Risk Analysis in Investment Decisions Sample Assignment

Risk Analysis in Investment Decisions

Multiple Choice Questions

1. Total risk is measured by _____ and systematic risk is measured by ____.
A. beta; alpha
B. beta; standard deviation
C. WACC; beta
D. standard deviation; beta
E. standard deviation; variance
F. None of the above.

2. When investment returns are less than perfectly positively correlated, the resulting diversification effect means that:
A. making an investment in two or three large stocks will eliminate all of the unsystematic risk.
B. making an investment in three companies all within the same industry will greatly reduce the systematic risk.
C. spreading an investment across five diverse companies will not lower the total risk.
D. spreading an investment across many diverse assets will eliminate all of the systematic risk.
E. spreading an investment across many diverse assets will eliminate some of the total risk.
F. None of the above.

3. Unsystematic risk:
A. can be effectively eliminated by portfolio diversification.
B. is compensated for by the risk premium.
C. is measured by beta.
D. is measured by standard deviation.
E. is related to the overall economy.
F. None of the above.

4. Which of the following are examples of diversifiable risk?

I. An earthquake damages Oakland, California.
II. The federal government imposes an additional $1,000 fee on all business entities.
III. Employment taxes increase nationally.
IV. Toymakers are required to improve their safety standards.
A. I and III only
B. II and IV only
C. II and III only
D. I and IV only
E. I, III, and IV only
F. None of the above.

5. Which of the following statements are correct concerning diversifiable, or unsystematic, risks?

I. Diversifiable risks can be largely eliminated by investing in thirty unrelated securities.
II. There is no reward for accepting diversifiable risks.
III. Diversifiable risks are generally associated with an individual firm or industry.
IV. Beta measures diversifiable risk.
A. I and III only
B. II and IV only
C. I and IV only
D. I, II, and III only
E. I, II, III, and IV
F. None of the above.

6. Which of the following statements concerning risk are correct?

I. Systematic risk is measured by beta.
II. The risk premium increases as unsystematic risk increases.
III. Systematic risk is the only part of total risk that should affect asset prices and returns.
IV. Diversifiable risks are market risks you cannot avoid.
A. I and III only
B. II and IV only
C. I and II only
D. III and IV only
E. I, II, and III only
F. None of the above.

7. Which one of the following is an example of systematic risk?
A. The Federal Reserve unexpectedly announces an increase in target interest rates.
B. A flood washes away a firm's warehouse.
C. A city imposes an additional one percent sales tax on all products.
D. A toymaker has to recall its top-selling toy.
E. Corn prices increase due to increased demand for alternative fuels.
F. None of the above.

8. The excess return earned by a risky asset, for example with a beta of 1.4, over that earned by a risk-free asset is referred to as a:
A. market risk premium.
B. risk premium.
C. systematic return.
D. total return.
E. real rate of return.
F. None of the above.

9. The dividend growth model can be used to compute the cost of equity for a firm in which of the following situations?

I. Firms that have a 100 percent retention ratio
II. Firms that pay an unchanging dividend
III. Firms that pay a constantly increasing dividend
IV. Firms that pay an erratically growing dividend
A. I and II only
B. I and IV only
C. II and III only
D. I, II, and III only
E. I, III, and IV only
F. None of the above.

10. The cost of equity for a firm:
A. tends to remain static for firms with increasing levels of risk.
B. increases as the unsystematic risk of the firm increases.
C. ignores the firm's risks when that cost is based on the dividend growth model.
D. equals the risk-free rate plus the market risk premium.
E. equals the firm's pretax weighted average cost of capital.
F. None of the above.

11. The pre-tax cost of debt:
A. is based on the current yield to maturity of the firm's outstanding bonds.
B. is equal to the coupon rate on the latest bonds issued by a firm.
C. is equivalent to the average current yield on all of a firm's outstanding bonds.
D. is based on the original yield to maturity on the latest bonds issued by a firm.
E. has to be estimated as it cannot be directly observed in the market.
F. None of the above.

