Description
investment decisions; payback period, discounted payback, book rate of return, internal rate of return (IRR), modified IRR, profitability index.
Net Present Value Leads to Better Investment Decisions than OtherMaster subtitle style Click to edit Criteria
Topics Covered
?Capital Budgeting ?NPV and its Competitors ?The Payback Period ?The Book Rate of Return ?Internal Rate of Return
Capital Budgeting
?Capital?
Capital Budgeting
?Capital?
Long term assets to be used ?Budgeting?
Capital Budgeting
?Capital?
Long term assets to be used ?Budgeting? Plan which details projected inflows and outflows during some future period ?Capital Budget?
Capital Budgeting
?Capital?
Long term assets to be used ?Budgeting? Plan which details projected inflows and outflows during some future period ?Capital Budget? Outline of planned investment in fixed assets ?Capital Budgeting?
Capital Budgeting
?Capital?
Long term assets to be used ?Budgeting? Plan which details projected inflows and outflows during some future period ?Capital Budget? Outline of planned investment in fixed assets ?Capital Budgeting? Process of analysing projects and deciding which ones to include
Importance of Cap. Bud.
?Defines strategic direction of the firm –
new product, service, markets, etc. ?Results of cap. Bud. Decisions continue for many years & investment in FA may lead to inflexibility ?Asset expansion based on future expected revenues – requires long term forecast
Investment Decision
? If firm invests too much – high depreciation
& other expenses ? If the firm invests too less – inadequate capacity may lose market share ? Timing – capital asset must be available when they are needed ? If known in advance, the firm can plan the acquisition of assets. Usually firms wait till full capacity and then order – may result in delay in acquiring assets ? Flip side – if actual is lower than forecasted – avoid investment
Ideas
?Cap. Bud. Projects are generated by
the firm ?Firm’s growth or to stay competitive – new products, ways to make a better product, ways to operate lower costs, better service, etc.
Types of Projects
Types of Projects
?Replacement – for maintenance ?Replacement – for cost reduction ?Expansion of existing product/ market ?Expansion for new product/ market ?Safety/ Environmental project ?R & D ?Others – office building, etc.
Cap. Bud. & Sec. Valuation
?Cost of project – Price to be paid for
stock ?Estimated cash flows for project – future dividends ?Salvage value – horizon value ?Riskiness & cost of capital must be estimated ?PV of expected cash flows ?PV of cash flows compared with initial outlay to take decision
Capital Budgeting Rules
?The Payback Period ?Discounted Payback ?The Book Rate of Return ?NPV ?Internal Rate of Return ?Modified IRR ?Profitability Index
Payback
?The payback period of a project is
the number of years it takes before the cumulative forecasted cash flow equals the initial outlay. ?The payback rule says only accept projects that “payback” in the desired time frame. ?This method is very flawed, primarily because it ignores later year cash flows and the present value of future cash flows.
Payback Criteria
?Shorter the payback better the project
Payback
Example
Examine the three projects and note the mistake we would make if we insisted on only taking projects with a payback period of 2 years or less. Payback Project C0 C1 C2 C3 NPV@ 10% Period A - 2000 500 500 5000 B - 2000 500 1800 0 C - 2000 1800 500 0
Payback
Example Examine the three projects and note the mistake we would make if we insisted on only taking projects with a payback period of 2 years or less.
Payback Project C0 C1 C2 C3 NPV@ 10% Period A - 2000 500 500 5000 3 + 2,624 B - 2000 500 1800 0 2 - 58 C - 2000 1800 500 0 2 + 50
Payback Drawbacks
Payback Drawbacks
?Payback rule ignores all CFs after
the cutoff date ?It gives equal weightage to all CFs before the cutoff date ?It does not take the entire life of the project ?Useful, where the future is hazy, in unstable political conditions, firms having liquidity crisis, or firms having short term goals
Discounted Payback
Discounted Payback
?Cash flows are discounted at firm’s
cost of capital and then payback calculated ?Discounted payback is like “breakeven” calculation
Discounted Payback
?Same drawback as Payback
Paybacks - Advantages
Paybacks - Advantages
?Provides information on how long
the funds would be tied up in the project ?Shorter the payback – greater the project’s liquidity ?Cash flows expected in distant future are generally more riskier than near term cash flows ?Payback is considered as indicator of a project’s riskiness
Book Rate of Return
Book Rate of Return - Average income divided by average book value over project life. Also called accounting rate of return.
book income Book rate of return = book assets
Managers rarely use this measurement to make decisions. The components reflect tax and accounting figures, not market values or cash flows.
