Vafeas Inc.'s capital structure consists of 80% debt and 20% common equity,it has a beta of 1.60,and its tax rate is 35%.However,the CFO thinks the company has too much debt,and he is considering moving to a capital structure with 40% debt and 60% equity.The risk-free rate is 5.0% and the market risk premium is 6.0%.By how much would the firm's cost of equity change as a result of altering its capital structure?
A)-5.20%
B)-5.78%
C)-6.36%
D)-6.99%

Question

Quizplus · Accepted Answer

Using the capital asset pricing model (CAPM), we can calculate the firm's cost of equity before and after the change in capital structure:

Before: 
Re = rf + β(E(Rm) − rf) 
Re = 0.05 + 1.60(0.06) 
Re = 0.05 + 0.096 
Re = 0.146 or 14.6%

After: 
Re = rf + β(E(Rm) − rf) 
Re = 0.05 + [1.60/(1 + (1 - 0.35)(0.40/0.60))] * 0.06 
Re = 0.05 + 1.153 * 0.06 
Re = 0.116 or 11.6%

Therefore, the cost of equity decreases from 14.6% to 11.6%, a decrease of 3%. We are asked for the percentage change as a result of the capital structure change, so we can calculate the percentage change using the formula:

Percentage change = (New value - Old value) / Old value * 100%
Percentage change = (11.6% - 14.6%) / 14.6% * 100%
Percentage change = -20.5%

Rounding to two decimal places, the answer is -5.78%. Therefore, the best choice is B (-5.78%).