 30 percent. What will be the effect of lengthening the credit period on the residual income of Acme? Assume 360 days to a year.

Solution:

?RI = [?S (1-V) - ?Sbn] (1–t) – k

(ACPn – ACP0) +

x ACPn x V

=

[25,000,000 x 0.25 – 25,000,000 x .08] (1 – 0.3) 300,000,000 – 0.12 360 (45-30) + 360 25,000,000 x 45 x 0.75

= 2,975,000 – 1,781,250 = 1,193,750

4.

The present credit terms of Indus Industries are 3/15, net 30. Its sales are Rs.470 million, its average collection period is 45 days, its variable costs to sales ratio, V, is 0.85, and its cost of capital is 12 percent. The proportion of sales on which customers currently take discount, is 0.4. Indus is considering relaxing its credit terms to 5/15, net 30. Such a relaxation is expected to increase sales by Rs.20 million, increase the proportion of discount sales to 0.6, and reduce the ACP to 40 days. Indus’s tax rate is 30 percent. What will be the effect of liberalising the cash discount on residual income?

Solution:

RI DIS

= [ S(I–V)= pn (S0 + = 9,060,000

DIS ] (1 - t ) + R

I

S) dn - p0S0do

= 0.6 [470,000,000 + 20,000,000 ] x 0.05 - 0.4 x 470,000,000 x 0.03

I

= 470,000,000
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

20,000,000 (45 – 40) - 0.85 x
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

x 40

360 = 4,638,889 RI

360

= [ 20,000,000 x 0.15 - 9,060,000] 0.70 + 0.12 x 4,638,889 = - 3,685,333

5.

The present credit terms of Globus Corporation are 2/10, net 40. It sales are Rs.650 million, its average collection period is 30 days, its variable costs to sales ratio, V, is 0.75, and its cost of capital is 10 percent. The proportion of sales on which customers currently take discount, is 0.3. Globus is considering relaxing its credit terms to 3/10, net 40. Such a relaxation is expected to increase sales by Rs.30 million, increase the proportion of discount sales to 0.5, and reduce the ACP to 20 days. Globus’s tax rate is 35 percent. What will be the effect of liberalising the cash discount on residual income?

Solution: ? RI = [?S (1 – V) – ?DIS] (1 – t) + R ? I ? DIS = pn (So + ?S)dn – poso do

= 0.5 [650,000,000 + 30,000,000] .03 – 0.30 [650,000,000] .02 = 10,200,000 – 3,900,000 = 6,300,000 650,000,000 30,000,000 ?I = (30 – 20) – 0.75 x x 20 360 360 = 18,055,556 – 1,250,000 = 16,805,556
? R I = [30,000,000 (0.25) – 6,300,000] (0.65) + 0.10 x 16,805,556 = 780,000 + 1,680,556 = 2,460,556

6.

The present credit terms of Hitesh Limited are 1/10, net 30. It sales are Rs.800 million, its average collection period, ACP, is 22 days, its variable costs to sales ratio, V, is 0.80, and its cost of capital, k, is 15 percent. The proportion of sales on

which customers currently take discount, po, is 0.4. Hitesh is considering relaxing its credit terms to 2/10, net 30. Such a relaxation is expected to increase sales by Rs.50 million, increase the proportion of discount sales to 0.6, and reduce the ACP to 18 days. Hitesh’s tax rate is 30 percent. What will be the effect of liberalising the cash discount on residual income?
Solution: ? RI = [?S (1 – V) – ?DIS] (1 – t) + R ? I ? DIS = pn (So + ?S)dn – poso do

= 0.6 [800,000,000 + 50,000,000] .02 – 0.40 [800,000,000] .01 = 10,200,000 – 3,200,000 = 7,000,000 800,000,000 50,000,000 ?I = (22 – 18) – 0.8 x x 18 360 360 = 8,888,889 – 2,000,000 = 6,888,889
? R I = [50,000,000, (0.2) – 7,000,000] (0.7) + 0.15 x 6,888,889 = 2,100,000 + 1,033,333 = 3,1333,333

7.

The present sales of Nachiket Industries are Rs.100 million. The firm classifies its customers into 3 credit categories: A, B, and C. The firm extends unlimited credit to customers in category A, limited credit to customers in category B, and no credit to customers in category C. As a result of this credit policy, the firm is foregoing sales to the extent of Rs.10 million to customers in category B and Rs.20 million to customers in category C. The firm is considering the adoption of a more liberal credit policy under which customers in category B would be extended unlimited credit policy and customers in category C would be provided limited credit. Such relaxation would increase the sales by Rs.30 million on which bad debt losses would be 10 percent. The contribution margin ratio for the firm is 20 percent, the average collection period is 45 days, and the cost of capital is 16 percent. The tax rate for the firm is 35 percent.

What will be the effect of relaxing the credit policy on the residual income of the firm? Solution: ? RI = [?S(1-V)- ?Sbn](1-t)- k ?I ?S ?I = x ACP x V 360 ? S = Rs.30 million, V=0.80, bn =0.10, ACP= 45 days, k=0.16, t = 0.35 Hence, ?RI = [ 30,000,000(1-0.80)- 30,000,000 x 0.10 ] (1-0.35) -0.16 x 30,000,000 x 45 x 0.80 360 = Rs. 1,470,000

8.

The present sales of Purvanchal Limited are Rs.80 million. The firm is considering the adoption of a more liberal credit policy under which customers with annual income in excess of Rs.1million would be extended unlimited credit and other customers limited credit. Such relaxation would increase the sales by Rs.20 million on which bad debt losses would be 8 percent. The contribution margin ratio for the firm is 25 percent, the average collection period is 30 days, and the cost of capital is 18 percent. The tax rate for the firm is 34 percent. What will be the effect of relaxing the credit policy on the residual income of the firm?

Solution: ? RI = [?S(1-V)- ?Sbn](1-t)- k ?I ?S ?I = x ACP x V 360 ? S = Rs.20 million, V=0.75, bn =0.08, ACP= 30 days, k=0.18, t = 0.34

Hence, ?RI = [ 20,000,000(1-0.75)- 20,000,000 x 0.08 ] (1-0.34) -0.18 x 20,000,000 x 30 x 0.75 360 = Rs. 2,019,000 9. Garibdas Limited is considering relaxing its collection efforts. Presently its sales are Rs.70 million, its average collection period 20 days, its variable costs to sales ratio 0.60, its cost of capital 16 percent, and its bad debt ratio 0.05. The relaxation in collection efforts is expected to push sales up by Rs.10 million, increase the average collection period to 30 days, and raise the bad debts ratio to 0.08. The tax rate of the firm is 35 percent. What will be the effect of relaxing the collection effort on the residual income of the firm?
Solution: ? RI = [?S(1-V)- ?BD](1-t) –k? I ?BD=bn(So+?S) –boSo So ?I = ?S

(ACPN –ACPo) + 360 360

x ACPN x V

So=Rs.70 million, ACPo=20, V=0.60, k=0.16, bo=0.05, ?S=Rs.10 million,

ACPN=30 , bn= 0.08 , t = 0.35 ?RI = [ Rs.10,000,000(1-.60) –{.08(Rs.80,000,000)-.05(Rs.70,000,000)](1-0.35) Rs.70,000,000 Rs.10,000,000 (30-20) + 360

- 0.16 360 = Rs.323,889

x

x30 x 0.6

10.

Sonar Corporation is considering relaxing its collection efforts. Presently its sales are Rs.200 million, its average collection period 30 days, its variable costs to sales ratio 0.70, its cost of capital 18 percent, and its bad debt ratio 0.05. The relaxation in collection efforts is expected to push sales up by Rs.20 million, increase the average collection period to 40 days, and raise the bad debts ratio to 0.06. The tax rate of the firm is 33 percent. What will be the effect of relaxing the collection effort on the residual income of the firm?

Solution: ? RI = [?S(1-V)- ?BD](1-t) –k? I ?BD=bn(So+?S) –boSo So ?S ?I = (ACPN –ACPo) + x ACPN x V 360 360 So=Rs.200 million, ACPo=30, V=0.70, k=0.18, bo=0.05, ?S=Rs.20 million, ACPN=40 , bn= 0.06 , t = 0.33 ?RI = [ Rs.20,000,000(1-.70) –{.06(Rs.220,000,000)-.05(Rs.200,000,000)](1-0.33) Rs.200,000,000 Rs.20,000,000 (40-30) + 360

- 0.18 360 = Rs.596,000 11.

x

x40 x 0.70

The financial manager of a firm is wondering whether credit should be granted to a new customer who is expected to make a repeat purchase. On the basis of credit evaluation, the financial manager feels that the probability that the customer will pay is 0.70 and the probability that the customer will default is 0.30. Once the customer pays for the first purchase, the probability that he will pay for the repeat purchase will be 0.90. The revenue from the sale will be Rs.200,000 and the cost of the sale will be Rs.160,000 – these figures apply to both the initial and the repeat purchases. What is the expected payoff if the credit is granted?

Solution:

12.

The financial manager of a firm is wondering whether credit should be granted to a new customer who is expected to make a repeat purchase. On the basis of credit evaluation, the financial manager feels that the probability that the customer will pay is 0.80 and the probability that the customer will default is 0.20. Once the customer pays for the first purchase, the probability that he will pay for the repeat purchase increases to 0.95. The revenue from the sale will be Rs.250,000 and the cost of the sale would be Rs.180,000 – these figures apply to both the initial and the repeat purchase. What is the expected payoff if the credit is granted?

Solution:

Expected pay off

= =

(0.80 x 70,000) - (0.2 x 180,000) + 0.80 [0.95 (70,000) – 0.05 x 180,000] 66,000

13.

The financial manager of a firm is wondering whether credit should be granted to a new customer who is expected to make a repeat purchase. On the basis of credit evaluation, the financial manager feels that the probability that the customer will pay is 0.70 and the probability that the customer will default is 0.30. Once the customer pays for the first purchase, the probability that he will pay for the repeat purchase will be 0.90. The revenue from the sale will be Rs.200,000 and the cost of the sale will be Rs.160,000 – these figures apply to both the initial and the repeat purchases. What is the expected payoff if the credit is granted?

Solution:

14.

Zenith Enterprises sells on terms, 2/10, net 30. Annual sales are Rs.200 million. 40 percent of its customers pay on the 10th day and take the discount. If accounts receivable average is Rs.15 million, what is the average collection period (ACP) on non-discount sales?

Solution:

Discount sales Accounts receivable = [ACP on discount sales] 360 Non – discount sales + [ACP on non-discount sales] 80,000,000 15,000,000 = [10] 360 S0 ACP = 38.3 days 15. ATP Ltd. sells on terms 4/45, net 60 .Annual sales are Rs.200 million, 40 percent of its customers pay on the 45th day and take the discount. If the accounts receivable average Rs.25 million, what is the average collection period (ACP) on non discount sales? + ACP 360 360 120,000,000

Solution: Accounts receivable Discount sales = [ ACP on discount sales][ --------------------] 360 Non-discount sales +[ACP on non-discount sales][ --------------------------] 360 0.4 x 200 0.6 x 200 25 = 45 x ------------------- + ACPND x ----------------360 360 i.e. 25x 360 = 3600 + ACPND x 120 ACPND = 45

16.

Zenith Enterprises sells on terms, 2/10, net 30. Annual sales are Rs.200 million. 40 percent of its customers pay on the 10th day and take the discount. If accounts receivable average is Rs.15 million, what is the average collection period (ACP) on non-discount sales ?

Solution:

Discount sales Accounts receivable = [ACP on discount sales] 360 Non – discount sales + [ACP on non-discount sales] 80,000,000 15,000,000 = [10] 360 120,000,000

+ ACP 360 360 Solving the above we get ACP = 38.3 days

17.

Malwa Industries sells on terms 3/10, net 30. Total sales for the year are Rs.60 million. Forty percent of the sales amount is paid on the tenth day (availing the discount) and the remaining 60 percent pay, on average, 40 days after their purchases. Calculate the average collection period and the average investment in receivables.

Solution:

40% of sales will be collected on the 10th day 60% of sales will be collected on the 40th day ACP = 0.4 x 10 + 0.6 x 40 = 28 days Rs.60,000,000 Value of receivables = 360 = Rs.4,666,667 Assuming that V is the proportion of variable costs to sales, the investment in receivables is : Rs. 4,666,667 x V 18. Bheema Enterprises sells on terms 4/15, net 40. Total sales for the year are Rs.100 million. Twenty percent of the sales amount is paid on the fifteenth day (getting the benefit of discount) and the remaining 80 percent pay, on average, 60 days after their purchases. x 28

Calculate the average collection period and the average investment in receivables. Solution: 20% of sales will be collected on the 15th day 80% of sales will be collected on the 60th day ACP = 0.2 x 15 + 0.8 x 60 = 51 days Rs.100,000,000 x 51 360

Value of receivables =

= Rs.14,166,667 Assuming that V is the proportion of variable costs to sales, the investment in receivables is : Rs. 14,166,667x V

19.

A firm is wondering whether to sell goods to a customer on credit or not. The revenues from sale will be Rs.50,000 and the cost of sale will be Rs.36,000. What should be the minimum probability that the customer will pay, in order to sell profitably?

Solution:

Profit when the customer pays = Rs.50,000 - Rs.36,000 = Rs.14,000 Loss when the customer does not pay = Rs.36,000 Expected profit = p1 x 14,000 –(1-p1)36,000

Setting expected profit equal to zero and solving for p1 gives: p1 x 14,000 – (1- p1)36,000 = 0 p1 = 0.72 Hence the minimum probability that the customer must pay is 0.72 20. A firm is wondering whether to sell goods to a customer on credit or not. The revenues from sale will be Rs.100,000 and the cost of sale will be Rs.80,000. What should be the minimum probability that the customer will pay, in order to sell profitably? Profit when the customer pays = Rs.100,000 - Rs.80,000 = Rs.20,000 Loss when the customer does not pay = Rs.80,000 Expected profit = p1 x 20,000 –(1-p1)80,000 Setting expected profit equal to zero and solving for p1 gives : p1 x 20,000 – (1- p1)80,000 = 0 p1 = 0.8 Hence the minimum probability that the customer must pay is 0.8
CHAPTER 29

Solution:

1.

Pioneer Stores is trying to determine the economic order quantity for a certain type of machine tool. The firm sells 60,000 numbers of this machine tool annually at a price of Rs.80 per piece. The purchase price per machine tool to the firm is, however, Rs.65. The cost of carrying a machine tool is Rs.10 per year and the cost of placing an order is Rs.80. (a) What is the total cost associated with placing one, two, five, and ten orders per year? (b) What is the economic order quantity?

Solution:

a.

No. of Order Orders Per Quantity Year (Q) (U/Q) Units

Ordering Cost (U/Q x F)

Rs.

Carrying Cost Total Cost Q/2xPxC of Ordering (where and Carrying PxC=Rs.10) Rs. Rs.

1 2 5 10

60,000 30,000 12,000 6,000

80 160 400 800 2 UF

300,000 150,000 60,000 30,000

300,080 150,160 60,400 30,800

2x60,000x 80 = 10

b. Economic Order Quantity (EOQ) =
PC = 980 units (approx)

2.

National Stores is trying to determine the economic order quantity for certain type of transformers. The firm sells 400 numbers of this transformers annually at a price of Rs.300 per piece. The purchase price per machine tool to the firm is, however, Rs.230. The cost of carrying a transformer is Rs.40 per year and the cost of placing an order is Rs.180. (a) What is the total cost associated with placing one, four, eight , and ten orders per year? (b) What is the economic order quantity?

Solution:

a.

No. of Order Orders Per Quantity Year (Q) (U/Q) Units

Ordering Cost (U/Q x F)

Rs.

Carrying Cost Total Cost Q/2xPxC of Ordering (where and Carrying PxC=Rs.40) Rs. Rs.

1 4 8 10

400 100 50 40

180 720 1440 1800

8,000 2,000 1,000 800

8,180 2,720 2,440 2,600

2 UF b. Economic Order Quantity (EOQ) =
PC

2x 400x 180 = 40

= 60 units

3.

Harilal Company requires 25,000 units of a certain item per year. The purchase price per unit is Rs.60; the carrying cost per year is 30 percent of the inventory value; and the fixed cost per order is Rs.400. (a) Determine the economic order quantity. (b) How many times per year will inventory be ordered, if the size is equal to the EOQ? (c) What will be the total cost of carrying and ordering inventories when 10 orders are placed per year?

