Dividend Discount Model Formula | Example and Calculation

Dividend discount model is used to calculate the growth rate of stock. Generally there is infinite life of stock. If there is a known growth rate of the dividends of the stock each year, it is evaluated as growing perpetuity. It is not possible to apply standard value tables on a growing perpetuity. But a mathematical identity makes it possible to find the present value of the perpetuity. Such mathematical identity is referred to as Dividend Discount Model (DDM). Dividend discount model is named as Gordon’s Growth Model and is given by the following formula

Dividend Discount Model Formula

P_o =   D_o (I + g)    =       D₁

            k – g                 k – g       

In the above equation “g” is the expected dividend growth rate, D_o is the current dividend, D₁ is the Dividend that will be paid next year. “k” is the discount factor which represents the riskiness of the stock. It is important assumption of the above model there is perpetual dividend stream along with the constant growth rate.

In certain situation, the riskiness of the particular stock according to the market at any moment can also be ascertained through Dividend Discount Model. In the above mentioned equation the current stock price and the current dividend can be observed. It is possible to estimate the dividend growth rate. But the discount rate “k” cannot be observed. The value of “k” can find out if other variables of the equation are known. The “k” is also referred to as shareholder’s required rate of return, which is given by

k = D_o (I + g) + g 

            P_o                  

“k” is in fact the sum of two components which are the expected growth rate on stock & the expected dividend yield. The “g” specifies the forecasted capital appreciation in the price of stock if the dividend yield is constant.

The Significance of Hitting the Earnings Estimate

The significance of hitting the Wall Street’s earnings estimates is clear to the corporate CFOs. The analysts base their estimates on sound information provided by the company because of their frequent contact with the company which enables them to understand the operations of the company. When the earnings report is disappointing, the market mostly penalizes the stock of the company substantially. This is correct when the estimated growth rate & required rate of return re high.

Example:

Suppose dividend payout ratio of certain company is 50%, and $1.10 is the expectation of analysts about the earnings in the next year. The dividend growth rate is 15% by consensus median and $27.5 is the current stock price. The shareholder’s required rate of return is given by the following formula of Dividend Discount Model

 r = D₁ + g 

       P_o  

r = 0.5 ($1.10) + 0.15

       $27.50     

r = 17%

This example is extended further for the stock price of the stock. Suppose $0.29 is the expected earnings in the upcoming quarter but the company reports only $0.27. This shows that the actual earnings were below expectations as indicated by the figures. As a result the estimate of future growth is reduced by the analysts so that discount rate can be boosted. The investors adjust the required rate of return to 18% and growth rate to 13%. The anticipated earnings per share will be $1.08 if the future estimates for the year remain on track. Now the stock price is ascertained by the following formula of DDM.

P_o = D₁

       k – g    

P_o = 0.5($1.80)   

        0.18 – 0.13   

P_o = $10.80

These results shows that why whisper number is significant. It is further indicated that CFOs do not prefer to provide incomplete information to the analysts who follow their firms.

The Multistage Dividend Discount Model

Usually small companies show high levels of growth whose persistence cannot be expected. In such situation, two growths should be used. Suppose the current dividend paid by a company is $1 which is expected to increase 20% for the next two years and thereafter increase by 5% annually. The growth rate that is expected to continue is referred as customable growth rate. In order to ascertain the price P_o paid by investor if the required rate of return is 17%, following formula of multistage Dividend Discount Model is used

P_o =   D₁     +     D₂       D₂(1.g) / (k – g)

       (1 + k)    (1 + k)²           (1 + k)²

Because the formula for the growing perpetuity is based on the dividend of next year so the term for the dividend in year three is discounted only twice. In other words the numerator of the equation is discounted only twice instead of three times.

Caveats about Dividend Discount Model

In security analysis, Dividend Discount Model is useful tool. However the future cannot be predicted by this method. In fact DDM assists the analyst to make a good decision rather than making decision by itself. There are certain shortcomings of DDM that should be considered.

The first short coming is that the equation of DDM cannot be used if the dividend growth rate is equal or greater required rate of return. The results are greatly affected by the minor differences in the selected growth rate. The second shortcoming is the assumption of constant dividend yield. The apparent growth rate is affected by the change in the dividend policy. Different values are generated from the model if there is a change in the growth rate. The last drawback of model is that it long term ROE is implicitly assumed to be constant. It is required by the model that the growth for every year should be identical. Rather long term growth rate is required to be constant.