Book Rate
AAR = Average annual Profit after Taxes / Average Investment over the life of the project AAR > ‘r’, accept the project Avg. Investment
Book Rate
?Not a good measure ?It is an average across all firm’s
activities
Example
Determine the Average rate of return, payback and NPV for the following 2 machines Particulars Cost PAT Year 1 Year 2 Year 3 Year 4 Year 5 Estimated life Estimated Salvage Value 3375 5375 7375 9375 11375 5 30000 11375 9375 7375 5375 3375 5 30000 Machine A 56125 56125
Machine B
NPV
?Forecast CFs generated by project over
its economic life ?Determine appropriate ‘r’ ?Use ‘r’ to discount future CFs ?Calculate NPV
NPV Tenet
?Money today is worth more than money
tomorrow ?It solely depends on ‘r’ & CFs – it could be affected by manager’s decisions – accounting method, etc. ?You can add PV of CF of different periods ?NPV depends on CFs and not accounting income ?It considers the total benefit arising out of the project ?Useful for mutually exclusive projects
NPV Rationale
?NPV = 0, signifies that the cash
flows are sufficient to repay the invested capital & provide required rate of return ?NPV +ve, it generates more money than is needed to service the debt and provide the required return to the shareholders. The excess accrues solely to the shareholders ?NPV –ve, converse to the above
Internal Rate of Return
?Internal rate of return is that return at
which NPV = 0 ?It is the discount rate at which the PV of all inflows is equal to the PV of all outflows NPV = C0 + C1/(1+r) = 0 r = -C0/C1 – 1 The discount rate that makes NPV = 0
IRR Criteria
?We accept the project if IRR is greater
than Opportunity cost of capital – it increases the shareholders’ value ?“Breakeven” characteristic ?Most Managers recommend this method in preference to NPV
Internal Rate of Return
Example You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment?
Internal Rate of Return
Example You can purchase a turbo powered machine tool gadget for 4,000. The investment will generate 2,000 and 4,000 in cash flows for two years, respectively. What is the IRR on this investment?
2,000 4,000 NPV = ?4,000 + + =0 1 2 (1 + IRR ) (1 + IRR )
Internal Rate of Return
Example You can purchase a turbo powered machine tool gadget for 4,000. The investment will generate 2,000 and 4,000 in cash flows for two years, respectively. What is the IRR on this investment?
2,000 4,000 NPV = ?4,000 + + =0 1 2 (1 + IRR ) (1 + IRR )
IRR = 28.08%
Internal Rate of Return
Example A project X costs Rs. 36 lacs and is expected to generate cash inflows of Rs. 11.2 lacs annual for 5 years. The salvage value at the end of 5 years is Rs. 6 lacs. Similarly Project Y Costs Rs. 36 lacs and has annual cashflows of for 5 years as Rs. 5.2 lacs, Rs. 8.8 lacs, Rs. 11.6 lacs, Rs. 13.5 lacs and Rs. 16.9 lacs. Its salvage value at the end of 5 years is Rs. 6 lacs. Project Z costs Rs. 45 lacs and has cash inflows of Rs. 5.6 lacs, Rs. 9.2 lacs, Rs. 13.4 lacs, Rs. 16.7 lacs and Rs. 22 lacs for 5 years. It salvage value at the end of 5 years is Rs. 5 lacs. Calculate the payback, AAR, NPV and IRR? Assume the Opportunity cost of capital as 15%
Internal Rate of Return
X Payback AAR IRR NPV 3.2 53.33% 20% 4.5 Y 3.8 53.33% 17% 1.9 Z 4.01 53.52% 14% -1.4
Internal Rate of Return
2500 2000 1500 NPV (,000s) 1000 500 0 -1000 -1500 -2000 Discount rate (%)
10
IRR=28%
-500
10
20
30
40
50
60
70
80
90
0
Internal Rate of Return
Pitfall 1 - Lending or Borrowing?
?With some cash flows (as noted below)
the NPV of the project increases as the discount rate increases. ?This is contrary to the normal relationship between NPV and discount rates.
Internal Rate of Return
Pitfall 1 - Lending or Borrowing?
? With some cash flows (as noted below) the NPV of the
project increases as the discount rate increases. ? This is contrary to the normal relationship between NPV and discount rates.
NPV Discount Rate
Borrowing or Lending
?Borrowing – IRR < occ ?Lending – IRR > occ ?In case of mixed CFs (positive and
negative), IRR > occ
Internal Rate of Return
Pitfall 2 - Multiple Rates of Return
? Certain cash flows can generate NPV=0 at
two different discount rates. ? The following cash flow generates NPV=0 at both (-50%) and 15.2%.
Internal Rate of Return
Pitfall 2 - Multiple Rates of Return
? Certain cash flows can generate NPV=0 at two different
discount rates. ? The following cash flow generates NPV=0 at both (50%) and 15.2%. IRR=15.
500 0 NPV -500 -1000 IRR=50%
2% Discou nt Rate
Rule of sign
?There can be many different IRRs for a
project as there are changes in sign of the cash flow – Descartes ‘rule of sign’
Pavilion Project: NPV and IRR?
0 -800 k= 10% 1 5,000 2 -5,000
NPV = -386.78 IRR = ERROR. Why?
We got IRR = ERROR because there are 2 IRRs. Non-normal CFs--two sign changes. Here’s a picture:
NPV
NPV Profile
IRR2 = 400%
450 0 100 IRR1 = 25% 400 k
-800
Logic of Multiple IRRs
1. At very low discount rates, the PV of CF2 is large & negative, so NPV < 0. 2. At very high discount rates, the PV of both CF1 and CF2 are low, so CF0 dominates and again NPV < 0. 3. In between, the discount rate hits CF2 harder than CF1, so NPV > 0.
Internal Rate of Return
Pitfall 3 - Mutually Exclusive Projects ? IRR sometimes ignores the magnitude of the project. ? The following two projects illustrate that problem.