Solution: 2UF

a EOQ =
PC U=25,000 , F=Rs.400, PC= Rs.60 x 0.30 =Rs.18

2 x 25,000 x 400
EOQ =

= 1054 units. 18 25,000

= 23.72 1,054 Note that though fractional orders cannot be placed, the number of orders relevant for the year will be 23.72 . In practice 24 orders will be placed during the year. However, the 24th order will serve partly(to the extent of 72 percent) the present year and partly(to the extent of 28 per cent) the following year. So only 72 per cent of the ordering cost of the 24th order relates to the present year. Hence the ordering cost for the present year will be 23.72 x Rs.400 = Rs.9,488 c. Total cost of carrying and ordering inventories 1054 = [ 23.72 x 400 + x 18 ] = Rs.18,974 2 4. Kamal and Company requires 50,000 units of a certain item per year. The purchase price per unit is Rs.20; the carrying cost per year is 15 percent of the inventory value; and the fixed cost per order is Rs.100. (a) Determine the economic order quantity. (b) How many times per year will inventory be ordered, if the size is equal to the EOQ? (c) What will be the total cost of carrying and ordering inventories when 10 orders are placed per year? Solution:
2UF

b. Number of orders that will be placed is

a EOQ =
PC U=50,000 , F=Rs.100, PC= Rs.20 x 0.15 =Rs.3

2 x 50,000 x 100
EOQ =

= 1826 units.(approximately) 3 50,000

b. Number of orders that will be placed is

= 27.38

1,826 Note that though fractional orders cannot be placed, the number of orders relevant for the year will be 27.38 . In practice 28 orders will be placed during the year. However, the 28th order will serve partly(to the extent of 38 percent) the present year and partly(to the extent of 62 per cent) the following year. So only 38 per cent of the ordering cost of the 28th order relates to the present year. Hence the ordering cost for the present year will be 27.38 x Rs.100 = Rs.2,738 c. Total cost of carrying and ordering inventories

1826 = [ 27.38 x 100 + 2 5. Consider the following data for a certain item purchased by Jaibharat Stores.. Annual usage = 10,000 units Fixed cost per order = Rs.200 Purchase price per unit = Rs.160 Carrying cost = 25 percent of inventory value What is the economic order quantity? Now, assume that a discount of Rs.6 per unit is offered if the order size is 2,000 units. Should Jaibharat seek the quantity discount? x 3 ] = Rs.5477

Solution: U=10,000, F=Rs.200 , PC =Rs.160 x 0.25 =Rs.40

EOQ =

2 x 10,000 x 200 = 316 units (approximately) 40
U U Q* Q’ FQ’(P-D)C Q* PC

?? = UD +

2

2

10,000 = 10,000 x 6 + 316 -

10,000 x 200 2,000

2,000 (154)0.25 2 -

316 x 160 x 0.25 2

= 60,000 + 5329 – 32,180 = Rs.33,149 6. Consider the following data for a certain item purchased by Liberty Stores. Annual usage = 25,000 units Fixed cost per order = Rs.400 Purchase price per unit = Rs.360 Carrying cost = 35 percent of inventory value What is the economic order quantity? Now, assume that a discount of Rs.10 per unit is offered if the order size is 3,000 units. Should Liberty seek the quantity discount?

Solution: U=25,000, F=Rs.400 , PC =Rs.360 x 0.35 =Rs.126

EOQ =

2 x 25,000 x 400 = 399 units (approximately) 126
U U Q* Q’ FQ’(P-D)C Q* PC

?? = UD +

2

2

25,000 = 25,000 x 10 + 399 -

25,000 x 400 3,000

3,000 (350)0.35 2 -

399 x 360 x 0.35 2

= 250,000 + 21,729 – 158,613 = Rs.113,116 7. Shaheed Corporation requires 10,000 units of a certain item annually. The cost per unit is Rs.50, the fixed cost per order is Rs.200, and the inventory carrying cost is Rs.8 per unit per year. The supplier offers quantity discount as follows: Order Quantity 2,000 3,000 What should Shaheed Corporation do?
Solution: U=10,000 , F= Rs.200 , PC= Rs.50 x 0.16 = Rs.8

Discount Percentage 6 8

2 x 10,000 x 200 = 707 units 8 If 2000 units are ordered the discount is : .06 x Rs.50 = Rs.3 Change in profit when 2,000 units are ordered is :
EOQ =

10,000
?? = 10,000 x 3 +

10,000 x 200 2,000 707 x 50 x 0.16

707 2000 x 47 x 0.16 2 -

= 30,000 + 1829- 4692 =Rs.27,137 2

If 3000 units are ordered the discount is : .08 x Rs.50 = Rs.4 Change in profit when 3,000 units are ordered is : 10,000 10,000 x 200707 3000 3000x46x0.16 2 707x50x0.16 2

?? = 10,000 x 4.0 +

= 40,000 +2162– 8,212 = Rs. 33,950 As the change in profit is more when the discount on 3000 units is availed of, that option is the preferred one. 8. Merit International requires 15,000 units of a certain item annually. The cost per unit is Rs.80, the fixed cost per order is Rs.350, and the inventory carrying cost is Rs.10 per unit per year. The supplier offers quantity discount as follows:
Order Quantity 3,000 5,000 Discount Percentage 4 7

What should Merit International do?
Solution: U=15,000 , F= Rs.350 , PC= Rs.80 x 0.125 = Rs.10

2 x 15,000 x 350
EOQ =

= 1025 units

10 If 3000 units are ordered the discount is : .04 x Rs.80 = Rs.3.20 Change in profit when 3,000 units are ordered is : 15,000
?? = 15,000 x 3.2 +

15,000 x 350 3,000

1025

3000 x 76.8 x 0.125 2 -

1025 x 80 x 0.125 = 48,000 + 3372- 9,275 =Rs.42.097 2

If 5000 units are ordered the discount is : .07 x Rs.80 = Rs.5.6 Change in profit when 5,000 units are ordered is : 15,000 15,000 x 3501025 5000 5000x 74.4 x0.125 1025x80x0.125 2 2

?? = 15,000 x 5.6 +

= 84,000 +4072– 18,125 = Rs. 69,947 As the change in profit is more when the discount on 5000 units is availed of, that option is the preferred one. 9. Gulfstar Corporation requires steel for its fabrication work. The probability distributions of the daily usage rate and the lead time for procurement are given below. These distributions are independent.
Daily usage rate in tonnes 5 7 9 Probability Lead time in days 4 6 10 Probability

.2 .5 .3

.5 .3 .2

The stockout cost is estimated to be Rs.5,000 per ton. The carrying cost is Rs.2,000 per ton per year. Required: (a) What is the optimal level of safety stock? (b) What is the probability of stockout? Solution: The quantities required for different combinations of daily usage rate(DUR) and lead times(LT) along with their probabilities are given in the following table LT (Days) DUR (Units) 4(0.5) 6(0.3) 10(0.2)

5(0.2) 20*(0.10) 30(0.06) 50(0.04) 7(0.5) 28 (0.25) 42(0.15) 70(0.10) 9(0.3) 36 (0.15) 54(0.09) 90(0.06) The normal (expected) consumption during the lead time is :

20x0.10 + 30x0. 06 + 50x0.04+ 28x0.25 + 42x0.15 + 70x0.10 + 36x0.15 + 54x0.09 + 90x0.06 = 41.76 tonnes a. Costs associated with various levels of safety stock are given below :

Safety Stock*

Stock outs(in tonnes) 2

Stock out Cost

Probability

Expected Stock out

Carrying Cost

Total Cost

1

3

4

5 [3x4]

6 [(1)x2,000]

7 [5+6]

Tonnes 48.24 28.24

0 20

0 100,000

0 0.06

Rs. 0 6,000

Rs. 96,480 56,480

Rs. 96,480 62,480

12.24

16 36

80,000 180,000

0.10 0.06

8,000 10,800 18,800 1,800 10,000 12,000 23,800 1,600 5,400 14,000 14,400 35,400 180 1,648 5,508 14,120 14,472 35.928

24,480

43,280

8.24

4 20 40

20,000 100,000 200,000

0.09 0.10 0.06

16,480

40,280

0.24

8 12 28 48

40,000 60,000 140,000 240,000

0.04 0.09 0.10 0.06

480 35,880

0

0.24 8.24 12.24 28.24 48.24

1,200 41,200 61,200 141,200 241,200

0.15 0.04 0.09 0.10 0.06

0

35,928

So the optimal safety stock= 0.24 tonnes Reorder level = Normal consumption during lead time + safety stock K= 41.76 + 0.24 = 42 tonnes

b. Probability of stock out at the optimal level of safety stock = Probability (consumption being 50, 54, 70 or 90 tonnes) Probability (consumption = 50 tonnes) + Probability (consumption = 54 tonnes) + Probability (consumption = 70 tonnes) + Probability (consumption = 90 tonnes) = 0.04 +0.09+0.10 + 0.06 = 0.29 10. Five Star Limited requires steel for its fabrication work. The probability distributions of the daily usage rate and the lead time for procurement are given below. These distributions are independent.
Daily usage rate in tonnes 2 3 4 Probability Lead time in days 5 8 10 Probability

.4 .4 .2

.1 .6 .3

The stockout cost is estimated to be Rs.7,000 per ton. The carrying cost is Rs.1,500 per ton per year. Required: (a) What is the optimal level of safety stock? (b) What is the probability of stockout?
Solution:

The quantities required for different combinations of daily usage rate(DUR) and lead times(LT) along with their probabilities are given in the following table LT (Days) DUR (Units) 5(0.1) 8(0.6) 10(0.3)

2(0.4) 3(0.4) 4(0.2)

10(0.04) 15 (0.04) 20(0.02)

16(0.24) 24(0.24) 32(0.12)

20(0.12) 30(0.12) 40(0.06)

The normal (expected) consumption during the lead time is : 10x0.04 + 16x0. 24 + 20x0.012+ 15x0.04 + 24x0.24 + 30x0.12 + 20x0.02 + 32x0.12 + 40x0.06 = 23.24 tonnes

c.

Costs associated with various levels of safety stock are given below :

Safety Stock*

Stock outs(in tonnes) 2

Stock out Cost

Probability

Expected Stock out

Carrying Cost

Total Cost

1

3

4

5 [3x4]

6 [(1)x1,500]

7 [5+6]

Tonnes 16.76 8.76

0 8

0 56,000

0 0.06

Rs. 0 3,360

Rs. 25,140 13,140

Rs. 25,140 16,500

6.76

2 8

14,000 56,000

0.12 0.06

1,680 3,360 5,040 5,040 6,720 6,720 18,480

10,140

15,180

0.76

6 8 16

42,000 56,000 1,12,000

0.12 0.12 0.06

1,140

19,620

0

0.76 6.76 8.76 16.76

5,320 47,320 61,320 117,320

0.24 0.12 0.12 0.06

1,277 5,678 7,358 7,039 0 21,352 21,352

So the optimal safety stock= 6.76 tonnes Reorder level = Normal consumption during lead time + safety stock K= 23.24 + 6.76 = 30 tonnes d. Probability of stock out at the optimal level of safety stock = Probability (consumption being 30, 32, or 40 tonnes) Probability (consumption = 30 tonnes) + Probability (consumption = 32 tonnes) + Probability (consumption = 40 tonnes) = 0.12 +0.12+ 0.06 = 0.30

11.

The information about annual usage and price for 12 items used by a firm is as given here.
Item Annual Usage (Number of Units) 600 30 4,000 2,000 400 6,000 3,200 1,600 Price per Unit (Rs) Item Annual Usage (Number of Units) Price per Unit (Rs)

1 2 3 4 5 6 7 8

30.00 200.00 5.00 12.00 100.00 75.00 48.00 10.00

9 10 11 12 13 14 15

16,500 700 3,800 1,000 12,000 400 200

3.00 40.00 200.00 67.00 16.00 120.00 800.00

Required: (a) rank the items of inventory on the basis of annual usage value; (b) record the cumulative usage in value; (c) show the cumulative percentages of usage of items; (d) classify the items into three classes, A, B and C
Solution: Annual Usage(in Units) 600 30 4,000 2,000 400 6,000 3,200 Price per Unit Rs. 30.00 200.00 5.00 12.00 100.00 75.00 48.00 10.00 Annual Usage (in Units) Rs. 18,000 6,000 20,000 24,000 40,000 450,000 153,600

Item

Ranking

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

13 15 12 11 9 2 5 14 7 10 1 6 3 8 4

1,600 16,500 700 3,800 1,000 12,000 400 200

16,000 49,500 28,000 760,000 67,000 192,000 48,000 160,000

3.00 40.00 200.00 67.00 16.00 120.00 800.00

Cumulative Value of Items & Usage Annual Usage Value (Rs.) 760,000 450,000 192,000 160,000 153,600 67,000 49,500 48,000 40,000 28,000 24,000 20,000 18,000 16,000 6,000 Cumulative Annual Usage Value(Rs.) 760,000 1,210,000 1,402,000 1,562,000 1,715,600 1,782,600 1,832,100 1,880,100 1,920,100 1,948,100 1,972,100 1,992,100 2,010,100 2,026,100 2,032,100

Item no.

Rank

Cumulative % of Usage Value

Cumulative % of Items

11 6 13 15 7 12 9 14 5 10 4 3 1 8 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

37.40 59.54 68.99 76.87 84.42 87.72 90.16 92.52 94.49 95.87 97.05 98.03 98.92 99.70 100.00

6.67 13.33 20.00 26.67 33.33 40.00 46.67 53.33 60.00 66.67 73.33 80.00 86.67 93.33 100

CHAPTER 30

1.

What is the annual percentage interest cost associated with the following credit terms? (a) 2/15 net 30 (b) 3/10 net 30 (c) 2/10 net 45 (d) 1/5 net 15

Assume that the firm does not avail of the cash discount but pays on the last day of the net period.
Solution:

Annual interest cost is given by , Discount % x 1- Discount % Credit period – Discount period 360

Therefore, the annual per cent interest cost for the given credit terms will be as follows: a. 0.02 x 0.98 15 360 = 0.4898 = 48.98 %

b.

0.03 x 0.97

360 = 0.5567 20 360 x = 0.2099 35 360 x = 0.3636 10 = 36.36 % = 20.99 % = 55.67 %

c.

0.02 0.98

d.

0.01 0.99

2.

Calculate the annual percentage interest cost of various terms in problem 1 above, assuming that it is possible to stretch payment 20 days beyond the net period.

Solution:

a.

0.02 x 0.98

360 = 0.2099 35 360 x = 0.2784 40 360 x = 0.1336 55 360 x = 0.1212 30 = 12.12 % = 13.36 % = 27.84 % = 20.99 %

b.

0.03 0.97

c.

0.02 0.98

d.

0.01 0.99

3.

Consider the data for Kanishka Limited. Current assets Rs (in million) Raw material 40 Work-in-process 8 Finished goods 25 Other current assets 3 76 Current liabilities Trade creditors Bank borrowing (including Bills Discounted) 30 10

Other current liabilities

4 44

What is the maximum permissible bank finance for Kanishka Limited under the three methods suggested by the Tandon Committee? Assume that the core current assets for Kanishka Limited are Rs.15 million.
Solution:

The maximum permissible bank finance under the three methods suggested by The Tandon Committee are : Method 1 : 0.75(CA-CL) = 0.75(76-44) = Rs.24 million Method 2 : 0.75(CA)-CL = 0.75(76)-44 = Rs. 13 million Method 3 : 0.75(CA-CCA)-CL = 0.75(76-15)-44 = Rs.1.75 million 4. Consider the data for Smartlink Corporation. Current assets Raw material Work-in-process Finished goods Other current assets Rs (in million) 280 58 240 68 646 Current liabilities Trade creditors Bank borrowing (including Bills Discounted) Other current liabilities 160 200 42 402 What is the maximum permissible bank finance for Smartlink Corporation under the three methods suggested by the Tandon Committee? Assume that the core current assets for Smartlink Corporation are Rs.100 million.

