1. Copyright © 2012 Pearson Prentice Hall. All rights reserved. Chapter 8 Investment Decision Rules

2. Chapter Outline 1. The NPV Decision Rule 2. Using the NPV Rule 3. Alternative Decision Rules 4. Choosing Between Projects 5. Evaluating Projects with Different Lives 6. Choosing Among Projects When Resources Are Limited 7. Putting it All Together 2

3. NET PRESENT VALUE (NPV) 3

4. 8.1 The NPV Decision Rule Most firms measure values in terms of Net Present Value–that is, in terms of cash today. Logic of the decision rule: –When making an investment decision, take the alternative with the highest NPV, which is equivalent to receiving its NPV in cash today. NPV = PV (Benefits) – PV (Costs) (Eq. 8.1) 4

5. Example 8.1 The NPV Is Equivalent to Cash Today Problem: After saving $1,500 waiting tables, you are about to buy a 42- inch plasma TV. You notice that the store is offering “one- year same as cash” deal. You can take the TV home today and pay nothing until one year from now, when you will owe the store the $1,500 purchase price. If your savings account earns 5% per year, what is the NPV of this offer? Show that its NPV represents cash in your pocket. Today In one year Cash flows: $ 1,500 –$ 1,500 5

6. 8.2 Using the NPV Rule A take-it-or-leave-it decision: –Researchers at Fredrick’s Feed and Farm have made a breakthrough. –A fertilizer company can create a new environmentally friendly fertilizer at a large savings over the company’s existing fertilizer. –The fertilizer will require a new factory that can be built at a cost of $81.6 million. Estimated return on the new fertilizer will be $28 million after the first year, and last four years. 6

7. 8.2 Using the NPV Rule Given a discount rate r, the NPV is: We can also use the annuity formula: If the company’s cost of capital is 10%, the NPV is $7.2 million and they should undertake the investment. (Eq. 8.2) (Eq. 8.3) 7

8. 8.2 Using the NPV Rule NPV of Fredrick’s project –The NPV depends on cost of capital. –NPV profile graphs the NPV over a range of discount rates. –Based on this data the NPV is positive only when the discount rates are less than 14%. –The lower the cost of capital is, the larger the NPV is in $. 8

9. 8.2 Using the NPV Rule FIGURE 8.1 NPV of Fredrick’s New Project 9

10. ALTERNATIVE DECISION RULES: PAYBACK PERIOD 10

11. 8.3 Alternative Decision Rules FIGURE 8.2 The Most Popular Decision Rules Used by CFOs 11

12. 8.3 Alternative Decision Rules The Payback Rule –Based on the notion that an opportunity that pays back the initial investment quickly is the best idea. Calculate the amount of time it takes to pay back the initial investment, called the payback period. Accept if the payback period is less than required Reject if the payback period is greater than required 12

13. Example 8.2 Using the Payback Rule Problem: Assume the fertilizer company requires all projects to have a payback period of two years or less. In this case would the firm undertake the project under this rule? Solution: In order to implement the payback rule, we need to know whether the sum of the inflows from the project will exceed the initial investment before the end of 2 years. The project has inflows of $28 million per year and an initial investment of $81.6 million. The sum of the cash flows from year 1 to year 2 is $28m x 2 = $56 million, this will not cover the initial investment of $81.6 million. Because the payback is > 2 years (3 years required $28 x 3 = $84 million) the project will be rejected. While simple to compute, the payback rule requires us to use an arbitrary cutoff period in summing the cash flows. Further, also note that the payback rule does not discount future cash flows. Instead it simply sums the cash flows and compares them to a cash outflow in the present. In this case, Fredrick’s would have rejected a project that would have increased the value of the firm. 13

14. Example 8.2b Using the Payback Rule Problem: Assume a company requires all projects to have a payback period of three years or less. For the project below, would the firm undertake the project under this rule? YearExpected Net Cash Flow 0-$10,000 1$1,000 2 3 4$500,000 14

15. Example 8.2b Using the Payback Rule Solution: The sum of the cash flows from years 1 through 3 is $3,000. This will not cover the initial investment of $10,000. Because the payback is more than 3 years the project will not be accepted, even though the 4 th cash flow is very high! While simple to compute, the payback rule requires us to use an arbitrary cutoff period in summing the cash flows. Further, also note that the payback rule does not discount future cash flows – in this case, a huge mistake! Instead it simply sums the cash flows and compares them to a cash outflow in the present. 15

