U3_Capital Budgeting.pptx Project Financing including NPV, IRR, PI, PB, DPB, and ARR methods
- 1. Project Appraisal and Financing: Profitability Index, PB, DPB, and ARR methods @ Ravindra Nath Shukla Assistant Professor ITM University, Gwalior
- 2. LEARNING OBJECTIVES • Understand the nature and importance of investment decisions • Explain the methods of calculating net present value (NPV) and internal rate of return (IRR) • Show the implications of net present value (NPV) and internal rate of return (IRR) • Describe the non-DCF evaluation criteria: payback and accounting rate of return • Illustrate the computation of the discounted payback • Compare and contrast NPV and IRR and emphasize the superiority of NPV rule
- 3. What is Capital Budgeting? • A capital budgeting decision may be defined as the firm’s decision to invest its current funds most efficiently in the long-term assets in anticipation of an expected flow of benefits over a series of years.
- 4. 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.
- 5. 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.
- 6. Importance of Investment Decisions • Growth • Risk • Funding • Irreversibility • Complexity
- 7. 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
- 8. Investment Evaluation Criteria • Three steps are involved in the evaluation of an investment: 1. Estimation of cash flows 2. Estimation of the required rate of return (the opportunity cost of capital) 3. Application of a decision rule for making the choice
- 9. 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.
- 10. 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) – Discounted payback period (DPB) – Accounting Rate of Return (ARR)
- 11. 1(a) Net Present Value Method • The net present value (NPV) method is the classic economic method of evaluating the investment proposals. It is a DCF technique that explicitly recognizes the time value of money. • 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. • Present value of cash flows should be calculated using the opportunity cost of capital as the discount rate. • Net present value should be found out by subtracting present value of cash outflows from present value of cash inflows. The project should be accepted if NPV is positive (i.e., NPV > 0).
- 12. Net Present Value Method • The formula for the net present value can be written as follows: n 1 t 0 t t 0 n n 3 3 2 2 1 C ) k 1 ( C NPV C ) k 1 ( C ) k 1 ( C ) k 1 ( C ) k 1 ( C NPV
- 13. 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.
- 14. Example : A company is considering the following investment projects: a) Rank the projects according to NPV methods, assuming discount rates of 10% and 30% respectively. b) Assuming the projects are independent, which one should be accepted? c) If the projects are mutually exclusive, which project is the best? Cash Flows in INR Projects C0 C1 C2 C3 A – 10,000 10,000 B – 10,000 17,500 7,500 C – 10,000 12,000 4,000 12,000 D – 10,000 10,000 3,000 13,000
- 15. Why is NPV Important? • Positive net present value of an investment represents the maximum amount a firm would be ready to pay for purchasing the opportunity of making investment, or the amount at which the firm would be willing to sell the right to invest without being financially worse-off. • The net present value can also be interpreted to represent the amount the firm could raise at the required rate of return, in addition to the initial cash outlay, to distribute immediately to its shareholders and by the end of the projects’ life, to have paid off all the capital raised and return on it.
- 16. 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.
- 17. 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 • Limitations: – Involved cash flow estimation – Discount rate difficult to determine – Mutually exclusive projects – Ranking of projects
- 18. Example : 1 • Calculate the net present value of the project at discount rates of 0, 10, 40, 50 and 100 per cent.
- 19. 1(b) INTERNAL RATE OF RETURN METHOD • The internal rate of return (IRR) method is another discounted cash flow technique, which takes account of the magnitude and timing of cash flows • 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. ∑ ∑
- 20. • It can be noticed that the IRR equation is the same as the one used for the NPV method. • In the NPV method, the required rate of return, k, is known and the net present value is found, • while in the IRR method the value of r has to be determined at which the net present value becomes zero.
- 21. 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.
- 22. Example • A project costs Rs.16,000 and is expected to generate cash inflows of Rs.8,000, Rs.7,000 and Rs.6,000 at the end of each year for next 3 years. • We know that IRR is the rate at which project will have a zero NPV. As a first step, we try (arbitrarily) a 20 per cent discount rate. The project’s NPV at 20 per cent is: • A negative NPV of Rs.1,004 at 20 per cent indicates that the project’s true rate of return is lower than 20 per cent. Let us try 16 per cent as the discount rate.
- 23. Example • A project costs Rs.16,000 and is expected to generate cash inflows of Rs.8,000, Rs.7,000 and Rs.6,000 at the end of each year for next 3 years.
