## The Dividend Discount Model

The Dividend Discount Model, also known as the Gordon Growth Model is a formula that allows us to calculate the intrinsic value of a stock. The model assumes that the fair value of a stock is the present value of all future dividends that the company pays to its shareholders. These dividends are discounted to present value by using the required rate of return for the stock.

We firstly assume a model where the dividend amounts are fixed.

$S_{0} = \sum_{t=1}^{n}\frac{ D_{t} }{ (1+r)^t }$

As $n \to \infty$

we obtain ${S_{0}=\frac{D_{t}}{r}}$

This result is what we call a perpetuity (an annuity that pays fixed cash flows at constant intervals until infinity). The model assumes that all company dividends are paid out therefore there is no growth in the company’s dividends. Very rarely, companies pay out all their earnings in dividends, instead a proportion of earnings are retained internally to help grow the company in the future. By adding this assumption we introduce the company’s “sustainable growth rate”. This is the constant rate at which we assume that the company and therefore the dividends will grow in the future.

$S_{0} = \sum_{t=1}^{n} \frac{ D_{t}(1+g)}{(1+r)^t}$

As $n \to \infty$

We obtain (a growing perpetuity):

$S_{0}=\frac{D_{t}}{r-g}$

Limitations

• The model isn’t applicable to companies that currently do not pay dividends.
• Dividend amounts may fluctuate over the course of the years, so it might not make sense to assume that they are constant. In such cases we need to look at more complicated models like a two-stage dividend growth model.
• The model requires precise estimation as the stock price is very sensitive to the assumptions that we place for the growth rate (g) and the required rate of return (r).

• Well known and relatively simple to use.
• Applicable to well established companies that have a long track record of paying out dividends.

Worked Examples

Question 1

Company A pays $80 in dividends and is expected to pay the same dividend amount forever. Investors require a 10% rate of return for this stock. What is the intrinsic value of the stock? ‘Answer: 80/0.10 =$800

Question 2

Company B pays $25 in dividends and is expected to pay the same dividend amount forever. Investors require a 5% rate of return for this stock. What is the intrinsic value of the stock? ‘Answer: 25/0.05 =$500

Question 3

Company C is expected to pay a dividend of $35 next year. The company’s sustainable growth rate is 5% this growth rate is expected to be constant. Investors require a 7% rate of return for this stock. What is the intrinsic value of the stock? ‘Answer: 35/(0.07-0.05) =$1750

Question 4

Company C is expected to pay a dividend of $2 next year. The company’s sustainable growth rate is 2% this growth rate is expected to be constant. Investors require a 12% rate of return for this stock. What is the intrinsic value of the stock? ‘Answer: 2/(0.12-0.02) =$20

Feel free to post any questions you may have. Happy Studying!

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