16. 8.3 Alternative Decision Rules Weakness of the Payback Rule –Ignores the time value of money. –Ignores cash-flows after the payback period. –Lacks a decision criterion grounded in economics –Arbitrary cut-off point is necessary. 16

17. ALTERNATIVE DECISION RULES: INTERNAL RATE OF RETURN 17

18. 8.3 Alternative Decision Rules The Internal Rate of Return Rule –Take any investment opportunity where IRR exceeds the opportunity cost of capital. 0123 CF 0 CF 1 CF 2 CF 3 CostInflows IRR is the discount rate that forces PV inflows = cost. This is the same as forcing NPV = 0. 18

19. NPV: Enter r, solve for NPV. IRR: Enter NPV = 0, solve for IRR. 19

20. 901,09090 01210 IRR = ? Q.How is a project’s IRR related to a bond’s YTM? A.They are the same thing. A bond’s YTM is the IRR if you invest in the bond. -1,134.2 IRR = 7.08% (use TVM or CF j ).... 20

21. Understanding NPV and IRR Suppose you borrow $1,000 from Citi Bank for one-year loan today –This means that you need to pay back $1,100 in one year. Suppose with $1,000, you invest on AAPL stocks today. In one year, you sell AAPL stocks for $1,100. Will you make a profit or loss? –Neither. You are break-even!!! How? –The present value of $1,100 at 10% is $1,000. –NPV = $1,000 (PV of $1,100) - $1,000 (cost) = $0 !!! –IRR = 10% from investment, and the cost of capital is 10%  Break-even 21

22. 8.3 Alternative Decision Rules Weakness in IRR –In most cases IRR rule agrees with NPV for stand- alone projects if all negative cash flows precede positive cash flows. –In other cases the IRR may disagree with NPV. Multiple IRRs – which IRR should we use? Mutually exclusive projects – Often IRR is misleading. 22

23. 8.3 Alternative Decision Rules Delayed Investments –Two competing endorsements: Star basketball player Evan Cole has dilemma with two competing endorsements. –Offer A: single payment of $1million upfront –Offer B: $500,000 per year at the end of the next three years –Estimated cost of capital is 10% 23

24. 8.3 Alternative Decision Rules The NPV is: –That is, positive cash flow from Option A means that Cole chose Option A. –A negative cash flow from Option B means that Cole pass up Option B. Set NPV to zero and solve for r to get IRR. Given:31,000,000-500,000 0 Solve for:23.38 Excel Formula: =RATE(NPER,PMT,PV,FV) = RATE(3,-500000,1000000,0) 24

25. 8.3 Alternative Decision Rules 23.38% > the 10% opportunity cost of capital, so according to IRR, Option A best. However, NPV shows that Option B is best, which makes sense better economically. To resolve the conflict we can show a NPV Profile 25

26. 8.3 Alternative Decision Rules When cash is upfront, a high interest rate discounts the future cash flow (in this case, cash out flow of three $500k) more heavily, yielding a higher NPV. For most investments expenses are upfront and cash is received in the future. In these cases, it is opposite, so a low IRR is preferred. Conclusion: In delayed investment, IRR is misleading! FIGURE 8.3 NPV of Cole’s $1 Million QuenchIt Deal 26

27. 8.3 Alternative Decision Rules Another issue with IRR: Multiple IRRs –Suppose the cash flows in the previous example change. –The company has agreed to make an additional payment of $600,000 in 10 years. The new timeline: The NPV of the new investment opportunity is: If we plot the NPV profile, we see that it has two IRRs! 27

28. 8.3 Alternative Decision Rules FIGURE 8.4 NPV of Evan’s Sports Drink Deal with Additional Deferred Payments 28

29. 8.3 Alternative Decision Rules Conclusions so far: –Do not use IRR if Cash flows are delayed Cash flow change signs more than once. 29

30. CHOOSING BETWEEN PROJECTS 30

31. 8.4 Choosing Between Projects Projects are: –independent, if the cash flows of one are unaffected by the acceptance of the other. –mutually exclusive, if the cash flows of one can be adversely impacted by the acceptance of the other. Mutually exclusive projects. –Can’t just pick the project with a positive NPV. –The projects must be ranked and the best one chosen. –Pick the project with the highest NPV. 31