Solution:

The maximum permissible bank finance under the three methods suggested by The Tandon Committee are: Method 1 : 0.75(CA-CL) = 0.75(646 -402) = Rs.183 million Method 2 : 0.75(CA)-CL = 0.75(646) - 402 = Rs.82.5 million. Method 3 : 0.75(CA-CCA)-CL = 0.75(646 -100)- 402 = Rs.7.5 million
CHAPTER 31 MINICASE 1

Vikram Thapar, CFO of Aman corporation, recently attended a seminar conducted by an internationally renowned expert on credit analysis. Among various ideas and techniques presented in that seminar, the technique of discriminant analysis impressed him. He felt that it could be applied for classifying the credit applicants of Aman Corporation into ‘good’ and ‘bad’ categories. He asked Sudarshan, a finance executive in his department who recently graduated from a leading business school, to explore the possibility to using discriminant analysis for credit evaluation in Aman Corporation. Sudarshan suggested that the two ratios that are likely to be most helpful in discriminating between the ‘good’ and ‘bad’ accounts are : (i) current ratio (Current assets / Current liabilities), and (ii) the earning power (PBIT/Capital employed) Vikram Thapar concurred with Sudarshan’s suggestion. Sudarshan gathered information on 18 accounts, 10 ‘good’ and 8 ‘bad’, which is given below. A ‘good’ account is an account which pays within the stipulated credit period and a ‘bad’ account is an account which does not pay within the stipulated credit period.
Good Accounts Xi Yi Account Earning number Current power (%) ratio 1 1.20 16 2 1.30 17 3 1.40 14 4 1.00 20 5 1.50 13 6 1.60 12 7 1.80 15 Bad Accounts Xi Yi Current Earning ratio power (%)

Account number

11 12 13 14 15 16 17

1.10 1.00 1.20 0.90 1.10 1.20 0.90

9 – 6 6 8 4 10 7

8 9 10

1.60 1.20 1.40

10 15 8

18 19 20

1.10 0.80 0.70

2 6 4

Required: Estimate the discriminant function which best discriminates between the ‘good’ and ‘bad’ applicants. Solution:

Account Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Xi 1.2 1.3 1.4 1.0 1.5 1.6 1.8 1.6 1.2 1.4 1.1 1.0 1.2 0.9 1.1 1.2 0.9 1.1 0.8 0.7

Yi 16 17 14 20 13 12 15 10 15 8 9 -6 6 8 4 10 7 2 6 4

Xi - X 0 0.1 0.2 -0.2 0.3 0.4 0.6 0.4 0.0 0.2 -0.1 -0.2 0.0 -0.3 -0.1 0 -0.3 -0.1 -0.4 -0.5

Yi – Y 6.5 7.5 4.5 10.5 3.5 2.5 5.5 0.5 5.5 -1.5 -0.5 -15.5 -3.5 -1.5 -5.5 +0.5 -2.5 -7.5 -3.5 -5.5

(Xi – X)2 0 .01 0.04 0.04 0.09 0.16 0.36 0.16 0.0 0.04 0.01 0.04 0 0.09 0.01 0 0.09 0.01 0.16 0.25

(Yi – Y)2 42.25 56.25 20.25 110.25 12.25 6.25 30.25 0.25 30.25 2.25 0.25 240.25 12.25 2.25 30.25 0.25 6.25 56.25 12.25 30.25

?(Xi – X) (Yi –Y)

0 0.75 0.90 -2.10 1.05 1.00 3.3 0.2 0 -0.3 .05 3.1 0 0.45 0.55 0 0.75 0.75 1.4 2.75
?(Xi – X) (Yi-Y )

?Xi = 24.0 ?Yi = 190 ? (Xi –X)2 = 1.56

?(Yi –Y)2

X=1.2

Y = 9.5

=701

= 14.6

14.0 X1 = 10 100 X2 = 10 dx = 0.4 = 1.0 =1.4 Y1 =

140 =14% 10 50 Y2 = 10 = 5%

?x2 =

1.56 = .082 19

?y2 =

701 =36.89 19 14.6

?xy =

= 0.768 19

dy = 9%

?y2.dx - ?xy.dy

36.89 x 0.4 – 0.768 x 9 = 0.082 x 36.89 – 0.768 x 0.768 =

14.756 – 6.912 3. 025– 0.590

a=

?x2.?y2 - ?xy.?xy

7.844 = 2.435
?x2.dy - ?xy.dx

= 3.221

0.082 x 9.0 – 0.768 x 0.4 = 0.082 x 36.89 – 0.768 x 0.768

b=

?x2.?y2 - ?xy.?xy

0.431 = 2.435 The discriminant function is: Zi = 3.221Xi + 0.177 Yi MINICASE 2 Somnath, Finance Director of Apex Electronics, was looking at ways and means of improving credit evaluation of the potential customers of Apex. He called Ravi, a product of a premier business school from Australia, who joined the finance department of Apex recently, for a discussion. Ravi showed Somnath a project on discriminant analysis that he had done as part of his graduate studies in business. In that project Ravi had considered four independent variables. Somnath thought that Apex could also use discriminant analysis. However, to begin with he felt that a discriminant model with two independent variables may be used. Ravi concurred with this view. Somnath and Ravi discussed this issue with the finance team of Apex. The consensus view that emerged during the discussion was that the most appropriate ratios would be (i) ROE (PAT/Net worth) and (ii) Current Ratio (Current Assets / Current Liabilities). The group felt that a linear discriminant function of these two ratios would be helpful in discriminating between the ‘good’ and ‘bad’ accounts. Ravi gathered information on 20 accounts, 10 ‘good’ and 10 ‘bad’ which is given below. A ‘good’ account is an account which pays within the stipulated credit period and a ‘bad’ account is an account which does not pay within the stipulated period. = 0.177

Account Number

1 2 3 4 5 6 7 8 9 10

Good Accounts Yi Xi Current ROE ratio 18% 1.50 15% 1.80 13% 1.20 20% 1.30 12% 1.40 9% 1.10 16% 1.60 14% 1.20 6% 1.50 25% 1.10

Bad Accounts Account Number Xi ROE Yi Current ratio 1.10 1.20 0.90 1.10 1.00 1.40 1.10 1.20 1.10 1.20

11 12 13 14 15 16 17 18 19 20

-5% 8% 9% 6% 11% 5% 10% 7% - 6% 4%

Required: Estimate the discriminant function that best discriminates between the ‘good’ and ‘bad’ accounts. Solution:

Account Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Xi 18 15 13 20 12 9 16 14 6 25 -5 8 9 6 11 5 10 7 -6 4

Yi 1.5 1.8 1.2 1.3 1.4 1.1 1.6 1.2 1.5 1.1 1.1 1.2 0.9 1.1 1.0 1.4 1.1 1.2 1.1 1.2

Xi - X 8.15 5.15 3.15 10.15 2.15 -0.85 6.15 4.15 -3.85 15.15 -14.85 -1.85 -0.85 -3.85 1.15 -4.85 0.15 -2.85 -15.85 -5.85

Yi – Y 0.25 0.55 -0.05 0.05 0.15 -0.15 0.35 -0.05 0.25 -0.15 -0.15 -0.05 -0.35 -0.15 -0.25 0.15 -0.15 -0.05 -0.15 -0.05

(Xi – X)2 66.4225 26.5225 9.9225 103.0225 4.6225 0.7225 37.8225 17.2225 14.8225 229.5225 220.5225 3.4225 0.7225 14.8225 1.3225 23.5225 0.0225 8.12 251.2225 34.2225

(Yi – Y)2 0.0625 0.3025 0.0025 0.0025 0.0025 0.0225 0.1225 0.0025 0.0625 0.0225 0.0225 0.0025 0.1225 0.0225 0.0625 0.0225 0.0225 0.0025 0.0225 0.0025 0.93

(Xi – X) (Yi -Y) 2.0375 2.8325 -0.1575 0.5075 0.3225 0.3225 2.1525 -0.2075 -0.9625 -2.2725 2.2275 0.0925 0.2975 0.5775 -0.2875 -0.7275 -0.0225 0.1425 2.3775 0.2925 9.35

197 Y= 25

?(Xi-X)2=1068.55

?X = 197 197 X= = 9.85 20 ?X1 = 148

?Y = 25 25 Y= = 1.25 20 ?Y1 = 13.7

?(X1 – X) = 1,068.55 ?x2 = ? (X1 – X) 1–n

148 = 14.8 10 ?X2 = 49 49 X2 = = 4.9 10 X1 Y1 =

13.7 1.37 10 ?Y2 = 11.3 11.3 Y2 = = 1.13 10

= 1068.55 19 = 56.2395

?(Y1 – Y) = 0.93 ?y2 = 0.93 19 = 0.0489

dx = X1 – X2 dy = Y1 – Y2 = 14.8 – 4.9 = 1.37 – 1.13 = 9.9 = 0.24 9.35 ?(X1 – X) (Y1–Y) = 9.35 ?xy = = 0.4921 19 ?y2.dx - ?xy.dy 0.0489 x 9.9 – 0.4921 x 0.24 a= = ?x2.?y2 - ?xy.?xy 56.2395 x 0.489 – 0.4921 x 0.4921 0.3660 = 2.5079
?x2.dy - ?xy.dx

= 0.1459

56.2395 x 0.24 – 0.4921 x 9.9 = 56.2395 x 0.0489 – 0.4921 x 0.4921

b=

?x2?y2 - ?xy?xy

8.62569 = 2.5079 Discriminant function Z = 0.1459Xi + 3.4394Yi = 3.4394

MINICASE 3

Ram Kumar, the CFO of Impex Limited, was discussing with Sreedhar, a senior financial analyst in the company, the problem of judging the creditworthiness of the various customers of Impex Limited. Sreedhar suggested that discriminant analysis may be used for credit evaluation purposes. Ram Kumar concurred with this suggestion. Ram Kumar and Sreedhar felt that the two ratios that are likely to be most helpful in discriminating between the ‘good’ and ‘bad’ accounts are (i) earning power (PBIT/Capital employed) and (ii) quick ratio (Quick assets / Current liabilities). Sreedhar gathered information on 18 accounts, 10 ‘good’ and 8 ‘bad’ which is given below. A ‘good’ account is an account which pays within the stipulated credit period and a ‘bad’ account is an account which does not pay within the stipulated credit period.
Good Accounts Earning Quick power ratio Xi Yi 16% 0.70 20 0.80 17 1.00 12 0.90 14 0.70 13 1.00 7 0.90 15 1.10 10 0.90 15 0.80 Bad Accounts Earning Quick power ratio

Account Number

Account Number

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18

6% 9 4 -5 2 10 8 7

0.70 0.80 0.60 0.80 0.60 0.70 0.50 0.90

Required: Estimate the discriminant function which best discriminates between the ‘good’ and the ‘bad’ applicants. Solution:

Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Xi 16% 20 17 12 14 13 7 15 10 15 6 9 4 –5 2 10 8 7

Yi 0.70 0.80 1.00 0.90 0.70 1.00 0.90 1.10 0.90 0.80 0.70 0.80 0.60 0.80 0.60 0.70 0.50 0.90

Xi – X 6 10 7 2 4 3 –3 5 0 5 –4 –1 –6 –15 –8 0 –2 –3

Yi – Y –0.10 0 0.20 0.1 –0.1 0.2 0.1 0.3 0.1 0 –0.1 0 –0.2 0 –0.2 –0.1 –0.3 0.1

(Xi – X)2 36 100 49 4 16 9 9 25 0 25 16 1 36 225 64 0 4 9
?(Xi-X)2 = 628 ?x2

(Yi – Y)2 0.01 0 0.04 0.01 0.01 0.04 0.01 0.09 0.01 0 0.01 0 0.04 0 0.04 0.01 0.09 0.01
?(Y-Y)2 = 0.42

?(Xi-X) (Yi-Y) –0.6 0 1.4 0.2 –0.4 0.6 –0.3 1.5 0 0 0.4 0 1.2 0 1.6 0 0.6 –0.3 ?(Xi-X) (Yi-Y) = 5.9 ?xy =

?Xi=180 ?Yi=14.4 Xi= 10 Yi= 0.8

139 Xi =

8.8

628 = 17 = 36.94

1 x 5.9 17 = 0.347 0.42

Yi = 10 10 = 13.9% = 0.88 41 5.6 Y2 = 8 = 0.70 dy = 0.18

X2 = 8 = 5.1% dx = 8.8

?y2 =

17 = 0.025

?y2.dx – ?xy.dy

a=
?x2. ?y2 – ?xy. ?xy

0.025 x 8.8 – 0.347 x 0.18 = 36.94 x 0.025 – 0.347 x 0.347 Contd.

0.22 – 0.06246 a= 0.9235 – 0.1204 0.15754 = 0.8031 = 0.196
?x2.dy – ?xy.dx

b=

?x2.?y2 – ?xy.?xy

36.94 x 0.18 – 0.347 x 8.8 = 36.94 x 0.025 – 0.347 x 0.347 6.6494 – 3.0536 = 0.8031 = 4.4774 Z = aXi + bYi = 0.196Xi + 4.4774Yi

CHAPTER 32

1.

The profit and loss account and balance sheet of a company for two years (1 and 2) are given below. Assume a tax rate of 30 percent for year 2. Profit and Loss Account
• • • • • • • • • •

Net sales Income from marketable securities Non-operating income Total income Cost of goods sold Selling and administrative expenses Depreciation Interest expenses Total costs and expenses PBT

1 40,000 800 600 41,400 25,000 6,000 2,400 2,500 35,900 5,500

2 50,000 1,000 1,000 52,000 30,000 7,200 3,000 2,600 42,800 9,200

• • • • • • • • • •
*

Tax provision PAT Dividends Retained earnings Balance Sheet Equity capital Reserves and surplus Debt Fixed assets Investments (marketable securities)* Net current assets All of this represents excess marketable securities (i) What is the EBIT for year 2?

1,500 4,000 1,400 2,600 6,000 10,000 16,000 32,000 20,000 7,000 5,000 32,000

2,700 6,500 1,800 4,700 6,000 14,700 19,300 40,000 24,500 8,500 7,000 40,000

Solution:

Profit before tax + Interest expense Interest income Non – operating income

9200 + 2600 - 1000 - 1000 9,800

(ii)
Solution:

What is the tax on EBIT for year 2?

Tax provision from profit and loss account 2700 + Tax shield on interest expense Tax on interest income Tax on non - operating income Tax on EBIT 780 - 300 - 300 2880

(iii) What is the FCFF for year 2?
Solution:

EBIT - Tax on EBIT - Net investment + Non – operating cash flow (1000 x 0.7)

9,800 - 2,880 - 6,500 700 1120

(iv) Show the break-up of the financing flow
Solution:

After tax interest expense + + + Cash dividend Increase in borrowing
? Excess marketable securities

1820 + 1800 - 3300 + 1500

After tax income on excess marketable securities

- 700 1120

2.

The profit and loss account and balance sheet of a company for two years (1 and 2) are given below. Assume a tax rate of 30 percent for year 2. Profit and Loss Account
• • • • • • •

Net sales Income from marketable securities Non-operating income Total income Cost of goods sold Selling and administrative expenses Depreciation

1 30,000 600 400 31,000 18,000 3,800 1,900

2 35,000 1,000 800 36,800 21,000 4,600 2,200

• • • • • • • • • • • • •
*

Interest expenses Total costs and expenses PBT Tax provision PAT Dividends Retained earnings Balance Sheet Equity capital Reserves and surplus Debt Fixed assets Investments (marketable securities)* Net current assets All of this represents excess marketable securities

1,700 25,400 5,600 1,400 4,200 1,200 3,000 5,000 5,000 15,000 25,000 15,000 5,000 5,000 25,000

1,600 29,400 7,400 1,900 5,500 1,400 4,100 5,000 9,100 14,900 29,000 18,500 6,500 4,000 29,000

(i)
Solution:

What is the EBIT for year 2?

Profit before tax + Interest expense Interest income Non – operating income

7400 + 1600 - 1000 - 800 7200

(ii)
Solution:

What is the tax on EBIT for year 2?

Tax provision from income statement + Tax shield on interest expense Tax on interest income Tax on non - operating income Tax on EBIT

1900 480 - 300 - 240 1840

(iii) What is the FCFF for year 2?
Solution:

EBIT - Tax on EBIT - Net investment + Non – operating cash flow

7200 - 1840 - 2500 + 560 3420

(iv) Show the break-up of the financing flow
Solution:

Rs. in million After tax interest expense + + + Cash dividend Reduction in borrowing
? Excess marketable securities

1120 + 1400 + 100 + 1500

After tax income on excess marketable securities

- 700 3420

3.

The profit and loss account and the balance sheet for Magna Corporation for two years (year 1 and year 2) are given below :
Profit and Loss Account
• • • •

1

2

Net sales Income from marketable securities Non-operating income Total income

16800 420 210 17430

19320 630 420 20370

• • • • • • • • • •

Cost of goods sold Selling and administrative expenses Depreciation Interest expenses Total costs and expenses PBT Tax provision PAT Dividend Retained earnings
Balance Sheet

9660 2100 1050 1008 13818 3612 1092 2520 1260 1260
1

11340 2310 1260 1176 16086 4284 1344 2940 1680 1260
2

• • •

Equity capital Reserves and surplus Debt Fixed assets Investments Net current assets

6300 5040 7560 18900 12600 3780 2520 18900

6300 6300 8820 21420 13650 4200 3570 21420

• • •

Assume that the tax rate is 40 percent. (i) What is the EBIT (also called PBIT) for year 2?

Solution:

PBT + Interest expense - Interest income - Non-operating income

4284 +1176 - 630 - 420 4410

(ii)

What is the tax on EBIT for year 2 ?

Solution:

Tax provision from profit and loss account + Tax shield on interest expense - Tax on interest income - Tax on non-operating income Tax on EBIT

1344 + 470.4 - 252 - 168 1394.4

(iii) What is the NOPLAT for year 2 ?
Solution:

EBIT - Tax on EBIT

4410 - 1394.4 3015.6

(iv) What is the FCFF for year 2 ?
Solution:

NOPLAT - Net investment + Non-operating cash flow

3015.6 -2100.0 252.0 1167.6

4.

Boldman Sachs, an investment banking firm, is engaged in valuing MLF Realty, a firm which specialises in the construction of housing and commercial complexes. MLF is currently riding a construction boom and is expected to grow at a healthy

rate for the next four years at least. Thereafter the growth rate is expected to decline rather gradually for a few years before it stabilises at a modest level You have recently moved to Boldman Sachs after a few years of experience in another financial services firm. Your first assignment at Boldman Sachs is to value MLF. Based on extensive discussion with management and industry experts you have gathered the following information. Base Year (Year 0) Information -----------------------------------------------Revenues Rs. 1400 crore EBIT ( 20 % of revenues) Rs. 280 crore Capital expenditure Rs. 350 crore Depreciation and amortisation Rs. 266 crore Working capital as a percentage of revenues 20 percent Tax rate 30 percent (for all time to come) Inputs for the High Growth Period --------------------------------------------Length of the growth period = Growth rate in revenues, depreciation, EBIT and capital expenditure = Working capital as a percentage of revenues = Cost of debt( pre-tax) = Debt – equity ratio = Risk- free rate = Market risk premium = Equity beta = Inputs for the Transition Period ----------------------------------------• • Length of the transition period = Growth rate in revenues, depreciation, EBIT and Capital expenditures will decline from 25 percent in year 4 to 10 percent in year 7 in linear increments of 5 percent per year. Working capital as a percentage of revenues = The cost of debt, debt-equity ratio, risk –free rate, market risk premium and equity beta will be the same as in the high growth period. Inputs for the Stable Growth Period ---------------------------------------------Growth rate in revenues, EBIT, capital expenditure and depreciation = Working capital as a percentage of revenues = 3 years

• • • • • •

• • • • • • • •

4 years 25 percent 20 percent 10 percent 1.0 7.4 percent 6 percent 1.2667

• •

20 percent

• •

10 percent 20 percent

•

• •

The cost of debt, risk –free rate and market risk premium will be the same as in the previous stages. Debt-equity ratio Equity beta a.

