Description
nature of investment decisions, types of investment decisions, investment evaluation criteria, investment decision rule, evaluation criteria. It also explains the concept of IRR and how IRR is calculated. It also differentiates between NPV and IRR.
Capital Budgeting Decisions
Nature of Investment Decisions
• The investment decisions of a firm are generally known as the capital budgeting, or capital expenditure decisions. • The firm’s investment decisions would generally include expansion, acquisition, modernisation and replacement of the long-term assets. Sale of a division or business (divestment) is also as an investment decision. • Decisions like the change in the methods of sales distribution, or an advertisement campaign or a research and development programme have long-term implications for the firm’s expenditures and benefits, and therefore, they should also be evaluated as investment decisions.
Features of Investment Decisions
• The exchange of current funds for future benefits. • The funds are invested in long-term assets. • The future benefits will occur to the firm over a series of years.
Importance of Investment Decisions
• Growth • Risk • Funding • Irreversibility • Complexity
Types of Investment Decisions
• One classification is as follows:
– Expansion of existing business – Expansion of new business – Replacement and modernisation
• Yet another useful way to classify investments is as follows:
– Mutually exclusive investments – Independent investments – Contingent investments
Investment Evaluation Criteria
• Three steps are involved in the evaluation of an investment:
– Estimation of cash flows – Estimation of the required rate of return (the opportunity cost of capital) – Application of a decision rule for making the choice
Investment Decision Rule
• It should maximise the shareholders’ wealth. • It should consider all cash flows to determine the true profitability of the project. • It should provide for an objective and unambiguous way of separating good projects from bad projects. • It should help ranking of projects according to their true profitability. • It should recognise the fact that bigger cash flows are preferable to smaller ones and early cash flows are preferable to later ones. • It should help to choose among mutually exclusive projects that project which maximises the shareholders’ wealth. • It should be a criterion which is applicable to any conceivable investment project independent of others.
Evaluation Criteria
• 1. Discounted Cash Flow (DCF) Criteria
– Net Present Value (NPV) – Internal Rate of Return (IRR) – Profitability Index (PI)
• 2. Non-discounted Cash Flow Criteria
– Payback Period (PB) – Accounting Rate of Return (ARR)
Net Present Value Method
• Cash flows of the investment project should be forecasted based on realistic assumptions. • Appropriate discount rate should be identified to discount the forecasted cash flows. The appropriate discount rate is the project’s opportunity cost of capital. • Present value of cash flows should be calculated using the opportunity cost of capital as the discount rate. • The project should be accepted if NPV is positive (i.e., NPV > 0).
Net Present Value Method
• Net present value should be found out by subtracting present value of cash outflows from present value of cash inflows. The formula for the net present value can be written as follows:
? C1 C3 Cn ? C2 + + +L+ ? C0 NPV = ? 2 3 n ? (1 + k ) (1 + k ) ? ? (1 + k ) (1 + k ) n Ct ? C0 NPV = ? t t =1 (1 + k )
Calculating Net Present Value
• Assume that Project X costs Rs 2,500 now and is expected to generate year-end cash inflows of Rs 900, Rs 800, Rs 700, Rs 600 and Rs 500 in years 1 through 5. The opportunity cost of the capital may be assumed to be 10 per cent.
? Rs 900 Rs 800 Rs 700 Rs 600 Rs 500 ? NPV = ? + + + + ? Rs 2,500 2 3 4 5 ? (1+0.10) (1+0.10) (1+0.10) ? ? (1+0.10) (1+0.10) NPV = [Rs 900(PVF1, 0.10 ) + Rs 800(PVF2, 0.10 ) + Rs 700(PVF3, 0.10 ) + Rs 600(PVF4, 0.10 ) + Rs 500(PVF5, 0.10 )] ? Rs 2,500 NPV = [Rs 900 × 0.909 + Rs 800 × 0.826 + Rs 700 × 0.751 + Rs 600 × 0.683 + Rs 500 × 0.620] ? Rs 2,500 NPV = Rs 2,725 ? Rs 2,500 = + Rs 225
Acceptance Rule
• Accept the project when NPV is positive NPV > 0 • Reject the project when NPV is negative NPV < 0 • May accept the project when NPV is zero NPV = 0 • The NPV method can be used to select between mutually exclusive projects; the one with the higher NPV should be selected.
