When an investor buys a stock, he typically expects to receive two types of cash flows:

dividends during the holding period,

expected price at the end of ownership.

To determine expected dividends, assumptions are made regarding expected future earnings growth rates and payout ratios. A stock's required return depends on its risk. Several models for assessing risk and profitability have been developed (CAPM, index models, arbitrage and factor models, etc.).

The dividend discount model (DDM) is a tool for assessing assets (the internal value of a company's shares) in order to identify overvaluation or undervaluation of the latter. ABOUT

The dividend discount model (DDM) is a tool for assessing assets (the internal value of a company's shares) in order to identify overvaluation or undervaluation of the latter.

again all similar models - calculating the present value of future dividend streams. This is a very useful tool as it allows an investor to determine the intrinsic value of a company without taking into account the influence of the current market situation.

All dividend discount models can be divided into two large groups: deterministic and stochastic. The former reflect the traditional approach to present value assessment, according to which it is assumed that the stream of future dividend payments is a well-defined value. The second approach was proposed relatively recently. It treats the future flow of dividends as uncertain. This is an important assumption, since in this case it becomes possible to construct a probability distribution of a random variable of present value, and, consequently, to find the confidence interval that will allow us to determine the significance of the result obtained. This is the main advantage of stochastic dividend models. After all, having received any result, it is difficult to say how much you can trust it, and whether an investor should rely on it in his further actions, assuming that the company’s shares are truly undervalued or vice versa. Thus, these types of models become important for the investment decision-making process.

Deterministic DDMs.

As mentioned above, the basis of all DMAs is the use of the present value method, which implies that the fair price of an asset represents the present value of expected future cash flows (in the case of shares, these are dividend payments that will be made). The basic model looks like

, (4.99)

Where R- theoretical share price;

D t-the expected amount of dividend that will be paid in the period t;

r t- discount rate, which corresponds to the level of risk of investing in shares of a given company.

The basic model considers an endless stream of dividends, making it impossible to calculate the value R. In this regard, it is necessary to make a number of assumptions, in particular, about the finiteness of dividend payments. In this case, the dividend flow is estimated for a finite period of time (say, N years), and a certain estimate of the future share price, which characterizes the reduced dividend flow of the post-forecast period, is discounted. Equation (4.99) then takes on the following form:

where P N is the expected share price at the end of period N, when it is planned to be sold.

With this assumption, it obviously becomes possible to estimate the future dividend stream as a reasonable time horizon is considered. However, the question arises about estimating this future value. Also uncertain is how to account for time-varying discount rates.

The next assumption is the assumption that the discount rate is constant. In this case, the discount rate r it will simply be considered as a certain weighted average of all rates for the period (this approach is very common, for example, calculating the yield of YTM bonds). Any inaccuracies caused by such an assumption are minimal compared to errors that may occur when attempting to estimate all future discount rates. Taking this into account, equation (4.100) will have the following form:

Now, to calculate the present value, it is necessary to predict or determine the following initial parameters:

expected final price (future value) ( P N);

expected dividend flow for N years ( D 1 - D N);

discount rate (r).

The most difficult thing is to estimate the future value. It represents the present value of all future dividend payments. In practice, this value is usually projected based on the company's dividends or earnings, and then adjusted based on profitability requirements, price/earnings ratio and capitalization rate. It is also necessary to keep in mind that P will be negligible and can be neglected in the case when N is very large. As for the discount rate, it is usually determined from the CAPM asset valuation model discussed above.

The next variation of DDM is deterministic constant growth model. This model assumes that dividend growth rates are constant throughout the life of the stock. In turn, this model suggests two more options: an additive growth model (growth in arithmetic progression) and a geometric growth model.

Additive constant growth model:

, (4.102)

Where d- increase in the amount of dividend.

The geometric growth model has the following form:

Where g - expected dividend growth rate, r – cost of attraction equity. Moreover, if N tend to infinity, we get:

(4.104)

This model is also known as the model Gordon. If we express the dividend of the next period in terms of the current one, we get:

(4.105)

Gordon's model is best suited to firms with growth rates equal to or lower than the economy's growth rate and with established dividend payout practices.

