Question

In: Finance

Suppose a firm will pay a $2 dividend next year and expects to increase dividends by...

Suppose a firm will pay a $2 dividend next year and expects to increase dividends by 20%, 15%, and 10% over the following three years. After that, dividends will increase at a rate of 5% per year indefinitely. If the required return is 17%, what is the price of the stock today?

Group of answer choices

$19.21

$21.50

$18.80

$22.14

$20.98

Solutions

Expert Solution

Sol:

Dividend at year 1 (D1) = 2

Dividend at year 2 (D2) = 2 (1 + 20%) = 2.40

Dividend at year 3 (D3)= 2.40 (1 + 15%) = 2.76

Dividend at year 4 (D4) = 2.76 (1 + 10%) = 3.036

Dividend growth rate (G) = 5%

Required rate of return (Re) = 17%

Market price at end of year 3 = D4 / (Re -G)

Market price at end of year 3 = 3.036 / (17% -5%)

Market price at end of year 3 = 3.036 / (0.17 - 0.05)

Market price at end of year 3 = 3.036 / 0.12 = $25.3

Price of the stock today = 2 / (1 + 17%)1 + 2.40 / (1 + 17%)2 + 2.76 / (1 + 17%)3 + 25.30 / (1 + 17%)3

Price of the stock today = 2 / (1 + 0.17)1 + 2.40 / (1 + 0.17)2 + 2.76 / (1 + 0.17)3 + 25.30 / (1 + 0.17)3

Price of the stock today = 2 / (1.17)1 + 2.40 / (1.17)2 + 2.76 / (1.17)3 + 25.30 / (1.17)3

Price of the stock today = 1.7094 + 1.7532 + 1.7233 + 15.7966

Price of the stock today = $20.98

Therefore price of the stock today is $20.98

jeff jeffy answered 2 years ago
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