Dye Industries currently uses no debt, but its new CFO is considering changing the capital structure to 40.0% debt (wd) by issuing bonds and using the proceeds to repurchase and retire common shares so the percentage of common equity in the capital structure (wc) = 1 ? wd. Given the data shown below, by how much would this recapitalization change the firm's cost of equity, i.e., what is rL ? rU? $$\begin{array} { l r l r }
\text { Risk-free rate, } \mathrm { r } _ { \mathrm { RF } } & 6.00 \% & \text { Tax rate, } \mathrm { T } & 40 \% \
\text { Market risk premium, } \mathrm { RP } _ { \mathrm { M } } & 4.00 \% & \text { Current } \mathrm { w } _ { \mathrm { d } } & 0 \% \
\text { Current beta, } \mathrm { b } _ { \mathrm { U } } & 1.15 & \text { Target } \mathrm { w } _ { \mathrm { d } } & 40 \%
\end{array}$$
A) 1.66%
B) 1.84%
C) 2.02%
D) 2.23%
E) 2.45%

Question

Dye Industries currently uses no debt, but its new CFO is considering changing the capital structure to 40.0% debt (wd) by issuing bonds and using the proceeds to repurchase and retire common shares so the percentage of common equity in the capital structure (wc) = 1 ? wd. Given the data shown below, by how much would this recapitalization change the firm's cost of equity, i.e., what is rL ? rU? $$\begin{array} { l r l r } 
\text { Risk-free rate, } \mathrm { r } _ { \mathrm { RF } } & 6.00 \% & \text { Tax rate, } \mathrm { T } & 40 \% \
\text { Market risk premium, } \mathrm { RP } _ { \mathrm { M } } & 4.00 \% & \text { Current } \mathrm { w } _ { \mathrm { d } } & 0 \% \
\text { Current beta, } \mathrm { b } _ { \mathrm { U } } & 1.15 & \text { Target } \mathrm { w } _ { \mathrm { d } } & 40 \%
\end{array}$$
A) 1.66%
B) 1.84%
C) 2.02%
D) 2.23%
E) 2.45%

Quizplus · Accepted Answer

The change in the firm's cost of equity can be calculated using the formula for levered beta: $ b_L = b_U \times (1 + (1 - T) \times \frac{w_d}{w_c}) $. Substituting the given values, $ b_L = 1.15 \times (1 + (1 - 0.4) \times \frac{0.4}{0.6}) = 1.15 \times 1.4 = 1.61 $. The new cost of equity $ r_L = r_{RF} + b_L \times RP_M = 6\% + 1.61 \times 4\% = 12.44\% $. The original cost of equity $ r_U = r_{RF} + b_U \times RP_M = 6\% + 1.15 \times 4\% = 10.6\% $. The change is $ r_L - r_U = 12.44\% - 10.6\% = 1.84\% $.

Dye Industries Currently Uses No Debt, but Its New CFO