However, studies have shown that these models provide inadequate results for cases where dividend growth rates are far from constant, although they may well be applicable when they approach such. The Gordon model is used to evaluate a company in a sustainable growth phase. Dividends and growth rates are maintained indefinitely. Gordon's model also applies to firms with growth rates equal to or lower than the economy's growth rate and with established dividend payout practices. Reputable companies pay stable dividends. In the US, the average payout ratio is 60%. There are three main methods for estimating growth rates:

determining growth rates based on fundamental indicators,

historical growth rates,

assessment by stock analysts.

Methods for estimating historical growth. To assess historical growth, arithmetic and geometric average models, log-linear regression models, time series models (autoregressive moving average model ARIMA- (Autoregressive integrated moving average)), and assessment by analysts are used. Analysts use various types of information about a company. In some cases, their forecasts are better than those based on historical data.

Example 11. Find the price of the stock if the following data are available.

Earnings per share in 2000 equal to 3.13 (EPS).

Dividend payout ratio ( )=69.97% (PR).

Dividends per share are 2.19 ( ).

Return on equity is 11.635 (ROE).

The cost of raising equity capital is determined using the CAPM model. Let in our case it be equal =9%.

Solution. The price according to the Gordon model is
.

Let us find g the expected growth rate.

The share price (or cost of equity) is
.

If shares on the day of analysis were sold at a price of 36.59, then they can be considered undervalued.

Example 12. REITs, established in 1970, are legally allowed to invest in real estate and pass on profits to investors tax-free. In 2000, the fund paid a dividend of 2.12 per share with earnings per share of $22.22. Find the price of a stock if the average beta for real estate investment trusts is 0.69, the risk-free interest rate is 5.4%, and the risk premium is 4%.

Solution. EPS = $22.22; ROE = 12.29%; D0 = $2.12; = 8.16%. Let's find the dividend payout ratio PR = D 0 /EPS = 2.12/22.22 = 0.95. The cost of attracted capital according to CAPM is equal to = 5.4 + 4* 0.69 = 8.16%. The expected growth rate is g = (1- 0.95) * 12.29 = 0.55%.

The share price is
= 2.12*(1+0.55)/(8.16-0.55) = $28.03. If on May 14, 2001, the fund's shares were selling at $36.57, then the shares were significantly overvalued.

To calculate the value of a share using a single-phase model, you need to know

Two-phase model.

In the case of long-term investments, models are used that attempt to take into account the life cycle of a stock. The simplest form of such models is two-phase model, which examines the period of accelerated dividend growth and the phase of stable growth rates. This model assumes that high growth rates can only be observed for a limited period of time, after which the company enters a phase of more stable development. Such a model can be described as follows:

, (4.106)

Where
. The first term of the equation shows, respectively, the size of all dividend payments made during the period of high growth rates, while the second - for the period starting from N+1 to infinity. Exceptional growth rates - and stable growth .

Application of a two-phase model.

The two-phase model is used for firms experiencing a period of rapid growth. For example, a company that has received a patent operates in an industry that is experiencing rapid growth and there are barriers to entry for other firms. Example of Procter&Gamble company. 12 For firms paying dividends as residuals cash flows(remaining after debt repayment, reinvestment).

Model N – two-phase model.

This model assumes that growth rates fall linearly.

Example 13. Two-phase model for P&G. The company faces two problems. Saturation of the US market, where the company receives half of its revenue. Increased competition. But let’s assume that the company will grow over the next 5 years by developing new markets and introducing new products. The company pays high dividends and has not accumulated significant volumes over the past ten years Money. Data for calculations are given below.

Cost of equity = 5,4 + 0,85*4 = 8,8%.

The expected growth can be calculated using one of the models G = KNI *ROE * (1-PR).

CIT is the coefficient of retained earnings, which in this case we take equal to 25% g = (1- 0.4567) * 0.25 = 13.58%. Beta is estimated to rise to 1, the cost of equity is = 5,4 + 4*1 = 9,4%.

Let the company's growth rate be equal to the economy's growth rate of 5%, and the return on equity will drop to 15% lower than the industry's 17.4%.

KNI = g/ROE = 5/15 = 33.33%. The dividend payout ratio is 1 - 0.3333 = 0.6666.

(4.107).

The first part of the formula is the present value of dividends, which is equal to

7,81$.

The second part is the present value of dividends in the second phase

59,18$

The share price is P= 7.81+59.18 = $66.99.

