Chapter 6: Making capital investment decisions

1. Chapter 6: Making capital investment decisions Corporate Finance Ross, Westerfield, and Jaffe

2. Outline 1. Relevant/incremental cash flows 2. An example 3. The equivalent annual cost method

3. TVM • We need to evaluate a new project using the TVM technique. • That is, we should discount future expected cash flows (specifically, FCFs) back to present time and compare PV to initial costs: whether NPV > 0? • Discount cash flows, not earnings.

4. Relevant cash flows • But before we do this, a few notions about cash flows need to be addressed. • The cash flows in the capital-budgeting time line need to be relevant cash flows; that is they need to be incremental in nature. • Incremental cash flows: those cash flows that will only occur if the project is accepted.

5. Ask the right question • You should always ask yourself “Will this cash flow occur ONLY if we accept the project?” • If the answer is “yes”, it should be included in the analysis because it is incremental. • If the answer is “no”, it should not be included in the analysis because it will occur anyway.

6. Sunk costs • A sunk cost is a cost that has already occurred regardless of whether the project is accepted. • Example: consulting fee for evaluating a project. • Sunk costs should not be taken into consideration when evaluating a project.

7. Opportunity costs • Opportunity costs (OCs) are the costs of giving up the second best use of resources. • Example: a vacant land. • Opportunity costs should be taken into consideration when evaluating the project.

8. Side effects • Accepting a new project may have side effects. • Erosion occurs when a new project reduces the sales and cash flows of existing projects. • Synergy occurs when a new project increases the sales and cash flows of existing projects. • Cash flows due to erosion and synergy are incremental cash flows.

9. An example, I • Baldwin Company is considering an investment project: producing colored bowling balls. • The estimated life of the project: 5 years. • The cost of test marketing: $250,000. • Would be produced in a vacant building owned by the firm; the property can be sold for $150,000 after taxes. • The cost of a new machine: $100,000. • The estimated market value of the machine at the end of 5 years: $30,000.

10. An example, II • Production by year for the 5-year life: 5,000 units, 8,000 units, 12,000 units, 10,000 units, and 6,000 units. • The price of bowling balls in the first year: $20. • The price of bowling balls will increase at 2% per year. • No debt financing; no interest expenses.

11. An example, III • First-year production costs: $10 per unit. • Production costs will increase at 10% per year. • Incremental/marginal corporate tax rate: 34%. • An initial investment (at year 0) in net working capital: $10,000. • NWC at the end of each year will be equal to 10% of sales for that year. • NWC at the end of the project is zero.

12. An example, IV

13. Depreciation • Depreciation for tax purpose in the U.S. is based on the Modified Accelerated Cost Recovery System (MACRS). • See Table 6.3 (p. 176) for IRS depreciation schedule. • For a 5-year depreciation, the depreciation schedule is: 20% (year 1), 32% (year 2), 19.2% (year 3), 11.5% (year 4), 11.5% (year 5), and 5.8% (year 6).

14. An example, V

15. After-tax salvage cash flow • OCF = sales – costs – taxes. • The estimated salvage market value of the machine is 30% of $100,000; that is, $30,000. • The machine will have been depreciated to 5.8% of $100,000 at that time; that is, $5,800. • The taxable amount is $24,200 ($30,000 - $5,800). • The after-tax salvage cash flow is: $30,000 – (34% × $24,200) = $21,772.

16. An example, VI

17. Decision • If the nominal discount rate (cost of equity) is less than 16%, we accept the project. • In other words, if the discount rate is higher than 16%, we have a negative NPV.

18. NPV • The firm uses no debt. Thus the appropriate discount rate is the cost of equity. • Suppose that cost of equity is 15%. • NPV = 5473.43 (> 0).

19. An example, VII

20. Alternative definitions of OCF • In our previous calculation, we used the top-down approach to compute OCF ( = sales – costs – taxes). • Another 2 alternative methods: the bottom-up method, and the tax shield method. • See pp. 186-189.

21. The equivalent annual cost method • This method is useful (1) when one tries to choose between 2 machines of unequal lives, or (2) whether one should replace an existing machine with a new one. • Whereas a general capital budgeting problem is often computed in nominal terms, the equivalent annual cost (EAC) method works best in real terms.

22. Nominal vs. real

23. 2 machines with unequal lives • Revenues per year are the same, regardless of machine. • The nominal discount rate (NR) is 13.3%. The expected inflation rate (E(I)) is 3%. The real discount rate (RR) is 10%. • (1 + NR) = (1 + RR) × (1 + E(I)) • (1 + 13.3%) = (1 + 10%) × (1 + 3%).

24. Real cost outflows w/ real discount rate

25. Equivalent annual cost • One needs to use real (nominal) discount rate to discount real (nominal) cash flows. • For A, the EAC is $321.05. • 798.42 PV; 3 N; 10 I/Y; CPT PMT. • For B, the EAC is $289.28. • 916.99 PV; 4 N; 10 I/Y; CPT PMT. • B has a lower equivalent annual cost. We should choose B.

26. End-of-chapter • Concept questions: 1-12. • Questions and problems: 1-20.