Question

(Ordinary share valuation) Assume the following:
• the investor’s required rate of return is 15%
• the expected level of earnings at the end of this year (E|) is $5.00
• the retention ratio is 50% • the return on equity (ROE) is 20% (i.e. it can earn 20% on reinvested earnings)
• similar shares sell at multiples of 10 times earnings per share.

Questions:

(a) Determine the expected growth rate for dividends.

(b) Determine the price/earnings ratio (P!E\) using equation.

(c) What is the share price using the P/E ratio valuation method?

(d) What is the share price using the dividend discount model?

(e) What would happen to the P/E ratio (P!E\) and share price if the firm could earn 25% 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?

Using the correct formulas, not excel calculators/cells

Answer 1

a)
Growth Rate = ROE x Plowback ratio
Growth Rate = 20% x 50%	10.00%
b)
P0 = DIV1/(r-g)
DIV 1 = E1 x ( 1 - 50%)	$2.50
P0 = $2.50/(15% - 10%)	$50.00
P/ E = $50/$5	10.00	Times
c)
P/E = Price / EPS = 10 = Price/$5
Price = 10 x $5	$50.00
d)
P0 = DIV1/(r-g)
DIV 1 = E1 x ( 1 - 50%)	$2.50
P0 = $2.50/(15% - 10%)	$50.00
e)
Growth Rate = ROE x Plowback ratio
Growth Rate = 25% x 50%	12.50%
P0 = DIV1/(r-g)
DIV 1 = E1 x ( 1 - 50%)	$2.50
P0 = $2.50/(15% - 12.50%)	$100.00
P/ E = $100/$5	20.00	Times
f)
The ROE increases, then growth rate also increases and PE ratio increases as the return on equity increases and decreases as the return on equity decreases.