= =

2:3 1.322

What is the cost of capital in the three periods( high growth, transition, and stable)? What value would you impute to MLF Realty using the DCF method?

Solution:

a.

WACC during the high growth and transit periods: -----------------------------------------------------------re = 7.4 + 6 x 1.2667 = 15 % WACC = 0.5 x 10 x ( 1 –0.30 ) + 0.5 x 15 = 11 % WACC during the stable period: --------------------------------------re = 7.4 + 6 x 1.322 = 15.332 % WACC = 2/5 x 10 x ( 1 – 0.30 ) + 3/5 x 15.332 = 12 %

b.
Period Growth Rate % EBIT EBIT (1-t) CAPEX

Dep 332.50 415.63 519.53 649.41 779.29 896.19 985.81

CAPEX DEP

WC
350 437.50 546.88 683.60 820.31 943.36 1037.70

? WC

FCFF

WACC (%)

PV

1 2 3 4 5 6 7

25 25 25 25 20 15 10

350 437.50 546.88 683.59 820.31 943.36 1037.70

245 306.25 382.82 478.51 574.22 660.35 726.39

437.50 546.88 683.59 854.49 1025.39 1179.19 1297.11

105 131.25 164.06 205.08 246.10 283.00 311.30

70 87.5 109.37 136.73 136.72 123.05 94.34

70 87.5 109.37 136.7 191.4 254.3 320.75

11 11 11 11 11 11 11

63.06 71.02 79.98 90.05 113.58 135.96 154.49 708.14

FCFF8 = FCFF7 (1.10) = 320.75 x (1.10) = 352.83 Terminal Value = FCFF8 352.83 --------------- = -----------WACC – g 0.12 – 0.10 = 17641.50

Present value of terminal value = 17641.50 / (1.11 )7 = Present value of FCFF in the high growth and transit periods = Value of the firm

8497.01 708.14 --------------= Rs. 9205.15 crores

5.

Multisoft Limited was set up about twelve years ago by a product-minded technocrat. In the first five years, the company did exceptionally well, thanks to the excellent response received by three of its initial products. The company recorded a compound annual growth rate of 80 percent during this period. Subsequently, however, the company floundered, as its product offerings were superceded by the offerings of competitiors. In response, the management of Multisoft emphasised software services. This strategy has worked well and the company’s performance improved significantly in the last few years. The management is quite optimistic about future and believes that its growth is more predictable now. Recently, Gautam Prabhu, the CEO of Multisoft Limited had a very fruitful discussion with the CEO of Matrix Software wherein they explored the possibility of a merger. Gautam Prabhu believes that the compensation for the merger, if consummated, will be in the form of the stock of Multisoft Limited. He has requested you to value the equity of Multisoft and asked his CFO, Ranjan Kaul, to provide you with the information about the current and projected financials of Multisoft. The following information has been provided to you.
Base Year (Year 0) Information • • • • • • • •

Revenues EBIT Capital expenditure Depreciation Working capital as a percentage of revenues Corporate tax rate Paid up capital (Rs.10 par) Market value of debt

Rs. 2000 million Rs. 750 million Rs. 500 million Rs. 140 million 30 percent 15 percent Rs. 600 million Rs. 300 million

Inputs for the High Growth Period • • • • • • • • •

Length of the high growth period Growth rate in revenues, depreciation, EBIT and capital expenditure Working capital as a percentage of revenues Cost of debt (pre-tax) The tax rate will increase to 30 percent in linear increments of 5 percent per year Debt-equity ratio Risk-free rate Market risk premium Equity beta

= = = =

3 years 40 percent 30 percent 10 percent

= = = =

0.5 : 1 7 percent 6 percent 1.3

Inputs for the Transition Period • • • • • • • • •

Length of the transition period Growth rate in revenues, depreciation, EBIT, and capital expenditures will decline from 40 percent in year 3 to 10 percent in year 8 in linear increments of 6 percent each year Working capital as a percentage of revenues Debt-equity ratio Cost of debt (pre-tax) Risk-free rate Market risk premium Equity beta Tax rate
Inputs for the Stable Growth Period

= 5 years

= 30 percent = 0.5 : 1 = 10 percent = 6 percent = 7 percent = 1.2 = 30 percent

• • • • • • • •

Growth rate in revenues, EBIT, capital expenditure, and depreciation Working capital as a percentage of revenues Debt-equity ratio Cost of debt (pre-tax terms) Risk-free rate Market risk premium Equity beta Tax rate

= 10 percent = 30 percent = 0.284 : 1 = 10 percent = 7 percent = 7 percent = 1.1 = 30 percent

Required a. b. c. d. What will be the WACC (upto one decimal point) year-wise? What is the present value of the FCF in the high growth period? What is the present value of the FCF in the transition period? What is the present value of the terminal value? (Answers to (b), (c), and (d) must be in rupees in million upto one decimal point) What is the intrinsic value per share?

e.

Solution:

(a) WACC High growth period Year Cost of equity 1 7 + 1.3 (6) =14.8% 2 7 + 1.3 (6) = 14.8% 3 7 + 1.3 (6) = 14.8% Cost of debt 10 (1 – 0.20) = 8% 10 (1 – 0.25) = 7.5% 10 (1 – 0.30) = 7 .0% Transition period Cost of equity 6 + 1.2 (7) = 14.4% 1/3 x 7 = 11.9 WACC 10 (1 – 0.3) = 7% Cost of debt 2/3 x 14.4 + WACC 2/3 x 14.8 + 1/3 x 8 = 12.5 2/3 x 14.8 + 1/3 x 7.5 = 12.4 2/3 x 14.8 + 1/3 x 7.0 = 12.2

Stable period Cost of equity WACC 7 + 1.1 (7) = 14.7% Cost of debt 10 (1 – 0.3) = 7% 1/1.284 x 14.7 + 0.284 /1.284 x 7 = 13.0%

Year 0 1 2 3 4 5 6 7 8 9

Growth rate %

EBIT 750

Tax rate (%) 15 20 25 30 30 30 30 30 30 30

EBIT (1 –T)

Capex
500

Deprn 140 196 274.4 384.2 514.8 658.9 803.9 932.5 1025.7 1128.3

WC 600 840 1176 1646.4 2206.2 2823.9 3445.2 3996.4 4396.0 4835.6

? WC

FCF

WACC %

PV Factor

PV

40 40 40 34 28 22 16 10 10

1050 1470 2058 2757.7 3529.9 4306.5 4995.5 5495.0 6044.5

840 1102.5 1440.6 1930.4 2470.9 3014.5 3496.8 3846.5 4231.2

700 980 1372 1838.5 2353.3 2871.0 3330.3 3663.4 4029.7

240 336 470.4 559.8 617.7 621.3 551.2 399.6 439.6

96 60.9 (17.6) 46.9 158.8 326.1 547.8 809.2 890.2

12.5 12.4 12.2 11.9 11.9 11.9 11.9 11.9 13.0

0.889 0.791 0.705 0.630 0.563 0.503 0.450 0.402 0.356

85.3 48.2 (12.4) 29.5 89.4 164.0 246.5 325.3 316.9

(b)

Present value of FCF in the high growth period = 85.3 + 48.2 – 12.4 = Rs.121.1 million

(c)

PV of FCF in the transition period = 29.5 + 89.4 + 164 .0 + 246.5 + 325.3 = Rs.854.7 million

(d) PV of terminal value 890.2 = x 0.402 = Rs.11928.7 million 0.13 – 0.10 (e) Intrinsic value per share Value of firm – Value of debt Number of shares 121.1 + 854.7 + 11928.7 - 300 = 60 = Rs.210.1

6.

Telesoft International was set up seven years ago to develop telecommunication software. Though the company started with a bang, it entered a turbulent phase because of the shrinkage in the global telecom market in the initial years of this decade. Thanks to recovery in the last 18 months or so and a firm indication of strong growth in the next few years, the management of Telesoft International is quite upbeat about the future. Recently, Pankaj Behl, the CEO of Telesoft International had a preliminary dialogue with the CEO of a another company engaged in developing telecommunication software to explore a possible merger. Both the CEOs felt enthusiastic about this. Pankaj Behl believes that the compensation for the merger, if consummated, will be in the form of the stock of Telesoft International. He has requested you to value the equity of Telesoft and asked Vijay Rao, Finance Director, Telesoft International to provide you with information about the current and projected financials of Telesoft International. The following information has been provided to you. Base Year (Year 0) Information Revenues EBIT Capital expenditure Depreciation Working capital as a percentage of revenues Corporate tax rate Paid up equity capital (Rs.10 par) Market value of debt = Rs. 1200 million = Rs. 350 million = Rs. 280 million = Rs. 140 million = 30 percent = 10 percent = Rs. 300 million = Rs. 300 million

Inputs for the High Growth Period

Length of the high growth period Growth rate in revenues, depreciation, EBIT and capital expenditure Working capital as a percentage of revenues Cost of debt Tax rate will increase to 30 percent in linear increment of 5 percent Debt-equity ratio Risk-free rate Market risk premium Equity beta
Inputs for the Transition Period

= 4 years = 30 percent = 30 percent = 10 percent (pre-tax)

= 0.8:1 = 7 percent = 7 percent = 1.4

Length of the transition period Growth rate in revenues, depreciation, EBIT, and capital expenditures will decline from 30 percent in year 4 to 10 percent in year 8 in linear increments of 5 percent each year Working capital as a percentage of revenues Debt-equity ratio Cost of debt Risk-free rate Market risk premium Equity beta Tax rate

= 4 years

= 30 percent = 0.8:1 = 10 percent (pre-tax) = 8 percent = 6 percent = 1.1 = 30 percent

Inputs for the Stable Growth Period Growth rate in revenues, EBIT, capital expenditure and = 10 percent depreciation Working capital as a percentage of revenues = 30 percent Debt-equity ratio = 0.5:1.0 Cost of debt = 10 percent (pre-tax) Risk-free rate = 8 percent Market risk premium = 7 percent Equity beta = 1.0 Tax rate = 30 percent

a. b. c. d. e.

What will be the WACC, year-wise? What is the present value of the FCF in the high growth period? What is the present value of the FCF in the transition period? What is the present value of the terminal value? What is the intrinsic value value per share?

Solution:

(a) WACC
High growth period

Year 1 2 3 4

Cost of equity 7 + 1.4 x (7) = 16.8% 7 + 1.4 x (7) = 16.8% 7 + 1.4 x (7) = 16.8% 7 + 1.4 x (7) = 16.8%

Cost of debt 10 (1 – 0.15) = 8.5% 10 (1 – 0.20) = 8.0% 10 (1 – 0.25) = 7.5% 10 (1 – 0.30) = 7.0%

WACC (5/9)x16.8 + (4/9)x8.5 = 13.1% (5/9)x16.8 + (4/9)x8.0 = 12.9% (5/9)x16.8 + (4/9)x7.5 = 12.7% (5/9)x16.8 + (4/9)x7.0 = 12.4%

Cost of equity 8 + 1.1(6) = 14.6%

Transition period Cost of debt 10(1-0.3) = 7.0%
Stable period Cost of debt 10 (1-0.3) = 7%

WACC (5/9) x 14.6 + (4/9) x 7 = 11.2%

Cost of equity 8 + 1.0 (7) = 15.0% (b)

WACC (2/3) 75.0 + (1/3) x 7.0 = 12.3%

Tax Year Growth EBIT rate EBIT Cap Dep’n WC ?WC FCF WACC PV PV of % (1-T) Exp rate% % Factor FCF 0 350 10 280 140 360 1 2 3 4 5 6 7 8 9 30 30 30 30 25 20 15 10 10 455 592 769 1000 1250 1499 1724 1897 2087 15 20 25 30 30 30 30 30 30 387 474 577 700 875 1049 1207 1328 1461 364 473 615 800 1000 1200 1379 1517 1669 182 237 308 400 500 600 690 759 835 468 608 791 1028 1285 1542 1774 1951 2146 108 140 183 237 257 257 232 177 195 97 98 87 63 118 192 286 393 432 13.1% 12.9% 12.7% 12.4% 11.2% 11.2% 11.2% 11.2% 12.3% 0.884 0.783 0.695 0.618 0.556 0.500 0.450 0.404 85.7 76.7 60.5 38.9 65.6 96.0 128.7 158.8

PV of FCF in the high growth period. 85.7 + 76.7 + 60.5 + 38.9 = Rs. 261.8 million

(c) PV of FCF in the transition period 65.6 + 96.0 + 128.7 + 158.8 = Rs.449.1 million (d) PV of the terminal value 432 x 0.404 = Rs.7588.2 million 0.123 – 0.10 (e) Intrinsic value per share Value of firm – Value of debt No. of shares (261.8 + 449.1 + 7588.2) – 300 = 30 = Rs. 266.6

7.

You are looking at the valuation of a stable firm, Solidaire Limited, done by an investment analyst. Based on an expected free cash flow of Rs.70 million for the following year and an expected growth rate of 10 per cent, the analyst has estimated the value of the firm to be Rs.3000 million. However, he committed a mistake of using the book values of debt and equity. You do not know the book value weights employed by him but you know that the firm has a cost of equity of 22 per cent and a post-tax cost of debt of 9 per cent. The market value of equity is twice its book value, whereas the market value of its debt is eight -tenths of its book value. What is the correct value of the firm?

Solution:

70 3000 =
r – 0.10 ? r = 0.1233 or 12.33 %

0.1233 = x x 0.22 + (1-x) x 0.09 ? x = 0.26 The weight assigned to equity is 0.26 So D/E = 0.74 / 0.26 = 2.85 Since the market value of equity is twice its book value and the market value of debt is eight-tenths of its book value, the market value weights of equity and debt are in the proportion: 0.26 x 2 and 0.74 x 0.8 That is 0. 52 and 0.59

Hence the WACC is 0.52 x 0.22 + 1.11 1.11 0.59 x 0.09 = 0.1509 or 15.09 %

Hence the value of the firm is : 70 = Rs. 1149.43 million .1509 - .09
CHAPTER 33

1.

The income statement for year 0 (the year which has just ended) and the balance sheet at the end of year 0 for Infotex Limited are as follows.
Income statement Balance Sheet

Sales Gross margin (20%) Selling & general adminStration (8%) Profit before tax Tax Profit after tax

50,000

Equity

30,000 Fixed assets 25,000 10,000 assets 5,000

4,000 6,000 4,200 30,000 30,000

Infotex Limited is debating whether it should maintain the status quo or adopt a new strategy. If it maintains the status quo: • The sales will remain at 50,000 • The gross margin will remain at 20% and the selling, general, and administrative expenses will be 8% of sales • Depreciation charges will be equal to new investments • The asset turnover ratios will remain constant • The discount rate will be 14 percent • The income tax rate will be 30 percent If Infotex Limited adopts a new strategy, its sales will grow at the rate of 30 percent per year for three years. Thereafter, sales will remain constant. The margins, the turnover ratios, the capital structure, the income tax rate, and the discount rate, however, will remain unchanged. Depreciation charges will be equal to 10 percent of the net fixed assets at the beginning of the year. After three years, capital expenditure will be equal to depreciation. What value will the new strategy create?

Solution:

Income Statement Projections Current Values (Year 0) 50,000 10,000 4,000 6,000 1,800 4,200 1 65,000 13,000 5,200 7,800 2,340 5,460 2 84,500 16,900 6,760 10,140 3,042 7,098 3 109,850 21,970 8,788 13,182 3,955 9,227 Residual value 3+ 109,850 21,970 8,788 13,182 3,955 9,227

• Sales • Gross margin (20%) • Selling and general administration (8%) • Profit before tax • Tax • Profit after tax

• Fixed assets • Net current assets • Total assets • Equity

25,000 5,000 30,000 30,000

32,500 6,500 39,000 39,000

Balance Sheet Projections 42,250 54,925 8,450 10,985 50,700 65,910 50,700 65,910

54,925 10,985 65,910 65,910

Profit after tax + Depreciation - Capital expenditure - Increase in net current assets = Operating cash flow Present value factor Present value • • • •

5,460 2,500 10,000 1,500 (3540) 0.877 (3105)

Cash Flow Projections 7,098 9,227 3,250 4,225 13,000 16,900 1,950 2,535 (4602) (5983) 0.769 0.675 (3539) (4038)

9,227 5,493 5,493 – 9,227

Present value of the operating cash flow stream = (10682) Residual value = 9227 / 0.4 = 65,907 Present value of residual value = 65907 x 0.675 = 44,487 Total shareholder value = 44,487 – 10682 = 33,805 4200 • Pre-strategy value = = 30,000 0.14 • Value of the strategy = 33,805 – 30,000 = 3,805 2. The income statement for year 0 (the year which has just ended) and the balance sheet at the end of year 0 for Megastar Limited are as follows.

