Given the following firm and market information,determine the value of the firm. $$\begin{array}{l}
\begin{array} { l l r }
\text {Net profit margin}&3 \% \
\text {Total asset turnover}&1.5 \
\text {Debt/equity}&0.5 \
\text {Plowback ratio}&0.5 \
\text {Last year's dividends per share}&\$ 2.00 \
\text {Firm beta}&1.2 \
\text {Risk-free rate}&5 \% \
\text {Market risk premium}&8 \%
\end{array}
\end{array}$$
A) $28.42
B) $18.42
C) $8.42
D) $38.42
E) none of these

Question

Given the following firm and market information,determine the value of the firm. $$\begin{array}{l}
\begin{array} { l l r } 
\text {Net profit margin}&3 \% \
\text {Total asset turnover}&1.5 \
\text {Debt/equity}&0.5 \
\text {Plowback ratio}&0.5 \
\text {Last year's dividends per share}&\$ 2.00 \
\text {Firm beta}&1.2 \
\text {Risk-free rate}&5 \% \
\text {Market risk premium}&8 \%
\end{array}
\end{array}$$
A) $28.42
B) $18.42
C) $8.42
D) $38.42
E) none of these

Quizplus · Accepted Answer

The value of the firm can be calculated using the Gordon Growth Model. First, calculate the required rate of return using the CAPM: $ r = 5\% + 1.2 \times 8\% = 14.6\% $. The growth rate $ g $ is the retention ratio (plowback ratio) times the return on equity (ROE). ROE can be calculated as Net Profit Margin $\times$ Total Asset Turnover $\times$ Equity Multiplier. The equity multiplier is $1 + \text{Debt/Equity} = 1.5$. So, ROE = $3\% \times 1.5 \times 1.5 = 6.75\%$. Therefore, $ g = 0.5 \times 6.75\% = 3.375\% $. Using the Gordon Growth Model: $ P = \frac{D_0 \times (1+g)}{r-g} = \frac{2 \times 1.03375}{0.146 - 0.03375} = 18.42 $.

Given the Following Firm and Market Information,determine the Value of the Firm