1 / 18

Quiz 4 solution sketches

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

rex
Download Presentation

Quiz 4 solution sketches

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. PV of Perpetuity • If Alexia receives $1,000 per year, forever, starting nine months from now, what is the total PV of all payments? Assume a stated annual interest rate of 16%, compounded every three months. • EAIR = (1.04)4 – 1 = 16.986% • PV = 1,000/.16986 * (1.16986)1/4 • PV = $6,122.69 She receives payments 3 months sooner than what is in perpetuity formula

  3. Balloon Payment • Sunny borrows $5,000 today. She makes monthly payments of $37.50 for 48 months, starting one month from today. She makes one additional payment 60 months from today to completely pay off the loan. How much will this payment be if the stated annual interest rate is 9%, compounded monthly?

  4. Balloon Payment • Interest-only loan for 48 months: • 5000 * (.09/12) = $37.50 • Balance after last regular payment in 48 months = $5,000 • Payment needed 12 months later = 5,000 * (1 + .09/12)12 = $5,469.03

  5. Profitability Index • Brady invests $500,000 in McKenzie Wealth Management today. He will receive $100,000 per year, forever, starting one year from now. What is the profitability index for this investment if the effective annual interest rate is 25%? • PV of benefits = 100,000/.25 = $400,000 • P.I. = 400,000/500,000 = 0.8

  6. Growing Dividends • Scrubby Dub Dub Ghost, Inc. will pay its first dividend three years from today, and will pay annually thereafter forever. The first dividend payment (in 3 years) is $10 per share. Each of the next two dividend payments will be 50% higher than the previous payment. After that, dividend payments will remain the same forever.

  7. Growing Dividends • What is the PV of this stock if the effective annual interest rate is 10%? • PV = 10/(1.1)3 + 15/(1.1)4 + 22.50/.1 * 1/(1.1)4 • PV = $171.44 $22.50 paid every year starting 5 years from now

  8. CAPM • KKQJ Products, Inc. currently has an expected return of 15%. The risk-free rate of return is 4% and the expected return on the market is 10%. What is the beta for KKQJ Products? • Exp. Ret. = Risk-free rate + β*risk premium • 15% = 4% + β * (10% - 4%) • 15% = β * 6% • β = 1.833

  9. Random Walk • Use the following information for the next two questions: Deucey Deuce Dance Productions stock exhibits price changes that are a random walk. In any given day, the value of the stock goes up by $2 with probability 0.4 and goes down by $1 with probability 0.6. The stock’s current value is $50.

  10. Random Walk • What is the probability that the value of the stock will be the same two days from today? • In 2 days, the stock cannot reach the same value given the problem’s set-up. • Probability = 0

  11. Random Walk • What is the probability that the value of the stock will be the same three days from today? • Three combinations will achieve the same stock value (with U=up and D=down): • UDD, DUD, DDU • Each has the same prob. = (.4)(.6)2 = .144 • Total probability = 3 * .144 = 43.2%

  12. Confidence Interval • Over Jan. 1, 1900 to Jan. 1, 2000, the historical average annual rate of return in Greece’s stock market was 12.5%. The annual standard deviation of the rate of return was 25.6%. What is the upper bound of the 95.4% confidence interval for the annual rate of return based on this information?

  13. Confidence Interval • Hint: you need to be within 2 standard errors of the average to find the upper and lower bounds of the 95.4% confidence interval. • Upper bound= 12.5% + 2 * 25.6%/(100)1/2= 12.5% + 5.12%=17.62%

  14. Confidence Interval • Hint: you need to be within 2 standard errors of the average to find the upper and lower bounds of the 95.4% confidence interval. • Upper bound= 12.5% + 2 * 25.6%/(100)1/2= 12.5% + 5.12%=17.62%

  15. Returns in States of the World • There are 3 states of the world, each with one-third probability of occurring: A, B, and C. When state A occurs, Stock P has a return of 20% and Stock Q has a return of 5%. When state B occurs, Stock P has a return of 30% and Stock Q has a return of 10%. When state C occurs, Stock P has a return of -8% and Stock Q has a return of 18%.

  16. Returns in States of the World • (a) What is the expected return for each company? (Note: both answers must be correct for credit on this part.) • ER(P) = 1/3 * [.2 + .3 + (-.08)] = .14 • ER(Q) = 1/3 * [.05 + .1 + .18] = .11

  17. Returns in States of the World • (b) What is the variance of Stock Q’s returns? • Var(Q) = 1/3 * [(.05-.11)2 + (.1-.11)2 + (.18-.11)2] • Var(Q) = 0.0028667

  18. Returns in States of the World • What is the covariance of the two stocks’ returns? • Cov(P,Q) = 1/3 * [(.2-.14)(.05-.11) + (.3-.14)(.1-.11) + (-.08-.14)(.18-.11)] • Cov(P,Q) = 1/3 * (-0.0206) • Cov(P,Q) = -0.006867

More Related