1. Chapter 7 Investment Decision Rules Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7-1

2. Chapter Outline Using the NPV Rule Alternative Decision Rules Choosing Between Projects Evaluating Projects with Different Lives Choosing Among Projects When Resources Are Limited Putting It All Together 7-2

3. Learning Objectives Use the NPV rule to make investment decisions Understand alternative decision rules and their drawbacks Choose between mutually exclusive alternatives Rank projects when a company’s resources are limited so that it cannot take all positive- NPV projects 7-3

4. Using the NPV Rule When making an investment decision, take the alternative with the highest NPV. Choosing this alternative is equivalent to receiving its NPV in cash today. 7-4

5. Using the NPV Rule Consider a take-it-or-leave-it investment decision involving a single, stand-alone project. 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 lasting four years. 7-5

6. Computing NPV The following timeline shows the estimated return: The cash flows are an immediate $81.6 million outflow followed by an annuity inflow of $28 million per year for 4 years. 7-6

7. Computing NPV 7-7 Therefore, given a discount rate r, the NPV of this project is: We can also use the annuity formula to write the NPV as

8. Computing NPV If the company’s cost of capital is 10%, the NPV is $7.2 million and they should undertake the investment. 7-8

9. NPV Profile The NPV of a project depends on cost of capital. Frequently there is uncertainty regarding the projects capital costs. In these cases an NPV profile, which 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%. 7-9

10. 7-10 Alternative Decision Rules

11. The Payback Rule Based on the notion that an opportunity that pays back the initial investment quickly is the best idea. 1.Calculate the amount of time it takes to pay back the initial investment, called the payback period. 2.Accept the project if the payback period is less than a pre-specified length of time—usually a few years. 3.Reject the project if the payback period is greater than that pre-specified length of time 7-11

12. Example 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? 7-12

13. Example - Using the Payback Rule Solution: Plan: 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. 7-13

14. Example Using the Payback Rule Execute: 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. 7-14

15. Example Using the Payback Rule Evaluate: 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. 7-15

16. Weakness of Payback Rule 1.Ignores the time value of money. 2.Ignores cash-flows after the payback period. 3.Lacks a decision criterion grounded in economics (what is the right number of years to require for a payback period?). 7-16

17. The Internal Rate of Return Rule IRR Investment Rule: Take any investment opportunity where IRR exceeds the opportunity cost of capital. Turn down any opportunity whose IRR is less than the opportunity cost of capital. 7-17

18. NPV, IRR, and Payback for Fertilizer Plant Summary of results using NPV Profile IRR decision would be to accept because the actual cost of capital is 10%, less than the IRR of 14%. 7-18

19. Weakness in IRR In most cases IRR rule agrees with NPV for stand alone project’s if all of the project’s negative cash flows precede the positive cash flows. In other cases the IRR may disagree with NPV. 7-19

20. Delayed Investments Two competing endorsements: Offer A: single payment of $1million upfront Offer B: $500,000 per year payable at the end of the next three years Estimated cost of capital is 10% Opportunity timeline: 7-20

21. Delayed Investments 7-21 The NPV of the investment is By setting the NPV to zero and solving for r, we find the IRR. We can use a financial calculator: Given:31,000,000-500,0000 Solve for:23.38 Excel Formula: =RATE(NPER,PMT,PV,FV) = RATE(3,-500000,1000000,0)

22. Delayed Investments The 23.38% is larger than then 10% opportunity cost of capital, according to IRR Option A is the best option. However NPV shows that Option B is best To resolve the conflict we can show a NPV Profile 7-22

23. Delayed Investment For most investment opportunities expenses are upfront and cash is received in the future. In these cases a low rate is best. When cash is upfront a high interest rate is best. 7-23

24. Offer A is extended from $1 million now so that it also includes $600,000 in 10 years.

25. Common Mistake: IRR Versus IRR Rule IRR Versus the IRR Rule. While we have pointed out the shortcomings of using the IRR rule to make investment decisions, the IRR itself remains a very useful tool. The IRR measures the sensitivity of the NPV to estimation error in the cost of capital and the average return of the investment. Thus knowing the IRR can be very useful, but relying on it to make investment decisions can be hazardous. 7-25

26. 7.2 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. 7-26

27. NPV Profile with Multiple IRRs 7-27

28. NPV Profile of MIRR There is now only a single IRR, at 15.25%. Because our cost of capital is 15%, we would properly accept the project using the IRR rule 7-28 CF Modified by combining PV of -1,540 in year 2 with -1,000 in year 0 (resulting in -2,164.46 in year 0, while compounding the 2,500 in year 1 to 2875 in year 2.