It is stated that at the time of the analysis on 05/14/2000, P&G shares were selling at a price of $63.90, therefore the shares are being sold at a discount.

Three-phase model.

A more complex variation of this model is three-phase model, within which the so-called transition phase is also considered. It proceeds from the fact that the company’s development is more progressive than abrupt, and therefore a transition period can also be distinguished between the phases of high and stable growth rates. The model in this case looks like:

Rice. 4.16. Three-phase model.

,

Depending on the company, the duration of these stages will naturally vary. Thus, young, rapidly developing companies will be characterized by a longer growth phase compared to mature companies. Interestingly, according to available data, on average, the growth and transition phases account for up to 25% of expected income, while the maturity stage accounts for up to 50%. However, this also depends on the company's policy. Thus, a company with high growth rates and low dividend payments transfers its relative contribution to the maturity stage, while companies with the opposite situation transfer their relative contribution to the growth and transition phases.

This model is also known as the E-model (E-earnings-income). The three-phase growth model is widely used by investors because it allows them to obtain quite adequate results. For example, it is used by Salomon Brothers.

Stochastic dividend discount models

Stochastic dividend discount models assume that the stream of future dividend payments is subject to a stochastic process, from which the present value is derived. In this case, processes with the characteristics of Markov motion are considered, which are well suited for temporary payments such as dividends. For the assessment process, the general history is not important - only the current value of the dividend and the probabilistic path of further development of this uncertain process are important. Markov's movement is precisely characterized by the fact that it does not take into account the previous history. These models are divided into two types: binomial (assuming two outcomes) and trinomial (respectively –3 possible outcomes).

Binomial models assume that dividend payments will either remain at the same level or change (in this case, a change in one direction is considered - usually an increase, but neither at once). In turn, they are divided into additive and geometric growth models.

The additive stochastic growth model has the following form:

with probability will increase

with probability
Will not change

Where: d– increase in dividends in cash;

p– the probability that the dividend will increase

(4.109)

It should be noted that this model is also indispensable for a situation where the rate of dividend growth is not constant.

It should be borne in mind that there is always the possibility of a company going bankrupt. Taking this into account, we can calculate a certain lower price level:

with probability R

D t +1 = with probability

0 with probability

where p B is the probability of bankruptcy.

(4.110)

The geometric model looks like this:

D t (1+ g) with probability R

D t +1 = D t with probability (1-r)

(4.111)

It is very important that, unlike all previous models, this model can be more or less successfully used in a situation of variable dividend growth rates. Here you can also determine a lower price level taking into account the likelihood of bankruptcy of the company:

(4.112)

Finally, consider the trinomial stochastic model, which is also known as the generalized Markov growth model. It is quite natural for companies to cut their dividend payments from time to time. This model allows us to take into account such a development of the situation. It thus assumes three possible outcomes: dividends rise, fall, or remain unchanged.

There are also two possible growth options here: in arithmetic and in geometric progressions.

The additive version of this model has the following form:

Dt + d with probability R U

D t +1 = D t - d with probability R D

D t with probability (1-r U -R D )

where: p U is the probability that the dividend will increase; R D - the likelihood of a dividend drop.

(4.113)

It is quite obvious that if the probability of a reduction in dividend payments is zero, then the model is automatically transformed into an equation characterizing the corresponding binomial model.

Taking into account the probability of bankruptcy, we have:

Consider the geometric model:

Dt (1+ g) with probability R U

D t +1 = D t (1- g) with probability R D

D t with probability ( 1st U -R D )

(4.115)

And also taking into account the possible bankruptcy of the company:

(4.116)

According to the conducted “tests” of these models, trinomial models give more correct estimation results compared to binomial ones. As for the choice between using additive or geometric models, no advantages were observed here - both types are equal, since for some companies more adequate results were obtained using the former, while for others geometric models were more suitable.

The main advantage of stochastic DDMs is the ability to construct the distribution of the value P, since it is a random variable. This makes it possible to assess how significant the result obtained by applying the DDM is. However, it is very difficult to determine the type of distribution of this present value, and even more so, its parameters (variance, etc.). Typically, a Monte Carlo simulation method is used to generate this distribution and estimates of its parameters. Sometimes, however, they start from the assumption that the distribution is normal. In this case, it seems possible to calculate the main characteristics of the distribution. The results are sometimes quite satisfactory and coincide with those obtained using the Monte Carlo method, however, such an assumption is not justified, so the best option is to use the above method.

