# Applying the Gordon stock model when there is one change in the dividend growth rate [closed]

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?
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?