what is the dividend discount model ddm 
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 investopedia zoe hansenunderstanding the ddma 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 originate 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 moneyimagine you gave 100 to your friend as an interest free loan after some time you go to them to collect your loaned money your friend gives you two options 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 1essentially 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 dividendsestimating 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 2alternatively if one spots 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 factorshareholders 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 their 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 3this 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 their shares the required rate of return can vary due to investor discretion 4companies 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 formulabased 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 cce dgr edps where edps expected dividend per sharecce cost of capital equitydgr dividend growth rate since the variables used in the formula include the dividend per share and the net discount rate represented by the required rate of return or cost of equity and the expected rate of dividend growth the value 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 that do not pay dividends by making assumptions about what dividend they would have paid otherwise 5ddm variationsthe 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 6this 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 r gd 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 ddmassume 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 of 2 08 2 12 2 16 2 20 and 2 24 between 2019 and 2024 in chronological order 7one can see a pattern of a consistent increase of 4 cents in walmart s dividend each year which equals an average growth of about 2 assume an investor has a required rate of return of 5 using an estimated dividend of 2 28 at the beginning of 2024 the investor would use the dividend discount model to calculate a per share value of 2 28 05 02 76 shortcomings of the ddmwhile the ggm method of the 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 dividends 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 5using the ddm for investmentsall 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 8investors who believe in the underlying principle that the present day intrinsic value of a stock is a representation of their discounted value of 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 the ddm however one should note that the 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 the 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 