Despite the fact that the use of stochastic models has not yet received sufficient application in practice, they provide more satisfactory results, and also allow us to draw a conclusion about the statistical significance of the models

The general disadvantage of DDM is, first of all, the problem of assessing the initial (necessary for calculation) data - how to more accurately determine, for example, the final price? The question remains open. Secondly, you need to understand that DMMs only talk about the relative value of a stock, but do not provide any information about when you can expect the market price of a stock to begin to move towards its theoretical/intrinsic value. This means that you can buy shares of a certain company, deciding on the basis of the analysis that they are undervalued, and wait a very uncertain period of time before they enter the price. But this is another question, more related to the investment strategy.

In general, DDMs are a very popular tool among investors because, being impartial to market influences, they allow one to obtain fairly reliable estimates of the company’s intrinsic value. However, even more reliable results can be obtained if they are used along with, for example, factor models.

Criticism of the model. The model provides too conservative a cost estimate. The model does not include other ways of returning money to shareholders. But this can be done in a modified version of the model.

Tests of the discounting model. The test of the model lies in its ability to predict overvalued and undervalued stocks. The results of the study show that the model produces excess returns in the long run.

Gordon's model. Gordon Growth Model)- the simplest model for estimating the value of a share - is to discount dividends paid to shareholders. The model is based on the following assumptions:

Stable business: the assumption is that the company has a stable business model and the company is not expected to significantly change its operations in the long term.

Sustained Growth: We can assume that the issuer's dividend (or FCFE) will grow at a constant, sustainable growth rate year after year.

Stable leverage (financial leverage): changes in the proportion of debt financing compared to equity can affect the cost of capitalCost of Equity. Stable business + Stable financial leverage => the cost of equity is constant.

Dividends and FCFE: The entire firm is paid in the form of dividends.

Formula and example

Three components are included in the Gordon model formula:

(1) D1 = expected annual dividend per share for next year

(2) K= required rate of return orCost of Equity

(3) g = expected stable long-term dividend growth rate

With these variables, the stock price can be calculated as:

D1/(K–g)

To illustrate the applicationGGM, take a look at the following example: Company A's shares are trading at$ 250. In addition, for company A the cost of equity is 8%. Next year, Company A will pay a dividend of $10 per share, and the dividend is expected to grow at 5% per year. Thus, the share price is calculated as:

Share price =$10 / (0,08 – 0,05)

Share price =$ 333,33

This result shows that Company A's stock is undervalued since the model assumes that the fair price of the stock is$ 333 .

Advantages

Gordon's model is applicable to stable companies with stable high cash flow and limited business expenses.

- GGMsimple, and the source data can be found in financial statements issuer.

The model does not take into account market conditions, so it can be used to evaluate or compare companies of different sizes and different industries.

The model is widely used in the real estate sector, where rental cash flows are well known

Disadvantages and Limitations

The assumption of stable dividend growth is the main limitation of the model. Companies find it difficult to maintain consistent dividend growth due to various market conditions, changes in business cycles, financial difficulties.

If the required rate of return is less than the growth rate, the model may result in a negative value, so the model is ineffective in such cases.

The model does not take into account market conditions or other factors such as the size of the Company, the value of the Company's brand, market perception, local and geopolitical factors. All these factors influence the actual price of a stock and hence the model does not provide a holistic picture.

GGM cannot be used for companies that have irregular cash flows, unstable dividend payments or changing debt ratios.

The model cannot be used for companies at the development stage without a long history of dividend payments.

Conclusion

Gordon's model, although simple to understand, is based on a number of critical assumptions and therefore has limitations. However, the model can be used for stable companies with a history of dividend payments and predictable future growth.

Calculation of terminal value in the modelDCFcan also be done usingGGM, but instead of dividends - free cash flow, and insteadcost of equitynessesary to use .

Constant growth model ( Dividend Discount Model, DDM) is a model in which it is assumed that dividends will grow from period to period in the same proportion, i.e. with the same growth rate. This model is widely used under the name ( Gordon Growth Model).

The model is named after M.J. Gordon, who originally published it in a study with Eli Shapiro: Capital Equipment Analysis: The Required Rate of Profit, Management Science, 3(1) (October 1956) .

