Answer to Question #180422 in Finance for Ketty

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.


1
Expert's answer
2021-04-19T18:45:58-0400

We solve by the following formula:

P=D0(1+g)kg×(1(1+g)n(1+k)n)+D0(1+g)n(1+g)(1+k)n(kg)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=4(1+0.1)0.110.1×(1(1+0.1)3(1+0.11)3)+4(1+0.1)3(1+g)(1+0.11)3(0.11g)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=440×0.0268+5.324(1+g)1.367631(0.11g)40=440\times0.0268+\frac{5.324(1+g\propto)}{1.367631(0.11-g\propto)}

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

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

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

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

0.797077.24608101×g=1+g0.79707-7.24608101\times g\propto=1+g\propto

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

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


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