Of the existing methods for assessing the value of a company in the terminal year, appraisers most often use the Gordon method, which is essentially similar to the approach based on income capitalization:
GV - value in the post-forecast period - at the end of the last year of the forecast period,
Cash flow of the first year of the post-forecast period,
Discount rate for the first year of the post-forecast period,
g - long-term growth rates of cash flow in the post-forecast period.
A feature of the methods of capitalization and discounting of cash flows is that, as a rule, only one of the methods is used, which is due to the conditions for applying these approaches to valuation.
However, this does not exclude the possibility of calculating the value of the company by two methods simultaneously.
The main prerequisites for using the direct capitalization method are as follows:
The amount of current income is stable, predictable, or changes at a constant growth rate, i.e. in the near future, income from the facility will remain at a level close to the current one;
Current activity companies can give some idea about its future activities.
The method based on discounted cash flows is more appropriate when a significant change in future income compared to current is expected, i.e. when the company's operations are expected to differ materially from its current or past performance.
Special attention it is necessary to pay to companies whose functioning will decline in the future (negative growth rate) or whose economic life will cease in the short term (bankruptcy is highly likely).
V this case the use of both methods may be questionable.
It should be noted that the approach based on discounting future cash flows relies on events that are only expected. Therefore, the value obtained using this approach directly depends on the accuracy of the forecast of the appraiser, analyst.
This approach should not be used when there is not enough data to form a reasonable forecast of net cash flow for a sufficiently long period in the future.
However, even using rough projections, a discounted approach to future earnings streams can be useful in determining a company's estimated value.
Among other things, it is necessary to take into account the stage life cycle companies and industries, and the type of company being valued.
It is obvious that the application of the capitalization method at the time of the company's active growth is unlikely to give an adequate value result.
Examples are telecommunications companies, high-tech businesses involved in the development of robotics, innovative products, companies in the process of restructuring, etc.
In addition, when capitalizing income, it is necessary to understand that for all subsequent periods, not only the amount of the company's income is transmitted, but also the structure of its capital, the rate of return, and the level of risk of the company.
Thus, in order to choose a method for calculating the cost, it is necessary to understand how income or income will change. cash flows companies in the near future, analyze not only financial condition of the company being valued and its development prospects, but also the macroeconomic situation in the world, country, industry to which the company belongs, as well as in related industries.
The purpose of the assessment itself and the intended use of its results play an important role in the choice of assessment method.
For example, in the case when it is required to determine the market value of a business as soon as possible using the methods income approach or to confirm the results obtained by methods within the framework of a comparative or cost approach, the capitalization method is optimal, since it will allow you to quickly get a relatively reliable result.
Also, the capitalization method is justified in the preparation of analytical materials when deep immersion in the company's financial flows is not required or it is not possible.
An almost ideal case for using the capitalization method is the rental business.
In all other cases, especially when the income approach is the only one in which the cost is calculated, in our opinion, the discounted cash flow method is more preferable.
The Gordon model is commonly used to calculate the reversion cost (terminal value) when using the discounted cash flow method (DCF) to determine the value of non-depreciating assets. At its core, the Gordon model formula is the sum of an infinite discounted income stream. The calculated dependence has the following form:
Сrev – cost of reversion;
CHOD - net operating income;
Y - discount rate;
g is the rate of change in NOR;
m is the number of the initial period;
Abbreviation for the formula of the Gordon model.
For depreciable assets, such as real estate, the cost of reversal is usually determined by other methods. As one of the calculation options, the method of direct capitalization of the NPV of the first year of the post-forecast period is used. The method of direct capitalization (PC) is also used as an independent method for determining the value of real estate.
However, unlike the DCF method, the PC method describes a different model of property ownership. This method assumes that the investor, investing in real estate, owns this object until the end of its life and at the same time accumulates funds for subsequent acquisition, after complete depreciation, similar object real estate. That is, thereby deliberately reduces the amount of incoming income by the rate of return of capital. The dependence for the PC method has the following form:
Co - the value of the property;
R is the capitalization ratio;
f- rate of return of capital;
index 0 - corresponds to the date of assessment;
index 1 corresponds to the first forecast period.