29. 7.3 Choosing Between Projects With mutually exclusive projects it is not enough to determine a project with a positive NPV. The projects must be ranked and the best one chosen. 7-29

30. Example 7.2 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? 7-30 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$75,0003%13%

31. Example 7.2 NPV and Mutually Exclusive Projects Solution: Plan: 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 7-31

32. Example 7.2 NPV and Mutually Exclusive Projects Execute: The NPVs are: 7-32 Based on the rankings the coffee shop should be chosen

33. Example 7.2 NPV and Mutually Exclusive Projects Evaluate 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. 7-33

34. Example 7.2a NPV and Mutually Exclusive Projects [deleted] 7-34

35. Example 7.2a NPV and Mutually Exclusive Projects [deleted] 7-35

36. Example 7.2a NPV and Mutually Exclusive Projects [deleted] 7-36

37. Example 7.2a NPV and Mutually Exclusive Projects [deleted] 7-37

38. 7.3 Choosing Between Projects Differences in Scale An important shortcoming of IRR: because it is a return, you cannot tell how much value has actually been created without knowing the basis for the return—a 10% IRR can have very different value implications for an initial investment of $1 million vs. an initial investment of $100 million. 7-38

39. 7-39 NPV of Javier’s Investment Opportunities CF: Girlfriend's is -10,000 now with 6,000 per year for 3 years. Two-computer project is -10,000 now and 5,000 per year for 3 years.

40. 7.3 Choosing Between Projects Change in Scale Note that the IRR is unaffected by the scale. Because your are scaling all the cash flows up by a factor of 5, a 10-machine Internet Cafe has exactly the same IRR as a two-machine Internet Cafe, so his girlfriend’s business still has a higher IRR than the Internet Café: 7-40 Given:3-50,00025,0000 Solve for:23.4 Excel Formula: =RATE(NPER,PMT,PV,FV) = RATE(3,25000,-50000,0)

41. 7-41 NPV of Javier’s Investment Opportunities

42. Example 7.3 Computing the Crossover Point Problem: Solve for the crossover point for Javier from Figure 7.8. 7-42

43. Example 7.3 Computing the Crossover Point Solution: Plan: 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 the Internet Café over his girlfriend’s business as the difference of the NPVs. At the crossover point the difference is 0 7-43

44. Example 7.3 Computing the Crossover Point Execute: Setting the difference equal to 0: 7-44 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:

45. Example 7.3 Computing the Crossover Point Execute: And we find that the crossover occurs at a discount rate of 20% (20.04% to be exact). 7-45 Given:3-40,00019,0000 Solve for:20.04 Excel Formula: =RATE(NPER, PMT, PV,FV) = RATE(3,19000, ‑ 40000,0)

46. Example 7.3 Computing the Crossover Point Evaluate: 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. 7-46

47. Timing of the Cash Flows 7-47 Given a cost of capital of 12%, it is better not to sell the Internet Café after one year, despite the higher IRR.

48. The Bottom Line on IRR As these examples make clear, picking the investment opportunity with the largest IRR can lead to a mistake. In general, it is dangerous to use the IRR in cases where you are choosing between projects, or anytime when your decision to accept or reject one project would affect your decision on another project. In such a situation, always rely on NPV. 7-48

49. 7.4 Evaluating Projects with Different Lives Often, a company will need to choose between two solutions to the same problem. 7-49

50. Example 7.4 Computing an Equivalent Annual Annuity Problem: You are about to sign the contract for Server A from Table 7.2 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? 7-50

51. Example 7.4 Computing an Equivalent Annual Annuity Solution: Plan: 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. 7-51

52. Example 7.4 Computing an Equivalent Annual Annuity Execute: Its annual cost of 5.62 is greater than the annual cost of Server A (5.02), so we should choose Server A. 7-52

53. Example 7.4 Computing an Equivalent Annual Annuity Evaluate: 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. 7-53

54. 7.5 Choosing Among Projects when Resources are Limited In some situations, 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. 7-54

55. 7-55 7.5 Choosing Among Projects when Resources are Limited

56. Profitability Index 7-56 (Eq. 7.3)

57. Example- Profitability Index with Capital 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 initial cost. NetIT has devoted only $190 million for its investments and is unable to raise additional funds to take all of its investment opportunities shown below: How should NetIT prioritize these projects? 7-57 ProjectNPVInitial CostPI Router$17.70$50.001.354 A$22.70$47.001.483 B$8.10$44.001.184 C$14.00$40.001.350 D$11.50$61.001.189 E$20.60$58.001.355 F$12.90$32.001.403 Total $107.50$332.00

58. Example Profitability Index with a Capital Constraint Problem: How should NetIt prioritize these projects? 7-58 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

59. Example 7.5 Profitability Index with a Human Resource Constraint Solution: Plan: The goal is to maximize the total NPV we can create with $190 millions (at most). We can use PI to sort out the basket of projects that would create the highest total NPV for the Company. Table below shows the result: 7-59 Ranking based on PI ProjectNPVInitial CostPI A22.7471.483 F12.9321.403 E20.6581.355 Router17.7501.354 C14401.350 D11.5611.189 B8.1441.184

60. Example 7.5 Profitability Index with a Human Resource Constraint Execute (cont’d): 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. 7-60 Selected Investments ProjectNPVInitial CostPI A22.7471.483 F12.9321.403 E20.6581.355 Router17.7501.354 73.9187

61. Example 7.5 Profitability Index with a Human Resource Constraint Evaluate 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. 7-61

62. 7-62 7.6 Putting It All Together

63. 7-63 7.6 Putting It All Together Table 7.5 Summary of Decision Rules

64. Chapter Quiz 1.Explain the NPV rule for stand-alone projects. 2.Under what conditions will the IRR rule lead to the same decision as the NPV rule? 3.What is the most reliable way to choose between mutually exclusive projects? 4.Explain why choosing the option with the highest NPV is not always correct when the options have different lives. 5.What does the profitability index tell you? 7-64