Internal Rate of Return
Pitfall 3 - Mutually Exclusive Projects
Mutually exclusive projects
?Look at IRR on incremental basis ?1st calculate the IRR of smaller
investment project ?The calculate the incremental CFs for the larger project ?Calculate the IRR of the incremental cashflows, if it is greater than cost of capital, accept the larger project
Construct NPV Profiles
Find NPVL and NPVS at different discount rates:
k 0 5 10 15 20 NPVL 50 33 19 ( 7 4 ) NPVS 40 29 20 12 5
NPV ($)
60 50 40 30 20 10 0 0 -10 5 10 15 20
k 0 5 10 15 20
Crossover Point = 8.7% S L
NPVL 50 33 19 7 (4)
NPVS 40 29 20 12 5
IRRS = 23.6% Discount Rate (%)
23.6
IRRL = 18.1%
NPV and IRR always lead to the same accept/reject decision for independent projects:
NPV ($) IRR > k and NPV > 0 Accept. k > IRR and NPV < 0. Reject.
IRR
k (%)
Mutually Exclusive Projects
NPV L k < 8.7: NPVL> NPVS , IRRS > IRRL CONFLICT k > 8.7: NPVS> NPVL , IRRS > IRRL NO CONFLICT
S k k 8.7
IRR S %
IRR L
To Find the Crossover Rate
Find cash flow differences between the projects. 2. Calculate IRR. Crossover rate = 8.68%, rounded to 8.7%. 3. Subtract S from L or vice versa, but better to have first CF negative. 4. If profiles don’t cross, one project dominates the other.
1.
Two Reasons NPV Profiles Cross
1. Size (scale) differences. Smaller project frees up funds at t = 0 for investment. The higher the opportunity cost, the more valuable these funds, so high k favors small projects. Timing differences. Project with faster payback provides more CF in early years for reinvestment. If k is high, early CF especially good, NPVS > NPVL.
2.
Internal Rate of Return
Pitfall 4 - Term Structure Assumption ?We assume that discount rates are stable during the term of the project. ?This assumption implies that all funds are reinvested at the IRR. ?This is a false assumption. ?Many firms use the IRR implicitly assuming that there is no difference between short- & long-term interest rates
Internal Rate of Return
?Calculating the IRR can be a laborious
task. ?IRR are easier to understand than NPV ?It does not use the concept of cost of capital explicitly ?It is consistent with the objective of maximizing wealth
Reinvestment Rate Assumptions
?NPV assumes reinvest at k
(opportunity cost of capital). ?IRR assumes reinvest at IRR. ?Reinvest at opportunity cost, k, is more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects.
Managers like rates--prefer IRR to NPV comparisons. Can we give them a better IRR? Yes, MIRR is the discount rate which causes the PV of a project’s terminal value (TV) to equal the PV of costs. TV is found by compounding inflows at WACC. Thus, MIRR assumes cash
MIRR
?PV of Costs = PV of Terminal Inflows
?PV Cost = TV / (1+MIRR)n ?PV – discounted at cost of capital
MIRR for Project L (k = 10%)
0 100 .0 10 % 1 2 10 .0 10 MIRR =% 16.5% $100 = 60 .0 10 %
3 80 .0
-100.0 PV outflow s
$158.1 (1+MIR RL)3 MIRRL = 16.5%
66. 0 15 8.1 12. TV 1 inflow s
Why use MIRR versus IRR?
?MIRR correctly assumes reinvestment at
opportunity cost = WACC. MIRR also avoids the problem of multiple IRRs. ? Managers like rate of return comparisons, and MIRR is better for this than IRR.
When there are nonnormal CFs and more than one IRR, use MIRR:
0 800,0 00 1 5,000, 000 2 5,000, 000
PV outflows @ 10% = -4,932,231.40. TV inflows @ 10% = 5,500,000.00. MIRR = 5.6%
?NO. Reject because MIRR = 5.6% < k =
Accept Project P?
10%.
?Also, if MIRR < k, NPV will be negative:
NPV = -$386,777.
S and L are mutually exclusive and will be repeated. k = 10%. Which is better? (000s) 0 Project S: (100) Project L: (100) 1 60 33. 5 2 60 33. 5 33. 5 33. 5 3 4
Example
S L CF0 -100,000 -100,000 CF1 60,000 33,500 Nj 2 4 I 10 10 NPV > NPVS. But is 6,190 4,132 NPVL L better? Can’t say yet. Need to perform common life analysis.
Example
?Note that Project S could be repeated
after 2 years to generate additional profits. ?Can use either replacement chain or equivalent annual annuity analysis to make decision.
Replacement Chain Approach (000s) Project S with Replication: 0 1 2 3 Project S: (100) (100) NPV = $7,547. 6 0 6 0 60 (100 ) (40)
4
6 0 6 0
6 0 6 0
If the cost to repeat S in two years rises to $105,000, which is best? (000s) 0 1 2 3 Project S: (100) 6 0 60 (105 )
4
6 0
6 0
NPVS = $3,415 (45) < NPVL = $6,190. Now choose L.
Profitability Index
?When resources are limited, the
profitability index (PI) provides a tool for selecting among various project combinations and alternatives ?A set of limited resources and projects can yield various combinations. ?The highest weighted average PI can indicate which projects to select.
