Green Tree Corporation is paying a dividend of $4 today. It expects dividends to grow at...

Green Tree Corporation is paying a dividend of $4 today. It expects dividends to grow at 25 percent for the next three years and to stabilize at 10 percent per year thereafter. If the required rate of return of this corporation is 15 percent, what is the current price of this corporation's stock? What percentage of the current stock price is due to the dividends in the first three years? What percentage of the current stock price is due to the dividends from Year 4 onwards?

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Expert Solution

Answer:

Last Dividend, D0 = $4.00

Growth Rate for next 3 years is 25% and a constant growth rate (g) of 10% thereafter

D1 = $4.0000 * 1.25 = $5.0000
D2 = $5.0000 * 1.25 = $6.2500
D3 = $6.2500 * 1.25 = $7.8125
D4 = $7.8125 * 1.10 = $8.5938

Required Return, rs = 15%

P3 = D4 / (rs - g)
P3 = $8.5938 / (0.15 - 0.10)
P3 = $171.8760

Present Value of Dividend in first 3 years = $5/1.15 + $6.25/1.15^2 + $7.8125/1.15^3
Present Value of Dividend in first 3 years = $14.21

Present Value of P3 = $171.876/1.15^3
Present Value of P3 = $113.01

Current Price = Present Value of Dividend in first 3 years + Present Value of P3
Current Price = $14.21 + $113.01
Current Price = $127.22

Percentage of Current Price due to Dividends in first 3 years = Present Value of Dividend in first 3 years / Current Price
Percentage of Current Price due to Dividends in first 3 years = $14.21 / $127.22
Percentage of Current Price due to Dividends in first 3 years = 0.1117 or 11.17%

Percentage of Current Price due to Dividends from Year 4 onwards = Present Value of P3 / Current Price
Percentage of Current Price due to Dividends in first 3 years = $113.01 / $127.22
Percentage of Current Price due to Dividends in first 3 years = 0.8883 or 88.83%

jeff jeffy answered 5 months ago

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