## What Is the Dividend Discount Model?

The dividend discount model (DDM) is a quantitative method used for predicting the price of a company's stock based on the theory that its present-day price is worth the sum of all of its future dividend payments when discounted back to their present value. It attempts to calculate the fair value of a stock irrespective of the prevailing market conditions and takes into consideration the dividend payout factors and the market expected returns. If the value obtained from the DDM is higher than the current trading price of shares, then the stock is undervalued and qualifies for a buy, and vice versa.

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## Understanding the DDM

A company produces goods or offers services to earn profits. The cash flow earned from such business activities determines its profits, which gets reflected in the company’s stock prices. Companies also make dividend payments to stockholders, which usually originates from business profits. The DDM model is based on the theory that the value of a company is the present worth of the sum of all of its future dividend payments.

## Time Value of Money

Imagine you gave $100 to your friend as an interest-free loan. After some time, you go to him to collect your loaned money. Your friend gives you two options: 1. Take your$100 now

## Discounting Factor

Shareholders who invest their money in stocks take a risk as their purchased stocks may decline in value. Against this risk, they expect a return/compensation. Similar to a landlord renting out his property for rent, the stock investors act as money lenders to the firm and expect a certain rate of return. A firm's cost of equity capital represents the compensation the market and investors demand in exchange for owning the asset and bearing the risk of ownership. This rate of return is represented by (r) and can be estimated using the Capital Asset Pricing Model (CAPM) or the Dividend Growth Model. However, this rate of return can be realized only when an investor sells his shares. The required rate of return can vary due to investor discretion.

Companies that pay dividends do so at a certain annual rate, which is represented by (g). The rate of return minus the dividend growth rate (r - g) represents the effective discounting factor for a company’s dividend. The dividend is paid out and realized by the shareholders. The dividend growth rate can be estimated by multiplying the return on equity (ROE) by the retention ratio (the latter being the opposite of the dividend payout ratio). Since the dividend is sourced from the earnings generated by the company, ideally it cannot exceed the earnings. The rate of return on the overall stock has to be above the rate of growth of dividends for future years, otherwise, the model may not sustain and lead to results with negative stock prices that are not possible in reality.

## DDM Formula

Based on the expected dividend per share and the net discounting factor, the formula for valuing a stock using the dividend discount model is mathematically represented as,

﻿ \begin{aligned}&\textit{\textbf{Value of Stock}}=\frac{\textit{\textbf{EDPS}}}{\textbf{(\textit{CCE}}-\textbf{\textit{DGR})}}\\&\textbf{where:}\\&EDPS=\text{expected dividend per share}\\&CCE=\text{cost of capital equity}\\&DGR=\text{dividend growth rate}\end{aligned}﻿

Since the variables used in the formula include the dividend per share, the net discount rate (represented by the required rate of return or cost of equity and the expected rate of dividend growth), it comes with certain assumptions.

Since dividends, and its growth rate, are key inputs to the formula, the DDM is believed to be applicable only on companies that pay out regular dividends. However, it can still be applied to stocks which do not pay dividends by making assumptions about what dividend they would have paid otherwise.

## DDM Variations

The DDM has many variations that differ in complexity. While not accurate for most companies, the simplest iteration of the dividend discount model assumes zero growth in the dividend, in which case the value of the stock is the value of the dividend divided by the expected rate of return.

The most common and straightforward calculation of a DDM is known as the Gordon growth model (GGM), which assumes a stable dividend growth rate and was named in the 1960s after American economist Myron J. Gordon.﻿﻿ This model assumes a stable growth in dividends year after year. To find the price of a dividend-paying stock, the GGM takes into account three variables:

﻿ \begin{aligned}&D = \text{the estimated value of next year's dividend}\\&r = \text{the company's cost of capital equity}\\&g = \text{the constant growth rate for dividends, in perpetuity}\end{aligned}﻿

Using these variables, the equation for the GGM is:

﻿ $\text{Price per Share}=\frac{D}{r-g}$﻿

A third variant exists as the supernormal dividend growth model, which takes into account a period of high growth followed by a lower, constant growth period. During the high growth period, one can take each dividend amount and discount it back to the present period. For the constant growth period, the calculations follow the GGM model. All such calculated factors are summed up to arrive at a stock price.

## Examples of the DDM

Assume Company X paid a dividend of $1.80 per share this year. The company expects dividends to grow in perpetuity at 5 percent per year, and the company's cost of equity capital is 7%. The$1.80 dividend is the dividend for this year and needs to be adjusted by the growth rate to find D1, the estimated dividend for next year. This calculation is: D1 = D0 x (1 + g) = $1.80 x (1 + 5%) =$1.89. Next, using the GGM, Company X's price per share is found to be D(1) / (r - g) = $1.89 / ( 7% - 5%) =$94.50.

A look at the dividend payment history of leading American retailer Walmart Inc. (WMT) indicates that it has paid out annual dividends totaling to $1.92,$1.96, $2.00,$2.04 and $2.08, between January 2014 and January 2018 in chronological order.﻿﻿ One can see a pattern of a consistent increase of 4 cents in Walmart's dividend each year, which equals to the average growth of about 2 percent. Assume an investor has a required rate of return of 5%. Using an estimated dividend of$2.12 at the beginning of 2019, the investor would use the dividend discount model to calculate a per-share value of $2.12/ (.05 - .02) =$70.67.

## Shortcomings of the DDM

While the GGM method of DDM is widely used, it has two well-known shortcomings. The model assumes a constant dividend growth rate in perpetuity. This assumption is generally safe for very mature companies that have an established history of regular dividend payments. However, DDM may not be the best model to value newer companies that have fluctuating dividend growth rates or no dividend at all. One can still use the DDM on such companies, but with more and more assumptions, the precision decreases.

The second issue with the DDM is that the output is very sensitive to the inputs. For example, in the Company X example above, if the dividend growth rate is lowered by 10 percent to 4.5 percent, the resulting stock price is $75.24, which is more than 20 percent decrease from the earlier calculated price of$94.50.

The model also fails when companies may have a lower rate of return (r) compared to the dividend growth rate (g). This may happen when a company continues to pay dividends even if it is incurring a loss or relatively lower earnings.

## Using DDM for Investments

All DDM variants, especially the GGM, allow valuing a share exclusive of the current market conditions. It also aids in making direct comparisons among companies, even if they belong to different industrial sectors.

Investors who believe in the underlying principle that the present-day intrinsic value of a stock is a representation of their discounted value of the future dividend payments can use it for identifying overbought or oversold stocks. If the calculated value comes to be higher than the current market price of a share, it indicates a buying opportunity as the stock is trading below its fair value as per DDM.

However, one should note that DDM is another quantitative tool available in the big universe of stock valuation tools. Like any other valuation method used to determine the intrinsic value of a stock, one can use DDM in addition to the several other commonly followed stock valuation methods. Since it requires lots of assumptions and predictions, it may not be the sole best way to base investment decisions.