Question

Hook Industries's capital structure consists solely of debt and common equity. It can issue debt at rd = 10%, and its common stock currently pays a $3.25 dividend per share (D0 = $3.25). The stock's price is currently $32.75, its dividend is expected to grow at a constant rate of 5% per year, its tax rate is 25%, and its WACC is 12.25%. What percentage of the company's capital structure consists of debt? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Let’s first calculate the cost of equity by using dividend discount model with constant dividend growth rate

Current Stock Price P0 = D0 * (1+g) / (r – g)

Where:

P0 = the current stock price = $32.75

Last dividend paid D0 = $3.25 per share

g = growth rate of dividends = 5% per year

re = required rate of return or cost of equity =?

Therefore

$32.75 = $3.25 * (1+5%) / (re - 5%)

Or $32.75 *(re - 5%) = $3.4125

Or $32.75 *re - $32.75 *5% = $3.4125

Or $32.75 *re - $1.6375 = $3.4125

Or $32.75 * re = $3.4125 + $1.6375 = $5.05

Or re =$5.05 /$32.75 = 0.1542 or 15.42%

Therefore the company’s cost of common equity is 15.42%

Now to calculate the weighted cost of capital (WACC), assume that weight of debt is X and weight of equity is (1-X)

WACC = wd *rd (1 - t) + we*re                 

Where,

WACC = 12.25%

we is the weight of equity = 1-X

wd is value of debt = X

rd is the before-tax cost of debt = 10%

t is the company’s tax rate = 25%

re is the cost of equity = 15.42%

Therefore,

12.25% = X * 10% * (1-25%) + (1-X) * 15.42%

Or 12.25% = 7.5% X + 15.42% - 15.42% X

Or 15.42% X -7.5% X = 15.42% - 12.25%

Or X = 3.17%/ 7.92% = 0.4002 or 40.02%

The percentage of the company's capital structure consists of debt is 40.02%