Evaluation of the NPV Method
• NPV is most acceptable investment rule for the following reasons:
– – – – – – – – Time value Measure of true profitability Value-additivity Shareholder value Involved cash flow estimation Discount rate difficult to determine Mutually exclusive projects Ranking of projects
• Limitations:
Internal Rate of Return Method
• The internal rate of return (IRR) is the rate that equates the investment outlay with the present value of cash inflow received after one period. This also implies that the rate of return is the discount rate which makes NPV = 0.
C0 = C3 Cn C1 C2 + + +L+ (1 + r ) (1 + r ) 2 (1 + r )3 (1 + r ) n
n t =1
C0 = ?
Ct (1 + r )t Ct ? C0 = 0 t (1 + r )
?
t =1
n
Calculation of IRR
• Uneven Cash Flows: Calculating IRR by Trial and Error
– The approach is to select any discount rate to compute the present value of cash inflows. If the calculated present value of the expected cash inflow is lower than the present value of cash outflows, a lower rate should be tried. On the other hand, a higher value should be tried if the present value of inflows is higher than the present value of outflows. This process will be repeated unless the net present value becomes zero.
Calculation of IRR
• Level Cash Flows
– Let us assume that an investment would cost Rs 20,000 and provide annual cash inflow of Rs 5,430 for 6 years. – The IRR of the investment can be found out as follows:
NPV = ?Rs 20,000 + Rs 5,430(PVAF6,r ) = 0 Rs 20,000 = Rs 5,430(PVAF6, r ) PVAF6, r Rs 20,000 = = 3.683 Rs 5,430
NPV Profile and IRR
A 1 NPV Profile 2 Cash Flow 3 -20000 4 5430 5 5430 6 5430 7 5430 8 5430 9 5430 B Discount rate 0% 5% 10% 15% 16% 20% 25% C D E F G H
NPV 12,580 7,561 3,649 550 0 (1,942) (3,974)
IR R
Figure 8.1 NPV Profile
Acceptance Rule
• • • • Accept the project when r > k. Reject the project when r < k. May accept the project when r = k. In case of independent projects, IRR and NPV rules will give the same results if the firm has no shortage of funds.
Evaluation of IRR Method
• IRR method has following merits:
– – – – Time value Profitability measure Acceptance rule Shareholder value
• IRR method may suffer from:
– Multiple rates – Mutually exclusive projects – Value additivity
Profitability Index
• Profitability index is the ratio of the present value of cash inflows, at the required rate of return, to the initial cash outflow of the investment.
Profitability Index
• The initial cash outlay of a project is Rs 100,000 and it can generate cash inflow of Rs 40,000, Rs 30,000, Rs 50,000 and Rs 20,000 in year 1 through 4. Assume a 10 per cent rate of discount. The PV of cash inflows at 10 per cent discount rate is:
PV = Rs 40,000(PVF 0.10 ) + Rs 30,000(PVF 0.10 ) + Rs 50,000(PVF 0.10 ) + Rs 20,000(PVF 0.10 ) 1, 2, 3, 4, = Rs 40,000× 0.909 + Rs 30,000× 0.826 + Rs 50,000× 0.751+ Rs 20,000× 0.68 NPV = Rs 112,350? Rs 100,000= Rs 12,350 PI = Rs1,12,350 = 1.1235. Rs1,00,000
Acceptance Rule
• The following are the PI acceptance rules:
– Accept the project when PI is greater than one. PI > 1 – Reject the project when PI is less than one. PI < 1 – May accept the project when PI is equal to one. PI = 1
• The project with positive NPV will have PI greater than one. PI less than means that the project’s NPV is negative.
