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Using CAPM and Dividend Growth to Estimate Stock Value

Article Quant Q&A · Author: Maximus
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Summary

The document outlines how to value a stock with the Gordon growth version of the dividend discount model. The model relates the next expected dividend to the difference between the required return on equity and the dividend growth rate. It explains that the required return is also called the cost of equity, and can be estimated as the risk-free rate plus an equity risk premium. The questioner’s uncertainty about deriving CAPM inputs from the supplied information is not resolved with a numerical calculation.

For growth, the answer points to the sustainable growth relationship: retention ratio multiplied by return on equity. It also notes that when return on equity and dividend growth vary between shorter and longer horizons, a two-stage approach such as the H-model may be appropriate. These formulas depend on assumptions including stable growth and a required return above the growth rate. The document offers a compact framework, but does not define how to obtain all market inputs or discuss uncertainty in forecasts.

Key ideas

  • The Gordon growth model values a share using its expected dividend, required return, and growth rate.
  • Required return on equity is another name for the cost of equity.
  • The answer describes the cost of equity as the risk-free rate plus an equity risk premium.
  • Sustainable growth can be estimated from the retention ratio and return on equity.
  • A two-stage model may help when growth differs across time horizons.

Tags

EquitiesFactor investing
Full text
# Dividend Discount Model for a stock and its derivatives


# Dividend Discount Model for a stock and its derivatives












This might be a bit basic but I've found this question and I'm definitely over-thinking it and now I've just completely confused myself. I'm just looking for some clarification.

I've been given the following information on a stock and its derivatives and I've been asked to determine the stock price using the Dividend Discount Model.

To calculate this I know I could use the Gordon Growth Formula, I have the dividend per share and I believe the growth rate of the dividend is 0, since it stays at £1. What I need is the cost of equity, which I think I can obtain using the CAPM. My problem here is that I'm not sure how to obtain the risk free rate, Beta of the stock, and the market risk premium. I've tried a few calculations but none seem correct (I get VERY low values).

If anyone could show me how I would obtain the values I need from the information given I would really appreciate it. I understand this might be a bit basic for this site but I've managed to overthink my way into a deep hole.

Thanks in advance

## Answer by Felix (score 1, accepted)

https://quant.stackexchange.com/a/63911

As you've said, you can apply a version of the DDM, namely the gordon growth model -- assuming a constant growth of dividends.

GGM = D1 / (r-g)

So you need the cost of equity, the future dividends, and a growth rate.

In your case, the required return on equity is basically the cost of equity -- it's just another word for it. Required return on equity is the return investors require for the equity: required return on equity = risk-free rate + equity risk premiums

From the companies point of view this required return investors demand is a cost, i.e., the cost of equity.

The growth rate in your case can be calculated as: g = Retention Ratio * ROE (see sustainable growth rate).

Then you have:

PV= (D0*(1+g))/(r-g)

BTW: Since you have long-term and short-term ROE you can calculate a long-term and short-term growth rate. So to consider that, you can use the H-model, for example.

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.