Question

Company X has 8 million shares of common stock outstanding. The current share price is $57, and the book value per share is $5. The company also has two bond issues outstanding. The first bond issue has a face value of $70.8 million and a coupon rate of 7 percent and sells for 107 percent of par. The second issue has a face value of $60 million and a coupon rate of 7 percent and sells for 109 percent of par. The first issue matures in 9 years, the second in 26 years. Suppose the company’s stock has a beta of 1.3. The risk-free rate is 3 percent, and the market risk premium is 7 percent. Assume that the overall cost of debt is the weighted average implied by the two outstanding debt issues. Both bonds make semiannual payments. The tax rate is 40 percent. What is the company’s WACC? (9 points)

Answer 1

Company's market value of equity = 8mil * $57 = $456 mil

Cost of Equity (by CAPM Method) = Risk Free Rate + (Beta * market Risk Premium)

Cost of Equity = 3% + (1.3 * 7%) = 12.1%

Now, we need to calculate YTM for both the bond issuances. We can do this using the following approximation formula:

Debt 1: C = 7%/2 * 70.8 mil (semi-annual) = $2.478 mil; F = $70.8 mil, P = $70.8 * 1.07 = $75.756 mil, n = 9 * 2 = 18 semi-annual periods

YTM₁ (approx.) = 2.203/73.278 = 3%

Market value of bond = $75.756 mil

Debt 2: C = 7%/2 * 60 mil (semi-annual) = $2.1 mil; F = $60 mil, P = $60 * 1.09 = $65.4 mil, n = 26 * 2 = 52 semi-annual periods

YTM₂ (approx.) = 2.203/73.278 = 3.18%

Market value of bond = $65.4 mil

Overall Pretax Cost of Debt = 75.756/(75.756 + 65.4) * 0.03 + 65.4/(75.756 + 65.4) * 0.0318 = 3.08%

Overall Post tax cost of debt = 3.08% * (1 - 40%) = 1.85%

WACC = 456/(456 + 75.756 + 65.4) * 12.1% + (75.756 + 65.4)/(456 + 75.756 + 65.4) * 1.85%

WACC = 9.68%