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

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 = R G = – 1 = 5.946%

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

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

Future Value Kokomo Jack invests $6,000 today, November 25, 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

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% * (19% – 6%) Exp. Ret. = 25.5%

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%.

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

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

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 B’s s.d. = (.0025) 1/2 =.05 ρ = Cov/[s.d.(A)*s.d.(B)] ρ = /(.01*.05) = -1

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

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.

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 = /.14 = $97.71

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

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/ (1.08)/ = -$0.3280