32. Example 8.3 NPV and Mutually Exclusive Projects Problem: You own a small piece of commercial land near a university. You are considering what to do with it. You have been approached recently with an offer to buy it for $220,000. You are also considering three alternative uses yourself: a bar, a coffee shop, and an apparel store. You assume that you would operate your choice indefinitely, eventually leaving the business to your children. You have collected the following information about the uses. What should you do? Initial Investment Cash flow in the First Year Growth rate Cost of capital Bar $400,000$60,0003.5%12% Coffee shop $200,000$40,0003%10% Apparel Store $500,000$85,0003%13% 32

33. Example 8.3 NPV and Mutually Exclusive Projects Solution: Since you can only do one project (you only have one piece of land), these are mutually exclusive projects. In order to decide which project is most valuable, you need to rank them by NPV. Each of these projects (except for selling the land) has cash flows that can be valued as a growing perpetuity, the present value of the inflows is CF 1 / (r-g). The NPV of each investment will be The NPVs are: Based on the rankings the coffee shop should be chosen. All of the alternatives have positive NPVs, but you can only take one of them, so you should choose the one that creates the most value. Even though the coffee shop has the lowest cash flows, its lower start-up cost coupled with its lower cost of capital (it is less risky), make it the best choice. 33

34. 8.4 Choosing Between Projects Differences in Scale –A 10% IRR can have very different value implications for an initial investment of $1 million vs. an initial investment of $100 million. 34

35. Figure 8.7 NPV of Javier’s Investment Opportunities 35 Given:3-10,0006,0000 Solve for:36.3 Excel Formula: =RATE(NPER,PMT,PV,FV) = RATE(3,6000,-10000,0) Identical Scale –NPV of Javier’s investment in his girlfriend’s business: –NPV of Javier’s investment in the Internet café:

36. 8.4 Choosing Between Projects Change in Scale: –Javier realizes he can just as easily install five times as many computers in the Internet café. –Setup costs would be $50,000 and annual cash flows would be $25,000. 36

37. Figure 8.8 NPV of Javier’s Investment Opportunities 37 Given:3-50,00025,0000 Solve for: 23.4 Excel Formula: =RATE(NPER,PMT,PV,FV) = RATE(3,25000,-50000,0) Change in Scale –IRR is unaffected by scale. –IRR of girlfriend’s business is the same.

38. Example 8.4 Computing the Crossover Point Problem: Solve for the crossover point for Javier from Figure 8.8. Solution: The crossover point is the discount rate that makes the NPV of the two alternatives equal. We can find the discount rate by setting the equations for the NPV of each project equal to each other and solving for the discount rate. In general, we can always compute the effect of choosing Project A over Project B as the difference of the NPVs. At the crossover point the difference is 0. Just as the NPV of a project tells us the value impact of taking the project, so the difference of the NPVs of two alternatives tells us the incremental impact of choosing one project over another. The crossover point is the discount rate at which we would be indifferent between the two projects because the incremental value of choosing one over the other would be zero. 38

39. Example 8.4 Computing the Crossover Point Execute: As you can see, solving for the crossover point is just like solving for the IRR, so we will need to use a financial calculator or spreadsheet: 39 Given:3-40,00019,0000 Solve for: 20.04 Excel Formula: =RATE(NPER, PMT, PV,FV) = RATE(3,19000, ‑ 40000,0)

40. 8.4 Choosing Between Projects Timing of the Cash Flows –Suppose Javier could sell the Internet café business at the end of the first year for $40,000. –Should he plan to sell it? 40

41. 8.4 Choosing Between Projects The Bottom Line on IRR –Picking the investment opportunity with the largest IRR can lead to a mistake. –In general, it is dangerous to use the IRR in choosing between projects. –Always rely on NPV. 41

42. NPV vs. IRR (Mutually Exclusive Projects with Different Scales) Option #1: You give me $1 now and I’ll give you $1.50 back at the end of the class period. Option #2: You give me $10 now and I’ll give you $11 back at the end of the class period. You can choose only one of two options. Assume a zero rate of interest because our class lasts only 1 hours. Which option would you choose? 42

43. NPV vs. IRR (Mutually Exclusive Projects with Different Cash Flow Timings) Project0123IRR NPV @5% Long-10010608018.1%$33Higher Short-10070502023.6%Higher$29 Which one should we take? Suppose r = 5%. 43

44. NPV ($) Discount Rate (%) IRR L = 18.1% IRR S = 23.6% Crossover Point = 8.7% 44

45. Which project(s) should be accepted at r=5%? If S and L are independent, accept both. NPV > 0. IRR S and IRR L > r = 5%. If Projects S and L are mutually exclusive, accept L because NPV S IRR L. Conflict !!! Choose between mutually exclusive projects on basis of higher NPV. Adds most value in dollar. 45

