Question

The common stock and debt of Northern Sludge are valued at $66 million and $34 million, respectively. Investors currently require a return of 15.6% on the common stock and a return of 8.1% on the debt. If Northern Sludge issues an additional $17 million of common stock and uses this money to retire debt, what happens to the expected return on the stock? Assume that the change in capital structure does not affect the interest rate on Northern’s debt and that there are no taxes.

(Do not round intermediate calculations. Enter your answer as a whole percent.)

What is the new return on equity %?

Answer 1

Solution:
	New return on equity = 14%
Working Notes:
	Old Equity value (E) = $66 million
	Old Debt value (D) = $34 million
	Total value of Capital (V) = E+ D = $66 + $34 = $100 million
	Return on Equity (re) =15.6%
	Return on debt (rd) = 8.10%
	Return on assets (ra) = Return on Equity x (E/V) + Return on debt x (D/V)
	ra = 15.6% x (66/100) + 8.10% x (34/100)
	ra = 13.05%
Now,
	Now , when new equity is issued and used to reduce debt , capital structure will change , but overall capital will remain same so return on assets will remain same ra = 13.05% and also change in capital structure does not affect the interest rate on Northern’s debt and that there are no taxes so rd= 8.10% will remain same but return on Equity will change New re
	New Equity value (E) = old Equity + $17 million = $66 + $17 =$83 million
	New Debt value (D) = Old debt - $17 = $34 - $17 = $17 million
	Total value of Capital (V) = E+ D = $83 + $17 = $100 million
	Return on assets ra = 13.05%
	New Return on Equity (re) =??
	Return on debt (rd) = 8.10%
	Return on assets (ra) =New Return on Equity (New re )x (E/V) + Return on debt x (D/V)
	13.05% = New re x (83/100) + 8.10% x (17/100)
	New Return on Equity (New re ) = (13.05% - 8.10% x (17/100) ) x (100/83)
	New Return on Equity (New re ) = (13.05% - 1.377% ) x (100/83)
	New Return on Equity (New re ) = 11.673% x (100/83)
	New Return on Equity (New re ) = 14.063855 %
	New Return on Equity (New re ) = 14 %
Please feel free to ask if anything about above solution in comment section of the question.