# Chapter 9: Net Present Value and Other Investment Criteria. Faculty of Business Administration Lakehead University Spring 2003 May 20, 2003

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1 Chapter 9: Net Present Value and Other Investment Criteria Faculty of Business Administration Lakehead University Spring 2003 May 20, 2003

2 Outline 9.1 Net Present Value 9.2 The Payback Rule 9.3 The Average Accounting Return 9.4 The Internal Rate of Return 9.5 The Profitability Index 9.6 The Practice of Capital Budgeting 1

3 9.1 Net Present Value The net present value (NPV) of a project measures the difference between the present value of the project s future cash flows and the present value of its costs. The process of valuing an investment by discounting its future cash flows is often called discounted cash flow (DCF) valuation. 2

4 9.1 Net Present Value: An Example Consider a project with an initial cost of \$30 and subsequent costs of \$14 per year. That is, some equipment is purchased at time 0 for \$30 and will cost \$14 per year to operate. The project is expected to generate a cash flow of \$24 per year for eight years. At the end of the eighth year, the equipment used in the project will be sold for \$2 (salvage value). What is the net present value of this project? 3

5 9.1 Net Present Value: An Example Timing of Cash Flows Year Initial cost -30 Inflows Outflows Salvage 2 Net cash flow

6 9.1 Net Present Value: An Example This project s cash flows can be divided in three parts: 1. An outlay of \$30 at time 0; 2. An annuity of \$10 per year for eight year, the first payment taking place in year 1; 3. A lump-sum payment of \$2 at the end of year 8. 5

7 9.1 Net Present Value: An Example Using a discount rate of 12%, the net present value of this project is NPV = ( 1 ( ) ) (1.12) 8 = \$ The NPV Rule: An investment should be accepted if its net present value is positive and should be rejected otherwise. 6

8 9.2 The Payback Rule The payback period of a project is the time it takes to recover the project s initial cost. The payback rule does not consider the time value of money. In the previous example, the payback period is exactly 3 years. 7

9 9.2 The Payback Rule What is the payback period for each of these projects? Year Project 1 Project

10 9.2 The Payback Rule Let CCF i cumulative cash flow from project i. Year Project 1 CCF 1 Project 2 CCF

11 9.2 The Payback Rule Project 1 s cost is paid back between year 4 and year 5. The exact time can be approximated as follows: Payback period = ( 2) = = 4.17 years. Project 2 s cost is paid back between year 3 and year 4. The exact time can be approximated as follows: Payback period = ( 5) = = 3.83 years. 10

12 9.2 The Payback Rule The Payback Rule: Accept any investment with a payback period below some prespecified number of years. Project 2 pays itself back before project 1. Is project 2 better than project 1? 11

13 9.2 The Payback Rule Let the discount rate be 12%. Then NPV of project 1 = \$9.61. NPV of project 2 = \$3.75. That is, if the payback rule were Only accept projects with a payback period under 4 years, then project 2 would be accepted and project 1 would be rejected, even though NPV of project 2 < 0 < NPV of project 1. 12

14 9.2 The Payback Rule Advantages of the Payback Rule 1. Easy to understand. 2. Adjusts for uncertainty of later cash flows. 3. Biased toward liquidity. 13

15 9.2 The Payback Rule Disadvantages of the Payback Rule 1. Ignores the time value of money. 2. requires an arbitrary cutoff point. 3. Ignores cash flows beyond the cutoff date. 4. Biased against long-term projects. 14

16 The Discounted Payback Rule The discounted payback period of a project is the time it takes to repay the project s initial cost with the discounted future cash flows. This rule thus takes into account the time value of money. The rule is that a project is accepted if its discounted payback period is below some prespecified number of years. 15

17 9.2 The Payback Rule Suppose r = 12%, and let CDCF i cumulative discounted cash flow from project i. Then Year Project 1 CCF 1 CDCF 1 Project 2 CCF 2 CDCF

18 The Discounted Payback Rule The discounted payback period for project 1 is between year 6 and year 7, whereas project 2 never pays back its initial cost with its discounted cash flows. The discounted payback rule never selects projects with negative net present value. 17

19 The Discounted Payback Rule Advantages of the Discounted Payback Rule 1. Takes the time value of money into account. 2. Easy to understand. 3. Does not accept projects with negative NPV. 4. Biased toward liquidity. 18

20 The Discounted Payback Rule Disadvantages of the Discounted Payback Rule 1. May reject projects with positive NPV. 2. requires an arbitrary cutoff point. 3. Ignores cash flows beyond the cutoff date. 4. Biased against long-term projects. 19

21 9.3 The Average Accounting Return The average accounting return (AAR) is measured as follows: Some measure of average accounting profit Some measure of average accounting value. We could use, for instance, Average net income Average book value of investment. 20

22 9.3 The Average Accounting Return Consider a project that requires an initial outlay of \$500. The project has a 5-year life, during which the initial investment depreciates linearly (straight-line depreciation) to zero. That is, the initial investment depreciates by \$100 each year, and thus its average book value is = 100( ) 6 = = =

23 9.3 The Average Accounting Return More specifically, note that (n 1) + n = n(n + 1). 2 22

