Homework #5A (Value and Expected rate of return on preferred stock) UPS preferred stock pays $12 in annual dividends. If your required rate of return is 6.69 percent, how much would you be willing to pay for one share of this preferred stock? =$12 / 6.69% = 179.37 Giant Co. has just issued preferred stock with a par value of $100 and an annual dividend rate of 9.57 percent. If your required rate of return is 13.33 percent, how much will you be willing to pay for one share of this preferred stock? =$100 * 9.57% / 13.33% = 71.79 Golden Rod Corp.'s preferred stock is currently selling for $70.12. The company pays $5.85 annual dividends on this preferred stock. Which rate of return does the investor expect to receive on this stock if the stock is purchased today? =$5.85 / $70.12 = (8.34)% Potter's Violin Co. has just issued nonconvertible preferred stock with a par value of $100 and an annual dividend rate of 15.35 percent. The preferred stock is currently selling for $147.21 per share. Which rate of return does the investor expect to receive on this stock if the stock is purchased today? =$100 * 15.35% / $147.21 = (10.43) % Homework #5B (Value of Common Stock, Expected Rate of return on Common Stock) The last dividend of Delta, Inc. was $14.14, the growth rate of dividends is expected to be 3.19 percent, and the required rate of return on this stock is 12.62 percent. What is the stock price according to the constant growth dividend model? =14.14*(1+3.19%) / (12.62%-3.19%) = 154.73 The next year the common stock of Gold Corp. will pay a dividend of $8.77 per share. If the company is growing at a rate of 3.22 percent per year, and your required rate of return is 11.49 percent, what is Gold's company stock worth to you? =8.77 / (11.49%-3.22%) = (106.05) The Black Forest Cake Company just paid an annual dividend of $4.28. If you expect a constant growth rate of 3.32 percent, and have a required rate of return of 9.89 percent, what is the current stock price according to the constant growth dividend model? =4.28*(1+3.32%) / (9.89%-3.32%) = (67.31) You are considering the purchase of a share of Alfa Growth, Inc. common stock. You expect to sell it at the end of one year for $66.42 per share. You will also receive a dividend of $2.80 per share at the end of the next year. If your required return on this stock is 12.86 percent, what is the most you would be willing to pay for Alfa Growth, Inc. common stock now? = (66.42+2.8) / (1+12.86%) = (61.33) Green Company's common stock is currently selling for $53.14 per share. Last year, the company paid dividends of $4.14 per share. The projected growth at a rate of dividends for this stock is 3.92 percent. Which rate of return does the investor expect to receive on this stock if it is purchased today? =4.14*(1+3.92%) / 53.14+3.92% = (12.02) % Digging Deep Company's common stock is currently selling for $185.95 per share. Next year, the company dividend is expected to be $14.80 per share. The projected growth at a rate of dividends for this stock is 4.53 percent per year. What rate of return does the investor expect to receive on this stock if he or she purchases the stock today? = (14.8/185.95) + 4.53% = (12.49) % Homework #5C (CAPM, Beta portfolio, Portfolio expected return) King Farm Manufacturing Company's common stock has a beta of 2.30. If the risk-free rate is 2.22 percent, and the market return is 7.10 percent, calculate the required return on King Farm Manufacturing's common stock. = 2.22%+2.3*(7.1%-2.22%) = 13.44% Try to determine the required rate of return on Tilden Woods Corporation's common stock. The firm's beta is 1.21. The rate on a 10-year Treasury bond is 2.07 percent, and the market risk premium is 6.60 percent. = 2.07%+1.21*(6.6%) = 10.06% You hold a portfolio with the following securities: Security Percent of portfolio Beta Stock A 60% 1.97 Stock B 13% 2.35 Stock C Please calculate it 1.75 Step 1: Find Stock C = 100% - 60% - 13% = 27% Step 2: = 60%*1.97 + 13%*2.35 + 27%*1.75 = (1.96) John invested the following amounts in three stocks: Security Investment Beta Stock A $220,555 0.91 Stock B $633,983 1.89 Stock C $116,911 1.23 Step 1: Calculate total investment (total value of the portfolio). $220,555 + $633,983 + $116,911 = $971,449 Step 2: Calculate weights of each stock in the portfolio. Stock A: $220,555 / $971,449 = 22.70% Stock B: $633,983/ $971,449 = 65.26% Stock C: $116,911 / $971,449 = 12.03% Step 3: Calculate beta portfolio as the weighted average of betas of stocks included in the portfolio: Beta portfolio = 22.70% *0.91 + 65.26% *1.89 + 12.03% * 1.23 = (1.59) Jack holds a portfolio with the following securities: Security Investment Return Stock A 836,130 10.6% Stock B 944,072 7.1% Stock C 159,552 9.2% Step 1: =836,130+944,072+159,552 =1,939,754 Step 2: =836130/1,939,754 =43.10% =944,072 /1,939,754 =48.67% =159,552 /1,939,754 =8.23% Step 3: =(10.6%*43.10%)+(7.1%*48.67%)+9.2%*8.23%) = 8.78% You hold a portfolio with the following securities: Security Percent of portfolio Return Stock A 31% -7.8% Stock B 11% 2.7% Stock C Please calculate it 8.9% Step 1: Find Stock C = 100% - 31% - 11% = 58% Step 2: = (31%*-7.8%) + (11%*2.7%) + (58%*8.9%) = 3.04% Homework #5D (Expected return and Standard deviation on stock using probabilities) Calculate the expected return on stock of Gamma Inc.: State of the economy Probability of the states Percentage returns Economic recession 24% -3.2% Steady economic growth 31% 4.1% Boom Please calculate it 14.5% Step 1: Find Stock C = 100% - 24% - 31% = 45% Step 2: = (24%*-3.2 %) + (31%*4.1 %) + (45%*14.5%) = 7.03% Calculate the expected standard deviation on stock: State of the economy Probability of the states Percentage returns Economic recession 16% -9% Steady economic growth 20% 6% Boom Please calculate it 14% Step 1: Find Stock C = 100% - 24% - 31% = 45% Step 2: = (24%*-3.2 %) + (31%*4.1 %) + (45%*14.5%) =8.34%