Evaluation of PI Method
• It recognises the time value of money. • It is consistent with the shareholder value maximisation principle. A project with PI greater than one will have positive NPV and if accepted, it will increase shareholders’ wealth. • In the PI method, since the present value of cash inflows is divided by the initial cash outflow, it is a relative measure of a project’s profitability. • Like NPV method, PI criterion also requires calculation of cash flows and estimate of the discount rate. In practice, estimation of cash flows and discount rate pose problems.
Payback
• Payback is the number of years required to recover the original cash outlay invested in a project. • If the project generates constant annual cash inflows, the payback period can be computed by dividing cash outlay by the annual cash inflow. That is:
C0 Initial Investment Payback = = Annual Cash Inflow C
• Assume that a project requires an outlay of Rs 50,000 and yields annual cash inflow of Rs 12,500 for 7 years. The payback period for the project is:
PB = Rs 50,000 = 4 years Rs 12,000
Payback
• Unequal cash flows In case of unequal cash inflows, the payback period can be found out by adding up the cash inflows until the total is equal to the initial cash outlay. • Suppose that a project requires a cash outlay of Rs 20,000, and generates cash inflows of Rs 8,000; Rs 7,000; Rs 4,000; and Rs 3,000 during the next 4 years. What is the project’s payback? 3 years + 12 × (1,000/3,000) months 3 years + 4 months
Acceptance Rule
• The project would be accepted if its payback period is less than the maximum or standard payback period set by management. • As a ranking method, it gives highest ranking to the project, which has the shortest payback period and lowest ranking to the project with highest payback period.
Evaluation of Payback
• Certain virtues: – Simplicity – Cost effective – Short-term effects – Risk shield – Liquidity • Serious limitations: – Cash flows after payback – Cash flows ignored – Cash flow patterns – Administrative difficulties – Inconsistent with shareholder value
Conventional and Non-conventional Cash Flows
• A conventional investment has cash flows the pattern of an initial cash outlay followed by cash inflows. Conventional projects have only one change in the sign of cash flows; for example, the initial outflow followed by inflows, i.e., – + + +. • A non-conventional investment, on the other hand, has cash outflows mingled with cash inflows throughout the life of the project. Non-conventional investments have more than one change in the signs of cash flows; for example, – + + + – ++ – +.
NPV Versus IRR
• Conventional Independent Projects: In case of conventional investments, which are economically independent of each other, NPV and IRR methods result in same accept-or-reject decision if the firm is not constrained for funds in accepting all profitable projects.
NPV Versus IRR
• Lending and borrowing-type projects : In case of conventional investments, which are economically independent of each other, NPV and IRR methods result in same accept-or-reject decision if the firm is not constrained for funds in accepting all profitable projects.
Cash Flows (Rs) Project X Y C0 -100 100 C1 120 -120 IRR 20% 20% NPV at 10% 9 -9
Case of Ranking Mutually Exclusive Projects
• Investment projects are said to be mutually exclusive when only one investment could be accepted and others would have to be excluded. • Two independent projects may also be mutually exclusive if a financial constraint is imposed. • The NPV and IRR rules give conflicting ranking to the projects under the following conditions: – The cash flow pattern of the projects may differ. That is, the cash flows of one project may increase over time, while those of others may decrease or vice-versa. – The cash outlays of the projects may differ. – The projects may have different expected lives.
Timing of Cash Flows
Cash Flows (Rs) Project M N C0 – 1,680 – 1,680 C1 1,400 140 C2 700 840 C3 140 1,510
NPV at 9% 301 321 IRR 23% 17%
Scale of Investment
Cash Flow (Rs) Project A B C0 -1,000 -100,000 C1 1,500 120,000 NPV at 10% 364 9,080 IRR 50% 20%
Project Life Span
Cash Flows (Rs) Project X Y C0 – 10,000 – 10,000 C1 12,000 0 C2 – 0 C3 – 0 C4 – 0 C5 – 20,120 NPV at 10% 908 2,495 IRR 20% 15%
NPV Versus PI
• A conflict may arise between the two methods if a choice between mutually exclusive projects has to be made. Follow NPV method:
Project C PV of cash inflows Initial cash outflow NPV PI 100,000 50,000 50,000 2.00
Project D 50,000 20,000 30,000 2.50
doc_522238928.pdf
nature of investment decisions, types of investment decisions, investment evaluation criteria, investment decision rule, evaluation criteria. It also explains the concept of IRR and how IRR is calculated. It also differentiates between NPV and IRR.
