Common stock valuation Assume the following the investors re

(Common stock valuation) Assume the following: the investor\'s required rate of return is 17 percent, the expected level of earnings at the end of this year (E1) is $5, the retention ratio is 45 percent, the return on equity (ROE) is 18 percent (that is, it can earn 18 percent on reinvested earnings), and similar shares of stock sell at multiples of 6.180 times earnings per share. Questions a. Determine the expected growth rate for dividends b. Determine the price earnings ratio (PIE1) c. What is the stock price using the P/E ratio valuation method? d. What is the stock price using the dividend discount model?

Solution

(i)

g = b x r

g = growth rate in dividends

b = retention ratio = 45% or 0.45

r = return on equity = 18% or 0.18

= 0.45 x 0.18

= 0.0810

= 8.10%

(ii)

Since similar shares of the stock are selling at 6.180 times of EPS, hence P/E Ratio is 6.180

(iii)

P/E Ratio = Market price of share/EPS

6.180 = Market price of share/5

Market price of share = 6.180 x 5

= $30.9

(iv)

EPS = $5

Retention ratio = 45%

Hence, dividend payout ratio = 55%

Hence, expected dividend (D₁) = 5 x 55%

= $2.75

P₀ = D₁/(K_e - g)

P₀ = Current market price

Ke = Investor\'s required rate of return = 17% = 0.17

= 2.75/(0.17 - 0.0810)

= 2.75/0.089

= $30.90