According to constant growth dividend discount model, we compute the intrinsic v

Question

According to constant growth dividend discount model, we compute the intrinsic value of stock at time 0 (today’s computed stock price), P0=D1/(k-g), where D1 is the expected dividend next year, and k is the required return or discount rate. Assuming the required return is 20% per year.

a.       If we assume dividend will grow at a constant rate of 8% infinitely. The stock price is $35 per share. If we assume the stock is correctly priced, i.e., the stock has intrinsic value equal to its market price, what is the dividend the firm is paying to its shareholders this year?

Hint: D1=D0*(1+g).

b.      Instead of assuming that the firm will have a constant dividend growth ratio of 8%, if we assume that the firm will have ROE (return on asset) of 15% per year, expected EPS (earns per share, E1) of $2.50, and the dividend payout ratio of 60%.   Will you buy or sell the stock?

c.       The firm just makes an announcement that it expects its future ROE will be altered.   Immediately after the announcement, the stock price surges 20%. Will the expected ROE greater or smaller than 15%? Why?

Explanation / Answer

a. P0=D1/(k-g)
P0 = $35
k = 20%
g = 8%
$35 = D1/(20% - 8%)
D1 = $4.20
D1 = D0 x (1+g) = $4.20 = D0 x (1+8%)
D0 = $3.89

b.
Sustainable growth rate = (1- Dividend payout ratio) × ROE
Sustainable growth rate (g)= (1-60%) x 15% = 6%
k= 20%
P/E = Dividend pay out ratio /(k - g) = 60%/(20%-6%) = 4.29 times
Stable period Payout Ratio = 1 - (Growth rate/ROE) = 1-(8%/15%) = 46.67%
P/E = Dividend pay out ratio /(k - g) = 46.67%/(20%-8%) = 3.89 times
The PE ratio increases as the payout ratio increases, for any given growth rate.
Buy the stock as P/E ratio has increased.
c.
The PE ratio increases as the return on equity increases and decreases as the return on equity decreases.so, ROE should be higher than 15%

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