1. Quiz 4 solution sketches 11:00 Lecture, Version A Note for multiple-choice questions: Choose the closest answer

2. Geometric Average On Nov. 1, 2013, Slacky Green Slacks was worth $100 per share. On Nov. 1, 2001, it was worth $50 per share. What is the geometric average rate of return over this 12-year period? (100/50) 1/12 = (2) 1/12 = 1.05946 R G = 1.05946 – 1 = 5.946%

3. Loan Amortization Gladman Goldie will borrow $100,000 on Jan. 1, 2014. He will make 15 yearly payments, on Nov. 1 of years 2015- 2029, to completely pay back the loan. How much will each payment be if the EAR is 12%?

4. Loan Amortization If paid on Jan. 1, 2015-2029: 100,000 = C/.12 * [1 – 1/1.12 15 ] 100,000 = 6.81086 * C C = $14,682 Add 10 months of interest to account for payments on Nov. 1: 14,682 * (1.12) 10/12 = $16,137

5. Future Value Kokomo Jack invests $6,000 today, November 25, 2013. Find the future value on November 25, 2025 if the stated annual interest rate is 10%, compounded every 18 months. Interest every 18 months =.1*18/12 =.15 Number of times compounded = 12/1.5 = 8 FV = 6000 * (1.15) 8 = $18,354

6. CAPM The risk-free rate of return is 6%. For a stock, assume that beta is 1.5. The market return of a well-diversified portfolio is 19%. What is the expected return for this stock? Exp. Ret. = Risk-free rate + β*risk premium Exp. Ret. = 6% + 1.5 * (19% – 6%) Exp. Ret. = 25.5%

7. Returns in States of the World For the following three questions, assume that there are two known states of the world, each with 50% probability of occurring: Good and Bad. When times are good, Stock A has a rate of return of 7% and Stock B has a return of 15%. When times are bad, Stock A has a rate of return of 9% and Stock B has a return of 5%.

8. Returns in States of the World What is the standard deviation of Stock A’s return? Avg return =.5 *.07 +.5 *.09 =.08 Var = 1/2 * [(.07-.08) 2 + (.09-.08) 2 ] Var = 1/2 * [.0001 +.0001] =.0001 Std. Dev. = (.0001) 1/2 =.01 = 1%

9. Returns in States of the World What is the covariance of the two stocks’ returns? A’s avg return =.5 *.07 +.5 *.09 =.08 B’s avg return =.5 *.15 +.5 *.05 =.10 Cov = 1/2 * [(.07-.08)(.15-.1) + (.09-.08)(.05-.1)] Cov = 1/2 * [-.0005 + (-.0005)] Cov = -0.0005

10. Returns in States of the World What is the correlation coefficient of the two stocks’ returns? A’s s.d. =.01 (from question 5) B’s variance = 1/2 * [(.15-.1) 2 + (.05-.1) 2 ] B’s variance = 1/2 * [.0025+.0025] =.0025 B’s s.d. = (.0025) 1/2 =.05 ρ = Cov/[s.d.(A)*s.d.(B)] ρ = -0.0005/(.01*.05) = -1

11. CAPM Assume that the risk-free rate is 9%. A stock has an expected return of 15%, and the expected return on the market is 14%. What is the beta for this stock? Exp. Ret. = Risk-free rate + β*risk premium 15% = 9% + β * (14% - 9%) 6% = β * 5% β = 1.2

12. Cash Cow & Retained Earnings Taco Bill Boots, Inc. is currently a cash cow. Without any re-investment of their earnings, they will earn $12 per share every year forever. The effective annual discount rate for owning this stock is 14%. Assume that the next dividend payment will be made later today.

13. Cash Cow & Retained Earnings Suppose that Cow Bell Boots could retain all of its earnings 5 years from today, and earn 8% on these earnings over the following year. (a) What is the PV of this stock if it continues to act as a cash cow? PV = 12 + 12/.14 = $97.71

14. Cash Cow & Retained Earnings (b) Should Taco Bill Boots retain its earnings 5 years from today? Why/why not? No, because: NPV is negative for this option Rate of return on retained earnings (8%) is less than the Discount rate (14%) Note that correct answers must use one of the two justifications

15. Cash Cow & Retained Earnings (c) How much does the present value of Taco Bill Boots change if the company retains its earnings 5 years from today? NPV of retaining earnings = -12/1.14 5 + 12(1.08)/1.14 6 = -$0.3280