Question

Assume the following:
• the investor's required rate of return is 15 percent,
• the expected level of earnings at the end of this year (E1) is $5
• the retention ratio is 50 percent,
• the return on equity (ROE) is 20 percent? (that is, it can earn 20 percent on reinvested earnings), and
• similar shares of stock sell at multiples of 10.000 times earnings per share.

Questions:
a. Determine the expected growth rate for dividends.
b. Determine the price earnings ratio (P/E1).
c. What is the stock price using the? P/E ratio valuation? method?
d. What is the stock price using the dividend discount? model?
e. What would happen to the P/E ratio ?(P/E1) and stock price if the firm could earn 25 percent on reinvested earnings ?(ROE)
f. What does this tell you about the relationship between the rate the firm can earn on reinvested earnings and P/E ratios

Answer 1

Answer to a.

Expected growth rate g = b X r, where b = retention ratio = 1-D/P ratio, = 50% or 0.5,

r = return on equity = 20%, so Expected growth rate g = 0.5X20% = 10%.

Answer to b,

One use of the P/E multipple is the relative valuation. so we can consider the P/E of this company also 10.

Answer to c.

Market price under P/E multpple model = Earnings X P/E,

So $5X10 = $50 is the price under PE ratio valuation method.

Answer to d,

stock price using the dividend discount model = D1 /(Ke-g),

d1 is the next year divident = next year earnings X (1-Retention ratio) = $5 X(1-0.5),

=$5 X 0.5 = $2.5,

Ke = (D1 / MP) + g,

Ke = (2.5/50) + 0.10,

So ke = 0.15 or 15%,

So MP = $2.5/(0.15-0.1) = $50,

Answer to e,

If the firm could earn 25 percent on reinvested earnings (ROE), g will be

Expected growth rate g = b X r, where b = retention ratio = 1-D/P ratio, = 50% or 0.5,

r = return on equity changes to 25% or 0.25,

g =0.5X25% = 12.5%, so the price will be

Price = D1/(ke-g),

=$2.5/(0.15-0.125)

=$2.5/0.025 = $100,

Then P/E ratio will be $100/$5 = 20,

Answer to f,

there is a 25% change in ROE (5/20X100) constituted 100% ( (20-10)/10X100 ) change in P/E ratio.

relationship between relationship between the rate the firm can earn on reinvested earnings and P/E ratio here it is 4 time.

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