Serendipity Inc.is re-evaluating its debt level.Its current capital structure consists of 80% debt and 20% common equity,its beta is 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 capital structure shift change the firm's cost of equity?
A) -5.20%
B) -5.78%
C) -6.36%
D) -6.99%
E) -7.69%

Question

Quizplus · Accepted Answer

$\begin{array}{lr}
\mathrm{b}_{\mathrm{L}}= & 1.60 \
\text { Current Debt\%  } & 80 \% \
\text { Target Debt\%  }= & 40 \% \
\text Current \mathrm{D} / \mathrm{E}=\mathrm{D} \% /(1-\mathrm{D} \%) = & 4.00\
\text Target  \mathrm{D} / \mathrm{E}=\mathrm{D} \% /(1-\mathrm{D} \%)  &  0.67 \
\text Tax  rate  = &  35 \% \
\ b_{U}=b_{I} /(1+(D / E)(1-T))  & 0.4444   \
\text new   b_{L}=b_{U} \times(1+(D / E) \times(1-T))= &  0.6370\
\text r_{R F}= &   5.00 \%\
\mathrm{RP}_{\mathrm{M}} &  6.00 \%\
\text r_{s 80 \%}  \mathrm{D}=\mathrm{r}_{\mathrm{RF}}+\mathrm{b}_{80 \% \mathrm{D}}\left(\mathrm{RP}_{\mathrm{M}}\right)= &   14.60 \% \
\text r_{4} 40 \% \mathrm{D}=\mathrm{r}_{\mathrm{RF}}+\mathrm{b}_{40 \% \mathrm{D}}\left(\mathrm{RP}_{\mathrm{M}}\right)= & 8.82 \%\
\text Change in equity cost & -5 .78\%
\end{array}$