# Stormy Weather has no attractive investment opportunities. Its return on equity equals the...

Stormy Weather has no attractive investment opportunities. Its return on equity equals the discount rate, which is 10 percent. Its expected earnings this year are 3 per share. Find the stock price, P/E ratio, and growth rate of dividends for plow-back ratios of: a. zero b. 0.40 c. 0.80 ## Common stock: Common stock is the ownership of the investor in the corporation. The common stockholders have voting rights in the company, and the earning of the business is distributed among the common stock shareholders as a dividend. ## Answer and Explanation: Calculating DPS: {eq}\begin{align*} \rm\text{DPS} &=\rm\text{ EPS} \times \left( 1 - \rm\text{Plowback ratio} \right)\\ \rm\text{a.DPS } &= \ 3 \times \left( 1 - 0 \right) = \$3\\ \rm\text{b.DPS }&= \$ 3\times \left( 1- 0.40 \right) = \$1.8\\ \rm\text{c.DPS } &= \$ 3 \times \left( 1 - 0.80 \right) = \0.6 \end{align*} {/eq} {eq}\begin{align*} \rm\text{P0 (MPS)} &= \dfrac{{{\rm\text{DPS}}}}{{{\rm\text{Ke - G}}}}\\ \rm\text{a.P0 (MPS)} &= \dfrac{{\ 3}}{{0.10 - 0.00}} = \$30\\ \rm\text{b.P0 (MPS) }&= \dfrac{{\$ 1.8}}{{0.10 - 0.04}} = \$30\\ \rm\text{c . P0 (MPS)} &= \dfrac{{\$ 0.6}}{{0.10 - 0.08}} = \30 \end{align*} {/eq} Calculating P/E ratio: {eq}\begin{align*} \rm\text{P/E ratio } &= \dfrac{\rm\text{MPS}}{\rm\text{EPS}}\\ \rm\text{a .P/E ratio} &= \dfrac{{\ 30}}{{\$3}} = 10\\ \rm\text{b.P/E ratio }&= \dfrac{{\$ 30}}{{\$3}} = 10\\ \rm\text{c.P/E ratio }&= \dfrac{{\$ 30}}{{\\$ 3}} = 10 \end{align*} {/eq}

Calculating growth of dividend:

{eq}\begin{align*} \rm\text{Growth of dividend} &=\rm\text{ ROE } \times \rm\text{ Plowback ratio}\\ \rm\text{a. Growth of dividend } &= 10 \times 0 = 0\\ \rm\text{b. Growth of dividend } &= 10 \times 40\% = 4\\ \rm\text{c. Growth of dividend } &= 10 \times 80\% = 8 \end{align*} {/eq} 