The common stock and debt of Northern Sludge are valued at $58
million and $24 million, respectively. Investors currently require
a 14% return on the common stock and an 6% 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.)
What is the expected return on the stock?
r(Assets) = [r(Debt) * w(Debt)] + [r(Equity) * w(Equity)]
= [0.06 * {24/(58+24)}] + [0.14 * {58/(58+24)}]
= 0.0176 + 0.0990 = 0.1166, or 11.66%
r(Equity) = r(Assets) + [(D/E) * {r(Assets) - r(Debt)}]
= 0.1166 + [{(24-5)/(58+5)} * (0.1166 - 0.06)]
= 0.1166 + [0.3016 * 0.0566]
= 0.1166 + 0.0171 = 0.1337, or 13.37%
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