The Treasury bill rate is 3% and the market risk premium is 7%.

The Treasury bill rate is 3% and the market risk premium is 7%. Project Beta Internal Rate of Return, % P 0.75 10 Q 0 8 R 1.00 12 S 0.15 9 T 0.90 9 a. What are the project costs of capital for new ventures with betas of .50 and 1.11? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Beta Cost of Capital 0.50 % 1.11 % b. Which of the following capital investments have positive NPVs? (You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer.) Tick P Tick Q T Tick R Tick S You are considering the purchase of real estate that will provide perpetual income that should average $64,000 per year. How much will you pay for the property if you believe its market risk is the same as the market portfolio’s? The T-bill rate is 6%, and the expected market return is 10.0%. Property value $ Explanation: If the systematic risk were comparable to that of the market, the discount rate would be 10.0%. The property would be worth $64,000/0.100 = $640,000. Stock A has a beta of .5, and investors expect it to return 5%. Stock B has a beta of 1.5, and investors expect it to return 12%. Use the CAPM to find the expected rate of return and the market risk premium on the market. (Do not round intermediate calculations. Round your answers to 1 decimal place.) Expected rate of return % Market risk premium % Explanation: r = rf + β(rm − rf) 5 = rf + 0.5(rm − rf) (stock A) 12 = rf + 1.5(rm − rf) (stock B) Solve these simultaneous equations to find that rf = 1.5% and rm = 8.5%. Market risk premium = rm − rf = 8.5% − 1.5% = 7.0% We Do Bankruptcies is a law firm that specializes in providing advice to firms in financial distress. It prospers in recessions when other firms are struggling. Consequently, its beta is negative, −.1. a. If the interest rate on Treasury bills is 4% and the expected return on the market portfolio is 14%, what is the expected return on the shares of the law firm according to the CAPM? Expected return % b. Suppose you invested 70% of your wealth in the market portfolio and the remainder of your wealth in the shares in the law firm. What would be the beta of your portfolio? (Round your answer to 2 decimal places.) Portfolio beta Explanation: a. r = rf + β(rm − rf) = 4% + [(−0.1) × (14% − 4%)] = 3% b. Portfolio beta = (0.70 × βmarket) + (0.30 × βlaw firm) = (0.70 × 1.0) + [0.30 × (−0.1)] = 0.67 Micro Spinoffs, Inc., issued 10-year debt a year ago at par value with a coupon rate of 9%, paid annually. Today, the debt is selling at $1,360. If the firm’s tax bracket is 35%, what is its after-tax cost of debt? (Do not round intermediate calculations. Round your answer to 2 decimal places.) After-tax cost of debt % Explanation: Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations. The yield to maturity for the bonds (since maturity is now 9 years) is the interest rate (r) that is the solution to the following equation: [$90 × annuity factor (r, 9 years)] + [$1,000/(1 + r)9] = $1,360 Using a financial calculator, enter n = 9, FV = 1,000, PV = (−)1,360, PMT = 90; then compute i = 4.13%. Therefore, the after-tax cost of debt is 4.13% × (1 − 0.35) = 2.68%. Micro Spinoffs has preferred stock outstanding. The stock pays a dividend of $6 per share, and the stock sells for $50. What is the return on preferred stock? Return on preferred stock % Explanation: r = DIV = $6 = 0.12 = 12% P0 $50 Micro Spinoffs, Inc., issued 10-year debt a year ago at par value with a coupon rate of 9%, paid annually. Today, the debt is selling at $1,360. The firm’s tax bracket is 35%. Micro Spinoffs also has preferred stock outstanding. The stock pays a dividend of $4 per share, and the stock sells for $40. Micro Spinoffs’s cost of equity is 12%. What is its WACC if equity is 60%, preferred stock is 10%, and debt is 30% of total capital? (Do not round intermediate calculations. Round your answer to 2 decimal places.) WACC % Explanation: Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations. The yield to maturity for the bonds (since maturity is now 9 years) is the interest rate (r) that is the solution to the following equation: [$90 × annuity factor (r, 1,360 years)] + [$1,000/(1 + r)9] = $1,360 Using a financial calculator, enter n = 9, FV = 1,000, PV = (−)1,360, PMT = 90; then compute i = 4.13%. r = DIV = $4 = 0.10 = 10% P0 $40 = [0.3 × 4.13% × (1 − 0.35)] + [0.1 × 10%] + [0.6 × 12%] = 9.01% Reactive Industries has the following capital structure. Its corporate tax rate is 40%. Security Market Value Required Rate of Return Debt $10 million 2% Preferred stock 20 million 4 Common stock 50 million 8 What is its WACC? (Do not round intermediate calculations. Round your answer to 2 decimal places.) WACC % Explanation: The total value of the firm is $80 million. The weights for each security class are as follows: Debt: D/V = 10/80 = 0.125 Preferred: P/V = 20/80 = 0.250 Common: E/V = 50/80 = 0.625 = [0.125 × 2% × (1 − 0.40)] + [0.250 × 4%] + [0.625 × 8%] = 6.15% Bunkhouse Electronics is a recently incorporated firm that makes electronic entertainment systems. Its earnings and dividends have been