Question

Examine the following book-value balance sheet for University Products Inc. The preferred stock currently sells for $30 per share and pays a dividend of $3 a share. The common stock sells for $16 per share and has a beta of 0.8. There are 4 million common shares outstanding. The market risk premium is 10%, the risk-free rate is 6%, and the firm’s tax rate is 40%.

BOOK-VALUE BALANCE SHEET (Figures 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 $0.10) 0.4 Plant and equipment 20.0 Additional paid-in stockholders’ equity 7.6 Retained earnings 11.0 Total $ 34.0 Total $ 34.0

a. What is the market debt-to-value ratio of the firm? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

b. What is University’s WACC? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Answer 1

All financials below are in $ mn. Nos. of shares outstanding is in mn and share price is in $ / share.

Part (a)

Face value, FV = 12

Bonds, coupon = 5%, paid annually; Hence PMT = 5% x FV = 5% x 12 = 0.60

Period = maturity = 10 years,

Rate = current yield to maturity = 6%

Hence, market value of bonds, D = - PV (Rate, period, PMT, FV) = - PV (6%, 10, 0.60, 12) = 11.12

Market value of equity, E = Current share price x Nos. of shares outstanding = 16 x 4 = 64

Market value of preferred stock, S = Current share price x Nos. of shares outstanding = 30 x Book value / Par value = 30 x 3 / 15 = 6

Hence, total capital = D + E + S = 11.12 + 64 + 6 = 81.12

the market debt-to-value ratio of the firm, Wd = D / Total capital = 11.12 / 81.12 = 13.70%

Part (b)

Proportion of equity in capital = We = E / Total capital = 64 / 81.12 = 78.90%

Proportion of preferred stock in capital = S / Total capital = 6 / 81.12 = 7.40%

Cost of debt, Kd = Current yield = 6%

Cost of equity, Ke = Risk free rate + Beta x market risk premium = 6% + 0.8 x 10% = 14%

Cost of preferred stock, Ks = Dividend / Current price = 3 / 30 = 10%

Tax rate, T = 40%

Hence, WACC = Wd x Kd x (1 - T) + We x Ke + Ws x Ks = 13.70% x 6% x (1 - 40%) + 78.90% x 14% + 7.40% x 10% = 12.28%

Hence,