Question

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.

Answer 1

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%