Question

Your company just paid a dividend of $2.00. The growth rate is expected to be 4...

Your company just paid a dividend of $2.00. The growth rate is expected to be 4 percent for 1 year, 5 percent the next year, then 6 percent for the following year, and then the growth rate is expected to be a constant 7 percent thereafter. The required rate of return on equity is 10 percent. What is the current stock price?

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Answer #1

Calculation of the dividends:-

Year 1 = 2 * (1.04) = $ 2.08

Year 2 = 2.08 * (1.05) = $ 2.184

Year 3 = $ 2.184 * (1.06) = $ 2.31504

Year 4 = $ 2.31504 * (1.07) = $ 2.4770928

From year 4, dividends are grow at 7% forever.So, we calculate the present value of dividends from year 4 at end of 3rd year.

PV of dividends from year 4 at end of year 3 = Year 4 dividend / (r - g)

= $ 2.4770928 / (0.10 - 0.07)

PV of dividends from year 4 at end of year 3 = $ 82.56976

Current stock price means Present value of all dividend from the stock.

Stock price :-

Years Dividends PVF@10% PV
year 1 2.08 0.909091 1.890909
year 2 2.184 0.826446 1.804959
year 3 2.31504 0.751315 1.739324
year 3 82.56976 0.751315 62.03588
Stock price $ 67.47107
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