Question

This morning, Fish Crown Inc. decided to take some leverage for the very first time in the company’s history. Specifically, the company just issued 3-year zero-coupon bonds with a face value of $1,000. All bonds were priced at $800.Following the issue of the bonds, the company WACC is calculated at 10%. The company’s tax rate is 35% and the required return on equity is15%. What fraction of the Fish Crown Inc’sassetsisinnet debt, and what fraction is inequity?

 

Answer 1

Before tax cost of debt = YTM of bonds

Issue price of bonds = face value / (1 + YTM)^{years to maturity}

$800 = $1,000 / (1 + YTM)³

YTM = (1000 / 800)^1/3 - 1

YTM = 7.72%

After tax cost of debt = Before tax cost of debt * (1 - tax rate)

After tax cost of debt = 7.72% * (1 - 35%) = 5.02%

Let us say the fraction of debt is X. Then, the fraction of equity = 1 - X

WACC = (weight of debt * after tax cost of debt) + (weight of common stock * cost of common stock)

10% = (X * 5.02%) + ((1 - X) * 15%)

0.10 = 0.0502X + 0.15 - 0.15X

0.0998X = 0.05

X = 0.50

Fraction of debt = 0.50

Fraction of equity = 1 - 0.50 = 0.50