1. Class 3 Investment Decisions and Capital Budgeting

2. Value of an Investment Project n Recall the four factors that determine the value of an investment:  Cost of the investment.  Magnitude of future cash flows.  Timing of future cash flows.  Risk of future cash flows. n We shall deal with the first three factors and defer the discussion of risk to a future date.

3. The Net Present Value (NPV) Rule n Net Present Value (NPV): CF t = after-tax cash flow in year t. r p = risk-adjusted discount rate for that investment. I = initial cost of the investment.

4. Net Present Value (NPV) n The NPV measures the amount by which the value of the firm’s stock will increase if the project is accepted. n NPV Rule:  Accept all projects for which NPV > 0.  Reject all projects for which NPV < 0.  For mutually exclusive projects, choose the project with the highest NPV.

5. NPV Example n Consider a drug company with the opportunity to invest $100 million in the development of a new drug that is expected to generate $20 million in after-tax cash flows for the next 15 years. What is the NPV of this investment project if the required return is 10%? What if the required return is 20%?

6. NPV Example (cont.) n r p = 10% n r p = 20%

7. Eurotunnel NPV n One of the largest commercial investment project’s in recent years is Eurotunnel’s construction of the Channel Tunnel linking France with the U.K. n The cash flows on the following page are based on the forecasts of construction costs and revenues that the company provided to investors in 1986. n Given the risk of the project, we assume a 13% discount rate.

8. Eurotunnel’s NPV

9. Special Topics: Comparing Projects with Different Lives n Your firm must decide which of two machines it should use to produce its output. n Machine A costs $100,000, has a useful life of 4 years, and generates after-tax cash flows of $40,000 per year. n Machine B costs $65,000, has a useful life of 3 years, and generates after-tax cash flows of $35,000 per year. n The machine is needed indefinitely and the discount rate is r p = 10%.

10. Comparing Projects with Different Lives n Step 1: Calculate the NPV for each project.

11. Comparing Projects with Different Lives n Step 2: Convert the NPVs for each project into an equivalent annual annuity.

12. Comparing Projects with Different Lives n Machine A 0 1 2 3 4 -100,000 40,000 40,000 40,000 40,000 8,453 8,453 8,453 8,453 n Machine B 0 1 2 3 - 60,000 35,000 35,000 35,000 8,863 8,863 8,863

13. Comparing Projects with Different Lives n The firm is indifferent between the project and the equivalent annual annuity. n Since the project is rolled over forever, the equivalent annual annuity lasts forever. n The project with the highest equivalent annual annuity offers the highest aggregate NPV over time.  Aggregate NPV A = $8,453/.10 = $84,530  Aggregate NPV B = $8,863/.10 = $88,630

14. Special Topics: Replacing an Old Machine n The cost of the new machine is $20,000 (including delivery and installation costs) and its economic useful life is 3 years. n The existing machine will last at most 2 more years. n The annual after-tax cash flows from each machine are given in the following table. n The discount rate is r p = 10%.

15. Replacing an Old Machine

16. n Step 1: Calculate the NPVof the new machine.

17. Replacing an Old Machine n Step 2: Convert the NPV for the new machine into an equivalent annual annuity.

18. Replacing an Old Machine n The NPV of the new machine is equivalent to receiving $6,544 per year for 3 years. n Operate the old machine as long as its after-tax cash flows are greater than EA New = $6,544. n Old machine should be replaced after one more year of operation. n How did we know that the new machine itself would not be replaced early?

19. Alternatives to NPV n Internal Rate of Return (IRR) n Payback n Profitability Index

20. Internal Rate of Return (IRR) n The IRR is the discount rate, IRR, that makes NPV = 0. n IRR Rule  Accept project if IRR > r p.  Reject project if IRR < r p.

21. IRR Example n Consider, once again, the drug company that has the opportunity to invest $100 million in the development of a new drug that will generate after-tax cash flows of $20 million per year for the next 15 years. What is the IRR of this investment?

22. IRR Example n The IRR makes NPV = 0. n Trial and error (or a financial calculator) gives IRR = 18.4%. n Accept the project if r p < 18.4%.

23. Problems with IRR n Borrowing or Lending? n Multiple IRRs n Mutually Exclusive Projects

24. IRR Problems: Borrowing or Lending? n Consider the following two investment projects faced by a firm with r p = 10%. n Both projects have an IRR = 50%, but only project A is acceptable.

25. NPV Profiles

26. IRR Problems: Multiple IRRs n Consider a firm with the following investment project and a discount rate of r p = 25%. n This project has two IRRs: one above r p and the other below r p. Which should be compared to r p ?

27. NPV Profile

28. IRR Problems: Mutually Exclusive Projects n Consider the following two mutually exclusive projects. The discount rate is r p = 20%. n Despite having a higher IRR, project A is less valuable than project B.

29. NPV Profiles

30. Payback Period n Payback is the number of years it takes to recoup your initial investment. n Payback Rule  Accept the project if the payback is less than the maximum payback allowed.  Reject the project if the payback is greater than the maximum payback allowed.

31. Payback Example n Consider the following two investment projects. Assume that r p = 20%. n Which project is accepted if the payback period criteria is 2 years?

32. Problems with Payback n Ignores the Time Value of Money n Ignores Cash Flows Beyond the Payback Period n Ignores the Scale of the Investment n Decision Criteria is Arbitrary

33. Profitability Index n Profitability Index PI = (I + NPV)/I = 1 + NPV/I n Used when the firm (or division) has a limited amount of capital to invest. n Rank projects based upon their PIs. Invest in the projects with the highest PIs until all capital is exhausted (provided PI > 1).

34. Profitability Index Example n Suppose your division has been given a capital budget of $6,000. Which projects do you choose?

35. Profitability Index Example n Suppose your budget increases to $7,000. n Choosing projects in decending order of PIs no longer maximizes the aggreagate NPV. n Projects A and C provide the highest aggregate NPV = $3,000 and stay within budget. n Linear programming techniques can be used to solve large capital allocation problems.