Chapter 7, Problem 38QP

a.

Summary Introduction

To determine: The sustainable growth rate.

Answer to Problem 38QP

The sustainable growth rateis 6%.

Explanation of Solution

Determine the sustainable growth rate

$\begin{array}{c}SustainableGrowthRate\left(g\right)=\left[PlowbackRatio\times \mathrm{Re}turnonEquity\left(ROE\right)\right]\\ =\left[0.30\times 20\%\right]\\ =6\%\end{array}$

Therefore, the sustainable growth rateis 6%.

b.

Summary Introduction

To determine: The stock price.

Answer to Problem 38QP

The stock priceis $35.

Explanation of Solution

Determine the stock price

$\begin{array}{c}Stock\mathrm{Pr}ice\left(P_0\right)=\left[\frac{CurrentDividends\left(D_1\right)\times \left(1-PlowbackRatio\right)}{\mathrm{Re}quired\mathrm{Re}turn\left(r\right)-GrowthRate\left(g\right)}\right]\\ =\left[\frac{\$3\times \left(1-0.30\right)}{12\%-6\%}\right]\\ =\left[\frac{\$2.10}{6\%}\right]\\ =\$35\end{array}$

Therefore, the stock priceis $35.

c.

Summary Introduction

To determine: The present value of growth opportunities.

Answer to Problem 38QP

The present value of growth opportunities is $10.

Explanation of Solution

Determine the present value of growth opportunities

$\begin{array}{c}PVGO=\left[CurrentStock\mathrm{Pr}ice-NoGrowth\mathrm{Pr}ice\right]\\ =\left[\$35-\left(\frac{\$3}{12\%}\right)\right]\\ =\left[\$35-\$25\right]\\ =\$10\end{array}$

Therefore, the present value of growth opportunities is $10.

d.

Summary Introduction

To determine: The P/E ratio.

Answer to Problem 38QP

The P/E ratiois 11.67.

Explanation of Solution

Determine the P/E ratio

$\begin{array}{c}PERatio=\left[\frac{CurrentStock\mathrm{Pr}ice\left(P_0\right)}{CurrentDividends\left(D_0\right)}\right]\\ =\left[\frac{\$35}{\$3}\right]\\ =11.67\end{array}$

Therefore, the P/E ratio is 11.67.

e.

Summary Introduction

To determine: The price and P/E ratio if firm paid all earnings as dividends.

Answer to Problem 38QP

The price is $25 and P/E ratiois 8.33 if firm paid all earnings as dividends.

Explanation of Solution

Determine the price and P/E ratio

The price of if firm paid all earnings as dividends is $25, which is nothing but the stock price using no growth model.

$\begin{array}{c}PERatio=\left[\frac{CurrentStock\mathrm{Pr}ice\left(P_0\right)}{CurrentDividends\left(D_0\right)}\right]\\ =\left[\frac{\$25}{\$3}\right]\\ =8.33\end{array}$

Therefore, the price is $25 and P/E ratio is 8.33 if firm paid all earnings as dividends.

e.

Summary Introduction

To discuss: The relationship between growth opportunities and PE ratio.

Explanation of Solution

The relationship between growth opportunities and PE ratio is as follows:

If the PE ratio is high, it directly reflects on higher present value of growth opportunities.