Capital Budgeting Decisions
Nature of Investment Decisions
• The investment decisions of a firm are generally known as the capital budgeting, or capital expenditure decisions. • The firm’s investment decisions would generally include expansion, acquisition, modernisation and replacement of the long-term assets. Sale of a division or business (divestment) is also as an investment decision. • Decisions like the change in the methods of sales distribution, or an advertisement campaign or a research and development programme have long-term implications for the firm’s expenditures and benefits, and therefore, they should also be evaluated as investment decisions.
Features of Investment Decisions
• The exchange of current funds for future benefits. • The funds are invested in long-term assets. • The future benefits will occur to the firm over a series of years.
Importance of Investment Decisions
• Growth • Risk • Funding • Irreversibility • Complexity
Types of Investment Decisions
• One classification is as follows:
– Expansion of existing business – Expansion of new business – Replacement and modernisation
• Yet another useful way to classify investments is as follows:
– Mutually exclusive investments – Independent investments – Contingent investments
Investment Evaluation Criteria
• Three steps are involved in the evaluation of an investment:
– Estimation of cash flows – Estimation of the required rate of return (the opportunity cost of capital) – Application of a decision rule for making the choice
Investment Decision Rule
• It should maximise the shareholders’ wealth. • It should consider all cash flows to determine the true profitability of the project. • It should provide for an objective and unambiguous way of separating good projects from bad projects. • It should help ranking of projects according to their true profitability. • It should recognise the fact that bigger cash flows are preferable to smaller ones and early cash flows are preferable to later ones. • It should help to choose among mutually exclusive projects that project which maximises the shareholders’ wealth. • It should be a criterion which is applicable to any conceivable investment project independent of others.
Evaluation Criteria
• 1. Discounted Cash Flow (DCF) Criteria
– Net Present Value (NPV) – Internal Rate of Return (IRR) – Profitability Index (PI)
• 2. Non-discounted Cash Flow Criteria
– Payback Period (PB) – Accounting Rate of Return (ARR)
Net Present Value Method
• Cash flows of the investment project should be forecasted based on realistic assumptions. • Appropriate discount rate should be identified to discount the forecasted cash flows. The appropriate discount rate is the project’s opportunity cost of capital. • Present value of cash flows should be calculated using the opportunity cost of capital as the discount rate. • The project should be accepted if NPV is positive (i.e., NPV > 0).
Net Present Value Method
• Net present value should be found out by subtracting present value of cash outflows from present value of cash inflows. The formula for the net present value can be written as follows:
? C1 C3 Cn ? C2 + + +L+ ? C0 NPV = ? 2 3 n ? (1 + k ) (1 + k ) ? ? (1 + k ) (1 + k ) n Ct ? C0 NPV = ? t t =1 (1 + k )
Calculating Net Present Value
• Assume that Project X costs Rs 2,500 now and is expected to generate year-end cash inflows of Rs 900, Rs 800, Rs 700, Rs 600 and Rs 500 in years 1 through 5. The opportunity cost of the capital may be assumed to be 10 per cent.
? Rs 900 Rs 800 Rs 700 Rs 600 Rs 500 ? NPV = ? + + + + ? Rs 2,500 2 3 4 5 ? (1+0.10) (1+0.10) (1+0.10) ? ? (1+0.10) (1+0.10) NPV = [Rs 900(PVF1, 0.10 ) + Rs 800(PVF2, 0.10 ) + Rs 700(PVF3, 0.10 ) + Rs 600(PVF4, 0.10 ) + Rs 500(PVF5, 0.10 )] ? Rs 2,500 NPV = [Rs 900 × 0.909 + Rs 800 × 0.826 + Rs 700 × 0.751 + Rs 600 × 0.683 + Rs 500 × 0.620] ? Rs 2,500 NPV = Rs 2,725 ? Rs 2,500 = + Rs 225
Acceptance Rule
• Accept the project when NPV is positive NPV > 0 • Reject the project when NPV is negative NPV < 0 • May accept the project when NPV is zero NPV = 0 • The NPV method can be used to select between mutually exclusive projects; the one with the higher NPV should be selected.