Profitability Index
NPV Profitability Index = Investment
Example We only have $300,000 to invest. Which do we select? Proj NPV Investment PI A 230,000 200,000 1.15 B 141,250 125,000 1.13 C 194,250 175,000 1.11 D 162,000 150,000 1.08
Profitability Index
Example - continued Proj NPV Investment PI A 230,000 200,000 1.15 B 141,250 125,000 1.13 C 194,250 175,000 1.11 D 162,000 150,000 1.08 Select projects with highest Weighted Avg PI WAPI (BD) = 1.13(125) + 1.08(150) + 0.0 (25) (300) (300) (300) = 1.01
Profitability Index
Example - continued Proj NPV Investment PI A 230,000 200,000 1.15 B 141,250 125,000 1.13 C 194,250 175,000 1.11 D 162,000 150,000 1.08
Select projects with highest Weighted Avg PI
WAPI (BD) = 1.01 WAPI (A) = 0.77 WAPI (BC) = 1.12
Choosing the Optimal Capital Budget
?Finance theory says to accept all positive
NPV projects. ?Two problems can occur when there is not enough internally generated cash to fund all positive NPV projects: ?An increasing marginal cost of
capital. ?Capital rationing
Increasing Marginal Cost of Capital
?Externally raised capital can have large
flotation costs, which increase the cost of capital. ?Investors often perceive large capital budgets as being risky, which drives up the cost of capital. ?If external funds will be raised, then the NPV of all projects should be estimated using this higher marginal cost of capital.
Capital Rationing
? Capital rationing occurs when a company
chooses not to fund all positive NPV projects. ? The company typically sets an upper limit on the total amount of capital expenditures that it will make in the upcoming year.
Capital Rationing
Reason: Companies want to avoid the direct costs (i.e., flotation costs) and the indirect costs of issuing new capital. Solution: Increase the cost of capital by enough to reflect all of these costs, and then accept all projects that still have a positive NPV with the higher cost of capital.
Capital Rationing
Reason: Companies don’t have enough managerial, marketing, or engineering staff to implement all positive NPV projects. Solution: Use linear programming to maximize NPV subject to not exceeding the constraints on staffing.
Linear Programming
?Maximize Cash flows or NPV ?Minimize costs
Capital Rationing
Reason: Companies believe that the project’s managers forecast unreasonably high cash flow estimates, so companies “filter” out the worst projects by limiting the total amount of projects that can be accepted. Solution: Implement a post-audit process and tie the managers’ compensation to the subsequent performance of the project.
Summary
? NPV & IRR Methods ? Similarities: ? Conventional investments – Initial outflow followed by inflows ? Independent Projects ? Differences ? Mutually exclusive Projects ? Technical Exclusiveness ? Size disparity ? Projects with unequal Lives ? Capital Rationing
Conclusion
? Large firms calculate all 6 methods ? Majority prefer IRR ? Payback & Discounted payback – indication of
risk & liquidity ? NPV – direct measure of cash benefit of the project to shareholders ? IRR – information of safety margin ? MIRR has virtues of NPV & IRR ? PI – indication of project risk
Foolish to ignore the information got from all of the above
Issues
?Cannot know the exact future cost of
capital or exact future cash flows. These inputs are estimates – errors can change NPV/ IRR calculations ?Thus quantitative methods provide valuable information but should not be used as the sole criteria ?Qualitative aspects should be considered
Issues
?Managers should question any project
that has high NPV/ IRR/ PI. ?In a perfectly competitive economy, there would be no +ve NPV project – all companies would have the same opportunities and would eliminate any +ve NPV.
Issues
? +ve NPV arises from some imperfection ? Be able to identify imperfections in market
place ? Longer the project life, longer the imperfection should last ? Should be able to explain why the imperfection will persist before accepting the project ? E.g. Patent, proprietary tech, first entrant, new product to meet unidentified customer need ? Firms have to develop some source of competitive advantage that would result in +ve NPV
Resultant
?If can’t identify reason for +ve NPV,
NPV may actually be –ve ?+ve NPV result of hard wok to develop competitive advantage ?Some competitive advantages do last longer – depending on competition’s capability to replicate – patents, control of scarce resource, strong economies of scale, R&D, work culture ?Bottom line – strive to develop nonreplicable sources of competitive advantage
Harold Biermer Survey
?All Fortune Cos use DCF ?84% use payback (not primary method) ?99% use IRR ?85% use NPV ?93% use w.a.c.c. for cap. Bud.
Small Companies
?21% use DCF ?Pre-occupied with liquidity – payback ?Lack of familiarity with DCF techniques ?DCF not worth the effort for small
projects
Post Audit
?Comparing actual results with those
predicted ?Explaining the differences
Post Audit Purpose
?Improve forecasts ?Improve operations ?Identify abandonment/ termination
opportunities
Post Audit
?Must recognize that each element of CF
forecast subject to uncertainty - % of all projects will go wrong ?Projects fail to meet expectations due to reasons beyond management control ?Although some projects are stand alone, the benefits/ savings are hard to measure
Use of Cap. Bud.
