Question

The common stock and debt of Northern Sludge are valued at $40 million and $15 million, respectively. Investors currently require a 13% return on the common stock and an 5% return on the debt. If Northern Sludge issues an additional $5 million of common stock and uses this money to retire debt, what is the new expected return on the stock? Assume that the change in capital structure does not affect the risk of the debt and that there are no taxes. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Expected stock return

Answer 1

Before change in capital structure:

Value of Debt = $15 million
Value of Equity = $40 million

Value of Firm = Value of Debt + Value of Equity
Value of Firm = $15 million + $40 million
Value of Firm = $55 million

Weight of Debt = Value of Debt / Value of Firm
Weight of Debt = $15 million / $55 million
Weight of Debt = 3 / 11

Weight of Equity = Value of Equity / Value of Firm
Weight of Equity = $40 million / $55 million
Weight of Equity = 8 / 11

Unlevered Cost of Capital = Weight of Debt * Cost of Debt + Weight of Equity * Cost of Equity
Unlevered Cost of Capital = (3/11) * 5.00% + (8/11) * 13%
Unlevered Cost of Capital = 10.82%

After change in capital structure:

Value of Debt = $15 million - $5 million
Value of Debt = $10 million

Value of Equity = $40 million + $5 million
Value of Equity = $45 million

Debt-Equity Ratio = Value of Debt / Value of Equity
Debt-Equity Ratio = $10 million / $45 million
Debt-Equity Ratio = 2 / 9

Cost of Equity = Unlevered Cost of Capital + (Unlevered Cost of Capital - Cost of Debt) * Debt-Equity Ratio
Cost of Equity = 0.1082 + (0.108182 - 0.05) * (2/9)
Cost of Equity = 0.1082 + 0.0129
Cost of Equity = 0.1211 or 12.11%

So, new expected stock return is 12.11%