Since the PC and DCF methods reflect somewhat different patterns of investor behavior, it is not surprising that, given certain initial data, they can give different results.
In order to demonstrate the correctness of the above descriptive model of the PC method, we transform dependence (2) into the following form:
Thus, we have received the classical formula for calculating the return on invested capital. For example, for the case of lending - the ratio of annual interest payments on the loan to the amount of the loan.
Since the rate of return of capital is calculated taking into account the term of the remaining economic life object (term of capital ownership), then it follows that the PC method is built on a model that assumes that the investor, after investing capital in an asset, will own it until the end of its economic life, which confirms the above.
To be fair, the DCF method for a non-depreciating asset that uses the Gordon model (since no return of capital is required) can also be viewed as a model that assumes perpetual ownership of the asset.
Dependence (3) can be written in the following form:
If NOR = const (g = 0), the first term in dependence (4) corresponds to the formula of the Gordon model in the absence of a change in NOR. Therefore, substituting formula (1) into (4) and transforming the resulting dependence, we obtain:
Dependence analysis (5) points to an unexpected, at first glance, result: a depreciable asset (having a finite life) generates an endless stream of income. This can be explained as follows. Since the PC method assumes the return of capital at the end of the life of the asset, in order to acquire a similar asset, then in fact the model described by the PC method assumes the infinite ownership of a periodically updated asset with a limited life.
If FOD is const (g 0), then depending on (5) one should use
Yo is the discount rate for the DCF method.
Transforming dependence (5) for this case, we obtain:
The analysis of dependence (6) allows us to conclude that the PC and DCF methods, in the general case, not only reflect different models of investor behavior, but are also characterized by different rates of return, which is quite logical, since different dates Ownership of an object involves different risks.
However, the fact that the rate of return for the PC method with a growing NOR is less than the discount rate for the DCF method, at first glance, does not seem entirely logical, since usually, the longer the asset holding period (asset life), the higher, in general, default risk. This explains, for example, that stock market The later the maturity of a bond, the higher its yield. However, in the case of a depreciating asset, the opposite effect seems to be observed in that over time, as the recovery fund accumulates and the value of the asset decreases, the amount of losses in case of default decreases. Therefore, the integral value of default risk is lower in this case.
In fact, the idea that when using the PC method, it is necessary to take into account the growth rate of NOR not only in the numerator, but in the denominator, was expressed, for example, in . However, the absence of an explicit formula has led to the fact that in practice this moment is usually not taken into account in the calculations. Apparently, in connection with this, the results of calculation by the PC and DCF methods with the same initial data, in the case of non-constant NOR and the same rates of return, differed, sometimes very significantly, from each other. Moreover, the result of the PC method, with increasing NOR, was always lower than the result of the DDP method. Accounting for the growth rate of NOR in the denominator makes it possible to reduce this discrepancy in the calculation results. But the difference in the results may remain, due to the initial differences in the models. Dependence (6) can also be recommended for use in the capitalization of the NOR of the post-forecast period in case of applying the DCF method.
Chapter 2. Evaluation market value JSC "Kalugapribor" (JSC "Kalugapribor")
The Gordon model is another stock valuation model based on the assumption that cash flows will grow forever at a constant growth rate. It is simpler in terms of calculations compared to, but is also based on the principle, that is, that fair value shares is equal to the value of future cash flows, reduced to the current moment.
Another name for this model is the Gordon growth model. It is so named because it assumes that future cash flows will grow forever at the same rate of growth, and the required rate of return will not change. Therefore, the Gordon model is best suited for valuing stocks that have stable cash flow growth rates.
For example, you have found a stock that has been paying dividends for a very long time and consistently, and that they grow by about 5% year on year. Per Last year dividends amounted to 5 rubles, which means that next year they will be 5 * 1.05 \u003d 5.25, in the second year 5.25 * 1.05 \u003d 5.5125 and so on. If you want a 12% return on your investment, then use this interest rate as your discount rate.
