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A stock you are evaluating just paid an annual dividend of $2.70. Dividends have grown at a constant rate of 2.4 percent over the last 15 years and you expect this to continue.If the required rate of return on the stock is 15.8 percent, what should the fair value be four years from today?

Answer :

TomShelby

Answer:

Value of the stock in four years: $22.69

Explanation:

We use the gordon model  to sovle for the intrinsic value (fair value) of the share according to their future cash flow:

[tex]\frac{divends_1}{return-growth} = Intrinsic \: Value[/tex]

the formula uses next year dividends so we need to calcualte:

2.70 x 1.024 = 2,7648‬

Now we can solve for the value of the stock:

g = 0.024

r = 0.158

[tex]\frac{2.7648}{0.158-0.024} = Intrinsic \: Value[/tex]

Present Value = 20.63283582

That is the value of the stock today.

Now we apply the grow factor for the next four year:

[tex]Principal \: (1+ r)^{time} = Amount[/tex]

Principal 20.63283582

time 4.00

rate 0.02400

[tex]20.6328358208955 \: (1+ 0.024)^{4} = Amount[/tex]

Amount 22.69

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