HW 6-Stocks-2023Solution

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School
Indiana University, Bloomington **We aren't endorsed by this school
Course
BUS F304
Subject
Finance
Date
Oct 29, 2023
Pages
3
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HW 6- Stocks 1) What is the dividend of a preferred stock if the required rate of return is 5% and the stock is currently trading at a price of $45.5? A preferred stock offers a fixed dividend and therefore it can be priced as the present value of a perpetuity. 𝑷 ? = 𝑫 𝒓 ??. ? = 𝑫 ?. ?? So D=2.275 2) If the firm pays a quarterly dividend of $0.87 and the discount rate is 5% (annual) what will be the value at the end of the year of all four dividend payments? This requires calculating the future value of an annuity but first converting the annual rate to a quarterly rate. 𝑭𝑽𝑨 = ? 𝒓 [(? + 𝒓) ? − ?] ∗ ?. ?? = ? ?. ???? (?. ???? ? − ?) ∗ ?. ?? = ?. ?? 3) A stock is expected to pay a dividend of $3 and has a dividend yield of 6%. If its total one-year return is expected to be 9% what is your estimate of next year's stock price? We need to find 𝑷 ? . From the total return formula we have 𝑯𝑷𝑹 = 𝑷 ? −𝑷 ? 𝑷 ? + 𝑫 ? 𝑷 ? We can also use the information on the dividend and the dividend yield to compute the current stock price as 𝑷 ? = $? ?.?? = $?? . Given that we can use the HPR formula to solve for the price ?. ?? = 𝑷 ? −?? ?? + ?. ?? So 𝑷 ? = ??. ? 4) A company just paid an annual dividend of $2. What is the expected dividend ten years from today if dividends are expected to grow at 4.2% per year over this period? To see what the dividend in ten years is solve, 𝑫 ?? = $?(?. ???) ?? = $?. ???
5) Jones corporation just paid a dividend of $2. This dividend is expected to grow at 5% indefinitely. What is the current stock price if the required return for the stock is 10%? Since the company's dividend grows at a constant rate we can use the present va lue of a growing perpetuity to solve for the price of the stock. 𝑷 ? = 𝑫 ? 𝒓 − 𝒈 = ?(?. ??) ?. ? − ?. ?? = ?? 6) A stock currently selling for $43 pays a dividend which grows at constant rate of 4% indefinitely. What is the capital gains yield on the stock? The capital gain is defined as 𝑷 ? −𝑷 ? 𝑷 ? . Since we have dividends which are growing at a constant rate we know that 𝑷 ? = 𝑫 ? 𝒓−𝒈 and that 𝑷 ? = 𝑫 ? 𝒓−𝒈 . Thus, 𝑷 ? − 𝑷 ? 𝑷 ? = 𝑫 ? − 𝑫 ? 𝑫 ? = 𝒈 = ?% 7) Zorba Foods just paid a dividend of $2.5. Dividends are expected to grow at 4% indefinitely. Investors require an expected return of 10% for the first two years and a return of 7% thereafter. What is the current stock price? Here we cannot simply use the present value of a growing perpetuity formula because the discount rate is not constant. The way to solve the problem is in two steps. First Step compute the price at t=2 𝑷 ? = 𝑫 ? 𝒓−𝒈 = ?.?∗?.?? ? ?.??−?.?? = ??. ? Second Step compute the price at t=0 𝑷 ? = 𝑫 ? ?.? + 𝑫 ? ?.? ? + 𝑷 ? ?.? ? = ?.?∗?.?? ?.? + ?.?∗?.???? ?.?? + ??.? ?.?? = ?? 8) AL & Zon Corporation is not expected to pay any dividends over the next four years. After that the company is expected to start paying a dividend of $1.5 which is expected to grow at a 3.8% rate indefinitely. What is the current stock price if the discount rate is 12%? Here, again, we have to solve the problem in two steps. First Step: Since the first non zero dividend is 𝑫 ? = ?. ? we can compute the price at t=4 as 𝑷 ? = 𝑫 ? 𝒓−𝒈 = ?.? ?.??−?.??? = ??. ?? Second Step compute the price at t=0 as 𝑷 ? = 𝑷 ? ?.?? ? = ??.?? ?.?? = ??. ?
9) LaLa clothing corporation is growing rapidly. Dividends are expected to grow at a rate of 25% over the next three years and then go down to a constant 4.5% rate thereafter. If the company just paid a dividend of $0.95 and shareholders rate of return is 10% what is the current stock price? Once again you cannot simply use the present value of a growing perpetuity formula to compute 𝑷 ? . Similar to before, you need to solve the problem in two steps. First Step compute the price at t=3 𝑷 ? = 𝑫 ? 𝒓−𝒈 = ?.??∗?.?? ? ∗?.??? ?.??−?.??? = ??. ?? Second Step compute the price at t=0 𝑷 ? = 𝑫 ? ?.? + 𝑫 ? ?.? ? + 𝑫 ? ?.? ? + 𝑷 ? ?.? ? = ?.??∗?.?? ?.? + ?.??∗?.?? ? ?.?? + ?.??∗?.?? ? ?.??? + ??.?? ?.??? = ??. ??
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