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Quiz 4 solution sketches

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

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Quiz 4 solution sketches

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  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 • RG = 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 – 1/1.1215]100,000 = 6.81086 * CC = $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= -12/1.145 + 12(1.08)/1.146= -$0.3280

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