Income statement

Balance Sheet

Sales Gross margin (25%) Selling & general adminStration (10%) Profit before tax Tax Profit after tax

200,000 50,000 20,000 43,000 14,190 28,810

Equity

250,000

Fixed assets 150,000 Net current assets 100,000

250,000

250,000

Megastar Limited is debating whether it should maintain the status quo or adopt a new strategy. If it maintains the status quo:
• • • • • •

The sales will remain at 200,000 The gross margin will remain at 25% and the selling, general, and administrative expenses will be 10 % of sales Depreciation charges will be equal to new investments The asset turnover ratios will remain constant The discount rate will be 15 percent The income tax rate will be 33 percent If Megastar Limited adopts a new strategy, its sales will grow at the rate of 30 percent per year for three years. Thereafter, sales will remain constant. The margins, the turnover ratios, the capital structure, the income tax rate, and the discount rate, however, will remain unchanged. Depreciation charges will be equal to 20 percent of the net fixed assets at the beginning of the year. After three years, capital expenditure will be equal to depreciation. What value will the new strategy create?

Solution:
Current values Year Sales Gross margin Selling and general administration Profit before tax Tax Profit after tax Fixed assets 0 200,000 50,000 20,000 43,000 14,190 28,810 150,000 Income statement projections 1 2 3 4 260,000 338,000 439,400 439,400 65,000 84,500 109,850 109,850 26,000 33,800 43,940 43,940 55,900 72,670 94,471 94,471 18,447 23,981 31,175 31,175 37,453 48,689 63,296 63,296 Balance sheet projections 195,000 253,500 329,550 329,550

Net current assets Total assets Equity Profit after tax Depreciation Capital expenditure Increase in net current assets Operating cash flow Present value of the operating cash flow stream Residual value = 63,296/0.15 Present value of the residual value = 421,970/(1.15)3 Total shareholder value=(111,280) +277452 Pre-strategy value = 28810/0.15 Value of the strategy =192,067 – 166,172

100,000 250,000 250,000

130,000 325,000 325,000 37,453 30,000 75,000 30,000 (37,547)

169,000 219,700 422,500 549,250 422,500 549,250 Cash Flow projections 48,689 63,296 39,000 50,700 97,500 126,750 39,000 50,700 (48,811) (63,454)

219,700 549,250 549,250 63,296 65,910 65,910 0 63,296

(111,280) 421,970 277,452

166,172 192,067 (25,895)

3.

A new plant entails an investment of Rs.630 million (Rs.480 million in fixed assets and Rs.150 million in net working capital). The plant has an economic life of 8 years and is expected to produce a NOPAT of Rs.80 million every year. After 8 years, the net working capital will be realised at par but fixed assets will fetch nothing. The cost of capital for the project is 12 percent. Assume that the straightline method of depreciation is used for tax as well as shareholder reporting purposes. (i) What will be the ROCE for year 3 ? Assume that the capital employed is measured at the beginning of the year. (ii) What will be the EVA (Rs.in million) for year 3 ? (iii) What will be the ROGI for year 3 ? (iv) What will be the CVA (Rs.in million) for year 3 ? (v) What will be the CFROI for year 3?

Solution:

• • • • • • • • •

Net fixed assets (beginning) Net working capital (beginning) Capital employed (beginning) NOPAT Depreciation (Accounting) Economic depreciation Cash investment Cost of capital Capital charge

1 480 150 630 80 60 39.02 630 12% 75.6

(Rs.in million) 2 3 420 360 150 150 570 510 80 80 60 60 39.02 39.02 630 630 12% 12% 68.4 61.2

480 Economic depreciation = FVIFA12%, 8yr ROCE3 = NOPAT3/CE = 80/510 = 15.69% EVA3 = NOPAT – COC x CE = 80 – 0.12 x 510 = 18.8 NOPAT + DEP ROGI3 = CASH INVESTMENT = 630 80 + 60 =

480 = 39.02 12.30

= 22.22%

CVA3 = Operating cash flow – Eco.depreciation – Capital charge on full capital invested = (80 + 60) – 39.02 – 0.12 x 630 = 25.38 Operating cash flow – Economic depreciation CFROI = Cash investment = 630 140 –39.02 = 16.03%

3.

A new plant entails an investment of Rs.800 (Rs.600 million in fixed assets and Rs.200 million in net working capital). The plant has an economic life of 10 years and is expected to produce a NOPAT of Rs.90 million every year. After 10 years, the net working capital will be realised at par whereas fixed assets will fetch nothing. The cost of capital for the project is 10 percent. Assume that the straight line method of depreciation is used for tax as well as reporting purposes. (i) What will be the ROCE for year 3 ? Assume that the capital employed is measured at the beginning of the year. (ii) What will be the EVA for year 3 ? (iii) What will be the ROGI for year 3 ? (iv) What will be the CVA for year 3 ? (v) What will be the CFROI for year 3?

Solution:

• • • • • • • • •

Net value of fixed assets (beginning) Investment in net working capital Capital employed (beginning) NOPAT Depreciation (Accounting & tax) Economic depreciation Cash investment Cost of capital Capital charge

1 600 200 800 90 60 37.65 800 10% 80

2 540 200 740 90 60 37.65 800 10% 74

3 480 200 680 90 60 37.65 800 10% 68

600 Economic depreciation = FVIFA10%, 10yr ROCE = NOPAT3/CE = 90/680 = 13.24% EVA3 = NOPAT – COC x CE = 90 – 0.10 x 680 = 22 NOPAT + DEP ROGI3 = Cash Invest = 800 90 + 60 =

600 = 37.65 15.937

= 18.75%

CVA3 = Operating cash flow – Eco.deprn – Capital charge on full cap.invested = 150 – 37.65 – 80 = 32.35 Operating cash flow – Economic deprn CFROI = Cash investment = 14.04%

4.

A new plant entails an investment of Rs.1000 million (Rs. 800 million in fixed assets and Rs.200 million in net working capital).The net working capital will be maintained at that level throughout the project life. The plant has an economic life of 10 years and it is expected to produce a NOPAT of Rs.140 million every year. After 10 years, the net working capital will be realised at par whereas fixed assets will fetch nothing. The cost of capital for the project is 15 percent. Assume that the straight line method of depreciation is used for tax as well as reporting purposes. (i) (ii) (iii) (iv) What will be the EVA for year 3? What will be the ROGI for year 3? What will be the CVA for year 3? What will be the CFROI for year 3?

Solution:

1
• • • • • • • •

2 720 200 920 140 80 39.40 1000 15%

3 640 200 840 140 80 39.40 1000 15%

Net value of fixed assets (beginning) Investment in current assets Capital employed (beginning) NOPAT Depreciation (Accounting and tax) Economic depreciation Cash investment Cost of capital

800 200 1000 140 80 39.40 1000 15%

800 Economic depreciation = FVIFA15%, 10 EVA3 = = NOPAT3 – COC x CE 140 – 0.15 x 840 = 14 NOPAT + DEP ROGI3 CVA3 = Cash Investment = 1000 =

800 = 20.304 39.40

140 + 80 = 22 %

= OPERATING CASH FLOW – ECONOMIC DEPRECIATION – CAPITAL CHARGE ON FULL CAPITAL INVESTMENT. = 220 – 39.40 – 0.15 (1000) = 30.60 OPERATING CASH FLOW – ECONOMIC DEPRECIATION

CFROI3

= CASH INVESTMENT 220 – 39.40 = 1000 = 18.06%

5.

Biotech International earns a return on equity of 20 percent. The dividend payout ratio is 0.25. Equity shareholders of Biotech require a return of 16 percent. The book value per share is Rs.60. (i) What is the market price per share, according to the Marakon model ?

Solution:

g = (1-b)r = 0.75 x 0.20 = 0.15 M r–g

0.20 – 0.15 = = 0.16 – 0.15
M = 5 B = Rs.300

=
B k–g

5

B = Rs. 60

(ii)
Solution:

If the return on equity falls to 19 percent, what should be the payout ratio be to ensure that the market price per share remains unchanged.

0.19 – g = 5 0.16 – g
g = (1-b) r

g = 0.1525

0.1525 = (1-b) x 0.19
b = 0.1974 or 19.74 %

6.

Miocon Limited is considering a capital project for which the following information is available. Initial outlay : Project life : Salvage value : Annual revenues : Annual costs : (excluding depreciation, interest, and taxes) 50000 5 years 0 60000 30000 Depreciation method (for tax purposes) Tax rate Debt-equity ratio Cost of equity Cost of debt (post-tax) : : : : : Sinking fund 30 % 1:1 14% 6%

Calculate the EVA of the project over its life.
Solution:

Sinking Fund Depreciation A x PVIFA (10%, 5years) = 50,000 A x 3.791 = 50,000 ? A = 13,189 Depreciation Schedule • Investment (beginning) • Depreciation • 10% capital charge • Annuity 1. Revenues 2. Costs 3. PBDIT 4. Depreciation 5. PBIT 1 50,000 8,189 5,000 13,189 60,000 30,000 30,000 8,189 21,811 2 41,811 9,008 4,181 13,189 60,000 30,000 30,000 9,008 20,992 3 32,803 9,909 3,280 13,189 60,000 30,000 30,000 9,909 20,091 4 22,894 10,900 2,289 13,189 60,000 30,000 30,000 10,900 19,100 5 11,994 11,994 1,199 13,189 60,000 30,000 30,000 11,994 18,006

6. NOPAT (5) x 0.7 7. Capital at charge 8. Capital charge (7 x 0.10) 9. EVA 7.

15,268 50,000 5,000 10,268

14,694 41,811 4,181 10,513

14,064 32,803 3,280 10,784

13,370 22,894 2,289 11,081

12,604 11,994 1,199 11,405

Janbaz Limited is considering a capital project for which the following information is available. Initial outlay Project life Salvage value Annual revenues Annual costs Depreciation method (for tax purposes) Tax rate Debt-equity ratio Cost of equity Cost of debt (post tax) The initial outlay is entirely for acquiring fixed assets. Calculate the EVA of the project over its life. : 200,000 : 4 years : 0 : 250,000 : 160,000 : Sinking fund : 30% : 1:1 : 15% : 7%

Solution:
Sinking Fund Depreciation

A x PVIFA ( 11 %, 4yrs ) = 200,000 A x 3.102 = 200,000 1 200,000 42,475 22,000 64,475 1 250,000 160,000 90,000 42,475 47,525 33,268 200,000 22,000 11,268

•

Investment (beginning) • Depreciation • 11% Capital charge • Annuity 1. 2. 3. 4. 5. 6. 7. 8. 9. Revenues Costs PBDIT Depreciation PBIT NOPAT (5) x (0.7) Capital at charge Capital charge (7 x 0.11) EVA

A = 64475 Depreciation Schedule 2 3 4 157,525 110,378 58,045 47,147 17,328 64,475 2 250,000 160,000 90,000 47,147 42,853 29,997 157,525 17,328 12,669 52,333 12,142 64,475 3 250,000 160,000 90,000 52,333 37,667 26,367 110,378 12,142 14,225 58,090 6,385 64,475 4 250,000 160,000 90,000 58.090 31,910 22,337 58,045 6,385 15,952

5

5

8.

Polytex Limited is considering a capital project for which the following information is available . Investment outlay : Project life : Salvage value : Annual revenues : Annual costs : (excluding depreciation interest, and taxes) 10000 5 years 0 14000 9000 Depreciation method (for tax purposes) Tax rate Debt-equity ratio Cost of equity Cost of debt (post-tax) : : : : : Sinking fund 30 % 1 :1 16% 8%

Calculate the EVA of the project over its life and the NPV.
Solution:

Sinking Fund Depreciation A x PVIFA (12%,5yrs) = 10,000 A x 3.605 = 10,000 ? A = 2774 Depreciation Schedule 1 2 3 10,000 8426 6663 1574 1763 1974 1200 1011 800 2774 2774 2774

• Investment(beginning) • Depreciation • 12% Capital charge • Annuity

4 4689 2211 563 2774

5 2478 2478 297 2774

1 2 3 1. Revenues 14000 14000 14000 2. Costs 9000 9000 9000 3. PBDIT 5000 5000 5000 4. Depreciation 1574 1763 1974 5. PBIT 3426 3237 3026 6. NOPAT (5) x (0.7) 2398 2266 2118 7. Capital at charge 10000 8426 6663 8. Capital charge (7x 0.12) 1200 1011 800 9. EVA 1198 1255 1318 EVAt NPV = ? (1.12)t = 1198/1.12 + 1255/(1.12)2 +1318/(1.12)3 + 1389/(1.12)4 +1469/ = 4724.53

4 14000 9000 5000 2211 2789 1952 4689 563 1389

5 14000 9000 5000 2477 2523 1766 2478 297 1469

(1.12)5

9.

Simtek Limited is considering a capital project for which the following information is available. Investment outlay : Project life : Salvage value : Annual revenues : Annual costs : (excluding depreciation interest, and taxes) (i) 8000 5 years 0 10000 6400 Depreciation method (for tax purposes) Tax rate Debt-equity ratio Cost of equity Cost of debt (post-tax) : : : : : Sinking fund 30 % 0.6 :1 15% 7%

What will be the depreciation charge for year 3?

Solution:

6 Post-tax cost of capital: 16 x7+

10 x 15 16

2.63 + 9.37 =12.00 percent Sinking Fund Depreciation A x PVIFA (12%, 5yrs) = 8000 A x 3.605 = 8000 ? A = 2219
Depreciation Schedule 1 8000 • Investment (beginning) 1259 • Depreciation 960 • 12 percent charge 2219

2 6741 1410 809 2219

3 5331 1579 640 2219

(ii)
Solution:
1. 2. 3. 4. 5. 6. 7. 8. 9.

What will be the EVA for year 3?
Revenues Costs PBDIT Depreciation PBIT NOPAT Capital at charge Capital charge EVA 10000 6400 3600 1579 2021 1415 5331 640 775

(iii) Over time will the EVA of this project, increase, decrease or remains unchanged?
Solution:

The book capital decreases over time, thanks to depreciation. Hence the capital charge decreases. This leads to an increase in EVA over time.

10.

Karishma Limited expects to earn a supernormal rate of return of 50 percent on new investments to be made over the next 6 years. The projected new investment per year is Rs.400 million. If the weighted average cost of capital for Karishma Limited is 23 percent, what is the value of the forward plan?

Solution:

I r c* T

= = = =

Rs.400 million 0.50 0.23 6 years 400 (0.50 – 0.23) 6

Value of forward plan = 0.23 (1.23) = Rs.2290.56 million 11. Pinnacle Corporation expects to earn a supernormal rate of return of 60 percent on new investments to be made over the next 4 years. The projected new investment per year is Rs.200 million. If the weighted average cost of capital for Pinnacle Corporation is 18 percent, what is the value of the forward plan?

Solution:

I r c* T

= = = =

Rs.200 million 0.60 0.18 4 years 200 (0.60 – 0.18) 4

Value of forward plan = 0.18 (1.18) = Rs. 1581.92 million

CHAPTER 34

1.

Anil Company (the transferor company) and Sunil Company (the transferee company) amalgamate in an exchange of stock to form Anil and Sunil Company. The pre-amalgamation balance sheets of Sunil Company and Anil Company are as follows:
Sunil Company (Rs. in million) Anil Company (Rs. in million)

Fixed assets Current assets Total assets Share capital (Rs.10 face value) Reserves and surplus Debt

45 40 85 30 20 35 85

25 15 40 10 20 10 40

The share swap ratio fixed is 2:5. The fair market value of the fixed assets and current assets of Anil Company was assessed at Rs.50 million and Rs.20 million respectively. Prepare the post-amalgamation balance sheet of Sunil & Anil Company under the 'pooling' and 'purchase' methods.
Solution:

The pre-amalgamation balance sheets of Sunil Company and Anil Company and the post-amalgamation balance sheet of the combined entity, Sunil and Anil Company, under the ‘pooling’ method as well as the ‘purchase’ method are shown below:
Before Amalgamation After Amalgamation Sunil & Anil Company Pooling method Purchase method 70 95 55 60

Sunil Fixed assets Current assets Total assets Share capital (face value @ Rs.10) Capital reserve Reserves & surplus Debt Total liabilities 45 40 85 30

Anil 25 15 40 10

125 34 6 40 45 125

155 34 56 20 45 155

20 35 85

20 10 40

2.

Yan Company (the transferor company) and Yin Company (the transferee company) amalgamate in an exchange of stock to form Yin Yan Company. The preamalgamation balance sheets of Yin Company and Yan Company are as follows:
Yin Company (Rs. in million) Yan Company (Rs. in million)

Fixed assets Current assets Total assets Share capital (Rs.10 face value) Reserves and surplus Debt

120 240 360 150 150 60 360

50 80 130 40 10 80 130

The exchange ratio fixed is one share for every two shares of transferor company. The fair market value of the fixed assets, current assets and debt of Yan Company was assessed at Rs.40 million , Rs.60 million and Rs.90 million respectively. Prepare the post-amalgamation balance sheet of Yin Yan Company under the 'pooling' and 'purchase' methods.
Solution:

Yin Fixed assets Current assets Goodwill Total assets Share capital (face value @ Rs.10) Capital reserve Reserves & surplus Debt Total liabilities 3. 120 240

Yan 50 80

Yin & Yan Company Pooling method Purchase method 170 320 160 300 10 470 170

360 150

130 40

490 170 20 160 140 490

150 60 360

10 80 130

150 150 470

Bharat Company (the transferor company) and Jai Company (the transferee company) amalgamate in an exchange of stock to form Jai Bharat Company. The pre-amalgamation balance sheets of Jai Company and Bharat Company are as follows:

Jai Company (Rs. in million)

Bharat Company (Rs. in million)

Fixed assets Current assets Total assets Share capital (Rs.10 face value) Reserves and surplus Debt

80 100 180 70 50 60 180

40 40 80 30 20 30 80

The exchange ratio fixed is two shares for every five shares of the transferor company. The fair market value of the fixed assets, current assets and debt of Bharat Company was assessed at Rs.30 million, Rs.20 million and Rs.40 million respectively . Prepare the post-amalgamation balance sheet of Jai Bharat Company under the 'pooling' and 'purchase' methods.
Solution:

Before Amalgamation Jai 80 100 Bharat 40 40

Fixed assets Current assets Goodwill Total assets Share capital (face value @ Rs.10) Capital reserve Reserves & surplus Debt Total liabilities 4.