As you can see on the graph, dividends tend to an infinitely large value (blue bars), their discounted value, on the contrary, decreases (orange bars), and their amount tends to some finite value (the red line reaches a plateau).
To make it clearer, I will explain more specifically: the present value of dividends in the next year is 4.6875, and in the year 100 0.007872. That is, the farther, the lower the present value, which can ultimately be neglected, because its effect on total amount discounted cash flows will only decrease over time. In the end, we come to a simple Gordon formula, with which you can calculate the value of a share.
Share price P = D1 / (k-g)
D1 is the amount of cash flow in the next year, which is calculated as D0*(1+g)
g is the growth rate of future cash flows
k is the discount rate.
In the above example, the price of a share would be 75 rubles.
If cash flows do not grow, then the formula is converted to the form P = D/k.
Both dividends and earnings per share (EPS) can act as cash flows.
By slightly changing this formula, you can calculate the profitability (profitability) of a stock r=EPS/P. It shows the ratio of earnings per share to the share price. This technique uses , calculating r, he compares it with the current yield on long-term government bonds. If r is less, then the stock is overvalued; if it is greater, it is undervalued.
Model Disadvantages
The first drawback of the Gordon model is that it can only be built into a constant growth rate of cash flows, that is, it is a single-phase model, which means it is not suitable for evaluating companies whose cash flows will vary greatly. For such companies, the multi-phase model is best suited.
It follows from this that such a model is best suited for valuing large mature companies that have already exhausted their growth potential. For example, EPS of Wells Fargo, one of the largest US banks, has grown by an average of 7% per year over the past 10 years, Coca-Cola by 5%, IBM by 9%. As you can see, their profits do not grow by more than 10% per year.
For Gordon's formula to make sense, g cannot be greater than the discount rate k - this is another drawback of the model. Moreover, growth rates should be close to the average growth rates of the economy, since no company can grow at a high rate forever, sooner or later it will hit the ceiling.
In addition to these limitations, the Gordon model has all the other disadvantages of the discounted cash flow model. That is, it is sensitive to input data, does not take into account the buyback of shares (when EPS can grow, but the company's profit at the same time fall), change dividend policy and others. Therefore, when using this model, it is imperative to use .
The most attractive for an investor are stocks of normal (permanent) and excessive growth. Normal growth stocks are stocks that are expected to increase dividends at a constant rate. This means that the amount of dividends at the end of the period of timet is equal to
Dt = D o(1 + g),
where g-expected growth rate of dividends.
For example, if the last dividend paid on one share of company X was one thousand rubles and growth of 6% is expected, then the dividend for the current year will be
D 1 = 1000 . (1 + 0.06) = 1060 rubles.
The internal price of the share (the price that should be today from the point of view of the investor) is again found from equation (2):
.
If the fraction<1, то есть ρ > g, then R is equal to the sum of an infinitely decreasing geometric progression with the denominator and the first termD O . . Hence,
(1)
The internal price of the stock in the above example withg= 6% and the required level of return ρ = 16.3% is equal to
rubles.
Equation (1) can be solved with respect to ρ and thus find the expected rate of return (yield). This yield is the sum of the dividend yield and the yield due to changes in the stock price.g, i.e.
If an investor bought a share for 10,000 rubles and expects a dividend of 1,030 rubles, with a profit growth rate for the current year of 6%, then the expected rate of return is
0.163 or 16.3%.
Let the share price on January 1, 2000 be 10,000 rubles and the dividend expected at the end of the year be 1,030 rubles. What will be the stock price at the beginning of 2001? The expected dividend for 2001 will beD 2001 = D 2000 . (1 + g) = 1030 . (1 + 0.06) = 1091.8 rubles.
rubles.
notice, that R(as of January 1, 2001) = 10600 =10000 . 1.06 = R(as of January 1, 2000) . 1.06
In general
That is, the share price constant growth increases at the same rate g, which is the dividend.
The expected income due to price changes is equal to 10600 - 10000 = 600 rubles. Therefore, the profitability due to price changes is equal to
.
In the general case, the following formula is valid
Yield due to price changes 
.
