Question #180422

1. Sky, Inc. paid a dividend of $4.00 per share on its common stock yesterday. Dividends are expected to grow at a constant rate of 10% for the next three years, at which point the dividends will begin to grow at a constant rate indefinitely. If the stock is selling for $40 today and the required return is 11%, what it the expected annual dividend growth rate after year three? Please share details.

Expert's answer

We solve by the following formula:

"P=\\frac{D0(1+g)}{k-g}\\times(1-\\frac{(1+g)^n}{(1+k)^n})+\\frac{D0(1+g)^n(1+g\\propto)}{(1+k)^n(k-g\\propto)}"

"40=\\frac{4(1+0.1)}{0.11-0.1}\\times(1-\\frac{(1+0.1)^3}{(1+0.11)^3})+\\frac{4(1+0.1)^3(1+g\\propto)}{(1+0.11)^3(0.11-g\\propto)}"

"40=440\\times0.0268+\\frac{5.324(1+g\\propto)}{1.367631(0.11-g\\propto)}"

"40=11.792+\\frac{5.324(1+g\\propto)}{1.367631(0.11-g\\propto)}"

"28.208=3.89286291\\times\\frac{(1+g\\propto)}{(0.11-g\\propto)}"

"7.24608101=\\frac{(1+g\\propto)}{(0.11-g\\propto)}"

"7.24608101\\times(0.11-g\\propto)=(1+g\\propto)"

"0.79707-7.24608101\\times g\\propto=1+g\\propto"

"-0.2029=8.24608101\\times g\\propto"

"g\\propto=-0.0246" or -2.46%

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