Alpha Corporation just paid a dividend of $2.50 per share on its common stock. D

Question

Alpha Corporation just paid a dividend of $2.50 per share on its common stock. Dividends are expected to grow at an annual rate of 8% for the next 3 years and then 3% thereafter. If you want to earn a minimum return of 9%, what is the most that you would be willing to pay for a share of Alpha Corporation today? Alpha Corporation just paid a dividend of $2.50 per share on its common stock. Dividends are expected to grow at an annual rate of 8% for the next 3 years and then 3% thereafter. If you want to earn a minimum return of 9%, what is the most that you would be willing to pay for a share of Alpha Corporation today?

Explanation / Answer

Current Dividend, D0 = $2.50

Growth rate for first 3 years is 8% and followed by a constant growth rate (g) of 3%
Required return, r = 9%

D1 = $2.5000 * 1.08 = $2.7000
D2 = $2.7000 * 1.08 = $2.9160
D3 = $2.9160 * 1.08 = $3.1493
D4 = $3.1493 * 1.03 = $3.2438

P3 = D4 / (r - g)
P3 = $3.2438 / (0.09 - 0.03)
P3 = $54.0626

P0 = $2.7000/1.09 + $2.9160/1.09^2 + $3.1493/1.09^3 + $54.0626/1.09^3
P0 = $49.11

So, price of share is $49.11

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