Evaluation of the NPV Method
• NPV is most acceptable investment rule for the following reasons:
– – – – – – – – Time value Measure of true profitability Value-additivity Shareholder value Involved cash flow estimation Discount rate difficult to determine Mutually exclusive projects Ranking of projects
• Limitations:
Internal Rate of Return Method
• The internal rate of return (IRR) is the rate that equates the investment outlay with the present value of cash inflow received after one period. This also implies that the rate of return is the discount rate which makes NPV = 0.
C0 = C3 Cn C1 C2 + + +L+ (1 + r ) (1 + r ) 2 (1 + r )3 (1 + r ) n
n t =1
C0 = ?
Ct (1 + r )t Ct ? C0 = 0 t (1 + r )
?
t =1
n
Calculation of IRR
• Uneven Cash Flows: Calculating IRR by Trial and Error
– The approach is to select any discount rate to compute the present value of cash inflows. If the calculated present value of the expected cash inflow is lower than the present value of cash outflows, a lower rate should be tried. On the other hand, a higher value should be tried if the present value of inflows is higher than the present value of outflows. This process will be repeated unless the net present value becomes zero.
Calculation of IRR
• Level Cash Flows
– Let us assume that an investment would cost Rs 20,000 and provide annual cash inflow of Rs 5,430 for 6 years. – The IRR of the investment can be found out as follows:
NPV = ?Rs 20,000 + Rs 5,430(PVAF6,r ) = 0 Rs 20,000 = Rs 5,430(PVAF6, r ) PVAF6, r Rs 20,000 = = 3.683 Rs 5,430
NPV Profile and IRR
A 1 NPV Profile 2 Cash Flow 3 -20000 4 5430 5 5430 6 5430 7 5430 8 5430 9 5430 B Discount rate 0% 5% 10% 15% 16% 20% 25% C D E F G H
NPV 12,580 7,561 3,649 550 0 (1,942) (3,974)
IR R
Figure 8.1 NPV Profile
Acceptance Rule
• • • • Accept the project when r > k. Reject the project when r < k. May accept the project when r = k. In case of independent projects, IRR and NPV rules will give the same results if the firm has no shortage of funds.
Evaluation of IRR Method
• IRR method has following merits:
– – – – Time value Profitability measure Acceptance rule Shareholder value
• IRR method may suffer from:
– Multiple rates – Mutually exclusive projects – Value additivity
Profitability Index
• Profitability index is the ratio of the present value of cash inflows, at the required rate of return, to the initial cash outflow of the investment.
Profitability Index
• The initial cash outlay of a project is Rs 100,000 and it can generate cash inflow of Rs 40,000, Rs 30,000, Rs 50,000 and Rs 20,000 in year 1 through 4. Assume a 10 per cent rate of discount. The PV of cash inflows at 10 per cent discount rate is:
PV = Rs 40,000(PVF 0.10 ) + Rs 30,000(PVF 0.10 ) + Rs 50,000(PVF 0.10 ) + Rs 20,000(PVF 0.10 ) 1, 2, 3, 4, = Rs 40,000× 0.909 + Rs 30,000× 0.826 + Rs 50,000× 0.751+ Rs 20,000× 0.68 NPV = Rs 112,350? Rs 100,000= Rs 12,350 PI = Rs1,12,350 = 1.1235. Rs1,00,000
Acceptance Rule
• The following are the PI acceptance rules:
– Accept the project when PI is greater than one. PI > 1 – Reject the project when PI is less than one. PI < 1 – May accept the project when PI is equal to one. PI = 1
• The project with positive NPV will have PI greater than one. PI less than means that the project’s NPV is negative.
