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Simpkins Corporation does not pay any dividends because it is expanding rapidly and needs to retain all of its earnings. However, investors expect Simpkins to begin paying dividends, with the first dividend of $2.00 coming 3 years from today. The dividend should grow rapidly - at a rate of 80% per year - during Years 4 and 5. After Year 5, the company should grow at a constant rate of 5% per year. If the required return on the stock is 13%, what is the value of the stock today (assume the market is in equilibrium with the required return equal to the expected return)

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Answer:

The answer is "$ 52.17"

Explanation:

Third-year dividend,  [tex]D_3 = \$ \ 2.00[/tex] Increasing at  [tex]80 \ \%[/tex] per year in years 4 and 5.

[tex]\to D_4 = 2.00(1.80)=3.6\\\\\to D_5 = 3.6 (1.80) = 4.48\\\\[/tex]

Now, rising at a steady rate of 5 percent per year in year 6

[tex]\to D_6 = 6.48(1.05) =6.804[/tex]

[tex]\text{Price of the stock} = \frac{Expected \ dividend}{(Required \ return - growth \ rate)}[/tex]

                            [tex]=\frac{6.804}{(0.13 - 0.05)}\\\\ =\frac{6.804}{(0.08)}\\\\ = \$ \ 85.05[/tex]

The present value of all flows of cash:

[tex]= \frac{2.00}{(1.13)^3} + \frac{3.6}{(1.13)^4} + \frac{(4.48+ 85.05)}{(1.13)^5}\\\\ = \frac{2.00}{1.442897} + \frac{3.6}{1.63047361} + \frac{(4.48+ 85.05)}{1.84243518}\\\\ = \frac{2.00}{1.442897} + \frac{3.6}{1.63047361} + \frac{(89.53)}{1.84243518}\\\\= 1.38 +2.20+ 48.59\\\\=52.17[/tex]

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