So, the expected return from a change in the price of a constant growth stock is constant and equal to the expected dividend growth rate, and the expected rate of returnρ for a constant growth stock is equal to the expected dividend yield plus the expected dividend growth rateg, i.e.
ρ = dividend yield + g.
Companies go through a number of stages in their development. The initial period of the company's activity is characterized by accelerated growth, exceeding the growth of the economy as a whole. Then stabilization occurs, in which the growth rate of dividends remains constant. An example of this is the company Microsoft »in the 90s. The stocks of such companies are called excess growth stocks. To estimate the stock price of excess growth, assuming that the growth rate becomes constant from some point, you need:
1) find the current value of the dividend paid during the period of excess growth;
2) find the expected stock price corresponding to the end of the period of excess growth;
3) add the results of the first and second steps.
Let the required rate of return ρ = 15%, overgrowth continued N = 3 years, growth rate of earnings and dividends during the period of excess growthg izb. R. = 30%; and a constant growth rate after a period of excess growthg= 10%; last dividend paid to dateD o = 1000 rubles. Let's find an estimate for the current stock price of excess growth with the specified parameters.
The amount of dividends for each year is equal to:
D 1 = D o. (1+ g fav.r. ) = 1000 . 1.3 = 1300 rubles,
D 2 = D o. (1+ g fav.r. ) 2 = 1000 . 1.69 = 1690 rubles,
D 3 = D o. (1+ g fav.r. ) 3 = 1000 . 2.197 \u003d 2197 rubles,
D 4 = D 3 (1 + g
ruble.
Adding this value toD 3 and discounted at an interest rate
ρ = 15%, we get
ruble.
Where does the current stock price come from
R\u003d 1130.43 + 1277.88 + 33244 \u003d 35652.31 rubles.
Gordon Model is a method of calculating the intrinsic value of a stock, excluding current market conditions. The model is a valuation method designed to determine the value of a share based on dividends paid to shareholders and the growth rate of those dividends. It is also called: Gordon Growth Model, Dividend Discount Model (DDM), Constant Growth Model. .
The model was named after Professor Myron J. Gordon in the 1960s, but Gordon was not the only financial scholar 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 multistage 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 - it is assumed to be constant)
Those. This formula allows you to calculate the future value of a share through a dividend, but on the condition that the growth rate of the dividend is the same.
Multistage growth model
If the dividend is not expected to grow at a constant rate, the investor must evaluate the dividend for each year separately, including the expected dividend growth rate for each year. However, the multi-stage growth model assumes that dividend growth eventually becomes permanent. Below is an example.
Examples
Stable (steady) Gordon model
Let's say Company XYZ intends to pay a dividend of $1 per share next year and you expect it to increase by 5% per year going forward. Assume also that the required rate of return on company XYZ stock is 10%. Company XYZ 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 share price is now $10
Now, using the formula above, we can calculate that intrinsic value one share of Company XYZ shares is equal to:
$1.00 / (0.10 - 0.05) = $20
Thus, according to the model, Company XYZ shares are worth $20 per share but are trading at $10; Gordon's growth model suggests that stocks are undervalued.
The stable model assumes that dividends grow at a constant rate. This is not always a realistic assumption, because things in companies do change, today they are doing wonderfully and they pay good dividends, and tomorrow they do not pay 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 multistage growth model
Let's assume that over the next few years, Company XYZ's dividend grows rapidly and then grows at a steady rate. 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% permanently. Using the elements of a robust model, but analyzing each year separately, we can calculate the current fair value of Company XYZ 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
Then we calculate the present value of each dividend during 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 calculation of the dividend for the fifth year:
D5 = $1.32 * (1.05) = $1.39
We then apply the Gordon Steady Growth Model formula to these dividends to determine their fifth year value:
$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 present value Company XYZ's future dividends to get the current intrinsic value of Company XYZ's shares:
$0.91 + $0.88 + $0.89 + $0.90 + $17.26 = $20.84
The multi-stage growth pattern also indicates that Company XYZ shares are undervalued (intrinsic value of $20.84 compared to a trading price of $10).
