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Exam Question. XYZ common just paid a dividend of $1 per share. What is the highest...

Exam Question. XYZ common just paid a dividend of $1 per share. What is the highest price that you are willing to pay, if you require a 13% rate of return, and if you expect that dividends will grow at an annual rate of 20% for the next five years, and at 8% thereafter.

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Answer #1
D(t+1) = D(t)*(1+g1)
D0 1
For the first two years
g1 0.2
D1 1.2
D2 1.44
D3 1.728
D4 2.0736
D5 2.48832
Find the price of the stock in year 5
g2 0.08
D6 = D5*(1+g2)
D6 2.687386
According to the dividend growth model.
P5 = D6/(R-g2)
where R is .13
P5 53.74771
Cash flow in year 5 = D5+P5
The value of the stock today = sum of present value of future cash flows.
Using R = .13
Year 1 2 3 4 5
Cash flow 1.2 1.44 1.728 2.0736 56.23603
Present value 1.06 1.13 1.20 1.27 30.52
sum of present values 35.18
The highest price you are willing to pay is $35.18.
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