?Evaluating Mergers & Acquisitions ?When deciding to downsize operations
or manpower
doc_108083805.pptx
investment decisions; payback period, discounted payback, book rate of return, internal rate of return (IRR), modified IRR, profitability index.
Net Present Value Leads to Better Investment Decisions than OtherMaster subtitle style Click to edit Criteria
Topics Covered
?Capital Budgeting ?NPV and its Competitors ?The Payback Period ?The Book Rate of Return ?Internal Rate of Return
Capital Budgeting
?Capital?
Capital Budgeting
?Capital?
Long term assets to be used ?Budgeting?
Capital Budgeting
?Capital?
Long term assets to be used ?Budgeting? Plan which details projected inflows and outflows during some future period ?Capital Budget?
Capital Budgeting
?Capital?
Long term assets to be used ?Budgeting? Plan which details projected inflows and outflows during some future period ?Capital Budget? Outline of planned investment in fixed assets ?Capital Budgeting?
Capital Budgeting
?Capital?
Long term assets to be used ?Budgeting? Plan which details projected inflows and outflows during some future period ?Capital Budget? Outline of planned investment in fixed assets ?Capital Budgeting? Process of analysing projects and deciding which ones to include
Importance of Cap. Bud.
?Defines strategic direction of the firm –
new product, service, markets, etc. ?Results of cap. Bud. Decisions continue for many years & investment in FA may lead to inflexibility ?Asset expansion based on future expected revenues – requires long term forecast
Investment Decision
? If firm invests too much – high depreciation
& other expenses ? If the firm invests too less – inadequate capacity may lose market share ? Timing – capital asset must be available when they are needed ? If known in advance, the firm can plan the acquisition of assets. Usually firms wait till full capacity and then order – may result in delay in acquiring assets ? Flip side – if actual is lower than forecasted – avoid investment
Ideas
?Cap. Bud. Projects are generated by
the firm ?Firm’s growth or to stay competitive – new products, ways to make a better product, ways to operate lower costs, better service, etc.
Types of Projects
Types of Projects
?Replacement – for maintenance ?Replacement – for cost reduction ?Expansion of existing product/ market ?Expansion for new product/ market ?Safety/ Environmental project ?R & D ?Others – office building, etc.
Cap. Bud. & Sec. Valuation
?Cost of project – Price to be paid for
stock ?Estimated cash flows for project – future dividends ?Salvage value – horizon value ?Riskiness & cost of capital must be estimated ?PV of expected cash flows ?PV of cash flows compared with initial outlay to take decision
Capital Budgeting Rules
?The Payback Period ?Discounted Payback ?The Book Rate of Return ?NPV ?Internal Rate of Return ?Modified IRR ?Profitability Index
Payback
?The payback period of a project is
the number of years it takes before the cumulative forecasted cash flow equals the initial outlay. ?The payback rule says only accept projects that “payback” in the desired time frame. ?This method is very flawed, primarily because it ignores later year cash flows and the present value of future cash flows.
Payback Criteria
?Shorter the payback better the project
Payback
Example
Examine the three projects and note the mistake we would make if we insisted on only taking projects with a payback period of 2 years or less. Payback Project C0 C1 C2 C3 NPV@ 10% Period A - 2000 500 500 5000 B - 2000 500 1800 0 C - 2000 1800 500 0
Payback
Example Examine the three projects and note the mistake we would make if we insisted on only taking projects with a payback period of 2 years or less.
Payback Project C0 C1 C2 C3 NPV@ 10% Period A - 2000 500 500 5000 3 + 2,624 B - 2000 500 1800 0 2 - 58 C - 2000 1800 500 0 2 + 50
Payback Drawbacks
Payback Drawbacks
?Payback rule ignores all CFs after
the cutoff date ?It gives equal weightage to all CFs before the cutoff date ?It does not take the entire life of the project ?Useful, where the future is hazy, in unstable political conditions, firms having liquidity crisis, or firms having short term goals
Discounted Payback
Discounted Payback
?Cash flows are discounted at firm’s
cost of capital and then payback calculated ?Discounted payback is like “breakeven” calculation
Discounted Payback
?Same drawback as Payback
Paybacks - Advantages
Paybacks - Advantages
?Provides information on how long
the funds would be tied up in the project ?Shorter the payback – greater the project’s liquidity ?Cash flows expected in distant future are generally more riskier than near term cash flows ?Payback is considered as indicator of a project’s riskiness
Book Rate of Return
Book Rate of Return - Average income divided by average book value over project life. Also called accounting rate of return.
book income Book rate of return = book assets
Managers rarely use this measurement to make decisions. The components reflect tax and accounting figures, not market values or cash flows.
