1.  Making Investment Decisions with the Net Present Value Rule Principles of Corporate Finance Brealey and Myers Sixth Edition Slides by Matthew Will Chapter 6 © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill

2. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 2 Topics Covered  What To Discount  IM&C Project  Project Interaction  Timing  Equivalent Annual Cost  Replacement  Cost of Excess Capacity  Fluctuating Load Factors

3. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 3 What To Discount Only Cash Flow is Relevant

4. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 4 What To Discount Only Cash Flow is Relevant

5. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 5 What To Discount  Do not confuse average with incremental payoff.  Include all incidental effects.  Do not forget working capital requirements.  Forget sunk costs.  Include opportunity costs.  Beware of allocated overhead costs. Points to “Watch Out For”

6. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 6  Be consistent in how you handle inflation!!  Use nominal interest rates to discount nominal cash flows.  Use real interest rates to discount real cash flows.  You will get the same results, whether you use nominal or real figures. Inflation INFLATION RULE

7. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 7 Inflation Example You own a lease that will cost you $8,000 next year, increasing at 3% a year (the forecasted inflation rate) for 3 additional years (4 years total). If discount rates are 10% what is the present value cost of the lease?

8. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 8 Inflation Example You own a lease that will cost you $8,000 next year, increasing at 3% a year (the forecasted inflation rate) for 3 additional years (4 years total). If discount rates are 10% what is the present value cost of the lease?

9. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 9 Inflation Example - nominal figures

10. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 10 Inflation Example - real figures

11. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 11 IM&C’s Guano Project Revised projections ($1000s) reflecting inflation

12. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 12 IM&C’s Guano Project  NPV using nominal cash flows

13. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 13 IM&C’s Guano Project Cash flow analysis ($1000s)

14. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 14 IM&C’s Guano Project Details of cash flow forecast in year 3 ($1000s)

15. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 15 IM&C’s Guano Project Tax depreciation allowed under the modified accelerated cost recovery system (MACRS) - (Figures in percent of depreciable investment).

16. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 16 IM&C’s Guano Project Tax Payments ($1000s)

17. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 17 IM&C’s Guano Project Revised cash flow analysis ($1000s)

18. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 18 Timing  Even projects with positive NPV may be more valuable if deferred.  The actual NPV is then the current value of some future value of the deferred project.

19. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 19 Timing Example You may harvest a set of trees at anytime over the next 5 years. Given the FV of delaying the harvest, which harvest date maximizes current NPV?

20. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 20 Timing Example - continued You may harvest a set of trees at anytime over the next 5 years. Given the FV of delaying the harvest, which harvest date maximizes current NPV?

21. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 21 Timing Example - continued You may harvest a set of trees at anytime over the next 5 years. Given the FV of delaying the harvest, which harvest date maximizes current NPV?

22. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 22 Equivalent Annual Cost Equivalent Annual Cost - The cost per period with the same present value as the cost of buying and operating a machine.

23. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 23 Equivalent Annual Cost Equivalent Annual Cost - The cost per period with the same present value as the cost of buying and operating a machine.

24. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 24 Equivalent Annual Cost Example Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using equivalent annual cost method.

25. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 25 Equivalent Annual Cost Example Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using equivalent annual cost method. Year Machine1234PV@6%EAC A1555528.37 B106621.00

26. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 26 Example Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using equivalent annual cost method. Year Machine1234PV@6%EAC A1555528.3710.61 B106621.0011.45 Equivalent Annual Cost

27. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 27 Machinery Replacement Annual operating cost of old machine = 8 Cost of new machine Year: 0 1 2 3 NPV @ 10% 15 5 5 5 27.4 Equivalent annual cost of new machine = 27.4/(3-year annuity factor) = 27.4/2.5 = 11 MORAL: Do not replace until operating cost of old machine exceeds 11.

28. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 28 Cost of Excess Capacity A project uses existing warehouse and requires a new one to be built in Year 5 rather than Year 10. A warehouse costs 100 & lasts 20 years. Equivalent annual cost @ 10% = 100/8.5 = 11.7 0... 5 6... 10 11... With project 0 0 11.7 11.7 11.7 Without project 0 0 0 0 11.7 Difference 0 0 11.7 11.7 0 PV extra cost = + +... + = 27.6 11.7 11.7 11.7 (1.1) 6 (1.1) 7 (1.1) 10

29. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 29 Fluctuating Load Factors

30. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 30 Fluctuating Load Factors

31. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 6- 31 Fluctuating Load Factors