The common stock and debt of Northern Sludge are valued at $120 million and $80 million,...

The common stock and debt of Northern Sludge are valued at $120 million and $80 million, respectively. Investors currently require a 14% return on the common stock and an 8% return on the debt. Assume that the change in capital structure does not affect the risk of the debt and that there are no taxes.

If Northern Sludge issues an additional $15 million of common stock and uses this money to retire debt, what is the expected return on the stock? (Round your answer to 4 decimal places.)

Expected return on the stock	%

Solutions

Expert Solution

Before Issuance of new common stock:

Value of Firm = Value of Equity + Value of Debt
Value of Firm = $120 million + $80 million
Value of Firm = $200 million

Weight of Debt = Value of Debt / Value of Firm
Weight of Debt = $80 million / $200 million
Weight of Debt = 0.40

Weight of Equity = Value of Equity / Value of Firm
Weight of Equity = $120 million / $200 million
Weight of Equity = 0.60

Return on Assets = Weight of Debt * Cost of Debt + Weight of Equity * Cost of Equity
Return on Assets = 0.40 * 8.00% + 0.60 * 14.00%
Return on Assets = 11.60%

After Issuance of new common stock:

Value of Equity = $120 million + $15 million
Value of Equity = $135 million

Value of Debt = $80 million - $15 million
Value of Debt = $65 million

Debt-Equity Ratio = Value of Debt / Value of Equity
Debt-Equity Ratio = $65 million / $135 million
Debt-Equity Ratio = 0.4815

Return on Equity = Return on Assets + [(Return on Assets - Return on Debt) * Debt-Equity Ratio]
Return on Equity = 0.1160 + [(0.1160 - 0.0800) * 0.4815]
Return on Equity = 0.1160 + 0.0173
Return on Equity = 0.1333 or 13.33%

jeff jeffy answered 1 year ago

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