12. The after-tax cost of debt generally increases when:

I. a firm's bond rating increases.
II. the market-required rate of interest for the company's bonds increases.
III. tax rates decrease.
IV. bond prices rise.
A. I and III only
B. II and III only
C. I, II, and III only
D. II, III, and IV only
E. I, II, III, and IV
F. None of the above.

Key facts and assumptions concerning FM Foods, Inc. at December 31, 2011, appear below.

13. Estimate FM's after-tax cost of equity capital.
A. 4.50%
B. 6.92%
C. 7.93%
D. 12.20%
E. 17.48%
F. None of the above.

14. Estimate FM's after-tax cost of debt capital.
A. 2.21%
B. 4.10%
C. 4.55%
D. 6.30%
E. 7.00%
F. None of the above.

15. Estimate the appropriate weight of equity to be used when calculating FM's weighted average cost of capital.
A. 11.5%
B. 19.3%
C. 80.7%
D. 88.5%
E. 100.0%
F. None of the above.

16. Estimate the appropriate weight of debt to be used when calculating FM's weighted average cost of capital.
A. 11.5%
B. 19.3%
C. 80.7%
D. 88.5%
E. 100.0%
F. None of the above.

17. Estimate FM's weighted-average cost of capital.
A. 6.46%
B. 6.58%
C. 11.27%
D. 11.32%
E. 11.52%
F. None of the above.

18. FM is contemplating an average-risk investment costing $100 million and promising an annual after-tax cash flow of $15 million in perpetuity. Which of the following statements is/are correct?

I. FM should reject the project because the IRR is greater than the firm's WACC.
II. FM should accept the project because the IRR is greater than the firm's WACC.
III. FM should accept the project because the NPV is greater than zero.
IV. FM should reject the project because the NPV is less than zero.
A. I only
B. II only
C. IV only
D. I and IV only
E. II and III only
F. None of the above.

19. Which of the following statements are correct?

I. Using the same risk-adjusted discount rate to discount all future cash flows adjusts for the fact that the more distant cash flows are often more risky than cash flows occurring sooner.
II. If you can borrow all of the money you need for a project at 5%, the cost of capital for this project is 5%.
III. The best way to obtain the cost of debt capital for a firm is to use the coupon rates on its bonds.
IV. The cost of capital, or WACC, is not the correct discount rate to use for all projects undertaken by a firm.
A. I and III only
B. II and IV only
C. I and II only
D. I and IV only
E. I, II, and III only
F. None of the above

20. The capital structure weights used in computing the weighted average cost of capital:
A. are based on the book values of total debt and total equity.
B. are based on the market value of the firm's debt and equity securities.
C. are computed using the book value of the long-term debt and the book value of equity.
D. remain constant over time unless the firm issues new securities.
E. are restricted to the firm's debt and common stock.
F. None of the above.

21. The discount rate assigned to an individual project should be based on:
A. the firm's weighted average cost of capital.
B. the actual sources of funding used for the project.
C. an average of the firm's overall cost of capital for the past five years.
D. the current risk level of the overall firm.
E. the risks associated with the use of the funds required by the project.
F. None of the above.

22. The weighted average cost of capital for a firm is the:
A. discount rate which the firm should apply to all of the projects it undertakes.
B. rate of return a firm must earn on its existing assets to maintain the current value of its stock.
C. coupon rate the firm should expect to pay on its next bond issue.
D. minimum discount rate the firm should require on any new project.
E. rate of return shareholders should expect to earn on their investment in this firm.
F. None of the above.

