Cartwright Communications is considering making a change to its capital structure to reduce its cost of capital and increase firm value. Right now, Cartwright has a capital structure that consists of 20% debt and 80% equity, based on market values. (Its D/S ratio is 0.25.) The risk-free rate is 6% and the market risk premium, rM σ rRF, is 5%. Currently the company's cost of equity, which is based on the CAPM, is 12% and its tax rate is 40%. What would be Cartwright's estimated cost of equity if it were to change its capital structure to 50% debt and 50% equity?
A) 13.00%
B) 13.64%
C) 14.35%
D) 14.72%
E) 15.60%

Question

Quizplus · Accepted Answer

Facts given: rs = 12%; D/E = 0.25; rRF = 6%; RPM = 5%; T = 40%.
 Step 1: Fird the firm's curent levered beta using the CAPM:
$\begin{aligned}
r _ { 5 } & = r _ { R F } + R P _ { M } ( b ) \
12 \% & = 6 \% + 5 \% ( b ) \
b & = 1.2
\end{aligned}$
Step 2: Find the firm's urilevered beta using the Harnada equation:
$\begin{aligned}
\mathrm { b } & = b [ 1 + ( 1 - T ) ( \mathrm { D } / \mathrm { E } ) ] \
1.2 & = b \mathrm { U } [ 1 + ( 0.6 ) ( 0.25 ) ] \
1.2 & = 1.15 \mathrm { bu } \
1.0435 & = b \mathrm { U } .
\end{aligned}$
Step 3: Find the new levered beta given the new capital structure usirg the Harnada equation:
$\begin{aligned}
\mathbf { b } & = b _ { U } [ 1 + ( 1 - T ) ( \mathrm { D } E ) ] \
& = 1.0435 [ 1 + ( 0.6 ) ( 1 ) ] \
& = 1.6696
\end{aligned}$
Btep 4: Find the firm'sriew cost of equity given its rew beta and the CAPM:
$\begin{aligned}
r _ { \mathbf { s } } & = r _ { \mathrm { R } } + \mathrm { RP } \mathrm { M } ( \mathrm { b } ) \
& = 6 \% + 5 \% ( 1.6696 ) \
& = 14.75 \%
\end{aligned}$

Cartwright Communications Is Considering Making a Change to Its Capital