Busfin1328 Spring 2024 Problem Set 1

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Feb 20, 2024

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BUSFIN 1328 Spring 2024 Problem Set 1 Show your work , please. TOTAL 100 points The assignment is due on Thursday, February 1, 2024, at 11 a.m. I need only one write-up back from each group with the first and last names of students forming the group (and your student ID numbers). Highlight your answers, please. Please upload it to Canvas. CAPM Question 1 (3 points) What is the beta of a portfolio with E(r P )=18%, if r f =6% and E(r M )=14%? Question 2 (7 points) The market price of a security is 50$. Its expected rate of return is 14%. The risk-free rate is 6% and the market risk premium is 8.5%. What will be the market price of the security if its covariance with the market portfolio doubles (and all other variables remain unchanged)? Assume that the stock is expected to pay a constant dividend in perpetuity. Hint: Recall that in the case of perpetual dividends price of the stock is equal to D/r Question 3 (2 points each, 4 points in total) Are the following true or false? a. Stocks with a beta of zero offer an expected rate of return of zero. b. The CAPM implies that investors require a higher return to hold highly volatile securities. Question 4 (6 points) A share of stock sells for $50 today. It will pay a dividend of $6 per share at the end of the year. Its beta is 1.2. R f =6%. R M =16%. What do investors expect the stock to sell for at the end of the year? Question 5 In 1997 the rate of return on short-term government securities (perceived to be risk-free) was about 5%. Suppose the expected rate of return required by the market for a portfolio with a beta of 1 is 12%. According to the CAPM (security market line): a. (3 points) What is the expected rate of return on the market portfolio? b. (3 points) What would be the expected rate of return on a stock with beta=0? c. (5 points) Suppose you consider buying a share of stock at $40. The stock is expected to pay $3 dividends next year and you expect it to sell then for $41. The stock risk has been evaluated by beta=-0.5. Is the stock overpriced or underpriced? 1
Stock Valuation Question 1 a. (10 points) You are a stock analyst in charge of valuing high-technology firms, and you are expected to come out with buy-sell recommendations for your clients. You are currently analyzing a firm called eGreg.com that specializes in Internet business communication. You are expecting explosive growth in this area. However, the company is not currently profitable even though you believe it will be in the future. Your projections are that the firm will pay no dividends for the next 10 years. Eleven years from now, you expect the stock to pay its first dividend of $2 per share. You expect dividends to increase at a rate of 25 percent per year for the nine years after that. At that point, the industry will start to mature and slow down; dividends will continue to grow but only at a rate of 9 percent per year. The stock is priced in the market at $15 per share. If you believe that a fair rate of return on a stock of this type is 14 percent, what is your estimate of the value of the stock, and should you issue a recommendation to buy or to sell? b. (10 points) The day after you make your estimate in part (a) news indicates that things are not going as smoothly as predicted for this business. Your estimates of the initial dividend and the growth rates remain the same, but the timing has changed. You now decide that the firm will pay its first dividend ($2) in 16 years. The high growth period (25 percent per year) will last for only four years before slowing to a growth of 9 percent per year. Given a rate of return of 14 percent, what is your new estimate of the value of the stock, and should you change your recommendation? Question 2 (10 points) An enterprise is expected to pay a dividend of $0.50 in one year. The dividend is expected to grow at a rate of 15 percent per year for the next four years up to and including year 5 as the firm goes through a period of rapid growth. After that, it is expected to grow at an average rate of 5 percent per year forever. If the required return is 20 percent, what is the value of a share? Question 3 You are estimating the price-earnings multiple to use to value Paramount Global by looking at the average price-earnings multiple of comparable firms. The following are the price-earning ratios of firms in the entertainment business. Firm PE Ratio Disney 22.09 Warner Bros Discovery Inc 36.00 Comcast 14.10 Netflix 26.70 Charter Communications 13.50 You can find more information about the companies at this link: https://disfold.com/united-states/industry/entertainment/companies/ 2
a. (3 points) Would you use all the comparable firms in calculating the average? Why or why not? b. (3 points) What is the average PE Ratio? Options Question 1 A call option has an exercise price of $10.00 and an expiry date of six months. The underlying stock is currently trading for $12.00. (a) (3 points) What is the minimum price an investor would pay for this option? Could an investor profit if the call option was actually trading at $1.00? (b) (3 points) What is the maximum price an investor would pay for this option? If the option was trading for $13.00, how could an investor earn a risk-free profit? This is a more analytical question than a quantitative one. Question 2 (10 points) A call option has a striking price of $8.10 and an expiry date of six months. The underlying stock is currently trading at $7.60 and has historically exhibited a standard deviation of 10.6 percent. The standard deviation is not expected to change. The interest rate is 5.4 percent. Using the Black-Scholes equation, estimate the value of the call option described above. What are some of the limitations of using the Black-Scholes equation? Question 3 (10 points) Suppose you have just purchased a share of stock in WYZ Corp for $50. The stock is not expected to pay a dividend during the time you plan to hold it. You have forecasted that the stock will be worth in one year either $ 65 or $40. Suppose further that you can sell a call option on WYZ stock with an exercise price of $52.50. It is a European-style contract that expires in exactly one year. What the option should sell for today if the one-year T-bill yield is 8%? Question 4 (7 points) Suppose that WYZ stock is currently valued at $53 and that call and put options on WYZ stock with an exercise price of $50 sell for $6.74 and $2.51 respectively. Both options can only be exercised in 6 months. You can also buy a 6-month T-bill with a $50 face value with an annualized rate/return of 6.25%. Does Put-Call parity hold? If not, what is the arbitrage trade you should make and what is the arbitrage profit? 3
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