1. 8- 1 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Fundamentals of Corporate Finance Sixth Edition Richard A. Brealey Stewart C. Myers Alan J. Marcus Slides by Matthew Will Chapter 7 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Net Present Value and Other Investment Criteria

2. 8- 2 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Topics Covered  Net Present Value  Other Investment Criteria  Mutually Exclusive Projects  Capital Rationing

3. 8- 3 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Net Present Value Net Present Value - Present value of cash flows minus initial investments. Opportunity Cost of Capital - Expected rate of return given up by investing in a project

4. 8- 4 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Net Present Value Example Q: Suppose we can invest $50 today & receive $60 later today. What is our increase in value? Initial Investment Added Value $50 $10 A: Profit = - $50 + $60 = $10

5. 8- 5 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Net Present Value Example Suppose we can invest $50 today and receive $60 in one year. What is our increase in value given a 10% expected return? This is the definition of NPV Initial Investment Added Value $50 $4.55

6. 8- 6 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Valuing an Office Building Step 1: Forecast cash flows Cost of building = C 0 = 350,000 Sale price in Year 1 = C 1 = 400,000 Step 2: Estimate opportunity cost of capital If equally risky investments in the capital market offer a return of 7%, then Cost of capital = r = 7%

7. 8- 7 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Valuing an Office Building Step 3: Discount future cash flows Step 4: Go ahead if PV of payoff exceeds investment

8. 8- 8 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Risk and Present Value  Higher risk projects require a higher rate of return  Higher required rates of return cause lower PVs

9. 8- 9 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Risk and Present Value

10. 8- 10 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Net Present Value NPV = PV - required investment

11. 8- 11 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Net Present Value Terminology C = Cash Flow t = time period of the investment r = “opportunity cost of capital”  The Cash Flow could be positive or negative at any time period.

12. 8- 12 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Net Present Value Net Present Value Rule Managers increase shareholders’ wealth by accepting all projects that are worth more than they cost. Therefore, they should accept all projects with a positive net present value.

13. 8- 13 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Net Present Value Example You have the opportunity to purchase an office building. You have a tenant lined up that will generate $16,000 per year in cash flows for three years. At the end of three years you anticipate selling the building for $450,000. How much would you be willing to pay for the building? Assume a 7% opportunity cost of capital

14. 8- 14 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Example - continued Net Present Value $16,000 $450,000 $466,000 0 1 2 3 Present Value 14,953 13,975 380,395 $409,323

15. 8- 15 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Net Present Value Example - continued If the building is being offered for sale at a price of $350,000, would you buy the building and what is the added value generated by your purchase and management of the building?

16. 8- 16 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Net Present Value Example - continued If the building is being offered for sale at a price of $350,000, would you buy the building and what is the added value generated by your purchase and management of the building?

17. 8- 17 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Payback Method Payback Period - Time until cash flows recover the initial investment of the project.  The payback rule specifies that a project be accepted if its payback period is less than the specified cutoff period. The following example will demonstrate the absurdity of this statement.

18. 8- 18 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Example The three project below are available. The company accepts all projects with a 2 year or less payback period. Show how this decision will impact our decision. Cash Flows Project C 0 C 1 C 2 C 3 PaybackNPV @10% A-2,000+1,000+1,000+10,000 B-2,000+1,000+1,000 0 C-2,000 0+2,000 0 Payback Method + 7,249 - 264 - 347 222222

19. 8- 19 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Other Investment Criteria Internal Rate of Return (IRR) - Discount rate at which NPV = 0. Rate of Return Rule - Invest in any project offering a rate of return that is higher than the opportunity cost of capital.

20. 8- 20 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Internal Rate of Return Example You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment?

21. 8- 21 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Internal Rate of Return Example You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment? IRR = 12.96%

22. 8- 22 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Internal Rate of Return

23. 8- 23 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Internal Rate of Return IRR=12.96%

24. 8- 24 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Internal Rate of Return Calculating the IRR can be a laborious task. Fortunately, financial calculators can perform this function easily. Note the previous example. HP-10BEL-733ABAII Plus -350,000CFj-350,000CFiCF 16,000CFj16,000CFfi2nd{CLR Work} 16,000CFj16,000CFi -350,000 ENTER 466,000CFj466,000CFi 16,000 ENTER {IRR/YR}IRR16,000 ENTER 466,000 ENTER IRRCPT All produce IRR=12.96

25. 8- 25 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Internal Rate of Return Example You have two proposals to choice between. The initial proposal (H) has a cash flow that is different than the revised proposal (I). Using IRR, which do you prefer?

26. 8- 26 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Internal Rate of Return 50 40 30 20 10 0 -10 -20 NPV $, 1,000s Discount rate, % 8 10 12 14 16 Revised proposal Initial proposal IRR= 14.29% IRR= 12.96% IRR= 12.26%

27. 8- 27 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Internal Rate of Return Pitfall 3 - Mutually Exclusive Projects  IRR sometimes ignores the magnitude of the project.  The following two projects illustrate that problem. Pitfall 1 - Lending or Borrowing?  With some cash the NPV of the project increases as the discount rate increases  This is contrary to the normal relationship between PV and discount rates. Pitfall 2 - Multiple Rates of Return  Certain cash flows can generate NPV=0 at two different discount rates.

28. 8- 28 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Internal Rate of Return Example You have two proposals to choice between. The initial proposal has a cash flow that is different than the revised proposal. Using IRR, which do you prefer?

29. 8- 29 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Project Interactions When you need to choose between mutually exclusive projects, the decision rule is simple. Calculate the NPV of each project, and, from those options that have a positive NPV, choose the one whose NPV is highest.

30. 8- 30 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Mutually Exclusive Projects Example Select one of the two following projects, based on highest NPV. assume 7% discount rate

31. 8- 31 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Investment Timing Sometimes you have the ability to defer an investment and select a time that is more ideal at which to make the investment decision. A common example involves a tree farm. You may defer the harvesting of trees. By doing so, you defer the receipt of the cash flow, yet increase the cash flow.

32. 8- 32 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Investment Timing Example You may purchase a computer anytime within the next five years. While the computer will save your company money, the cost of computers continues to decline. If your cost of capital is 10% and given the data listed below, when should you purchase the computer?

33. 8- 33 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Investment Timing Example You may purchase a computer anytime within the next five years. While the computer will save your company money, the cost of computers continues to decline. If your cost of capital is 10% and given the data listed below, when should you purchase the computer? YearCostPV SavingsNPV at PurchaseNPV Today 050702020.0 145702522.7 240703024.8 3367034 Date to purchase 25.5 433703725.3 531703924.2

34. 8- 34 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Equivalent Annual Annuity Equivalent Annual Cost - The cash flow per period with the same present value as the cost of buying and operating a machine.

35. 8- 35 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Equivalent Annual Annuity Example Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using equivalent annual annuity method. Year Mach.1234PV @6% E.A.A. F-15-4-4-4 G-10-6-6 -25.69 -21.00 - 9.61 -11.45

36. 8- 36 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Equivalent Annual Annuity Example (with a twist) Select one of the two following projects, based on highest “equivalent annual annuity” (r=9%). 2.82 2.78.87 1.10

37. 8- 37 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Capital Rationing Capital Rationing - Limit set on the amount of funds available for investment. Soft Rationing - Limits on available funds imposed by management. Hard Rationing - Limits on available funds imposed by the unavailability of funds in the capital market.

38. 8- 38 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Profitability Index Ratio of net present value to initial investment.

39. 8- 39 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Profitability Index

40. 8- 40 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Capital Budgeting Techniques

41. 8- 41 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Web Resources