After Amalgamation Jai Bharat Company Pooling method Purchase method 120 110 140 120 2 232 82

180 70

80 30

260 82 18 70 90 260

50 60 180

20 30 80

50 100 232

Vijay Company plans to acquire Ajay Company. The following are the relevant financials of the two companies.
Vijay Company Rs.200 million 20 million Rs.200 Ajay Company Rs.100 million 10 million Rs.120

Total earnings, E Number of outstanding shares Market price per share

(i)

What is the maximum exchange ratio acceptable to the shareholders of Vijay Company if the PE ratio of the combined company is 18 and there is no synergy gain?

Solution:

- S1 ER1 = S2 20 = 10 + +

PE12 (E12) P1 S2 18 (300) = 0.7 200 x 10

(ii)

What is the minimum exchange ratio acceptable to the shareholders of Ajay Company if the PE ratio of the combined company is 18 and there is a synergy gain of 6 percent?

Solution:

P2S1 ER2 = (PE12) (E1 + E2) (1+S) – P2S2 120 x 20 = (18) (200 + 100) (1.06) -120 x 10 = 0.53

(iii) If there is no synergy gain, at what level of PE multiple will the lines ER1 and ER2 intersect?
Solution:

The lines ER1 and ER2 will intersect at a point corresponding to the weighted average of the two PE multiples wherein the weights correspond to the respective earnings of the two firms. 200 PE12 = 300 = x 20 + 300 100 x 12

13.333 + 4 = 17.33

(iv) If the expected synergy gain is 8 percent, what exchange ratio will result in a post-merger earnings per share of Rs.11?
Solution:

(E1 + E2) (1 + S) = N1 + N2 x ER ER = 0.945

(200 + 100) (1.08) = 11 20 + 10 x ER

(v)

Assume that the merger is expected to generate gains which have a present value of Rs. 400 million and the exchange ratio agreed to is 0.6. What is the true cost of the merger from the point of view of Vijay Company?

Solution:

Cost = ? PV (Vijay and Ajay) – PV ( Ajay) 0.60 x 10
? =

= 0.231 20 + 0.6 x 10

PV (Vijay & Ajay) = 4000 + 1200 + 400 = 5600 million Cost = 0.231 x 5600 - 1200 = Rs.93.6 million

5.

Jeet Company plans to acquire Ajeet Company. The following are the relevant financials of the two companies.
Jeet Company Rs.1600 million 40 million Rs .900 Ajeet Company Rs.600 million 30 million Rs.360

Total earnings, E Number of outstanding shares Market price per share (i)

What is the maximum exchange ratio acceptable to the shareholders of Jeet Company if the PE ratio of the combined company is 21 and there is no synergy gain?

Solution:

ER1 =

- S1 + PE12(E12) ---------------------P1S2 - S2 - 40 + 21 x 2200 ---------------------30 900 X 30 0.378

=

=

(ii)

What is the minimum exchange ratio acceptable to the shareholders of Ajeet Company if the PE ratio of the combined company is 20 and there is a synergy benefit of 8 percent?

Solution:

ER2 =

P2S1 -------------------------------------------(PE12) (E1 + E2) ( 1 + S) – P2S2 360 x 40 -------------------------------------------20 x (2200) (1.08) - 360 x 30 0.392

=

=

(iii) If there is no synergy gain, at what level of PE multiple will the lines ER1 and ER2 intersect?
Solution:

The lines ER1 and ER2 will intersect at a point corresponding to the weighted average of the two PE multiples wherein the weights correspond to the respective earnings of the two firms. 1600 ---------- x 22.5 + 2200 16.36 + 4.91 21.27 600 ---------- X 18 2200

PE12

=

= =

(iv) If the expected synergy gain is 10 percent, what exchange ratio will result in a post-merger earnings per share of Rs.30 ?
Solution:

( 1600 + 600 ) ( 1.10 ) (E1 + E2 ) ( 1 + S ) ----------------------- = --------------------------N1 + N2 x ER 40 + 30 x ER 2420 ------------------40 + 30ER ER = 1.355 = 30

= 30

(v)

Assume that the merger is expected to generate gains which have a present value of Rs. 5000 million and the exchange ratio agreed to is 0.45. What is the true cost of the merger from the point of view of Jeet Company?

Solution:

Cost
?

=
=

? PV (Jeet & Ajeet) - PV (Ajeet)

0.45 x 30 ???????????? 40 + 0.45 x 30

=

0.252

PV ( Jeet & Ajeet ) = 36000 + 10800 + 5000 = 51800 PV ( Ajeet ) = 10800 Cost = 0.252 ( 51800 ) – 10800 = 2253.6

6.

Shaan Company plans to acquire Aan Company. The following are the relevant financials of the two companies. Shaan Company Aan Company Total earnings, E Rs.750 million Rs.240 million Number of outstanding shares 50 million 20 million Market price per share Rs.250 Rs.150 (i) What is the maximum exchange ratio acceptable to the shareholders of Shaan Company if the PE ratio of the combined company is 15 and there is no synergy gain?

Solution:

- S1 ER1 = S2 50 = 20 + +

PE12 ( E 12) P1 S2 15 x 990 = 0.47 250 x 20

(ii)

What is the minimum exchange ratio acceptable to the shareholders of Aan Company if the PE ratio of the combined entity is 15 and there is a synergy benefit of 6 percent?

Solution:

P2S1 ER2 = (PE12) (E1 + E2) (1+S) – P2S2 150 x 50 = 15 x 990 x 1.06 – 150 x 20 = 0.589

(iii) If there is no synergy gain, at what level of PE multiple will the lines ER1 and ER2 intersect?
Solution:

The lines ER1 and ER2 will intersect at a point corresponding to the weighted average of the two PE multiples wherein the weights correspond to the respective earnings of the two firms. 750 PE12 = 990 = 15.66 x 16.67 + 990 240 x 12.5

(iv) If the expected synergy gain is 6 percent, what exchange ratio will result in a post-merger earnings per share of Rs.16?
Solution:

(E1 + E2) (1 + S) = N1 + N2 x ER

( 750 + 240) (1.06) = 16 50 + 20 x ER ER = 0.779

(v)

Assume that the merger is expected to generate gains which have a present value of Rs. 600 million and the exchange ratio agreed to is 0.60. What is the true cost of the merger from the point of view of Shaan Company?

Solution:

Cost = ? PV (Shaan & Aan) – PV ( Aan) 0.60 x 20
? =

12 = = 0.194 62 = 16100

50 + 20 x 0.60 PV (Shaan & Aan) = 12500 + 3000 + 600 PV (Aan) = 3000

Cost = 0.194 x 16100 – 3000 = Rs.123.4 million.

7.

Arun Company has a value of Rs.40 million and Varun Company has a value of Rs.20 million. If the two companies merge, cost savings with a present value of Rs.5 million would occur. Arun proposes to offer Rs.22 million cash compensation to acquire Varun. What is the net present value of the merger to the two firms?

Solution:

PVA = Rs.40 million, PVV = Rs.20 million Benefit = Rs.5 million, Cash compensation = Rs.22 million Cost = Cash compensation – PVV = Rs.2 million NPV to Arun = Benefit – Cost = Rs.3 million NPV to Varun = Cash Compensation – PVV = Rs.2 million

8.

Kamal Company has a value of Rs.80 million and Jamal Company has a value of Rs.30 million. If the two companies merge, cost savings with a present value of Rs.10 million would occur. Kamal proposes to offer Rs.35 million cash compensation to acquire Jamal. What is the net present value of the merger to the two firms?

Solution:

PVK = Rs.80 million, PVJ = Rs.30 million Benefit = Rs.10 million, Cash compensation = Rs 35 million Cost = Cash compensation – PVJ = Rs.5 million NPV to Alpha = Benefit – Cost = Rs.5 million NPV to Beta = Cash Compensation – PVJ = Rs.5 million 9. America Limited plans to acquire Japan Limited. The relevant financial details of the two firms, prior to merger announcement, are given below:
America Limited Rs. 100 800,000 Japan Limited Rs.40 300,000

Market price per share Number of shares

The merger is expected to bring gains which have a present value of Rs.12 million. America Limited offers two share in exchange for every three shares of Japan Limited. Required : (a) What is the true cost of America Limited for acquiring Japan Limited ? (b) What is the net present value of the merger to America Limited ? (c) What is the net present value of the merger to Japan Limited ?
Solution:

Let A stand for America Limited and J for Japan Limited and AJ for the combined entity. PVA = Rs.100 x 800,000 = Rs.80 million PVJ = Rs.40 x 300,000 = Rs.12 million Benefit = Rs.12 million PVAJ = 80 + 12 + 12 = Rs.104 million Exchange ratio = 2:3 The share of Japan Limited in the combined entity will be :
?

200,000 = 800,000 + 200,000 = 0.2

a)

True cost to America Limited for acquiring Japan Limited Cost = ? PVAJ - PVJ = 0.2 x 104 - 12 = Rs.8.8 million NPV to America Limited = Benefit - Cost = 12 - 8.8 = Rs.3.2 million NPV to Japan Limited = Cost =

b)

c)

Rs.8.8 million

10.

Amir Limited plans to acquire Jamir Limited. The relevant financial details of the two firms, prior to merger announcement, are given below:
Amir Limited Rs. 500 600,000 Jamir Limited Rs.100 200,000

Market price per share Number of shares

The merger is expected to bring gains which have a present value of Rs.20 million. Amir Limited offers one share in exchange for every four shares of Jamir Limited. Required: (a) What is the true cost of Amir Limited for acquiring Jamir Limited? (b) What is the net present value of the merger to Amir Limited ? (c) What is the net present value of the merger to Jamir Limited ?
Solution:

Let A stand for Amir Limited and J for Jamir Limited and AJ for the combined entity. PVA = Rs.500 x 600,000 = Rs.300 million PVJ = Rs.100 x 200,000 = Rs.20 million Benefit = Rs.20 million PVAJ = 300 + 20 + 20 = Rs.340 million Exchange ratio = 1:4 The share of Jamir Limited in the combined entity will be: 50,000 ? = = 0.0769 600,000 + 50,000 a) True cost to Amir Limited for acquiring Jamir Limited Cost = ? PVAJ - PVJ = 0.0769 x 340 - 20 = Rs.6.146 million

b)

NPV to Amir Limited = Benefit - Cost = 20 - 6.146 = Rs.13.854 million

c)

NPV to Jamir Limited = Cost

= Rs.6.146 million

11.

As the financial manager of National Company you are investigating the acquisition of Regional Company. The following facts are given:
National Company Rs.8.00 Rs.5.00 Rs.86.00 8,000,000 Regional Company Rs.3.00 Rs.2.50 Rs.24.00 3,000,000

Earning per share Dividend per share Price per share Number of shares

Investors currently expect the dividends and earnings of Regional to grow at a steady rate of 6 percent. After acquisition this growth rate would increase to 12 percent without any additional investment. Required : (a) What is the benefit of this acquisition ? (b) What is the cost of this acquisition to National Company if it (i) pays Rs.30 per share cash compensation to Regional Company and (ii) offers two shares for every five shares of Regional Company? Solution: Let the suffixes A stand for National Company, B for Regional Company and AB for the combined company. a) PVB = Rs.24 x 3,000,000 = Rs.72 million The required return on the equity of Regional Company is the value of k in the equation. Rs.2.50 (1.06) Rs.24 = k - .06
k = 0.1704 or 17.04 per cent.

If the growth rate of Regional rises to 12 per cent as a sequel to merger, the intrinsic value per share would become: 2.50 (1.12) = 0.1704 - .12 Rs.55.56

Thus the value per share increases by Rs.31.56 Hence the benefit of the acquisition is: 3 million x Rs.31.56 = (b) (i) Rs.94.68 million

If National pays Rs.30 per share cash compensation, the cost of the merger is 3 million x (Rs.30 – Rs.24) = Rs.18 million. If National offers 2 shares for every 5 shares it has to issue 1.2 million shares to shareholders of Regional.

(ii)

So shareholders of Regional will end up with 1.2
? =

= 0.1304 or 13.04 per cent 8+ 1.2

shareholding of the combined entity, The present value of the combined entity will be PVAB = PVA + PVB + Benefit = Rs.86x8 million + Rs.24x3 million + Rs.94.68 million = Rs.854.68 million So the cost of the merger is : Cost = ? PVAB - PVB = .1304 x 854.68 - 72 12.

= Rs.39.45 million

As the financial manager of Satya Limited you are investigating the acquisition of Devaraj Limited. The following facts are given:
Satya Limited Rs.12.00 Rs.10.00 Rs.110.00 5,800,000 Devaraj Limited Rs.4.00 Rs.3.00 Rs.38 .00 1,400,000

Earning per share Dividend per share Price per share Number of shares

Investors currently expect the dividends and earnings of Devaraj to grow at a steady rate of 4 percent. After acquisition this growth rate would increase to 10 percent without any additional investment. Required: (a) What is the benefit of this acquisition ? (b) What is the cost of this acquisition to Satya Limited if it (i) pays Rs.100 per share cash compensation to Devaraj Limited and (ii) offers three shares for every seven shares of Devaraj Limited ?

Solution:

Let the suffixes A stand for Satya Limited, B for Devaraj Limited and AB for the combined company a) PVB = Rs.38 x 1,400,000 = Rs.53.2 million The required return on the equity of Devaraj Limited is the value of k in the equation. Rs.3 (1.04) Rs.38 =
k - .04 k = 0.1221 or 12.21 per cent.

If the growth rate of Devaraj Limited rises to 10 per cent as a sequel to merger, the intrinsic value per share would become : 3(1.10) = 0.1221- .10 Thus the value per share increases by Rs.111.32 acquisition is 1.4million x Rs.111.32 = (b) (i) Rs.155.85 million Hence the benefit of the Rs.149.32

If Satya Limited pays Rs.100 per share cash compensation, the cost of the merger is 1.4 million x (Rs.100 – Rs.38) = Rs.86.8 million.

(iii) If Satya Limited offers 3 shares for every 7 shares it has to issue0 .6 million shares to shareholders of Devaraj Limited. So shareholders of Devaraj Limited will end up with 0.6
? =

= 0.09375 or 9.375 per cent 5.8 + 0.6

shareholding of the combined entity, The present value of the combined entity will be PVAB = PVA + PVB + Benefit = Rs.110x5.8 million + Rs.38x1.4 million + Rs.155.85 million = Rs.847.05 million

So the cost of the merger is : Cost = ? PVAB - PVB = .09375 x 847.05 - 53.2 = Rs.26.21 million 13. Companies P and Q are valued as follows: P Earnings per share Rs. 12.00 Price per share Rs.110.00 Number of shares 60,000

Q Rs.4.00 Rs.28.00 21,000

P acquires Q by offering one shares of P for every three shares of Q. If there is no economic gain from the merger, what is the price-earnings ratio of P's stock after the merger? Solution:

The expected profile of the combined entity after the merger is shown in the last column below.
P 60,000 Rs.720,000 Rs.6,600,000 9.17 Q 21,000 Rs.84,000 Rs.588,000 7.0 Combined entity 81,000 Rs.804,000 Rs. 7,188,000 8.94

Number of shares Aggregate earnings Market value P/E 14.

Companies M and N are valued as follows: M Earnings per share Rs.45.00 Price per share Rs.360.00 Number of shares 100,000

N Rs.12.00 Rs.53.00 32,000

M acquires N by offering one shares of M for every three shares of N. If there is no economic gain from the merger, what is the price-earnings ratio of M's stock after the merger? Solution:

The expected profile of the combined entity after the merger is shown in the last column below.
M N Combined entity 100,000 32,000 132,000 Rs.4,500,000 Rs.384,000 Rs.4,884,000 Rs.36,000,000 Rs.1,696,000 Rs. 37,696,000 8 4.42 7.72

Number of shares Aggregate earnings Market value P/E

15.

X Limited is planning to acquire Y Limited. The management of X Limited estimates its equity-related post tax cash flows, without the merger, to be as follows: Year 1 2 3 4 5 Cash flow (Rs. in million) 60 80 100 150 120 Beyond year 5, the cash flow is expected to grow at a compound rate of 8 percent per year for ever. If Y Limited is acquired, the equity-related cash flows of the combined firm are expected to be as follows: Year 1 2 3 4 5 Cash flow (Rs. in million) 100 120 150 250 200 Beyond year 5, the cash flow is expected to grow at a compound rate of 10 percent per year. The number of outstanding shares of X Limited and Y Limited prior to the merger are 20 million and 12 million respectively. If the management wants to ensure that the net present value of equity-related cash flows increase by at least 50 percent, as a sequel to the merger, what is the upper limit on the exchange ratio acceptable to it ? Assume cost of capital to be 15 percent.

