Question

12. The stock that is selling for GH¢12 today is expected to pay GH¢ 1 next year, GH¢2 the year after and GH¢ 3 the following year. How much are you expecting to sell it for after the third dividend if you buy it today? Your discount rate is 32%.

Answer 1

The expected share price after the third dividend is GH¢ 20.22

What is stock price?

The stock price can be determined as the present value of future dividends, years 1-3 and the present value of all dividends beyond year 3 which is known as the terminal value(i.e. the unknown selling price after the third dividend as required in this case)

The terminal value is the present value of future dividends after 3 years which needs to be discounted 3 years backward in the process of computing share price

Share price=12

Year 1 dividend=1

Year 2 dividend=2

Year 3 dividend=3

Terminal value=unknown (assume it is X)

discount rate=32%

Each future dividend can be discounted using the present value formula of a single cash flow shown below:

PV=FV/(1+r)^N

FV=each future cash flow/dividends

r=discount rate=32%

N=the year of dividends, 1 for year 1, 2 for year 2

12=1/(1+32%)^1+2/(1+32%)^2+3/(1+32%)^3+X/(1+32%)^3

12=3.20978378829618+X/(1+32%)^3

12-3.20978378829618=X/(1+32%)^3

(12-3.20978378829618)*(1+32%)^3=X

X=(12-3.20978378829618)*(1+32%)^3

X=GH¢ 20.22

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