As we know, the discounting formula assumes that the present value of a share PV (determining its price at the initial point in time) can be represented as:

To simplify the calculations, M.J. Gordon suggested: since the validity of the stock is theoretically unlimited, we assume that the stream of cash payments represents an endless stream of dividends (there will be no liquidation amount, since the stock exists indefinitely). In addition, Gordon proposed to consider all values ​​of the growth rate of annual payments (g) to be the same, that is, dividends increase annually by (1 + g) times, and the value (g) does not change indefinitely. Taking this assumption into account, the formula will take the form:

Thus, the calculation of cost in accordance with the Gordon model is carried out according to the formula:

In addition to the above simplifications, Gordon's model assumes that:

Magnitude k there should always be more g, otherwise the stock price becomes uncertain. This requirement is quite logical, since the rate of dividend growth g may at some point exceed the required rate of return of the stock k. However, this will not happen if we assume the chosen discount period is infinite, because in this case dividends would constantly increase at a higher rate than the rate of return of the stock, which is impossible.

The company must pay dividends regularly, otherwise the Gordon model is not applicable. Moreover, the requirement of invariance of the value g means that the company always allocates the same share of its income to pay dividends.

Requirement of invariance of quantities k And g limits the capital structure of the enterprise to infinity: it is believed that the only source of financing for the company is its own funds, and there are no external sources. New capital enters the company only through the retained share of income; the higher the share of dividends in the enterprise's income, the lower the level of capital renewal.

Application of the Gordon model in business valuation

When assessing a business, when forecasting income, due to the fact that free cash flow cannot be predicted more than several years in advance, provisions have been introduced on the nature of changes in these cash flows - an assessment of the residual (terminal) value is assumed

business as of the end date of the explicitly stated forecast period.

According to the Gordon model, annual income of the post-forecast period is capitalized into a value indicator using a capitalization factor calculated as the difference between the discount rate and long-term growth rates (the Gordon model is used within the framework of the income approach).

In the absence of growth rates, the capitalization rate will be equal to the discount rate.

The final cost is calculated in accordance with the model under consideration using the following formula:

The relative size of the terminal value increases as the duration of the forecast period decreases and becomes a significant value as the forecast horizon moves away. Depending on the discount rate for forecasts beyond 10 years, the terminal cost becomes a much less significant element.

The essence of the Gordon model is as follows: The value of the company at the beginning of the first year of the post-forecast period is equal to the amount of capitalized income of the post-forecast period (i.e. the sum of the values ​​of all annual future income in the post-forecast period).

If the rate of profit growth is too high, the Gordon model cannot be used, since such indicators are possible with significant additional investments, which this formula does not take into account.

In A. Gregory's practical guide, this model, being modified to calculate capital, takes the following form:

To find the current value of an enterprise, this terminal value must be discounted by the average WACC and added to the current value of all free cash flow indicators for a specific forecast period.

When using this formula, it is important to understand how reasonable assumptions are made about g, the long-term (to infinity) growth rate.

Gordon's model can use historical, current or projected earnings, and often the latter is calculated by multiplying the last period's earnings by the expected long-term growth rate, in which case the formula becomes:

Limitations when using the Gordon model:

• the company's income growth rate must be stable;
• the rate of income growth cannot be higher than the discount rate;
• capital investments in the post-forecast period should be equal to depreciation charges (for the case when cash flow acts as income).

Literature:

1. Astrakhantseva I.A. Accounting and analysis: Textbook / Federal State Budgetary Educational Institution of Higher Professional Education “Ivanovo State Energy University named after V.I. Lenin. - Ivanovo, 2014. - 344 p.
2. Asaul A.N. Basics of business in the market valuable papers: textbook / A.N. Asaul, N.A. Asaul, R.A. Faltinsky; edited by Doctor of Economics Sciences, Professor A.N. Asaula. - St. Petersburg: ANO "IPEV", 2008. - 207 p.
3. Gregory A. Strategic assessment of companies ( Practical guide) - M.: Kvinto-Consulting, 2003. - 224 p.
4. Palace N.N. Estimation of enterprise (business) value: Educational and methodological manual. - M.: MARTIT, 2008. - 136 p.
5. Kallaur N.A. Dividends of the organization // Economic and legal bulletin. 2008. No. 12. - 160 s.

