Capital Budgeting Topics Investments of Unequal Lives

1. Capital Budgeting TopicsInvestments of Unequal Lives • There are times when application of the NPV rule can lead to the wrong decision. Consider an investment in equipment required in the production process: • There are two choices: • The “Auto Machine” costs $40,000 today, has annual operating costs of $1,000 and lasts for 10 years. • The “Manual Machine” costs $10,000 today, has annual operating costs of $5,000 and lasts for 5 years. • Which one should we choose? FIN 307 - Capital Budgeting Topics - Dr. Menahem Rosenberg

2. Investments of Unequal Lives At first glance, the “Manual” has the lower NPV (r = 10%): This overlooks the fact that the Auto Machine lasts twice as long. When we incorporate that, the Auto Machine is actually cheaper. FIN 307 - Capital Budgeting Topics - Dr. Menahem Rosenberg

3. -$1,000 –500 -500 -500 -500 -1,500 -500 -500 -500 -500 -500 0 1 2 3 4 5 6 7 8 9 10 Investments of Unequal Lives - Replacement Chain The “Manual Machine” time line of cash flows over ten years with a replacement at the end of its life: FIN 307 - Capital Budgeting Topics - Dr. Menahem Rosenberg

4. Investments of Unequal Lives • Replacement Chain - Matching Cycle • Repeat the projects forever, find the PV of that perpetuity. • Assumption: Both projects can and will be repeated. • Repeat projects until they begin and end at the same time—like we just did with the air cleaners. • Compute NPV for the “repeated projects”. • The Equivalent Annual Cost Method FIN 307 - Capital Budgeting Topics - Dr. Menahem Rosenberg

5. Investments of Unequal Lives: EAC • The Equivalent Annual Cost Method • Applicable to a much more robust set of circumstances than replacement chain. • The Equivalent Annual Cost is the value of the level payment annuity that has the same PV as our original set of cash flows. • NPV = EAC × {annuity factor} FIN 307 - Capital Budgeting Topics - Dr. Menahem Rosenberg

6. Investments of Unequal Lives: EAC • For example, the EAC for the Auto Machine is • Using the annuity factor FIN 307 - Capital Budgeting Topics - Dr. Menahem Rosenberg

7. Financial Leverage and Beta Financial leverage is the sensitivity of a firm’s fixed costs of financing. • The relationship between the betas of the firm’s debt, equity, and assets is given by: • Financial leverage always increases the equity beta relative to the asset beta. FIN 307 - Capital Budgeting Topics - Dr. Menahem Rosenberg

8. Financial Leverage and Beta: Example The XYZ, Inc., is currently all-equity and it has a beta of 1.10. The firm has decided to lever up to a capital structure of 25% debt and 75% equity. Since the firm will remain in the same industry, its asset beta should remain 0.90. However, assuming a zero beta for its debt, its equity beta would become twice as large: FIN 307 - Capital Budgeting Topics - Dr. Menahem Rosenberg

9. The Project versus the Firm • Any project’s cost of capital depends on the use (the project) to which the capital is being put—not the source of capital. • Therefore, it depends on the risk of the project and not the risk of the firm. FIN 307 - Capital Budgeting Topics - Dr. Menahem Rosenberg

10. Incorrectly accepted negative NPV projectsLowers firm Value Incorrectly rejected positive NPV projects Missed opportunity rf bFIRM Capital Budgeting & Project Risk A firm that uses one discount rate for all projects may over time increase the risk of the firm while decreasing its value. Project IRR Hurdle rate Firm’s risk (beta) FIN 307 - Capital Budgeting Topics - Dr. Menahem Rosenberg

11. Capital Budgeting & Project Risk Suppose a firm is made of three equal size departments. The company’s cost of equity capital is based on the CAPM. The risk-free rate is 4%; the market risk premium is 10% The breakdown of the company’s departments. Electronic parts dep. b = 1.1Electric equipment dep. b = 1.4Computer parts dep. b = 2.0 Average b of assets = 1.5 Cost of Equity = 4% + 1.5 × [14% – 4%] = 19% When evaluating a new computer parts project, which cost of capital should be used? FIN 307 - Capital Budgeting Topics - Dr. Menahem Rosenberg

12. Capital Budgeting & Project Risk Suppose a computer part project with an IRR of 20% is accepted. It will change the firm division into 50% computer parts and 25% for each other department. New Average b of assets = 1.725 The firm required return = 4% +1.725*10%= 21.25% Which is definitely above the firm actual return FIN 307 - Capital Budgeting Topics - Dr. Menahem Rosenberg

13. The Cost of Capital with Debt • The Weighted Average Cost of Capital is given by: • It is because interest expense is tax-deductible that we multiply the last term by (1- tC) making the true cost of debt rD(1- tC) FIN 307 - Capital Budgeting Topics - Dr. Menahem Rosenberg

14. Estimating Widget Inc. Cost of Capital • First, we estimate the cost of equity and the cost of debt. • We estimate an equity beta to estimate the cost of equity. • We can often estimate the cost of debt by observing the YTM of the firm’s debt. • Second, we determine the WACC by weighting these two costs. FIN 307 - Capital Budgeting Topics - Dr. Menahem Rosenberg

15. Estimating Widget’s Cost of Capital • The industry average beta is 1.30; the risk free rate is 4% and the market risk premium is 5.6%. • Thus the cost of equity capital is FIN 307 - Capital Budgeting Topics - Dr. Menahem Rosenberg

16. Estimating Widget’s Cost of Capital • The yield on the company’s debt is 7.2% (relative to similar maturity treasury bonds and credit risk) and the firm is in the 36% marginal tax rate. • The debt is 26% of the total firm value: 9.55% percent is Widget’s cost of capital. It should be used to discount any project where the project’s risk is equal to the risk of the firm as a whole, and the project is financed with the same leverage as the whole firm. FIN 307 - Capital Budgeting Topics - Dr. Menahem Rosenberg