Question

Beta company pays out 10% of earnings in dividends, and its latest earning was $5 per share. it earns an ROE on new investments of 15%. Suppose Jenny rewuires 14% return
a. how much should she pay for a share of stock of Beta company if she believes that this company can maintain its current retention ratio and ROE in new investment in the long run.
b. how much should she pay if the payout ratio was 60% and ROE was 19%?

Answer 1

a)

Stock price will be calculated under Constant-growth Dividend Discount Model  

P = D₀ (1 + g) (k - g)

Where,

D₀ (1 + g) or D₁ is next year's dividend amount.

g = company growth rate

k = required rate of return/capitalization rate

Retention Ratio = 1 - Payout Ratio = 1 - 0.10 = 0.90 or 90%

RoE = 15%

k = 14%

Growth rate (g) = RoE x Retention Ratio = 15% x 90% = 13.5%

Current EPS = $5

D₀ = Payout Ratio x EPS = 10% x $5 = $0.50

P = $0.50 (1 + 13.5%) (14%- 13.5%)

P = $113.50

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b)

Retention Ratio = 1 - Payout Ratio = 1 - 0.60 = 0.40 or 40%

RoE = 19%

k = 14%

Growth rate (g) = RoE x Retention Ratio = 19% x 40% = 7.60%

Current EPS = $5

D₀ = Payout Ratio x EPS = 60% x $5 = $3.0

P = $3.0 (1 + 7.60%) (14%- 7.60%)

P = $50.44

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