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,r_M -r_RF,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: r_s = 12%; D/E = 0.25; r_RF = 6%; RP_M = 5%; T = 40%. Step 1: $ \quad $ Find the firm's curent levered beta using the CAPM: $$\begin{aligned} r _ { s } & = r _ { R F } + R P _ { h } ( b ) \ 12 \% & = 6 \% / 5 \% ( b ) \ b & = 1.2 \end{aligned}$$ Step 2: $ \quad $Find the firm's unlevered beta using the Hanede equation: $$\begin{aligned} \mathrm { b } & = \mathrm { b } _ { \mathrm { U } } [ 1 + ( 1 - T ) ( \mathrm { D } E ) ] \ 1.2 & = \mathrm { b } _ { \mathrm { U } } [ 1 + ( 0 .6 ) ( 0.25 ) ] \ 1.2 & = 1.15 \mathrm {~b} _ { \mathrm { U } } \ 1.0435 & = \mathrm { b } _ { \mathrm { U } } . \end{aligned}$$ Step 3: $ \quad $ Find the new levered beta given the new cagital stucture usin the Hanadar equation: $$\begin{aligned} \mathrm { b } & = \mathrm { b } _ { \mathrm { U } } [ 1 + ( 1 - T ) ( \mathrm { D } / \mathrm { E } ) ] \ & = 1.0435 [ 1 + ( 0 .6 ) ( 1 ) ] \ & = 1.6696 . \end{aligned}$$ Step 4: $ \quad $Find the firm's new cast of equuity yiven its new beta and the CApM: $$\begin{aligned} r _ { s } & = r _ { \mathrm { RF } } + \mathrm { RP } _ { \mathrm { M } } ( \mathrm { b } ) \ & = 6 \% + 5 \% / (1.6696 ) \ & = 14.35 \% \end{aligned}$$

Cartwright Communications Is Considering Making a Change to Its Capital