Evaluation of PI Method
• It recognises the time value of money. • It is consistent with the shareholder value maximisation principle. A project with PI greater than one will have positive NPV and if accepted, it will increase shareholders’ wealth. • In the PI method, since the present value of cash inflows is divided by the initial cash outflow, it is a relative measure of a project’s profitability. • Like NPV method, PI criterion also requires calculation of cash flows and estimate of the discount rate. In practice, estimation of cash flows and discount rate pose problems.
Payback
• Payback is the number of years required to recover the original cash outlay invested in a project. • If the project generates constant annual cash inflows, the payback period can be computed by dividing cash outlay by the annual cash inflow. That is:
C0 Initial Investment Payback = = Annual Cash Inflow C
• Assume that a project requires an outlay of Rs 50,000 and yields annual cash inflow of Rs 12,500 for 7 years. The payback period for the project is:
PB = Rs 50,000 = 4 years Rs 12,000
Payback
• Unequal cash flows In case of unequal cash inflows, the payback period can be found out by adding up the cash inflows until the total is equal to the initial cash outlay. • Suppose that a project requires a cash outlay of Rs 20,000, and generates cash inflows of Rs 8,000; Rs 7,000; Rs 4,000; and Rs 3,000 during the next 4 years. What is the project’s payback? 3 years + 12 × (1,000/3,000) months 3 years + 4 months
Acceptance Rule
• The project would be accepted if its payback period is less than the maximum or standard payback period set by management. • As a ranking method, it gives highest ranking to the project, which has the shortest payback period and lowest ranking to the project with highest payback period.
Evaluation of Payback
• Certain virtues: – Simplicity – Cost effective – Short-term effects – Risk shield – Liquidity • Serious limitations: – Cash flows after payback – Cash flows ignored – Cash flow patterns – Administrative difficulties – Inconsistent with shareholder value
Conventional and Non-conventional Cash Flows
• A conventional investment has cash flows the pattern of an initial cash outlay followed by cash inflows. Conventional projects have only one change in the sign of cash flows; for example, the initial outflow followed by inflows, i.e., – + + +. • A non-conventional investment, on the other hand, has cash outflows mingled with cash inflows throughout the life of the project. Non-conventional investments have more than one change in the signs of cash flows; for example, – + + + – ++ – +.
NPV Versus IRR
• Conventional Independent Projects: In case of conventional investments, which are economically independent of each other, NPV and IRR methods result in same accept-or-reject decision if the firm is not constrained for funds in accepting all profitable projects.
NPV Versus IRR
• Lending and borrowing-type projects : In case of conventional investments, which are economically independent of each other, NPV and IRR methods result in same accept-or-reject decision if the firm is not constrained for funds in accepting all profitable projects.
Cash Flows (Rs) Project X Y C0 -100 100 C1 120 -120 IRR 20% 20% NPV at 10% 9 -9
Case of Ranking Mutually Exclusive Projects
• Investment projects are said to be mutually exclusive when only one investment could be accepted and others would have to be excluded. • Two independent projects may also be mutually exclusive if a financial constraint is imposed. • The NPV and IRR rules give conflicting ranking to the projects under the following conditions: – The cash flow pattern of the projects may differ. That is, the cash flows of one project may increase over time, while those of others may decrease or vice-versa. – The cash outlays of the projects may differ. – The projects may have different expected lives.
Timing of Cash Flows
Cash Flows (Rs) Project M N C0 – 1,680 – 1,680 C1 1,400 140 C2 700 840 C3 140 1,510
NPV at 9% 301 321 IRR 23% 17%
Scale of Investment
Cash Flow (Rs) Project A B C0 -1,000 -100,000 C1 1,500 120,000 NPV at 10% 364 9,080 IRR 50% 20%
Project Life Span
Cash Flows (Rs) Project X Y C0 – 10,000 – 10,000 C1 12,000 0 C2 – 0 C3 – 0 C4 – 0 C5 – 20,120 NPV at 10% 908 2,495 IRR 20% 15%
NPV Versus PI
• A conflict may arise between the two methods if a choice between mutually exclusive projects has to be made. Follow NPV method:
Project C PV of cash inflows Initial cash outflow NPV PI 100,000 50,000 50,000 2.00
Project D 50,000 20,000 30,000 2.50
doc_522238928.pdf