Analysts often include an estimated price and sale date in these calculations if they know they won't hold the stock indefinitely. Coupon payments can also 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 exception allows investors to compare companies across 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, to make the Gordon model effective, two things are necessary. 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 be negative.
The Gordon model, especially the multi-stage growth model, often requires users to make several unrealistic and complex estimates of dividend growth rates (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, stocks become more valuable when their dividend increases, the investor's required rate of return decreases, or the expected dividend growth rate increases. The Gordon Growth Model also assumes that the stock price rises at the same rate as dividends.
It is extremely important to be able to assess what kind of profitability will bring in the future investments in various projects.
It is very difficult to predict the size of dividends, since this size is completely determined by the results economic activity enterprises.
At the same time, it is difficult to assess the degree of influence of numerous entrepreneurial risks, from which even the most stable company is not insured.
For this case, special models have been developed that allow, as far as possible, to predict the amount of future dividend payments as accurately as possible.
So, when the most difficult tasks of assessment and tax planning arise, the model of eternal growth of dividends or the Gordon model is used. The calculation formula and business valuation methods based on it are in the article.
Model of constant growth (Gordon Growth Model)
A 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 of the Gordon Growth Model.
The model is named after MJ Gordon, who originally published it in a joint study with Eli Shapiro: Capital Equipment Analysis: The Required Rate of Profit, Management Science, 3(1) (October 1956) .
The discounting formula assumes that the present value of a share, PV (which determines its price at the initial point in time), can be represented as:
M. J. Gordon, to simplify the calculations, suggested that since the validity of the stock is theoretically unlimited, we consider that the cash flow is an endless stream of dividends (there will no longer be a liquidation amount, since the share exists indefinitely).
In addition, Gordon proposed to consider all the growth rates of annual payments (g) the same, i.e., dividends increase annually by (1 + g) times, and the value (g) does not change indefinitely.Given this assumption, the formula will take the form:
Thus, the calculation of the cost in accordance with the Gordon model is carried out according to the formula:
In addition to the above simplifications, the Gordon model assumes that:
- The value of k must always be greater than g, otherwise the stock price becomes uncertain. This requirement is quite logical, since the rate of growth of dividends g may at some point exceed the required rate of return on shares k.
However, this will not happen if we assume the chosen discounting period to be infinite, because in this case the dividends would constantly grow at a higher rate than the rate of return of the share, which is impossible.
- The company must pay dividends regularly, otherwise the Gordon model is not applicable. Moreover, the requirement that the value of g remain unchanged means that the company always allocates the same share of its income to dividend payments.
- The requirement that the values of k and g remain constant up to infinity limits the structure of the company's capital: 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 at the expense of the retained share of income, the higher the share of dividends in the income of the enterprise, the lower the level of capital renewal.
Application in business valuation
When evaluating a business, when forecasting income, due to the fact that free cash flow cannot be predicted for more than a few years in advance, provisions have been introduced on the nature of the change in these cash flows - it is assumed that the residual (terminal) value of the business is estimated at the end date of the explicit forecast period.
According to the Gordon model, the annual income of the post-forecast period is capitalized into a value indicator using a capitalization ratio calculated as the difference between the discount rate and long-term growth rates (the Gordon model is used as part of the income approach).In the absence of growth rates, the capitalization ratio will be equal to the discount rate.
The calculation of the final cost in accordance with the model under consideration is carried out according to the following formula:
The relative size of the terminal cost 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 projections over 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 value of the capitalized income of the post-forecast period (ie the sum of the values of all annual future income in the post-forecast period).If the profit growth rate 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 the 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 about g, the long-term (to infinity) growth rate, are being used.
The Gordon model can use historical, current, or projected earnings, and often the latter is calculated by multiplying recent earnings by the expected long-term growth rate, in which case the formula becomes:
Limitations when using the Gordon model:
- the growth rate of the company's income must be stable;
- income growth rates cannot be higher than the discount rate;
- capital investments in the post-forecast period should be equal depreciation charges(for the case when cash flow acts as income).