Gordon model is a method of calculating the intrinsic value of a stock excluding current market conditions. The model is a valuation technique designed to determine the value of a stock based on the dividends paid to shareholders and the growth rate of those dividends. It is also called the Gordon growth model, the dividend discount model (DDM), and the constant growth rate model. .

The model was named after Professor Myron J. Gordon in the 1960s, but Gordon was not the only financial scientist to popularize the model. In the 1930s, Robert F. Wise and John Burr Williams also did significant work in this area.

There are two main forms of the model: stable model And multi-stage growth model.

Stable model

Share price = D 1 / (k - g)

D 1 = expected annual dividend per share next year

g = expected dividend growth rate (note - this is assumed to be constant)

Those. This formula allows you to calculate the future value of a share through the dividend, but provided that the growth rate of the dividend is the same.

Multi-stage growth model

If dividends are not expected to grow at a constant rate, an investor should evaluate each year's dividends separately, including the expected rate of dividend growth for each year. However, the multi-stage growth model assumes that dividend growth eventually becomes permanent. Below is an example.

Examples

Stable (stable) Gordon model

Let's say XYZ Company intends to pay a dividend of $1 per share next year, and you expect it to increase by 5% per year thereafter. Let's also assume that the required rate of return on XYZ Company stock is 10%. XYZ Company's stock is currently trading at $10 per share. That is, once again:

Planned dividend of $1 per share

The dividend will grow by 5% per year

Profit rate 10%

The stock price is currently $10.

Now, using the formula above, we can calculate that the intrinsic value per share of XYZ Company stock is:

$1.00 / (0.10 - 0.05) = $20

Thus, according to the model, XYZ Company's stock is worth $20 per share but is trading at $10; Gordon's growth model suggests the stock is undervalued.

The stable model assumes that dividends grow at a constant rate. This is not always a realistic assumption, because things do change in companies, today they are doing great and paying good dividends, and tomorrow they are not paying them at all. Therefore, this method, with a stable model, when the dividend is the same every year, still gives way to a multi-stage growth model.

Gordon's multi-stage growth model

Let's assume that XYZ Company's dividends will increase rapidly over the next few years and then increase at a steady rate thereafter. Next year's dividend is expected to still be $1 per share, but the dividend will increase annually by 7%, then 10%, then 12%, and then increase by 5% continuously. Using elements of the robust model, but looking at each year separately, we can calculate the current fair value of XYZ Company's shares.

Initial data:

g1 (dividend growth rate, year 1) = 7%

g2 (dividend growth rate, year 2) = 10%

g3 (dividend growth rate, year 3) = 12%

gn (dividend growth rate in subsequent years) = 5%

Since we have estimated the dividend growth rate, we can calculate the actual dividends for these years:

D2 = $1.00 * 1.07 = $1.07

D3 = $1.07 * 1.10 = $1.18

D4 = $1.18 * 1.12 = $1.32

We then calculate the present value of each dividend over the unusual growth period:

$1.00 / (1.10) = $0.91

$1.07 / (1.10) 2 = $0.88

$1.18 / (1.10) 3 = $0.89

$1.32 / (1.10) 4 = $0.90

We then estimate dividends arising during a period of stable growth, starting with the fifth year dividend calculation:

D5 = $1.32 * (1.05) = $1.39

We then apply the Gordon steady growth model formula to these dividends to determine their value in the fifth year:

$1.39 / (0.10-0.05) = $27.80

The present value of these dividends over a period of stable growth is calculated as follows:

$27.80 / (1.10) 5 = $17.26

Finally, we can add the present value of XYZ Company's future dividends to get the current intrinsic value of XYZ Company shares:

$0.91 + $0.88 + $0.89 + $0.90 + $17.26 = $20.84

The multi-stage growth model also indicates that XYZ Company's stock is undervalued ($20.84 intrinsic value vs. $10.00 trading price).

Analysts often include an estimated price and sale date in these calculations if they know they won't hold the stock indefinitely. Also, coupon payments can be used instead of dividends when analyzing bonds.

Conclusion

The Gordon Growth Model allows investors to calculate the value of a stock without taking into account current market conditions. This exclusion allows investors to compare companies across different industries, and for this reason the Gordon model is one of the most widely used stock analysis and valuation tools. However, some are skeptical about it.