Book Rate
AAR = Average annual Profit after Taxes / Average Investment over the life of the project AAR > ‘r’, accept the project Avg. Investment
Book Rate
?Not a good measure ?It is an average across all firm’s
activities
Example
Determine the Average rate of return, payback and NPV for the following 2 machines Particulars Cost PAT Year 1 Year 2 Year 3 Year 4 Year 5 Estimated life Estimated Salvage Value 3375 5375 7375 9375 11375 5 30000 11375 9375 7375 5375 3375 5 30000 Machine A 56125 56125
Machine B
NPV
?Forecast CFs generated by project over
its economic life ?Determine appropriate ‘r’ ?Use ‘r’ to discount future CFs ?Calculate NPV
NPV Tenet
?Money today is worth more than money
tomorrow ?It solely depends on ‘r’ & CFs – it could be affected by manager’s decisions – accounting method, etc. ?You can add PV of CF of different periods ?NPV depends on CFs and not accounting income ?It considers the total benefit arising out of the project ?Useful for mutually exclusive projects
NPV Rationale
?NPV = 0, signifies that the cash
flows are sufficient to repay the invested capital & provide required rate of return ?NPV +ve, it generates more money than is needed to service the debt and provide the required return to the shareholders. The excess accrues solely to the shareholders ?NPV –ve, converse to the above
Internal Rate of Return
?Internal rate of return is that return at
which NPV = 0 ?It is the discount rate at which the PV of all inflows is equal to the PV of all outflows NPV = C0 + C1/(1+r) = 0 r = -C0/C1 – 1 The discount rate that makes NPV = 0
IRR Criteria
?We accept the project if IRR is greater
than Opportunity cost of capital – it increases the shareholders’ value ?“Breakeven” characteristic ?Most Managers recommend this method in preference to NPV
Internal Rate of Return
Example You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment?
Internal Rate of Return
Example You can purchase a turbo powered machine tool gadget for 4,000. The investment will generate 2,000 and 4,000 in cash flows for two years, respectively. What is the IRR on this investment?
2,000 4,000 NPV = ?4,000 + + =0 1 2 (1 + IRR ) (1 + IRR )
Internal Rate of Return
Example You can purchase a turbo powered machine tool gadget for 4,000. The investment will generate 2,000 and 4,000 in cash flows for two years, respectively. What is the IRR on this investment?
2,000 4,000 NPV = ?4,000 + + =0 1 2 (1 + IRR ) (1 + IRR )
IRR = 28.08%
Internal Rate of Return
Example A project X costs Rs. 36 lacs and is expected to generate cash inflows of Rs. 11.2 lacs annual for 5 years. The salvage value at the end of 5 years is Rs. 6 lacs. Similarly Project Y Costs Rs. 36 lacs and has annual cashflows of for 5 years as Rs. 5.2 lacs, Rs. 8.8 lacs, Rs. 11.6 lacs, Rs. 13.5 lacs and Rs. 16.9 lacs. Its salvage value at the end of 5 years is Rs. 6 lacs. Project Z costs Rs. 45 lacs and has cash inflows of Rs. 5.6 lacs, Rs. 9.2 lacs, Rs. 13.4 lacs, Rs. 16.7 lacs and Rs. 22 lacs for 5 years. It salvage value at the end of 5 years is Rs. 5 lacs. Calculate the payback, AAR, NPV and IRR? Assume the Opportunity cost of capital as 15%
Internal Rate of Return
X Payback AAR IRR NPV 3.2 53.33% 20% 4.5 Y 3.8 53.33% 17% 1.9 Z 4.01 53.52% 14% -1.4
Internal Rate of Return
2500 2000 1500 NPV (,000s) 1000 500 0 -1000 -1500 -2000 Discount rate (%)
10
IRR=28%
-500
10
20
30
40
50
60
70
80
90
0
Internal Rate of Return
Pitfall 1 - Lending or Borrowing?
?With some cash flows (as noted below)
the NPV of the project increases as the discount rate increases. ?This is contrary to the normal relationship between NPV and discount rates.
Internal Rate of Return
Pitfall 1 - Lending or Borrowing?
? With some cash flows (as noted below) the NPV of the
project increases as the discount rate increases. ? This is contrary to the normal relationship between NPV and discount rates.
NPV Discount Rate
Borrowing or Lending
?Borrowing – IRR < occ ?Lending – IRR > occ ?In case of mixed CFs (positive and
negative), IRR > occ
Internal Rate of Return
Pitfall 2 - Multiple Rates of Return
? Certain cash flows can generate NPV=0 at
two different discount rates. ? The following cash flow generates NPV=0 at both (-50%) and 15.2%.
Internal Rate of Return
Pitfall 2 - Multiple Rates of Return
? Certain cash flows can generate NPV=0 at two different
discount rates. ? The following cash flow generates NPV=0 at both (50%) and 15.2%. IRR=15.
500 0 NPV -500 -1000 IRR=50%
2% Discou nt Rate
Rule of sign
?There can be many different IRRs for a
project as there are changes in sign of the cash flow – Descartes ‘rule of sign’
Pavilion Project: NPV and IRR?
0 -800 k= 10% 1 5,000 2 -5,000
NPV = -386.78 IRR = ERROR. Why?
We got IRR = ERROR because there are 2 IRRs. Non-normal CFs--two sign changes. Here’s a picture:
NPV
NPV Profile
IRR2 = 400%
450 0 100 IRR1 = 25% 400 k
-800
Logic of Multiple IRRs
1. At very low discount rates, the PV of CF2 is large & negative, so NPV < 0. 2. At very high discount rates, the PV of both CF1 and CF2 are low, so CF0 dominates and again NPV < 0. 3. In between, the discount rate hits CF2 harder than CF1, so NPV > 0.
Internal Rate of Return
Pitfall 3 - Mutually Exclusive Projects ? IRR sometimes ignores the magnitude of the project. ? The following two projects illustrate that problem.