46. 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 r favors small projects. 2.Timing differences. Project with faster payback provides more CF in early years for reinvestment. If r is high, early CF especially good, NPV S > NPV L. 46

47. Reinvestment Rate Assumptions NPV assumes reinvest at r (opportunity cost of capital). IRR assumes reinvest at IRR. Reinvest at opportunity cost, r, is more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects. 47

48. MODIFIED INTERNAL RATE OF RETURN (MIRR) 48

49. 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 the cost of capital. Thus, MIRR assumes cash inflows are reinvested at the cost of capital. 49

50. 8.3 Alternative Decision Rules Modified Internal Rate of Return (MIRR) –Used to overcome problem of multiple IRRs –Computes the discount rate that sets the NPV of modified cash flows to zero –Possible modifications Bring all negative cash flows to the present and incorporate into the initial cash outflow Leave the initial cash flow alone and compound all of the remaining cash flows to the final period of the project. 8-50

51. Figure 8.6 NPV Profile of MIRR 51

52. MIRR = 16.5% 10.080.060.0 0123 10% 66.0 12.1 158.1 Starbucks estimates the cash flows for the new project, “Mocha.” Find MIRR. r = 10%. -100.0 10% TV inflows -100.0 PV outflows MIRR L = 16.5% $100 = $158.1 (1+MIRR L ) 3 52

53. To find TV with a calculator, enter in CF j : I = 10 NPV = 118.78 = PV of inflows. Enter PV = -118.78, N = 3, I = 10, PMT = 0. Press FV = 158.10 = FV of inflows. Enter FV = 158.10, PV = -100, PMT = 0, N = 3. Press I = 16.50% = MIRR. CF 0 = 0, CF 1 = 10, CF 2 = 60, CF 3 = 80 53

54. Accept Project ? YES. Accept because MIRR = 16.50% > r = 10%. Also, if MIRR > r, NPV will be positive: NPV = +$18.78. 54 Why use MIRR rather than IRR? MIRR correctly assumes reinvestment at opportunity cost = the cost of capital. MIRR also avoids the problem of multiple IRRs. Managers like rate of return comparisons, and MIRR is better for this than IRR.

55. EVALUATING PROJECTS WITH DIFFERENT LIVES 55

56. 8.5 Evaluating Projects with Different Lives Often, a company will need to choose between two solutions to the same problem. TABLE 8.2 Cash Flows ($ Thousands) for Network Server Options 56

57. 8.5 Evaluating Projects with Different Lives 57

58. 8.5 Evaluating Projects with Different Lives Server A is equivalent to spending $5,020 per year (versus $6,030 per year). Server A is the less expensive solution. TABLE 8.3 Cash Flows ($ Thousands) for Network Server Options, Expressed as Equivalent Annual Annuities 58

59. Example 8.5 Computing an Equivalent Annual Annuity Problem: You are about to sign the contract for Server A from Table 8.2 when a third vendor approaches you with another option that lasts for 4 years. The cash flows for Server C are given below. Should you choose the new option or stick with Server A? 59

60. Example 8.5 Computing an Equivalent Annual Annuity Solution: In order to compare this new option to Server A, we need to put it an equal footing by computing its annual cost. We can do this 1.Computing its NPV at the 10% discount rate we used above 2.Computing the equivalent 4-year annuity with the same present value. Its annual cost of 5.62 is greater than the annual cost of Server A (5.02), so we should choose Server A. In this case, the additional cost associated with purchasing and maintaining Server C is not worth the extra year we get from choosing it. By putting all of these costs into an equivalent annuity, the EAA tool allows us to see that. 60

61. Example 8.5a Computing an Equivalent Annual Annuity Problem: You considering a maintenance contract from two vendors. Vendor Y charges $100,000 upfront and then $12,000 per year for the three-year life of the contract. Vendor Z charges $85,000 upfront and then $35,000 per year for the two-year life of the contract. Compute the NPV and EAA for each vendor assuming an 8% cost of capital. 61

62. Example 8.5a Computing an Equivalent Annual Annuity Execute: 62

63. Example 8.5a Computing an Equivalent Annual Annuity Execute (cont’d): The annual cost of Vendor Z is greater than the annual cost of Vendor Y, so we should choose Vendor Y. Evaluate: In this case, the higher upfront cost associated with Vendor Y is worth the extra year we get from choosing it. By putting all of these costs into an equivalent annuity, the EAA tool allows us to see that. 63