growing at a rate of 40%, and the current dividend yield is 2%. Its beta is .9, the market risk premium is 11%, and the risk-free rate is 4%. a-1. Calculate the firm’s cost of equity by using the Dividend Discount Model. Cost of equity % a-2. Calculate the firm’s cost of equity by using the CAPM. (Do not round intermediate calculations. Round your answer to 1 decimal place.) Cost of equity % b. Which estimate seems more reasonable to you? CAPM rev: 05_12_2012 Explanation: a-1. Using the recent growth rate of 40% and the dividend yield of 2%, one estimate would be: DIV1/P0 + g = 0.02 + 0.40 = 0.42 = 42% a-2. Another estimate, based on the CAPM, would be: r = rf + β(rm − rf) = 4% + 0.9 × (11%) = 13.9% b. The estimate of 42% seems far less reasonable. It is based on a historic growth rate that is impossible to sustain. The DIV1/P0 + g rule requires that the growth rate of dividends per share must be viewed as highly stable over the foreseeable future. In other words, it requires the use of the sustainable growth rate. Examine the following book-value balance sheet for University Products, Inc. The preferred stock currently sells for $12 per share and the common stock for $16 per share. There are 4 million common shares outstanding. BOOK VALUE BALANCE SHEET (all values in millions) Assets Liabilities and Net Worth Cash and short-term securities $ 2.0 Bonds, coupon = 5%, paid annually (maturity = 10 years, current yield to maturity = 6%) $ 12.0 Accounts receivable 4.0 Preferred stock (par value $15 per share) 3.0 Inventories 8.0 Common stock (par value $0.1) 0.4 Plant and equipment 20.0 Additional paid-in stockholders’ equity 7.6 Retained earnings 11.0 Total $ 34.0 Total $ 34.0 What is the capital structure of the firm on the basis of market values? (Do not round intermediate calculations. Enter your answers in millions rounded to 2 decimal places and percentage values to 2 decimal places.) Security Market Value Percent Bonds $ million % Preferred stock million % Common stock million % Total $ million % Explanation: Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations. The bonds are selling below par value because the yield to maturity is greater than the coupon rate. The price per $1,000 par value is: PV = [$50 × annuity factor (6%, 10 years)] + ($1,000/1.0610) The total market value of the bonds is: $12 million par value × $926.40 market value = $11.12 million $1,000 par value There are $3 million/$15 = 200,000 shares of preferred stock. The market price of the preferred stock is $12 per share, so the total market value of the preferred stock is $2.4 million. There are $0.4 million/$0.1 = 4.0 million shares of common stock. The market price of the common stock is $16 per share, so the total market value of the common stock is $64 million. Examine the following book-value balance sheet for University Products, Inc. The preferred stock currently sells for $14 per share and the common stock for $20 per share. There are 3 million common shares outstanding. BOOK VALUE BALANCE SHEET (all values in millions) Assets Liabilities and Net Worth Cash and short-term securities $ 1.0 Bonds, coupon = 8%, paid annually (maturity = 10 years, current yield to maturity = 9%) $ 5.0 Accounts receivable 4.0 Preferred stock (par value $20 per share) 3.0 Inventories 8.0 Common stock (par value $0.2) 0.2 Plant and equipment 20.0 Additional paid-in stockholders’ equity 16.8 Retained earnings 8.0 Total $ 33.0 Total $ 33.0 If the preferred stock pays a dividend of $4 per share, the beta of the common stock is 0.7, the market risk premium is 10%, the risk-free rate is 6%, and the firm’s tax rate is 20%, what is University’s weighted-average cost of capital? (Do not round intermediate calculations. Round your answer to 2 decimal places.) WACC % Explanation: Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations. The bonds are selling below par value because the yield to maturity is greater than the coupon rate. The price per $1,000 par value is: PV = [$80 × annuity factor (9%, 10 years)] + ($1,000/1.0910) The total market value of the bonds is: $5 million par value × $935.82 market value = $4.68 million $1,000 par value There are $3 million/$20 = 150,000 shares of preferred stock. The market price of the preferred stock is $14 per share, so the total market value of the preferred stock is $2.1 million. There are $.2 million/$.2 = 1.0 million shares of common stock. The market price of the common stock is $20 per share, so the total market value of the common stock is $20 million. Therefore, the capital structure is: Security Market Value Percent Bonds $ 4.68 million 17.47 % Preferred Stock 2.10 million 7.84 Common Stock 20.00 million 74.69 Total $ 26.78 million 100.00 % The yield to maturity for the firm's debt is rdebt = 9%. The rate for the preferred stock is rpreferred = $4/$14 = 0.2857 = 28.57%. The rate for the common stock is: requity = rf + β(rm − rf) = 6% + (0.7 × 10%) = 13.00% Using the capital structure derived in the previous problem, we can calculate WACC as: = [0.1747 × 9% × (1 − 0.20)] + [0.0784 × 28.57%] + [0.7469 × 13.00%] = 13.21%