23. Blue Diamond Equipment has 80,000 bonds outstanding that are selling at par. Bonds with similar characteristics are yielding 6.75 percent. The company also has 750,000 shares of 7 percent preferred stock and 2.5 million shares of common stock outstanding. The preferred stock sells for $53 a share. The common stock has a beta of 1.34 and sells for $42 a share. The U.S. Treasury bill is yielding 2.8 percent and the return on the market is 11.2 percent. The corporate tax rate is 38 percent. What is the firm's weighted average cost of capital?
A. 10.39 percent
B. 10.64 percent
C. 11.18 percent
D. 11.30 percent
E. 11.56 percent
F. None of the above.

24. Honest Abe's is a chain of furniture retail stores. Integral Designs is a furniture maker and a supplier to Honest Abe's. Honest Abe's has a beta of 1.38 as compared to Integral Designs' beta of 1.12. Both firms carry no debt, i.e., are 100% equity-financed. The risk-free rate of return is 3.5 percent and the market risk premium is 8 percent. What discount rate should Honest Abe's use if it considers a project that involves the manufacturing of furniture?
A. 12.46 percent
B. 12.92 percent
C. 13.50 percent
D. 14.08 percent
E. 14.54 percent
F. None of the above.

Short Answer Questions

Key facts and assumptions concerning Costco Company, at December 31, 2011, appear below.

25. Use the above information to answer the following questions.

a. Estimate Costco's cost of equity capital.
b. Estimate Costco's weighted-average cost of capital.

26. Explain the difference between systematic and unsystematic risk, and why one of these types of risks is rewarded with a risk premium while the other type is not.

27. Suppose that your company's weighted-average cost of capital is 9 percent. Your company is planning to undertake a project with an internal rate of return of 12%, but you believe that this project is not a good investment for the firm. What logical arguments might you use to convince your boss to forego the project despite its high rate of return? Is it possible that making investments with expected returns higher than your company's cost of capital will destroy value? If so, how?

28. The standard deviation of returns on Wildcat Oil Drilling is very high. Does this necessarily imply that Wildcat Oil Drilling is a high-risk investment when investors hold diversified portfolios? Explain why or why not.

29. Investments A and B both cost $100,000 and each promises a single payoff in one year. The distribution of payoffs for each investment appears below.
Ignoring possible differences in nondiversifiable risk, which investment would a risk-averse investor prefer, and why?

30. What is the present value of a cash flow stream of $10,000 per year annually for 11 years that then grows at 2 percent per year forever? Assume the appropriate discount rate is 12 percent.

Risk Analysis in Investment Decisions Answer Key

Multiple Choice Questions

Difficulty: 1 Easy

Key facts and assumptions concerning FM Foods, Inc. at December 31, 2011, appear below.

13. Estimate FM's after-tax cost of equity capital.
A. 4.50%
B. 6.92%
C. 7.93%
D. 12.20%
E. 17.48%
F. None of the above.

K_E = gov't borrowing rate + equity beta * market risk premium = .044 + 1.2(.065) = 0.122

Difficulty: 1 Easy

14. Estimate FM's after-tax cost of debt capital.
A. 2.21%
B. 4.10%
C. 4.55%
D. 6.30%
E. 7.00%
F. None of the above.

The correct approach is to use the YTM on the firm's bonds for the before-tax cost. Thus, after-tax cost = 6.3% (1 - .35) = 4.10%.

Difficulty: 1 Easy

15. Estimate the appropriate weight of equity to be used when calculating FM's weighted average cost of capital.
A. 11.5%
B. 19.3%
C. 80.7%
D. 88.5%
E. 100.0%
F. None of the above.

Market value of equity = $40 * 240 million = $9,600 million. Weight of equity = 9,600/(9,600 + 1,250) = .8848 or 88.5%.

Difficulty: 1 Easy

16. Estimate the appropriate weight of debt to be used when calculating FM's weighted average cost of capital.
A. 11.5%
B. 19.3%
C. 80.7%
D. 88.5%
E. 100.0%
F. None of the above.

Market value of equity = $40 * 240 million = $9,600 million.
Weight of debt = 1,250/(9,600 + 1,250) = .1152 or 11.5%.

