Eccles Inc., a zero growth firm, has an expected EBIT of $100,000 and a corporate tax rate of 30%. Eccles uses $500,000 of 12.0% debt, and the cost of equity to an unlevered firm in the same risk class is 16.0%.
-Refer to the data for Eccles Inc.Assume that the firm's gain from leverage according to the Miller model is $126,667. If the effective personal tax rate on stock income is TS = 20%, what is the implied personal tax rate on debt income?
A) 16.4%
B) 18.2%
C) 20.2%
D) 22.5%
E) 25.0%

Question

Eccles Inc., a zero growth firm, has an expected EBIT of $100,000 and a corporate tax rate of 30%. Eccles uses $500,000 of 12.0% debt, and the cost of equity to an unlevered firm in the same risk class is 16.0%.
-Refer to the data for Eccles Inc.Assume that the firm's gain from leverage according to the Miller model is $126,667. If the effective personal tax rate on stock income is TS = 20%, what is the implied personal tax rate on debt income?
A) 16.4%
B) 18.2%
C) 20.2%
D) 22.5%
E) 25.0%

Quizplus · Accepted Answer

$ \mathrm{T}_{\mathrm{c}}: 30 \% $  $ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$\text { Gain from leverage: } \$ 126,667$
$ \mathrm{T}_{\mathrm{s}}:20 \% $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $Debt: $ \$ 500,000 $ 
 
$\begin{array}{l}
\begin{array} { l } 
{\left[1-\left(1-\mathrm{T}_{\mathrm{c}}\right)\left(1-\mathrm{T}_{\mathrm{s}}\right) /\left(1-\mathrm{T}_{\mathrm{d}}\right)\right] \mathrm{D} } &=\$ 126,667 \
{[1-(0.7)(0.8) / \mathrm{X}] \$ 500,000 } &=\$ 126,667 \
1-0.56 / \mathrm{X} &=0.25333 \
0.56 / \mathrm{X} &=0.74667 \
\mathrm{X} &=0.75000 \
1-\mathrm{T}_{\mathrm{d}} &=0.75000 \
\mathrm{~T}_{\mathrm{d}} &=\mathbf{2 5 . 0 0 \%} \%
\end{array}
\begin{array} { l } 
\left(1-T_{c}\right) &=0.70 \
\left(1-T_{s}\right) &=0.80 \
\left(1-T_{c}\right) \times\left(1-T_{s}\right) &=0.56 \
\text { Gain } D \text { ebt } &=0.25333 \
\text { Gain } D e b t-1 &=-0.7466 \
X=-0.56 /-0.74666 &=0.75000 \
X &=1-T_{d} \
T_{d} &=0.25000
\end{array}
\end{array}$