Mathematically, two things are necessary to make Gordon's model effective. First, the company must pay dividends. Second, the dividend growth rate (g) cannot exceed the investor's required rate of return (k). If g is greater than k, the result will be negative and stocks cannot have negative values.

The Gordon model, especially the multi-stage growth model, often requires users to make several unrealistic and complex estimates of the dividend growth rate (g). It is important to understand that the model is sensitive to changes in g and k, and many analysts perform sensitivity analyzes to evaluate how different assumptions change the estimate. According to Gordon's model, a stock becomes more valuable when its dividend increases, the investor's required rate of return decreases, or the expected rate of dividend growth increases. The Gordon growth model also assumes that the share price rises at the same rate as the dividend.

The Gordon model is used to estimate the value of a business and other investment objects. The author of the model is economist M. J. Gordon. The essence of the Gordon model is defined as follows: “The value of an investment object at the beginning of the post-forecast period will be equal to the sum of the current values ​​of all future values ​​of annual cash flows in the post-forecast period.” Thus, annual income is capitalized, forming the value of the business. A is calculated as the difference between the discount rate and long-term growth rates.

You can download an example of how Gordon's formula works in Excel.

Gordon proposed a simplified equation:

FV = CF(n+1) / (DR - t)

To calculate the formula, the following indicators are taken:

• FV is the value of the object in the post-forecast period;
• CF(n+1) – income flow at the beginning of the post-forecast period;
• DR – discount rate;
• t is the long-term growth rate of the income stream in the residual period.

The peculiarity of the Gordon model determines the business valuation

The peculiarity is that, if certain conditions are met, the equation becomes equivalent to the general flow discounting equation monetary units. To determine the current value of equity capital (FV), the business needs to divide the expected cash flows for a certain period (CF(n+1)) by the difference between the discount rate (DR) and the growth rate (t). Gordon needed to find a solution for calculating dividends, which is why it was originally called the “dividend model.” This equation is generalized. The difference DR – t is also interpreted as the capitalization rate. For example, the result of dividing 1/(DR – t) is considered a multiplier (in other words, a coefficient) to income. Accordingly, it is quite rational to consider the Gordon model to be compatible with the general assessment model. Business valuation according to this model is determined by multiplying income by a coefficient. In this way, by turning to the method of calculation using the Gordon formula, you can analyze information about the stock or the business as a whole. Sometimes in the literature the term GROWTH model appears (this is practically a synonym). Its forecast calculations are useful and are actively used both in business management and in its purchase/sale.

Myron Gordon created the discounted cash flow model

The Gordon model is used to provide difficult-to-decide valuations, for tax planning, and for valuing shares with uniform dividend growth by stock market. This model can be effectively applied:

• if there is a volume of the sales market;
• stable supplies of raw materials and material resources for production are traced;
• there is durability of the technologies and equipment used, a guarantee of innovative upgrades;
• financial resources are available for the development of the enterprise;
• the economic situation is stable.

Myron J. Gordon developed such a model back in 1959. However, for the above-mentioned model, there are alternatives in the general context of discounted cash flows (DCF). It should be borne in mind that dividends can only be paid according to the results of the enterprise’s economic activities. To do this, it is extremely important to have sufficiently reliable data to predict expected dividend payments. Forecasting dividends is an extremely difficult task, since there are various business risks (even if the company has received a high rating for business stability). Special techniques have been developed that make it possible to approximate future dividend payments with the greatest possible accuracy. Only with such an assessment will the formula be rationally applicable. It is in the Gordon model that assumptions about a stable growth rate of dividend payments are used. This model is a variation of dividend discount models and is also a way to determine stock prices or value a business as a whole. For example, over-the-counter companies. By the way, this particular segment is almost impossible to evaluate using other methods.

The Gordon model calculates the cash flow growth forecast

When the forecast period expires, it is assumed that the rate of increase in sales and profits will be stable, and the depreciation rate is equal to the rate of capital investment. This cost will be determined with the obligatory indication of the discount rate as a percentage, the rate of increase money turnover in the percentage ratio for the annual time period. It is important to remember that the value indicator at the end of the forecasted period using the Gordon formula is determined only at the end of the forecast period. But if we are talking about the first year in the post-forecast period, then these data are compiled separately with the obligatory influence of the growth of flows financial resources. The same discount rate is used.

A proposal is a model of reality that is presented to us during the presentation process.