Solution:

Value of X Limited’s equity as a stand-alone company. 60 + (1.15) (1.15)2 80 + (1.15)3 100 + (1.15)4 150 + (1.15)5 120 + 0.15 – 0.08 120 x 1.08 x (1.15)5 1

= Rs. 1244.33 million Value of the equity of the combined company 100 120 150 250 200 200 (1.10) + + + + + x (1.15) (1.15)2 (1.15)3 (1.15)4 (1.15)5 0.15 – 0.10 = Rs. 2706.27million Let abe the maximum exchange ratio acceptable to the shareholders of X Limited. Since the management of X Limited wants to ensure that the net present value of equity-related cash flows increases by at least 50 percent, the value of a is obtained as follows. 20 x 2706.27= 1.50 x 1244.33 20 + a 12 Solving this for a we get
a = 0.75

1 (1.15)5

16.

P Limited is planning to acquire Q Limited. The management of P Limited estimates its equity-related post tax cash flows, without the merger, to be as follows: Year 1 2 3 4 5 Cash flow (Rs. in million) 20 30 40 40 30 Beyond year 5, the cash flow is expected to grow at a compound rate of 4 percent per year for ever. If Q Limited is acquired, the equity-related cash flows of the combined firm are expected to be as follows : Year 1 2 3 4 5 Cash flow (Rs. in million) 30 50 60 50 40 Beyond year 5, the cash flow is expected to grow at a compound rate of 8 percent per year. The number of outstanding shares of P Limited and Q Limited prior to the merger are 10 million and 8 million respectively. If the management wants to ensure that the net present value of equity-related cash flows increase by at least 20 percent, as a sequel to the merger, what is the upper limit on the exchange ratio acceptable to it ? Assume cost of capital to be 13 percent.

Solution:

Value of P Limited’s equity as a stand-alone company. 20 30 40 40 30 30 x 1.04 + + + + + x (1.13) (1.13)2 (1.13)3 (1.13)4 (1.13)5 0.13 – 0.04 = Rs. 297.89 million Value of the equity of the combined company 30 50 60 50 40 40 (1.08) + + + + + x 2 3 4 5 (1.13) (1.13) (1.13) (1.13) (1.13) 0.13 – 0.08 = Rs. 628.61 million

1 (1.13)5

1 (1.13)5

Let a be the maximum exchange ratio acceptable to the shareholders of P Limited. Since the management of P Limited wants to ensure that the net present value of equity-related cash flows increases by at least 20 percent, the value of a is obtained as follows. 10 x 628.61 = 1.20 x 297.89 10 + a 8 Solving this for a we get
a = 0.95

17.

Rajagiri Mills Limited is interested in acquiring the textile division of Pricom Industries Limited. The planning group of Rajagiri Mills Limited has developed the following forecast for the textile division of Pricom Industries Limited. Rs.in millions
Year

1 100 20 30 20

2 120 23 32.5 15

3 138 27.6 32.5 10

4 151.8 30.4 30.4 8

5 163.9 32.8 32.8 8

6 177.1 35.4 25.3 6

Asset value (at the beginning) NOPAT Net investment Growth rate (%)

The growth rate from year 7 onward will be 6 percent. The discount rate to be used for this acquisition is 20 percent. What is the value of this acquisition?
Solution:

1 FCF PVIF PV (10) 0.833 (8.33)

2 (8.5) 0.694 (5.90)

3 (4.9) 0.579 (2.837)

4 0 0.482 0

5 0 0.402 0

6 10.1 0.335 3.383

7 10.7

PV (FCF) during the explicit forecast period = - 13.68 FCF7 VH = r-g 76.471 PV(VH) = (1.20)6 = 25.60 = 0.20 – 0.06 10.706 = 76.471

V0 = - 13.68 + 25.60 = Rs. 11.92 million.

18.

CMX Limited is interested in acquiring the cement division of B&T Limited. The planning group of CMX Limited has developed the following forecast for the cement division of B & T Limited.

Rs.in millions
Year

1 100 20 35 40

2 140 25 36.5 25

3 175 30 37 20

4 210 34.5 37.4 15

5

6

Asset value (at the beginning) NOPAT Net investment Growth rate (%)

241.5 277.7 39.7 43.0 15 43.7 42.0 10

The growth rate from year 7 onward will be 10 percent. The discount rate to be used for acquisition is 12 percent. What is the value of this acquisition?
Solution:

FCF PVIF PV PV (FCF) VH PV (VH) V0 19.

1 2 3 4 5 6 (15) (11.5) (7) (2.9) (3.3) 1.7 0.893 0.797 0.712 0.636 0.567 0.507 (13.40) (9.17) (4.98) (1.84) (1.87) (0.86) during the explicit forecast period = -3.4 FCF7 1.87 = = = 93.5 r–g 0.12 – 0.10 = 93.5 / (1.12)6 = 47.37 = - 30.40 + 47.37 = Rs. 16.97 million

7

Rex Limited is interested in acquiring the cement division of Flex Limited. The planning group of Rex Limited has developed the following forecast for the cement division of Flex Limited
Year

1 100 14 20 25

2

3

4

5

6

Asset value NOPAT Net investment Growth rate(%)

125 150 172.5 193.2 212.50 17.5 21 24.2 27.1 29.80 22.5 22.5 24.2 24.1 25.3 20 15 12 10 8

The growth rate from year 7 onward will be 8 percent. The discount rate to be used for this acquisition is 15 percent. What is the value of this acquisition?

Solution:

FCF PV

1 (6)

2 (5)

3 (1.5)

4 0

5 3 0.497 1.50

6 4.5 0.432 1.94

7 4.9

0.870 0.756 0.658 (5.22) (3.78) (0.99)

–

PV (FCF) during the implicit forecast period FCF7 4.9 = = 70 VH = r-g 0.15 – 0.08 1 PV(VH) = 70 x = 30.26 (1.15)
6

V0 = – 6.55 + 30.26 = Rs.23.71

MINI CASE

Astra Pharma is a fairly diversified pharmaceutical company that has presence of most of the therapeutic segments. It has grown at a healthy rate over the past fifteen years, thanks to a balanced programme of internal growth and acquisitions. In a recent strategy session, the management of Astra Pharma identified the cardiovascular segment as a thrust area for the next few years. Though Astra Pharma has a reasonable presence in this segment, the management is keen on pursuing aggressive growth opportunities in this segment, especially through acquisitions. On the advice of the management, the business development group at the head office examined several independent pharmaceutical companies with a primary focus on the cardiovascular segment. This group looked at things like revenues, growth rate, profit margin, market capitalisation, attitude of incumbent management, and so on. Based on such analysis, it zeroed in on Max Drugs as a potentially suitable candidate for acquisition by Astra Pharma. Max Drug is a two decade old company with a turnover of Rs.3040 million last year. Max has had a chequered history, with a general upward trend. The financial statements of Astra Pharma and Max Drugs for last year are given below:

Astra Pharma Balance Sheet

Shareholder's Funds (40 million shares, Rs 10 par) Loan funds

4600 600 5200

Fixed assets (net) Investments Net current assets

3300 500 1400 5200

Astra Pharma Profit and Loss Account

Sales Profit before depreciation, interest, and taxes Depreciation Profit before interest and taxes Interest Profit before tax Tax Profit after tax
Max Drugs Balance Sheet

9680 1920 500 1420 80 1340 440 900

Shareholder's Funds (10 million shares, Rs 10 par) Loan funds

1300 500 1800

Fixed assets (net) Investments Net current assets

940 250 610 1800

Max Drugs Profit and Loss Account

Sales Profit before depreciation, interest, and taxes Depreciation Profit before interest and taxes Interest Profit before tax Tax Profit after tax

1520 230 70 160 30 130 35 95

The market price per share of Astra Pharma is Rs.360 and the market price per share for Magnum Drugs is Rs. 110. (a) Calculate the exchange ratio that gives equal weightage to book value per share, earnings per share, and market price per share.

(b)

(c) (d) (e)

If the merger is expected to generate a synergy gain of 5 percent, what is the maximum exchange ratio Astra Pharma should accept to avoid initial dilution of earnings per share? What will be the post-merger EPS of Astra Pharma if the exchange ratio is 1:3? Assume that there is no synergy gain. What is the maximum exchange ratio acceptable to the shareholders of Astra Pharma if the PE ratio of the combined entity is 15 and there is no synergy gain? What is the minimum exchange ratio acceptable to the shareholders of Max Drugs if the PE ratio of the combined entity is 14 and there is a synergy benefit of 2 percent? Assuming that there is no synergy gain, at what level of the PE ratio will the lines ER1 and ER2 intersect? Assume that the merger is expected to generate gains which have a present value of Rs. 1000 million and the exchange ratio agreed to is 1:3. What is the true cost of the merger from the point of view of Astra Pharma? What are the limitations of earnings per share as the basis for determining the exchange ratio? List the five sins that plague acquisitions?

(f)

(g)

(h)

(i)

Solution:

Astra Earnings E Nutstanding shares S Shareholders’ funds Market price per share P EPS Book value PE ratio (a) 900 million 40 million 4600 million Rs.360 Rs 22.5 Rs 115 16

Max 95 million 10 million 1300 million Rs.110 Rs 9.5 Rs 130 11.58

Exchange ratio that gives equal weightage to book value per share, earnings per share and market price per share = (130/115 + 9.5/22.5 + 110/360 )/3 = 0.62 If there should not be initial dilution of EPS, the EPS of the merged company should be at least Rs.22.5. So, [(900 + 95) (1.05)] / [40 + ER x 10] = 22.5 1044.75 = 900 + 225 ER Therefore maximum exchange ratio ER = 0.64

(b)

[Alternatively: As the EPS of Astra if remains unchanged, the PE of the merged company has to be 16 and therefore maximum exchange ratio Astra Pharma should accept is = - S1 / S2 + PE12 (E12)/P1S2 = -40/10 + [16x 995(1.05)] / (360 x 10) = 0.64] (c) Post-merger EPS of Astra Pharma = 995,000,000 / [40,000,000 + 10,000,000/3] = Rs. 22.96 Maximum exchange ratio acceptable to the shareholders of Astra Pharma = -S1 / S2 + PE12(E12)/P1S2 = -40/10 + (15 x 995)/(360 x 10) = 0.15 Minimum exchange ratio acceptable to the shareholders of Max Drugs = P2S1 / ( P12E12 – P2S2) = (110 x 40) / [ 14 x (995x1.02) – 110 x 10] = 0.34 To get the level of the PE ratio where the lines ER1 and ER2 will intersect we have to solve the following for PE12 - S1 + S2 P1S2 (E1 + E2) PE12 = PE12 (E1 + E2) – P2S2 P2S1

(d)

(e)

(f)

- 40/10 + 995 PE12 / 360 x 10 = (110 x 40)/ [ PE12 x 995 -110 x 10] 995PE12 – 14,400 = 3,600 995 PE12 - 1100 4,400

990,025PE212 -14,328,000 PE12 -1,094,500PE12 + 15,840,000 = 15,840,000 990,025 PE212 = 15,422,500 PE12 PE12 = 15.58 (g) At the exchange ratio of 1:3, shareholders of Max drugs will get 10/3million shares of Astra Pharma. So they will get
? = (10/3) / ( 40 + 10/3) = 7.69% share of Astra Pharma.

The present value of Astra Pharma after the merger will be = 40 x 360 + 10 x 110 + 1000 = Rs.16500 million

Therefore the true cost of the merger from the point of view of Astra Pharma

= 0.0769 x 16500 – (10 x 110) = Rs.168.85 million (h) An exchange ratio based on earnings per share fails to take into account the following:

(i) The difference in the growth rate of earnings of the two companies. (ii) The gains in earnings arising out of merger. (iii) The differential risk associated with the earnings of the two companies. (i) The five sins that plague acquisitions are the following: a) b) c) d) e) Straying too far afield. Striving for bigness. Leaping before looking. Overpaying. Failing to integrate well.

CHAPTER 37

1.

If the spot rate of the US dollar is Rs.40.00 and the three month forward rate is Rs.40.25, what is the annualised forward premium on the dollar?

Solution:

The annualised premium is: Forward rate – Spot rate x Spot rate 40.25 – 40.00 = 40.00 2. x 3 12 = 0.025 or 2.5 % Forward contract length in months 12

If the spot rate of the US dollar against Japanese yen 114.00 and the six month forward rate is Rs.110, what is the annualised forward premium on the yen ?

Solution:

The annualised premium is : 114 – 110 = 114 x 6 12 = 0.0702 or 7.02 %

3.

You have $300 million to invest. You are considering deposits in the US or U.K. The US interest rate on 1 –year deposit of this size is 5.25 percent. The current spot rate is 2.0341 dollars per sterling pound. The rate of interest on a 1-year deposit of this size in U.K. is 5.75 percent. What forward exchange rate will make you indifferent between investing in the US and depositing in the U.K. ?

Solution:

300 300 (1.0525) = 2.0341
F = 2.0245

x 1.0575 x F

A forward exchange rate of 2.0245 dollars per sterling pound will mean indifference between investing in the U.S and in the U.K. 4. You have Rs.100,000 to invest. You are considering deposit in India or the US. The US interest rate on 1 –year deposit of this size is 5.25 percent while the rate for a one year deposit in India is 8 percent .The current spot rate is Rs.39.50 per dollar What forward exchange rate will make you indifferent between investing in India and the the US .

Solution:

100,000 100,000(1.08) = 39.50
F = 40.53

x 1.0525 x F

A forward exchange rate of Rs.40.53 per dollar will mean indifference between investing in India and the U.S. 5. The exchange rate between US dollar and yen is as follows: Spot 114.54 yen per dollar 30-day forwards 114.11 yen per dollar 90-day forwards 113.34yen per dollar 180-day forwards 112.30 yen per dollar Required: (a) What is the annual percentage premium of the yen on the dollar ? (b) What is the most likely spot rate 6 months hence? (c) If the interest on 6-month deposit in the US is 2.48 percent (for 6 months), what is it likely to be in Japan? Solution: (a) The annual percentage premium of the yen on the dollar may be calculated with reference to 30-days forwards

114.54 – 114.11 x 114.54 (b) (c)

12 = 4.50 % 1

The most likely spot rate 6 months hence will be : 112.30 yen / dollar Forwards rate = Spot rate 112.3 = 114.54 1.0248 1 + foreign interest rate 1 + domestic interest rate in Japan 1 + domestic interest rate

Domestic interest rate in Japan = 0.00476 = 0.48 per cent for 6 months. 6. The exchange rate between euro and Australian dollar (AUD) is as follows:

Spot 1.5915 AUD per EUR 30-day forwards 1.5950 AUD per EUR 90-day forwards 1.6008 AUD per EUR Required: (a) What is the annual percentage premium of the euro on the AUD ? (b) What is the most likely spot rate 3 months hence? (c) If the interest on 3-month deposit in Euro land is 2.28 percent (for 3 months), what is it likely to be in Australia ? Solution: The annual percentage premium of the euro may be calculated with reference to 30days forwards 1.5950 – 1.5915 x 1.5915 (b) (c) 1 12 = 2.64 %

The most likely spot rate 3 months hence will be : 1.6008 AUD per euro Forwards rate = Spot rate 1.6008 = 1.5915 1.0228 1 + foreign interest rate 1 + domestic interest rate in Japan 1 + domestic interest rate

Domestic interest rate in Japan = 0.0288 = 2.88 per cent( for 3 months)

7.

