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Below is a problem I did. I am hoping somebody can confirm I did it correctly, or tell me where I went wrong.

Problem:
ABC Corp. has just paid a dividend of \$3 per share. You—an experienced analyst—feel quite sure that the growth rate of the company’s dividends over the next 10 years will be 15% per year. After 10 years you think that the company’s dividend growth rate will slow to the industry average, which is about 5% per year. If the cost of equity for ABC is 12%, what is the value today of one share of the company?
Answer:
Let $p_{10}$ be the value of one share of stock $10$ years from now. The Gordon model is: $$ P_0 = \dfrac{D_0(1+g) } {r_e - g} $$ We have: \begin{align*} D_0 &= 3(1+.15)^{10} = 3(1.15^{10}) \\ g &= 0.05 \\ r_e &= 0.12 \\ p_{10} &= \dfrac{3(1.15^{10})(1+0.05) } {0.12 - 0.05} \\ p_{10} &= \dfrac{3(1.15^{10})(1.05) } {0.07} \\ p_{10} &= \dfrac{3.15(1.15^{10}) } {0.07} \\ p_{10} &= 182.0501 \end{align*} Let $p$ be the value of the security today. $$ p = \sum_{i = 1}^{10} \dfrac{ (1.15^i)(3) }{1.12^{i}} + \, \dfrac{ p_{10} }{1.12^{10}} $$ Using Python, I find that: $$ p = 93.4098 $$ Is my solution right?

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  • $\begingroup$ @AIRacoon If you could post your comment as an answer, I would accept it and close the question. $\endgroup$
    – Bob
    Apr 16, 2022 at 2:22

1 Answer 1

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Looks right to me. This is the two stage dividend growth model. The dividend at the end of the growth phase is projected one period forward and the standard Gordon Growth model is applied to arrive at year 10 value; which is then discounted for the 10 periods. Each of the other dividends is discounted at the cost of equity.

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