Consider a Gordon growth rule: s1 = d2 r g where s1 is the current stock price i

Question

Consider a Gordon growth rule: s1 = d2 r g

where s1 is the current stock price in period 1, d2 is the expected dividend payment received in period 2, r is the market interest rate, and g is the dividend growth rate.

a) If s1 = $100, d2 = $2, and r = 8%, what is the dividend growth rate? If the dividend payment is proportional to the earnings in each period, Equation (??) can be rewritten as:

s1 = d × e2/ r g

where d is the dividend payout ratio and e2 is the earnings in period 2.

b) Given e2 = $10, d = 20%, and P/E = 10, what is the growth rate g?

c) Given e2 = $10, d = 20%, and P/E = 50, what is the growth rate g?

Explanation / Answer

Answer:

a)

after putting all values in given formula:

100 = 2/(0.08-g)

100(0.08-g) = 2

8 - 100g = 2

100g = 6

g = 6/100 = 0.06

b)

P/E = stock price / earning per share

10 = Stock price / (10x0.2) (Formula: earningper share = e2 x d)

10 x 2 = stock price

Stock price = $20

putting all values in formula:

20 = (0.2x10)/(0.08-g)

20x0.08-20g = 2

1.6-20g = 2

0.4=20g

g = 0.4/20 = 0.02 = 2%

c) Stock price when P/E is 50

50 = stock price / 10 x 0.2

50 x 2 = stock price

100 = stock price

putting values in given formula:

100 = (0.2x 10) / (0.08-g)

100x0.08-100g = 2

8 -2 = 100g

6 = 100g

g = 6/100 = 0.06 = 6%

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