64. CHOOSING AMONG PROJECTS WHEN RESOURCES ARE LIMITED 64

65. 8.6 Choosing Among Projects when Resources are Limited Sometimes different investment opportunities demand different amounts of a particular resource. If there is a fixed supply of the resource so that you cannot undertake all possible opportunities, simply picking the highest- NPV opportunity might not lead to the best decision. 65

66. 8.6 Choosing Among Projects when Resources are Limited 66 TABLE 8.4 Possible Projects for $200 Million Budget (Eq. 8.4)

67. Example 8.6 Profitability Index with a Human Resource Constraint Problem: Your division at NetIt, a large networking company, has put together a project proposal to develop a new home networking router. The expected NPV of the project is $17.7 million, and the project will require 50 software engineers. NetIt has a total of 190 engineers available, and is unable to hire additional qualified engineers in the short run. Therefore, the router project must compete with the following other projects for these engineers: 67

68. Example 8.6 Profitability Index with a Human Resource Constraint Problem (cont’d): How should NetIt prioritize these projects? ProjectNPV ($ millions) Engineering Headcount Router17.750 Project A22.747 Project B8.144 Project C14.040 Project D11.561 Project E20.658 Project F12.932 Total107.5332 68

69. Example 8.6 Profitability Index with a Human Resource Constraint Execute: The goal is to maximize the total NPV we can create with 190 employees (at most). We can use Eq. 8.4 to determine the profitability index for each project. In this case, since engineers are our limited resource, we will use Engineering Headcount in the denominator. Once we have the profitability index for each project, we can sort them based on the index. 69

70. Example 8.6 Profitability Index with a Human Resource Constraint Execute : We now assign the resource to the projects in descending order according to the profitability index. The final column shows the cumulative use of the resource as each project is taken on until the resource is used up. To maximize NPV within the constraint of 190 employees, NetIt should choose the first four projects on the list. By ranking projects in terms of their NPV per engineer, we find the most value we can create, given our 190 engineers. There is no other combination of projects that will create more value without using more engineers than we have. This ranking also shows us exactly what the engineering constraint costs us—this resource constraint forces NetIt to forgo three otherwise valuable projects (C, D, and B) with a total NPV of $33.6 million. 70

71. Example 8.6a Profitability Index with a Human Resource Constraint Problem: AaronCo is considering several projects to undertake. All of the projects currently under consideration have a positive NPV, but AaronCo has a fixed capital budget of $300 million. The company does not believe they will be able to raise any additional funds. How should AaronCo prioritize the projects (listed on the following slide)? 71

72. Example 8.6a Profitability Index with a Human Resource Constraint Problem (cont’d): 72

73. Example 8.6a Profitability Index with a Human Resource Constraint The goal is to maximize the total NPV we can create with $300 million (at most). We can use Eq. 8.3 to determine the profitability index for each project. In this case, since money is our limited resource, we will use Initial Cost in the denominator. Once we have the profitability index for each project, we can sort them based on the index. 73

74. Example 8.6a Profitability Index with a Human Resource Constraint Execute: We now assign the resource to the projects in descending order according to the profitability index. The final column shows the cumulative use of the resource as each project is taken on until the resource is used up. To maximize NPV within the constraint of $300 million, AaronCo should choose the first four projects on the list. By ranking projects in terms of their NPV per engineer, we find the most value we can create, given our $300 million budget. There is no other combination of projects that will create more value without using more money than we have. This ranking also shows us exactly what the budget constraint costs us—this resource constraint forces AaronCo to forgo three otherwise valuable projects (B, D, and E) with a total NPV of $110 million. 74

75. Capital Rationing There is one case that the PI is preferred to the NPV. It is called “capital rationing” situation. Capital rationing occurs when a company chooses not to fund all positive NPV projects. –Or simply the firm does not have sufficient funds to undertake all positive NPV project. In these cases, the company typically sets an upper limit on the total amount of capital expenditures that it will make in the upcoming year. In some cases, 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. Use profitability index, instead of NPVs. Why? 75

76. Capital Rationing Example 76

77. 8.7 Putting It All Together TABLE 8.5 Summary of Decision Rules 77

78. 8.7 Putting It All Together TABLE 8.5 Summary of Decision Rules (cont.) 78

79. Capital Budgeting In Practice We should consider several investment criteria when making decisions. NPV and IRR are the most commonly used primary investment criteria. Payback is a commonly used secondary investment criteria. Use more than one Also exercise qualitative judgments in conjunction with quantitative analysis. 79