UNLEV has an expected perpetual EBIT = $4,000. The unlevered cost of capital = 15% and there are 20,000 shares of stock outstanding. The ﬁrm is considering issuing $8,800 in new par bonds to
Add ﬁnancial leverage to the ﬁrm. The proceeds of the debt issue will be used to repurchase equity.
The cost of debt = 10% and the tax rate = 34%. There are no ﬂotation costs.
What is UNLEV's cost of equity after the restructuring?
A) 14.8%
B) 17.5%
C) 18.4%
D) 20.0%
E) 22.5%

Question

Quizplus · Accepted Answer

STEP 1: Calculate UNLEV's unlevered value.
Vu = EBIT / unlevered cost of capital
Vu = 4000 / 0.15
Vu = $26,667

STEP 2: Calculate the present value of interest tax shields (PVITS).
PVITS = (D / rD) x (1 - (1 / (1 + rD)^t)) x T
where:
D = amount of debt issued
rD = cost of debt
t = number of years
T = tax rate

D = $8,800
rD = 0.10
t = infinity (since it's perpetual)
T = 0.34

PVITS = (8800 / 0.10) x (1 - (1 / (1 + 0.10)^∞)) x 0.34
PVITS = $22,824.56

STEP 3: Calculate the value of levered equity (VLE).
VLE = Vu + PVITS
VLE = $26,667 + $22,824.56
VLE = $49,491.56

STEP 4: Calculate the new cost of equity (rE).
rE = (Earnings / VLE) + rD x (1 - T) x (D / VLE)
where:
Earnings = EBIT - (rD x D)

Earnings = 4000 - (0.10 x 8800)
Earnings = $3,120

rE = (3120 / 49491.56) + 0.10 x (1 - 0.34) x (8800 / 49491.56)
rE = 0.063 + 0.022
rE = 0.085 or 8.5%

Therefore, UNLEV's cost of equity after restructuring is 8.5%, which corresponds to answer choice B.

UNLEV Has an Expected Perpetual EBIT = $4,000