Internal Rate of Return
Pitfall 3 - Mutually Exclusive Projects
Mutually exclusive projects
?Look at IRR on incremental basis ?1st calculate the IRR of smaller
investment project ?The calculate the incremental CFs for the larger project ?Calculate the IRR of the incremental cashflows, if it is greater than cost of capital, accept the larger project
Construct NPV Profiles
Find NPVL and NPVS at different discount rates:
k 0 5 10 15 20 NPVL 50 33 19 ( 7 4 ) NPVS 40 29 20 12 5
NPV ($)
60 50 40 30 20 10 0 0 -10 5 10 15 20
k 0 5 10 15 20
Crossover Point = 8.7% S L
NPVL 50 33 19 7 (4)
NPVS 40 29 20 12 5
IRRS = 23.6% Discount Rate (%)
23.6
IRRL = 18.1%
NPV and IRR always lead to the same accept/reject decision for independent projects:
NPV ($) IRR > k and NPV > 0 Accept. k > IRR and NPV < 0. Reject.
IRR
k (%)
Mutually Exclusive Projects
NPV L k < 8.7: NPVL> NPVS , IRRS > IRRL CONFLICT k > 8.7: NPVS> NPVL , IRRS > IRRL NO CONFLICT
S k k 8.7
IRR S %
IRR L
To Find the Crossover Rate
Find cash flow differences between the projects. 2. Calculate IRR. Crossover rate = 8.68%, rounded to 8.7%. 3. Subtract S from L or vice versa, but better to have first CF negative. 4. If profiles don’t cross, one project dominates the other.
1.
Two Reasons NPV Profiles Cross
1. Size (scale) differences. Smaller project frees up funds at t = 0 for investment. The higher the opportunity cost, the more valuable these funds, so high k favors small projects. Timing differences. Project with faster payback provides more CF in early years for reinvestment. If k is high, early CF especially good, NPVS > NPVL.
2.
Internal Rate of Return
Pitfall 4 - Term Structure Assumption ?We assume that discount rates are stable during the term of the project. ?This assumption implies that all funds are reinvested at the IRR. ?This is a false assumption. ?Many firms use the IRR implicitly assuming that there is no difference between short- & long-term interest rates
Internal Rate of Return
?Calculating the IRR can be a laborious
task. ?IRR are easier to understand than NPV ?It does not use the concept of cost of capital explicitly ?It is consistent with the objective of maximizing wealth
Reinvestment Rate Assumptions
?NPV assumes reinvest at k
(opportunity cost of capital). ?IRR assumes reinvest at IRR. ?Reinvest at opportunity cost, k, is more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects.
Managers like rates--prefer IRR to NPV comparisons. Can we give them a better IRR? Yes, MIRR is the discount rate which causes the PV of a project’s terminal value (TV) to equal the PV of costs. TV is found by compounding inflows at WACC. Thus, MIRR assumes cash
MIRR
?PV of Costs = PV of Terminal Inflows
?PV Cost = TV / (1+MIRR)n ?PV – discounted at cost of capital
MIRR for Project L (k = 10%)
0 100 .0 10 % 1 2 10 .0 10 MIRR =% 16.5% $100 = 60 .0 10 %
3 80 .0
-100.0 PV outflow s
$158.1 (1+MIR RL)3 MIRRL = 16.5%
66. 0 15 8.1 12. TV 1 inflow s
Why use MIRR versus IRR?
?MIRR correctly assumes reinvestment at
opportunity cost = WACC. MIRR also avoids the problem of multiple IRRs. ? Managers like rate of return comparisons, and MIRR is better for this than IRR.
When there are nonnormal CFs and more than one IRR, use MIRR:
0 800,0 00 1 5,000, 000 2 5,000, 000
PV outflows @ 10% = -4,932,231.40. TV inflows @ 10% = 5,500,000.00. MIRR = 5.6%
?NO. Reject because MIRR = 5.6% < k =
Accept Project P?
10%.
?Also, if MIRR < k, NPV will be negative:
NPV = -$386,777.
S and L are mutually exclusive and will be repeated. k = 10%. Which is better? (000s) 0 Project S: (100) Project L: (100) 1 60 33. 5 2 60 33. 5 33. 5 33. 5 3 4
Example
S L CF0 -100,000 -100,000 CF1 60,000 33,500 Nj 2 4 I 10 10 NPV > NPVS. But is 6,190 4,132 NPVL L better? Can’t say yet. Need to perform common life analysis.
Example
?Note that Project S could be repeated
after 2 years to generate additional profits. ?Can use either replacement chain or equivalent annual annuity analysis to make decision.
Replacement Chain Approach (000s) Project S with Replication: 0 1 2 3 Project S: (100) (100) NPV = $7,547. 6 0 6 0 60 (100 ) (40)
4
6 0 6 0
6 0 6 0
If the cost to repeat S in two years rises to $105,000, which is best? (000s) 0 1 2 3 Project S: (100) 6 0 60 (105 )
4
6 0
6 0
NPVS = $3,415 (45) < NPVL = $6,190. Now choose L.
Profitability Index
?When resources are limited, the
profitability index (PI) provides a tool for selecting among various project combinations and alternatives ?A set of limited resources and projects can yield various combinations. ?The highest weighted average PI can indicate which projects to select.