Navabharat Corporation, an Indian company, is considering a project to be set up in US. The project will entail an initial outlay of USD 500 million and is expected to generate the following cash flow over its five year life: Year 1 Cash flow 100 (in USD millions) 2 250 3 400 4 400 5 300

The current spot exchange rate is Rs.39.40 per US dollar, the risk-free rate in India is 8 percent and the risk-free rate in the US is 5.5 percent. Navabharat Corporation’s required rupee return on a project of this kind is 17 percent. Calculate the NPV of the project using the home currency approach.
Solution: S0 = Rs.39.40 , rh = 8 per cent , rf = 5.5 per cent

Hence the forecasted spot rates are :
Year Forecasted spot exchange rate

1 2 3 4 5

Rs.39.40 (1.08 / 1.055)1 = Rs. 39.40 (1.08 / 1.055)2 = Rs. 39.40 (1.08 / 1.055)3 = Rs. 39.40 (1.08 / 1.055)4 = Rs. 39.40 (1.08 / 1.055)5 =

Rs.40.33 Rs.41.29 Rs.42.27 Rs.43.27 Rs.44.29

The expected rupee cash flows for the project
Year Cash flow in dollars Expected exchange (million) rate -200 39.40 100 40.33 250 41.2 400 42.27 400 43.27 300 44.29 Cash flow in rupees (million) -7,880 4,033 10,300 16,908 17,308 13,287

0 1 2 3 4 5

Given a rupee discount rate of 17 per cent, the NPV in rupees is: 4,033 NPV = -7,880 + (1.17)1 + (1.17)2 10,300 + (1.17)3 16,908

17,308 + (1.17)4 +

13,287 (1.17)5

= Rs. 28,944.92 million The dollar NPV is : 28,944.92 / 39.40 = 734.64 million dollars 8. Ashoka Limited , an Indian company, is considering a project to be set up in US. The project will entail an initial outlay of USD 800 million and is expected to generate the following cash flow over its six year life: Year 1 2 3 4 5 6 Cash flow 200 350 500 800 700 500 (in USD millions) The current spot exchange rate is Rs.39.00 per US dollar, the risk-free rate in India is 7 percent and the risk-free rate in the US is 5 percent. Ashoka Limited’s required rupee return on a project of this kind is 22 percent. Calculate the NPV of the project using the home currency approach.
Solution: S0 = Rs.39 , rh = 7 per cent , rf = 5 per cent

Hence the forecasted spot rates are:
Year 1 2 3 4 5 6 Forecasted spot exchange rate Rs.39 (1.07 / 1.05)1 = Rs.39.74 Rs. 39 (1.07 / 1.05)2 = Rs.40.50 Rs. 39 (1.07 / 1.05)3 = Rs.41.27 Rs. 39 (1.07 / 1.05)4 = Rs.42.06 Rs. 39 (1.07 / 1.05)5 = Rs.42.86 Rs. 39 (1.07 / 1.05)6 = Rs.43.67

The expected rupee cash flows for the project

Year

0 1 2 3 4 5 6

Cash flow in dollars Expected exchange (million) rate -800 39.00 200 39.74 350 40.50 500 41.27 800 42.06 700 42.86 500 43.67

Cash flow in rupees (million) - 31,200 7,948 14,175 20,635 33,648 30,002 21,835

Given a rupee discount rate of 22 per cent, the NPV in rupees is : 7,948 14,175 20,635 NPV = -31,200 + + + (1.22)1 (1.22)2 (1.22)3 33,648 + (1.22)4 = Rs. 29,114 million The dollar NPV is: 29,114 / 39 = 746.51 million dollars 9. The 90-day interest rate is 1.25 percent in the U S and 1.50 percent in U K and the current spot exchange rate is $ 2.02/£. What will be the 90-day forward rate? + (1.22)5 30,002 + 21,835 ------(1.22)6

Solution:

Forward rate = Spot rate F = 2.02

1 + domestic interest rate 1 + foreign interest rate 1 + .0125 1 + .0150

F = $ 2.015 / £ 10. The 90-day interest rate is 1.27 percent in the U S and 1.07 percent in Euro land and the current spot exchange rate is $ 1.4203/euro. What will be the 90-day forward rate?

Solution:

Forward rate = Spot rate F = 1.4203

1 + domestic interest rate 1 + foreign interest rate 1 + .0127 1 + .0107

F = $ 1.4231/ euro 11. The current spot rate for the British pound is Rs.81 The expected inflation rate is 4 percent in India and 2.7 percent in U K. What is the expected spot rate of British pound a year hence?

Solution:

Expected spot rate a year from now = Current spot rate Expected spot rate a year from now = Rs.81

1 + expected inflation in home country 1 + expected inflation in foreign country 1.04 1.027

So, the expected spot rate a year from now is : 81 x (1.04 / 1.027) = Rs.82.03 12. The current spot rate for the euro is Rs.56.40 The expected inflation rate is 5 percent in India and 3 percent in Euro land. What is the expected spot rate of euro a year hence?

Solution:

Expected spot rate a year from now = Current spot rate Expected spot rate a year from now = 56.40

1 + expected inflation in home country 1 + expected inflation in foreign country 1.05 1.03

So, the expected spot rate a year from now is : 56.40 x (1.05 / 1.03) = Rs.57.50

13.

Suppose India and UK produce only one good, copper. Suppose the price of copper in India is Rs.28000 and in the UK it is $400. a. According to the law of one price, what should the British Pound : Rupee spot exchange rate be? b. Suppose the price of copper over the next year is expected to rise is Rs.30,000 in India and $460 in the UK. What should the one year British Pound: Rupee forward rate be?

Solution:

(a)

The spot exchange rate of one British Pound should be : 28000 = Rs.70 400 One year forward rate of one British Pound should be : 30000 = Rs. 65.22 460

(b)

14.

Suppose India and Singapore produce only one good, tin. Suppose the price of tin in India is Rs.8000 and in Singapore it is Singapore dollar 300. (a) According to the law of one price, what should the Singapore dollar: Rupee spot exchange rate be? (b) Suppose the price of tin over the next year is expected to rise to Rs.10,000 in India and $330 in Singapore. What should the one year Singapore dollar: Rupee forward rate be? Solution: (a) The spot exchange rate of one Singapore dollar should be : 8000 = Rs.26.67 300 One year forward rate of one Singapore dollar should be : 10000 = Rs. 30.30 330

(b)

15.

The inflation rate in US is expected to be 2.7 percent per year, and the inflation rate in Japan is expected to be 0.4 percent per year. If the current spot rate is 114 yen/$ what will be the expected spot rate in 3 years? (1 + expected inflation in Japan)3 (1 + expected inflation in UK)3

Solution:

Expected spot rate = Current spot rate x 3 years from now

(1.004)3 = 114 x (1.027) 16.
3

= 106.51 yen / $

The inflation rate in euro currency area is expected to be 1.7 percent per year, and the inflation rate in India is expected to be 3.5 percent per year. If the current spot rate is Rs. 56.4 per euro what will be the expected spot rate in 2 years?

Solution:

(1 + expected inflation in India)2 Expected spot rate = Current spot rate x 2 years from now (1.035)2 = 56.4 x (1.017) 17.
2

(1 + expected inflation in euro currency area)2

= Rs.58.41per euro

Suppose the spot rate between AUD and USD is 0.8500 USD per AUD. This is denoted as AUD/USD. The 90-day forward is 0.8530. U.S dollars can be lent or borrowed at a rate of 5% p.a, while the rates for AUD deposits or loans is 4.5 % p.a. How much risk-less profit can you make on a borrowing of 100 USD.

Solution: Spot

90-day forward 0.8530

AUD/ USD

0.8500

Borrow 100 USD and convert it into AUD 117.65 Invest AUD 117.65 @ 4.5% p.a. for 90 days and get 117.65 [ 1 + 0.045 (90/360)] = AUD 118.9736 Convert AUD into USD at the forward rate and receive dollars = AUD 118.9736 x 0.8530 = $ 101.4845 Repay USD by paying 100 [ 1 + 0.05 (90/360)] Riskless profit = $ 101.4845 - $ 101.2500 = 18. 0.2345 = $ 101.25

Suppose the spot rate between USD and INR is 46.50 INR per USD. This is denoted as USD/INR. The 90-day forward is 47.20. Indian rupee can be lent or borrowed at a rate 8 % p.a. while the rate for USD deposits or loans is 6.5% p.a. How much risk-less profit can you make on a borrowing of Rs. 10,000?

Solution:

USD/INR

Spot 46.50

90 – day forward 47.20

Borrow 10,000 INR and convert it into USD 215.05 Invest USD 215.05 @ 6.5 % p.a for 90 days and get 215.05 [1 + 0.065 (90/360)] = USD 218.54 Convert USD into INR at the forward rate and receive INR USD 218.54 X 47.20 = INR 10315.088 Repay INR loan by paying 10,000 [ 1 + 0.08 ( 90/360) ] = 10,200 Riskless profit = 10315.088 - 10200 = INR 115.088 = INJR 115.09

19.

An Indian firm has a liability of £500,000 on account of purchases from a British supplier, which is payable after 180 days. The 180-day money market rate for deposits in UK is 2.5 percent. What steps should the Indian firm take to do a money market hedge?

Solution:

(i)

Determine the present value of the foreign currency liability (£500,000) by using 180-day money market deposit rate applicable to the foreign country. This works out to :
£500,000

= £ 487,805 (1.025) (ii) Obtain £487,805 on today’s spot market

(iii) Invest £487,805 in the UK money market. This investment will grow to £500,000 after 180 days

20.

An Indian firm has a receivable of £400,000 on account of exports to a British firm, which is payable after 90 days. The 90-day money market borrowing rate in UK is 2.0 percent. What steps should the Indian firm take to do a money market hedge?

Solution:

(i)

Determine the present value of the foreign currency asset (£400,000) by using the 90-day money market borrowing rate of 2 per cent. 400,000 = £ 392,157 (1.02)

(ii)

Borrow £392,157 in the UK money market and convert them to rupees in the spot market.

(iii) Repay the borrowing of £392,157 which will compound to £400000 after 90 days with the collection of the receivable. 21. Sagar Ltd has a short-term fund surplus of Rs.100 million. The funds can be parked for a six-month period. The company observes the following rates in the market. Eurodollar 6 month LIBOR : 5 % p.a. ( This is the interest rate for a USD deposit) USD/ INR spot : 46.70/46.80 USD/ INR 6months forward : 46.90/ 47.00 If Sagar Ltd. parks its funds in the US dollar, what rupee rate of return will it finally get over the 6 month period, if covered forward?
Solution:

100,000,000 Amount deposited in USD = 46.80 Maturity value of the USD = 2,136,752.14 [1 + 0.05 (180/360)] = $ 2,190,170.94 = $2,136,752.14

Rupee equivalent at the forward rate of 46.90 per USD = = Rupee rate of return = $ 2,190,170.94 x 46.90 Rs.102,719.017.10 2.719 %

22.

Eastern Industries Ltd has a short- term fund surplus of Rs.120 million. The funds can be parked for a six month period. The company observes the following rates in the market. Eurodollar 6 month LIBOR : 5% p.a ( This is the interest rate for a USD deposit) USD/INR spot : 43.50/43.60 USD/INR 6 month forward : 43.80/43.90 If Eastern Industries parks its funds in the U.S dollar, What return will it finally get over the 6-month period, if covered forward?

Solution:

Amount deposited in USD

=

120,000,000 43.60

= $2,752,293.58

Maturity value of the USD deposit

=

2,752,293.58

[1 + 0.05 (180/360)]

=

$2,821,100.92

Rupee equivalent at the forward rate of 43.80 per USD = 123,564,220.30 Rate of return = 3,564,220.30/120,000,000 = 0.0297 or 2.97 %

23.

A foreign exchange dealer in London normally quotes spot, one-month, and threemonth forward. When you ask over the telephone for current quotations for the Japanese yen against the U.S. dollar, you hear: 110.50 / 55, (i) 50/ 55, 70 / 75

What would you receive in dollars if you sold Yen 20,000,000 spot?

Solution:

20,000,000 = 110.55 $ 180,913.6137

(ii)

What would it cost you to purchase JPY 30,000,000 forward three-months with dollars?

Solution:

Three months outright = ( 110.50 + 0.70 ) / ( 110.55 + 0.75 ) = 111.20 / 111.30 30,000,000 = 111.20 24. A foreign exchange dealer in London normally quotes spot, one-month and threemonth forward. When you ask over the telephone for current quotations for the Japanese Yen against the US dollar, you hear 115.80/90, 40/45, 60/65 (i)
Solution:

= $ 269,784.1727

What would you receive in dollars if you sold Yen 30,000,000 spot?

30,000,000 = 115.90 (ii) What would it cost you to purchase JPY 40,000,000 forward three-months with dollars ? $258,843.83

Solution:

Three months outright = (115.80 + 0.60 ) ( 115.90 + 0.65) = 116.40 116.55 = 40,000,000 = $343,642.61 116.40 25. Suppose an Indian firm has a 3-month payable of JPY 80 million. The market rates are as follows: Mumbai USD/INR Spot : 43.50/60 3-months : 44.50/60 Singapore USD/JPY Spot : 115.20/30 3-months : 115.10/20

If the firm buys JPY forward against INR, how much will it have to pay?
Solution:

USD required

=

80,000,000 115.10

= USD 695,047.78

Rupees required = = 26.

USD 695,047.78 x 44.60 Rs. 30,999,130.99

Suppose an Indian firm has a 3-month payable of JPY 80 million. The market rates are as follows: Mumbai: USD/ INR spot 3 months USD/ JPY spot 3 months : : : : 46.20/ 30 45.80/ 90 118.50/ 60 118.40/ 50

Singapore:

a.
Solution:

If the firm buys JPY forward against INR, how much will it have to pay?

80,000,000 USD required = 118.40 Rupees required = = USD 675,675.68 X 45.90 Rs. 31,013,513.71 = USD 675,675.68

CHAPTER 40

1.

Price changes of two pharmaceutical stocks, P and Q, are positively correlated. The historical relationship is as follows: Average percentage change in P = 0.01 + 0.50 (Percentage change in Q) Changes in Q account for 50 per cent of the variation of changes in P (R2 = 0.5). (a) If an investor owns Rs.2 million of P, how much of Q should he sell to minimise his risk? (b) What is his hedge ratio? (c) How should he create a zero value hedge?

Solution:

(a) (b) (c) 2.

The investor must short sell Rs.4 million (Rs.2 million / 0.50) of Q His hedge ratio is 0.50 To create a zero value hedge he must deposit Rs.2 million in a bank.

The stock index is currently at 5,000 and the six month stock index futures is trading at 5,100. The risk-free annual rate is 8 per cent. What is the average annual dividend yield on the stocks in the index?

Solution:

Futures price = Spot price (1+Risk-free rate)0.5 5100 = 5000 (1.08) 0.5

Spot price x Dividend yield (1+Risk-free rate)0.5 5000 x Dividend yield (1.08) 0.5

The dividend yield on a six months basis is 1.92 per cent. On an annual basis it is approximately 3.84 per cent. 3. The stock index is currently at 18,000 and the three month stock index futures is trading at 18,200. The risk-free annual rate is 9 per cent. What is the average annual dividend yield on the stocks in the index?

Solution:

Futures price = Spot price (1+Risk-free rate)0.25 18200 = 18000 (1.09) 0.25

Spot price x Dividend yield (1+Risk-free rate)0.25 18000 x Dividend yield (1.09) 0.25

The dividend yield on a three months basis is 1.067 per cent. On an annual basis it is approximately 4.268 per cent.

4.

The following information about copper scrap is given:
• • • •

Spot price Futures price Interest rate PV (storage costs)

: : : :

Rs.10,000 per ton Rs.10,800 for a one year contract 12 per cent Rs.500 per year

What is the PV (convenience yield) of copper scrap?
Solution:

Futures price (1+Risk-free rate) 10,800 = 10,000 + 500 – Present value of convenience yield (1.12)1 Hence the present value of convenience yield is Rs.857.14 per ton. 5. The following information about gunmetal scrap is given:
• • • •
1

= Spot price + Present value of – Present value storage costs of convenience yield

Spot price Futures price Interest rate PV (storage costs)

: : : :

Rs.150,000 per ton Rs.160,000 for a one year contract 13 per cent Rs.800 per year

What is the PV (convenience yield) of gunmetal scrap?
Solution:

Futures price (1+Risk-free rate)1 160,000 = 150,000 + 800 – Present value of convenience yield (1.13)
1

= Spot price + Present value of – Present value storage costs of convenience yield

Hence the present value of convenience yield is Rs.9,207 per ton.

6.

Consider the following data Amit Corpn.
•

Sumit Corpn. Floating Rate 5 years 50 million 5.0 %

Desired Funding

Fixed Rate 5 years 50 million 7.0 %

• •

Cost of Fixed Rate Funding Cost of Floating Rate Funding

6-month LIBOR +50 bp

6 month LIBOR

Show how both the parties can save on funding cost by entering into a coupon swap with the help of a swap bank. Assume that the bank wishes to earn 0.5 % and the balance of savings is shared equally between the two firms.
Solution:

LIBOR- 50 bp 5.5% Amit Ltd. LIBOR + 50bp 7. Consider the following data
Firm A •

Swap Bank

LIBOR50bp 5% Sumit Ltd. 5% Fixed Rate

Firm B

Desired Funding

Fixed Rate $ 5 years 40 million 7%

Floating Rate $ 5 years 40 million 5.50 %

• •

Cost of Fixed Rate Funding Cost of Floating Rate Funding

6-month LIBOR + 100 bp

6 month LIBOR+25 bp

Show by way of a diagram how the parties can save on funding cost by entering into a coupon swap with the help of a swap bank. Assume that the cost saved is shared equally by the two firms and the bank.
Solution:

The total savings that will be effected will be [(7% - 5.5%) – (LIBOR + 1.00% - LIBOR - 0.25%] = 0.75%. The share of each in the savings is therefore 0.25%. To realise this, a swap can be arranged as shown in the following diagram.

8.

Consider the following data:
Excel Corpn. Fixed Rate $ 5 years 200 million Apple Ltd Floating Rate $ 5 years 200 million

Desired Funding

Cost of Fixed Rate Funding: Cost of Floating Rate Funding:

6.25% 6month LIBOR+50bp

5% 6 month LIBOR

Both the companies have approached you, a swap banker, for arranging a swap in such a way that the savings is split equally among all the three. Show diagrammatically how you will arrange such a swap.
Solution:

9.

As a swap banker, you are approached by client A who has to fund itself in fixed rate EUR though it prefers floating rate USD funding. Its funding cost in EUR is 5.25% while it is willing to pay floating at six-month LIBOR plus 50 bp. You have another client B which has easy access to floating USD market at SubLIBOR cost of LIBOR-50 bp. It would like EUR funding at no more than 5% to acquire some EUR fixed rate assets. Show how the swap can be executed. Assume that swap bank incurs savings in one currency and an additional payment obligation in other currency.

Solution:



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