Dividend Discount Model (DDM) Formula, Variations, Examples, and Shortcomings

Dividend Discount Model

Investopedia / Zoe Hansen

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.


Dividend Discount Model

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
  2. Take your $100 after a year

Most individuals will opt for the first choice. Taking the money now will allow you to deposit it in a bank. If the bank pays a nominal interest, say 5%, then after a year, your money will grow to $105. It will be better than the second option where you get $100 from your friend after a year. Mathematically,

Future   Value = Present   Value   ( 1 + interest   rate % ) ( for   one   year ) \begin{aligned}&\textbf{Future Value}\\&\qquad\mathbf{=}\textbf{Present Value }\mathbf{^*(1+}\textbf{interest rate}\mathbf{\%)}\\&\hspace{2.65in}(\textit{for one year})\end{aligned} Future Value=Present Value (1+interest rate%)(for one year)

The above example indicates the time value of money, which can be summarized as “Money’s value is dependent on time.” Looking at it another way, if you know the future value of an asset or a receivable, you can calculate its present worth by using the same interest rate model.

Rearranging the equation,

Present   Value = Future   Value ( 1 + interest   rate % ) \begin{aligned}&\textbf{Present Value}=\frac{\textbf{Future Value}}{\mathbf{(1+\textbf{interest rate}\%)}}\end{aligned} Present Value=(1+interest rate%)Future Value

In essence, given any two factors, the third one can be computed.

The dividend discount model uses this principle. It takes the expected value of the cash flows a company will generate in the future and calculates its net present value (NPV) drawn from the concept of the time value of money (TVM). Essentially, the DDM is built on taking the sum of all future dividends expected to be paid by the company and calculating its present value using a net interest rate factor (also called discount rate).

Expected Dividends

Estimating the future dividends of a company can be a complex task. Analysts and investors may make certain assumptions, or try to identify trends based on past dividend payment history to estimate future dividends.

One can assume that the company has a fixed growth rate of dividends until perpetuity, which refers to a constant stream of identical cash flows for an infinite amount of time with no end date. For example, if a company has paid a dividend of $1 per share this year and is expected to maintain a 5% growth rate for dividend payment, the next year’s dividend is expected to be $1.05.

Alternatively, if one spot a certain trend—like a company making dividend payments of $2.00, $2.50, $3.00 and $3.50 over the last four years—then an assumption can be made about this year’s payment being $4.00. Such an expected dividend is mathematically represented by (D).

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,

Value   of   Stock = EDPS ( CCE DGR ) where: E D P S = expected dividend per share C C E = cost of capital equity D G R = dividend growth rate \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} Value of Stock=(CCEDGR)EDPSwhere:EDPS=expected dividend per shareCCE=cost of capital equityDGR=dividend growth rate

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 their growth rate, are key inputs to the formula, the DDM is believed to be applicable only to 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:

D = the estimated value of next year’s dividend r = the company’s cost of capital equity g = the constant growth rate for dividends, in perpetuity \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} D=the estimated value of next year’s dividendr=the company’s cost of capital equityg=the constant growth rate for dividends, in perpetuity

Using these variables, the equation for the GGM is:

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

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% 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%. 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% to 4.5%, the resulting stock price is $75.24, which is more than a 20% 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.

Article Sources
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  4. The International Financial Reporting Standards Foundation. “Illustrative Examples to Accompany IFRS 13 Fair Value Measurement: Unquoted Equity Instruments Within the Scope of IFRS 9 Financial Instruments.” Page 39.

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  8. Walmart. "Dividend History."

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