Profitability Index
NPV Profitability Index = Investment
Example We only have $300,000 to invest. Which do we select? Proj NPV Investment PI A 230,000 200,000 1.15 B 141,250 125,000 1.13 C 194,250 175,000 1.11 D 162,000 150,000 1.08
Profitability Index
Example - continued Proj NPV Investment PI A 230,000 200,000 1.15 B 141,250 125,000 1.13 C 194,250 175,000 1.11 D 162,000 150,000 1.08 Select projects with highest Weighted Avg PI WAPI (BD) = 1.13(125) + 1.08(150) + 0.0 (25) (300) (300) (300) = 1.01
Profitability Index
Example - continued Proj NPV Investment PI A 230,000 200,000 1.15 B 141,250 125,000 1.13 C 194,250 175,000 1.11 D 162,000 150,000 1.08
Select projects with highest Weighted Avg PI
WAPI (BD) = 1.01 WAPI (A) = 0.77 WAPI (BC) = 1.12
Choosing the Optimal Capital Budget
?Finance theory says to accept all positive
NPV projects. ?Two problems can occur when there is not enough internally generated cash to fund all positive NPV projects: ?An increasing marginal cost of
capital. ?Capital rationing
Increasing Marginal Cost of Capital
?Externally raised capital can have large
flotation costs, which increase the cost of capital. ?Investors often perceive large capital budgets as being risky, which drives up the cost of capital. ?If external funds will be raised, then the NPV of all projects should be estimated using this higher marginal cost of capital.
Capital Rationing
? Capital rationing occurs when a company
chooses not to fund all positive NPV projects. ? The company typically sets an upper limit on the total amount of capital expenditures that it will make in the upcoming year.
Capital Rationing
Reason: Companies want to avoid the direct costs (i.e., flotation costs) and the indirect costs of issuing new capital. Solution: Increase the cost of capital by enough to reflect all of these costs, and then accept all projects that still have a positive NPV with the higher cost of capital.
Capital Rationing
Reason: Companies don’t have enough managerial, marketing, or engineering staff to implement all positive NPV projects. Solution: Use linear programming to maximize NPV subject to not exceeding the constraints on staffing.
Linear Programming
?Maximize Cash flows or NPV ?Minimize costs
Capital Rationing
Reason: Companies believe that the project’s managers forecast unreasonably high cash flow estimates, so companies “filter” out the worst projects by limiting the total amount of projects that can be accepted. Solution: Implement a post-audit process and tie the managers’ compensation to the subsequent performance of the project.
Summary
? NPV & IRR Methods ? Similarities: ? Conventional investments – Initial outflow followed by inflows ? Independent Projects ? Differences ? Mutually exclusive Projects ? Technical Exclusiveness ? Size disparity ? Projects with unequal Lives ? Capital Rationing
Conclusion
? Large firms calculate all 6 methods ? Majority prefer IRR ? Payback & Discounted payback – indication of
risk & liquidity ? NPV – direct measure of cash benefit of the project to shareholders ? IRR – information of safety margin ? MIRR has virtues of NPV & IRR ? PI – indication of project risk
Foolish to ignore the information got from all of the above
Issues
?Cannot know the exact future cost of
capital or exact future cash flows. These inputs are estimates – errors can change NPV/ IRR calculations ?Thus quantitative methods provide valuable information but should not be used as the sole criteria ?Qualitative aspects should be considered
Issues
?Managers should question any project
that has high NPV/ IRR/ PI. ?In a perfectly competitive economy, there would be no +ve NPV project – all companies would have the same opportunities and would eliminate any +ve NPV.
Issues
? +ve NPV arises from some imperfection ? Be able to identify imperfections in market
place ? Longer the project life, longer the imperfection should last ? Should be able to explain why the imperfection will persist before accepting the project ? E.g. Patent, proprietary tech, first entrant, new product to meet unidentified customer need ? Firms have to develop some source of competitive advantage that would result in +ve NPV
Resultant
?If can’t identify reason for +ve NPV,
NPV may actually be –ve ?+ve NPV result of hard wok to develop competitive advantage ?Some competitive advantages do last longer – depending on competition’s capability to replicate – patents, control of scarce resource, strong economies of scale, R&D, work culture ?Bottom line – strive to develop nonreplicable sources of competitive advantage
Harold Biermer Survey
?All Fortune Cos use DCF ?84% use payback (not primary method) ?99% use IRR ?85% use NPV ?93% use w.a.c.c. for cap. Bud.
Small Companies
?21% use DCF ?Pre-occupied with liquidity – payback ?Lack of familiarity with DCF techniques ?DCF not worth the effort for small
projects
Post Audit
?Comparing actual results with those
predicted ?Explaining the differences
Post Audit Purpose
?Improve forecasts ?Improve operations ?Identify abandonment/ termination
opportunities
Post Audit
?Must recognize that each element of CF
forecast subject to uncertainty - % of all projects will go wrong ?Projects fail to meet expectations due to reasons beyond management control ?Although some projects are stand alone, the benefits/ savings are hard to measure
Use of Cap. Bud.
?Evaluating Mergers & Acquisitions ?When deciding to downsize operations
or manpower
doc_108083805.pptx