# Net Present Value and Other Investment Criteria

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1 Net Present Value and Other Investment Criteria

2 Topics Covered Net Present Value Other Investment Criteria Mutually Exclusive Projects Capital Rationing

3 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 Net Present Value Example Q: Suppose we can invest \$50 today & receive \$60 later today. What is our increase in value? A: Profit = - \$50 + \$60 = \$10 \$10 \$50 Added Value Initial Investment

5 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? Profit = This is the definition of NPV 1.10 \$4.55 \$4.55 Added Value \$50 Initial Investment

6 Net Present Value NPV = PV - required investment NPV C 0 Ct ( 1 r) t NPV C 0 C1 C2 Ct ( 1 r) ( 1 r) ( 1 r) t

7 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.

8 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.

9 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?

10 Net Present Value Example - continued \$466,000 \$450,000 \$16,000 \$16,000 \$16,000 Present Value ,953 14, ,395 \$409,323

11 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?

12 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? NPV NPV 16, , , 000 ( 107. ) ( 107. ) \$59, , 000 ( 107. ) 1 2 3

13 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.

14 Payback Method 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 Payback A ,249 B C

15 Using the Payback Rule

16 Using the Payback Rule

17 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. Rate of Return = C 1 - investment investment

18 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?

19 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? 0 350, , , , 000 ( 1 IRR) ( 1 IRR) ( 1 IRR) IRR = 12.96%

20 Internal Rate of Return Calculating IRR by using a spreadsheet Year Cash Flow Formula 0 (350,000.00) IRR = 12.96% =IRR(B3:B7) 1 16, , ,000.00

21 NPV (,000s) Internal Rate of Return IRR=12.96% Discount rate (%)

22 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? NPV (1 IRR) (1 IRR) (1 IRR) % NPV (1 IRR) %

23 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? Project C 0 C 1 C 2 C 3 IRR Initial Proposal % \$ 24,000 Revised Proposal % \$ 59,000

24 NPV \$, 1,000s Internal Rate of Return Revised proposal Initial proposal IRR= 12.26% IRR= 12.96% IRR= 14.29% Discount rate, %

25 Internal Rate of Return Pitfall 1 - Mutually Exclusive Projects IRR sometimes ignores the magnitude of the project. The following two projects illustrate that problem. Pitfall 2 - Lending or Borrowing? With some cash flows (as noted below) the NPV of the project increases as the discount rate increases. This is contrary to the normal relationship between NPV and discount rates. Pitfall 3 - Multiple Rates of Return Certain cash flows can generate NPV=0 at two different discount rates.

26 NPV of Star s \$1 million Book Deal When the benefits of an investment occur before the costs, the NPV is an increasing function of the discount rate. Copyright 2007 Pearson Addison-Wesley. All rights reserved.

27 NPV of Lecture Contract No IRR exists because the NPV is positive for all values of the discount rate. Thus the IRR rule cannot be used. Copyright 2007 Pearson Addison-Wesley. All rights reserved.

28 NPV of Star s Book Deal with Royalties In this case, there is more than one IRR, invalidating the IRR rule. If the opportunity cost of capital is either below 4.723% or above %, Star should make the investment. Copyright 2007 Pearson Addison-Wesley. All rights reserved.

29 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 Mutually Exclusive Projects Example Select one of the two following projects, based on highest NPV. System Faster C C C C NPV Slower assume 7% discount rate

31 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 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 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? Year Cost PV Savings NPV at Purchase NPV Today Date to purchase

34 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. Equivalent annual annuity = present value of cash flows annuity factor

35 Annuity Factor 1 1 Annuity Factor t,r = r (1 r) t

36 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 E.A.A. F G

37 Equivalent Annual Annuity Example (with a twist) Select one of the two following projects, based on highest equivalent annual annuity (r=9%). Project C0 C1 C2 C3 C4 A B NPV EAA

38 Capital Rationing Capital Rationing - Limit set on the amount of funds available for investment. The act of placing restrictions on the amount of new investments or projects undertaken by a company. This is accomplished by imposing a higher cost of capital for investment consideration or by setting a ceiling on the specific sections of the budget. Companies may want to implement capital rationing in situations where past returns of investment were lower than expected.

39 Capital Rationing ABC Corp. has a cost of capital of 10% but that the company has undertaken too many projects, many of which are incomplete. This causes the company's actual return on investment to drop well below the 10% level. As a result, management decides to place a cap on the number of new projects by raising the cost of capital for these new projects to 15%. Starting fewer new projects would give the company more time and resources to complete existing projects.

40 Capital Rationing 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.

41 Profitability Index

42 Profitability Index Profitability Project PV Investment NPV Index J /3 =.33 K /5 =.20 L /7 =.43 M /6 =.33 N /4 =.25

43 Profitability Index with a Human Resource Constraint

44 Profitability Index with a Human Resource Constraint

45 Capital Budgeting Techniques

46 EVA in Period n (When Capital Lasts Forever)

47 Calculating EVA When Invested Capital is Constant

48 Calculating EVA When Invested Capital is Constant

49 EVA in Period n (When Capital Depreciates)

50 Calculating EVA When Invested Capital Changes

51 Calculating EVA When Invested Capital Changes

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