- 24. • At 16 per cent, the project’s NPV is: • Since the project’s NPV is still negative at 16 per cent, a rate lower than 16 per cent should be tried. Let’s try to calculate NPV at 15 per cent as the trial rate.
- 25. • When we select 15 per cent as the trial rate, we find that the project’s NPV is Rs.200. Thus the true rate of return should lie between 15–16 per cent. • We can find out a close approximation of the rate of return by the method of linear interpolation as follows: The 15% discount rate the project’s NPV is :
- 26. 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. If the opportunity cost of capital is 10 per cent, what is the investment’s NPV? • The Rs.5,430 is an annuity for 6 years. The NPV can be found as follows: – The IRR of the investment can be found out as follows
- 27. • The rate, which gives a PVFA of 3.683 for 6 years, is the project’s internal rate of return. Looking up PVFA in Table across the 6-year row, we find it approximately under the 16 per cent column. Thus, 16 per cent is the project’s IRR that equates the present value of the initial cash outlay (Rs.20,000) with the constant annual cash inflows (Rs.5,430 per year) for 6 years.
- 28. 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.
- 29. 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
- 30. Example • 2. A project costs Rs.81,000 and is expected to generate net cash inflow of Rs.40,000, Rs.35,000 and Rs.30,000 over its life of 3 years. Calculate the internal rate of return of the project. • 3. A machine will cost Rs.100,000 and will provide annual net cash inflow of Rs.30,000 for six years. The cost of capital is 15 per cent. Calculate the machine’s net present value and the internal rate of return. Should the machine be purchased?
- 31. Examples • 4. Consider the following three investments: The discount rate is 12 per cent. Compute the net present value and the rate of return for each project.
- 32. Example • 5. Consider the following two mutually exclusive investments: • (a) Calculate the NPV for each project assuming discount rates of 0, 5, 10, 20, 30 and 40 per cent; • (b) draw the NPV graph for the projects to determine their IRR, • (c) show calculations of IRR for each project confirming results in (b). • Also, state which project would you recommend and why?
- 33. Example • 6. For Projects X and Y, the following cash flows are given: • (a) Calculate the NPV of each project for discount rates 0, 5, 8, 10, 12 and 20 per cent. Plot these on an PV graph. • (b) Read the IRR for each project from the graph in (a). • (c) When and why should Project X be accepted? • (d) Compute the NPV of the incremental investment (Y – X) for discount rates, 0, 5, 8, 10, 12 and 20 per cent. Plot them on graph.
- 34. 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. • The formula for calculating benefit-cost ratio or profitability index is as follows: ∑
- 35. 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 percent rate of discount. The PV of cash inflows at 10 percent discount rate is: ∑
- 36. 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.
- 37. Evaluation of PI Method • Time value:It recognises the time value of money. • Value maximization: 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. • Relative profitability: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.
- 38. Example • A company is considering the following six projects: You are required to calculate the profitability index for each project and rank them ?
- 39. Solution Projects 2 and 1 are best in terms of PI.
- 40. 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: C C Inflow Cash Annual Investment Initial = Payback 0
- 41. Example • 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: years 4 12,000 Rs 50,000 Rs PB
- 42. 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
- 43. 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.
- 44. 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
- 45. DISCOUNTED PAYBACK PERIOD • The discounted payback period is the number of periods taken in recovering the investment outlay on the present value basis. • The discounted payback period still fails to consider the cash flows occurring after the payback period. Discounted Payback Illustrated
- 46. ACCOUNTING RATE OF RETURN METHOD • The accounting rate of return is the ratio of the average after-tax profit divided by the average investment. The average investment would be equal to half of the original investment if it were depreciated constantly. • A variation of the ARR method is to divide average earnings after taxes by the original cost of the project instead of the average cost. or
- 47. Example • A project will cost Rs 40,000. Its stream of earnings before depreciation, interest and taxes (EBDIT) during first year through five years is expected to be Rs 10,000, Rs 12,000, Rs 14,000, Rs 16,000 and Rs 20,000. Assume a 50 per cent tax rate and depreciation on straight-line basis.
- 48. Calculation of Accounting Rate of Return
- 49. Acceptance Rule • This method will accept all those projects whose ARR is higher than the minimum rate established by the management and reject those projects which have ARR less than the minimum rate. • This method would rank a project as number one if it has highest ARR and lowest rank would be assigned to the project with lowest ARR.
- 50. Evaluation of ARR Method • The ARR method may claim some merits Simplicity Accounting data Accounting profitability • Serious shortcomings Cash flows ignored Time value ignored Arbitrary cut-off
- 51. THANK YOU!