Dividend Discount Model

The Dividend Discount Model (DDM) is a widely used approach to value common stocks. Financial theory states that the value of any securities is worth the present value of all future cash flow the owner will receive. If we assume that stock investor receive all their cash fow in the form of dividend, a DDM will give the intrinsic value for a stock.

A common stock can be tough as the right to receive future dividends. A stock's intrincic value can be defined as the value of all future dividends discounted at the appropriate discount rate. In its simpliest form, the DDM uses, as discount rate, the investor's required rate of return.

Mathematically, it can be expressed as: $V_{0}=\sum _{t=1}^{N}{\frac {D_{t}}{(1+k)^{n}}}$,

where $D_{t}$ is the expected dividend in period Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k} is the required rate of return for the investor.

From this formula, one can deduct that the most important components of the value of a stock are likely to be the size and the timing of the expected dividend. The larger it is, and the more quick the shareholder receive it, the higher the share value will be.

Assumptions of the model

• The future value of dividend is know by the investor.
• Dividends are expected to be distributed at the end of each year until infinity.
• Dividends are the only way inversors get money back from the company. This implies that any share buyback would be ignored.

Inputs to the model

To estimate the value of a common share, one must know at least:

• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle D_1} : the expected dividend to be received in one year;
• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k} : the required rate of return on the investment. There are many methods to estimate this required rate of return, the most common is the Nobel-prize rewarded Capital Asset Pricing Model;
• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g} : the expected growth rate in dividends.

If no growth in dividends

In the case where the dividend is not expected to growth in the future (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g=0} ), then the stock is also known as a perpetuity.

In that case, the price of the stock would be equal to:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P_0=\frac{D}{1+k}+\frac{D}{(1+k)^2}+\frac{D}{(1+k)^3}+...=\frac{D}{k}} ,

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle D} is the expected constant dividend and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k} is the required rate of return for the investor.

Constant growth of the dividend

In the case where the dividend is expected to grow at a definite constant growth rate Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g} , the value of the stock will be equal to

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P_0=\frac{D}{1+k}+\frac{D(1+g)}{(1+k)^2}+\frac{D(1+g)^2}{(1+k)^3}+...}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P_0=\frac{D_1}{(k-g)}} ,

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle D_1} is the expected constant dividend at period Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1} (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle D_1=D_0*(1+g)} ), Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g} is the dividend growth rate and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k} is the required rate of return for the investor.

It is also known as the Gordon Model for evaluating stocks.

Supernormal growth model

In many cases, companies do not growth at a constant rate during their life. They are expected to growth at a "supernormal" growth rate at the beginning of their activities and then, at maturity, the growth rate will be reduce to a constant "normal" growth rate.

In that case, we will have to adjust the calculation to take in account those two diffents growth periods.

If we assume that a company will have its dividend growing at a rate Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g_1} during the first Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N} periods and thereafter, until infinity, at a lower rate Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g_2} , the value of the company will be equal to:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_0=\sum_{t=1}^{N}\frac{D_0*(1+g_1)^t}{(1+k)^t}+\frac{\frac{D_N*(1+g_2)}{(k-g_2)}}{(1+g_2)^N}}

Where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle D_0} is the dividend distributed today, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k} is the required rate of return or the investor.

This method is usually used by analysts in valuing companies as the short-term growth is,in most cases, higher than the long-term growth (generally set at the general economic growth rate).

See Also

Gordon Model