Difficulty: 1 Easy

17. Estimate FM's weighted-average cost of capital.
A. 6.46%
B. 6.58%
C. 11.27%
D. 11.32%
E. 11.52%
F. None of the above.

The following table presents FM's WACC using market values (where possible):

Difficulty: 2 Medium

The IRR of the investment is 15/100 = 15%. FM's WACC of 11.27% is shown in the table below. The NPV of the investment at the WACC = -100 + 15/.1127 = $33.1 million.

Difficulty: 3 Hard

Difficulty: 2 Medium

Difficulty: 1 Easy

R_e = 0.028 + 1.34 (0.112 - 0.028) = 0.14056; R_p = (0.07 ´ $100)/$53 = 0.13208
Market values of: debt = 80,000*$1,000 = $80.00M; preferred = 750,000*$53 = $39.75M; and common = 2.5M * $42 = $105.00M. These sum to $224.75M. Thus, the WACC = ($105M/$224.75M) (0.14056) + ($39.75M/$224.75M) (0.13208) + ($80M/$224.75M) (0.0675) (1 - 0.38) = 10.39 percent.

Difficulty: 2 Medium

K_E = gov't borrowing rate + equity beta*market risk premium = 0.035 + 1.12(0.08) = 0.1246 or 12.46 percent

Difficulty: 1 Easy

Short Answer Questions

Key facts and assumptions concerning Costco Company, at December 31, 2011, appear below.

25. Use the above information to answer the following questions.

a. Estimate Costco's cost of equity capital.
b. Estimate Costco's weighted-average cost of capital.

a. K_E = gov't borrowing rate + equity beta*market risk premium
K_E = 3.28 + 0.80 (6.10) = 8.16%

b. The table below presents the weighted-average cost of capital for Costco:

Difficulty: 2 Medium

26. Explain the difference between systematic and unsystematic risk, and why one of these types of risks is rewarded with a risk premium while the other type is not.

Unsystematic, or diversifiable, risk affects a limited number of securities and can be eliminated by investing in securities from various industries and geographic regions. Unsystematic risk is not rewarded because it can be eliminated by investors. Systematic risk is risk that affects most, or all, securities and cannot be diversified away. Since systematic risk cannot be eliminated by investors it is rewarded with a risk premium. Systematic risk is measured by beta.

Difficulty: 2 Medium

If the investment is above the company's average risk, the company's cost of capital is not an appropriate benchmark. Equivalently, you might argue that the high risk of the investment places it below the security market line. Such investments destroy value because they promise returns that, while greater than the company's WACC, are still below those available on similar-risk investments available. Other possible arguments include: the investment is not consistent with the strategic plan; and, the cash flow estimates are too optimistic.

Difficulty: 2 Medium

The equation for beta in chapter 8 shows that the nondiversifiable risk of an asset is the product of its standard deviation of returns and the correlation of those returns with those on a well-diversified portfolio. Wildcat Oil Drilling may have a high standard deviation of returns, but if those returns are poorly correlated with those on a well-diversified portfolio, as is likely the case, nondiversifiable risk may be low.

Difficulty: 2 Medium

These investments have the same expected outcome but different dispersions of possible outcomes. Risk-averse investors will prefer investment B because it has the same return as A but at lower risk.

Difficulty: 2 Medium

30. What is the present value of a cash flow stream of $10,000 per year annually for 11 years that then grows at 2 percent per year forever? Assume the appropriate discount rate is 12 percent.

Divide the cash flows into two periods: An 11-year annuity of $10,000, and a growing perpetuity beginning in the 11^th year. The value of the 11-year annuity is
$59,376.99. The value of the growing perpetuity (using the formula provided in the chapter for a growing dividend into perpetuity) at time 11 is $10,000(1 + .02)/(.12-.02) = $102,000. Its value at time zero is $102,000/(1.12)¹¹ = $29,322.56. Adding these present values, $29,322.56 + $59,376.99 = $88,699.55.

Difficulty: 2 Medium