Valuing a Two-Stage Dividend Growth Stock
Summary
The document explains how to value a stock whose dividends grow quickly for a limited period before settling into a lower constant growth rate. It applies a two-stage dividend discount method: project dividends during the initial phase, estimate the share value at the transition using the Gordon growth model, then discount those cash flows and the transition value to today at the cost of equity.
The worked example uses the stated dividend, growth rates, transition horizon, and required return to calculate a present value. The accompanying answer confirms the approach: the terminal value uses the dividend one period after the high-growth phase, and each interim dividend is discounted separately. The treatment assumes the growth rates and discount rate are known and that constant growth is appropriate after the transition. It is an illustrative valuation exercise, not evidence that the forecasts or resulting share value are accurate.
Key ideas
- A two-stage dividend model can represent a temporary high-growth period followed by stable growth.
- The Gordon model estimates the value at the point when stable dividend growth begins.
- The terminal value should use the dividend expected one period after the transition.
- Discount interim dividends and the terminal value to the present using the cost of equity.
- The result depends on the assumed growth rates and discount rate.
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Full text
# Applying the Gordon stock model when there is one change in the dividend growth rate
# Applying the Gordon stock model when there is one change in the dividend growth rate
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?
## Answer by AlRacoon (score 1, accepted)
https://quant.stackexchange.com/a/70552
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.