24 9.3 The Average Accounting Return If an asset of value A depreciates to 0 over n years, this means that it loses A n of its value each year, and thus its average book value (ABV) is ABV = A + ( A A ) ( ) n + A 2A n A n + A n + 0 n + 1 A = n n + A n (n 1) + A n (n 2) A n 2 + A n n + 1 A = (n + (n 1) + (n 2) ) n(n + 1) = = A 2. A n(n + 1) n(n + 1) 2 23

25 9.3 The Average Accounting Return Back to our example, suppose the project is expected to generate the following net incomes: Year Net income The average net income is then =

26 9.3 The Average Accounting Return The average accounting return in our example is then AAR = = The Average Accounting Return Rule: A project is acceptable if its AAR is above some target AAR. 25

27 9.3 The Average Accounting Return Advantages of the ARR Rule 1. Easy to calculate. 2. Needed information usually available. 26

28 9.3 The Average Accounting Return Disadvantages of the ARR Rule 1. Ignores the time value of money. 2. Uses an arbitrary cutoff rate. 3. Based on book values instead of cash flows or market values. 27

29 9.4 The Internal Rate of Return The internal rate of return (IRR) is the most important alternative to NPV. It provides the discount rate at which an investment has a zero net present value. The IRR Rule: If the IRR of an investment is greater than the required rate of return, then the investment is worth undertaking. 28

30 9.4 The Internal Rate of Return: An Example Year Cash flow The internal rate of return in this example is 10.71%: (1.1071) (1.1071) (1.1071) (1.1071)

31 9.4 The Internal Rate of Return With an IRR of 10.71%, will the project be undertaken? If the firm requires a return of 12%, say, or higher on any of its projects, then this one won t be undertaken. If, on the other hand, the firm requires a return of 9% or higher on any of its projects, then this one will be undertaken. 30

32 9.4 The Internal Rate of Return There exists a positive IRR to any project with a positive NPV. A project with a negative NPV, i.e. a project that never pays back the initial investment, has a negative IRR. Given a certain discount rate, the fact that project A, say, has a greater NPV than project B does not imply that A s IRR is greater than B s IRR, and vice versa. A single project may have more than one IRR. 31

33 Problems with the IRR Multiple IRRs Consider the following stream of cash flows: Year Cash flow This project would have two IRRs: 25% and 33.33%. The maximum number of IRRs a project can have is equal to the number of times cash flows change sign. 32

34 Problems with the IRR Mutually Exclusive Investments Is the IRR the right rule to use when a firm has access to mutually exclusive projects? Consider the two following projects: Year Project A Project B

35 Problems with the IRR Mutually Exclusive Investments From these cash flows, we find: IRR A = 16.71% and IRR B = 18.69%. Is project B better than project A? The NPV of B is not always greater than that of A. 34

36 Mutually Exclusive Investments Problems with the IRR Rate NPV A NPV B 5% % % % % %

37 Problems with the IRR Mutually Exclusive Investments Project A and project B have the same NPV when the discount rate is around %. This is the crossover rate. The Crossover rate is the internal rate of return of A B. Let r c denote the crossover rate. Then, when r = r c, NPV A = NPV B NPV A NPV B = 0. 36

38 Problems with the IRR Mutually Exclusive Investments Let CF A,t and CF B,t denote the cash flow at time t of project A and project B, respectively. Then NPV A NPV B = 8 t=0 CF A,t (1 + r) t 8 t=0 CF B,t (1 + r) t = 8 t=0 CF A,t CF B,t (1 + r) t = NPV A B. 37

39 Mutually Exclusive Investments Problems with the IRR Year Project A Project B A B

40 Problems with the IRR Mutually Exclusive Investments When r < %, then NPV A > NPV B and thus the IRR rule may contradict the NPV rule. There is no conflict when When r > %. Looking at different streams of cash flows, can you tell whether the IRR and the NPV rules contradict each other? 39

41 The IRR Rule Advantages Closely related to the NPV rule. Easy to understand and communicate. Disadvantages May provide multiple answers. May provide the wrong answer when comparing mutually exclusive projects. 40

42 9.5 The Profitability Index The profitability index (PI) is a benefit/cost ratio. If a project costs \$25 and the present value of its future cash flows is \$37.5, then this project has a profitability index of = 1.5. A project with a positive NPV will have a PI greater than one. A project with a negative NPV will have a PI smaller than one. 41

43 9.5 The Profitability Index Mutually Exclusive Investments This measure may also lead to the wrong decision when selecting among mutually exclusive projects. Suppose project A costs \$5 and pays off \$11 in one year. Suppose project B costs \$100 and pays off \$121 in one year. If the discount rate is 10%, then PI A = 2 > 1.5 = PI B but NPV A = 5 < 10 = NPV B. 42

44 9.5 The Profitability Index Advantages Closely related to the NPV rule. Easy to understand and communicate. Useful when capital available is limited. Disadvantages May lead to incorrect decisions when comparing mutually exclusive projects. 43

45 9.6 The Practice of Capital Budgeting Since the NPV tells us what we want to know, why do these other measures exist? The NPV is only an approximation. The actual cash flows may be really different from what is expected. Firms usually use multiple criteria to evaluate a proposal. For instance, a positive NPV, a short payback period and a high AAR mean that the project is probably a good one. If, on the other hand, the firm receives conflicting signals (positive NPV, long payback period and low AAR), then it must be more careful when making its decision. 44

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