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Examine the following book-value balance sheet for University Products Inc. The preferred stock currently sells for $15 per share and pays a dividend of $3 a share. The common stock sells for $16 per share and has a beta of 0.9. There are 3 million common shares outstanding. The market risk premium is 10%, the risk-free rate is 6%, and the firm’s tax rate is 21%.

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Answer:

a. What is the market debt-to-value ratio of the firm?

  • 18.45%

b. What is University’s WACC?

  • 13.87%

Explanation:

total equity = 3,000,000 stocks x $16 = $48,000,000

cost of preferred stock debt = $3 / $15 = 20%

market risk premium = 10%

risk free rate = 6%

beta = 0.9

cost of equity = 6% x (0.9 x 10%) = 15%

some information was missing:

  • total preferred stocks = $2,000,000 $20 (par value) = 100,000 preferred stocks
  • total outstanding bonds $10,000,000 (8% coupon but with a 9% yield to maturity) 10 years to maturity

market value of bonds:

PV of maturity value = $10,000,000 / (1.09)¹⁰ = 4,224,108

PV of coupons = $8,000,000 x {1 - [1 / (1 + 0.09)¹⁰]} / 0.09 = $5,134,126

total = $9,358,234

total capitalization = total common stocks + total preferred stocks + total outstanding bonds = $48,000,000 + (100,000 x $15) + $9,358,234 = $58,858,234

debt to value ratio = total debt / (debt + equity)

total debt = $1,500,000 + $9,358,234 = $10,858,234

total capitalization = $58,858,234

debt to value ratio = $10,858,234 / $58,858,234 = 18.45%

University’s WACC = (E/V x cost of equity) + (preferred stocks/V x cost of preferred stocks) + [bonds/V x YTM x (1 - 21%)] = ($48,000,000/$58,858,234 x 15%) + ($1,500,000/$58,858,234 x 20%) + [$9,358,234/$58,858,234 x 9% x (1 - 0.21)] = 12.23% + 0.51% + 1.13% = 13.87%

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