Source: "afdanalyse.ru"
The Gordon model is a formula for evaluating business and investment objects
The Gordon model is used to evaluate the value of a business and other investment objects. The author of the model is the economist M. J. Gordon.
The essence of the Gordon model is defined as follows: “The cost investment object at the beginning of the post-forecast period will be equal to the sum of the current values of all future annual cash flows in the post-forecast period.
Thus, the annual income is capitalized, forming the value of the business. A is calculated as the difference between the discount rate and the long-term growth rate.
Gordon proposed a simplified equation:
FV = CF(n+1) / (DR - t)
To calculate the formula, the following indicators are taken:
FV is the cost of the object in the post-forecast period;
CF(n+1) – income stream 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.
To determine the current value of equity (FV) for a business, it is necessary 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 at first its name was “dividend model”. This equation is generalized. The difference DR - t is also interpreted as a 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 highly rational to consider the Gordon model as compatible with the general evaluation model.
Business valuation according to this model is determined by the product of income by the coefficient. In this way, by referring to the method of calculating the Gordon formula, you can analyze information about the stock or the business as a whole.
Sometimes the term GROWTH model is found in the literature (it is practically a synonym). Its forecast calculations are useful and actively used both in business management and in its purchase / sale.
Cash flow discount model
The Gordon model is used to provide a difficult to solve valuation, in tax planning, in the valuation of a share with a uniform increase in dividend in the stock market. This model can be effectively applied:
- if there is a volume of the sales market;
- there are stable supplies of raw materials, material resources for production;
- there is a durability of the applied technologies and equipment, a guarantee of innovative upgrades;
- financial resources are available for the development of the enterprise;
- stable economic situation.
Myron J. Gordon developed such a model as early as 1959. However, there are alternatives to the above mentioned model in the general context of discounted cash flows (DCF).
It should be borne in mind that dividends can be paid only according to the results of the economic activity of the enterprise. To do this, it is extremely important to have enough reliable data to predict the expected dividend payments.Forecasting dividends is an extremely difficult task, as there are various economic risks (even if the company has received a high rating for business stability). Special techniques have been developed that make it possible to make an approximation of 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. Such a model is a variation on dividend discount models, as well as a way to determine stock prices or value a business as a whole. For example, OTC companies. By the way, it is this segment that is almost impossible to evaluate by other methods.
Cash flow growth forecast
When the forecast period expires, it is assumed that the level of increase in sales and profits will be stable, and the rate of depreciation is equal to the rate of capital investment. This cost will be determined with the obligatory indication of the discount rate in percentage, at an increasing rate cash flow as a percentage for an annual period.
It is important to remember that the cost indicator at the end of the forecast period according to 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 summarized separately with the obligatory influence of the growth in financial flows. Use the same discount rate.
Source: "businessideas.com.ua"
Methods for calculating residual value
For determining residual value enterprises at the end of the forecast period, the following methods can be used:
- Gordon model;
- proposed sale;
- cost net assets;
- liquidation value.
Gordon's model comes from the following main provisions:
- the owner of the company does not change;
- in the residual period, depreciation and investment are equal;
- the forecast period should continue until the growth rate of the enterprise stabilizes; it is assumed that in the residual period, stable long-term growth rates should be maintained.
The proposed sale method consists in recalculating the cash flow or profit at the end of the forecast period using special coefficients.
Method of valuation by net asset value - the expected residual book value of assets at the end of the forecast period is used as the residual value. Not the best approach for evaluating an ongoing profitable enterprise.Salvage value method – the expected salvage value of assets at the end of the forecast period is used as the residual value. It is also not the best approach for evaluating an existing profitable enterprise.
According to any of these methods, the value of the residual value of the enterprise is calculated at the end of the forecast period, and in this regard, when determining the estimated value of the enterprise, this amount must be discounted (reduced to the current value).
Source: "bet-select.ru"
Gordon model for stock valuation
The Gordon model is another stock valuation model based on the assumption that cash flows will grow forever at a constant growth rate.
It is easier to calculate than discounting dividends, but is also based on the time value of money principle, i.e. that the fair value of a share equals the value of future cash flows adjusted to the current moment.
Another name for this model is the Gordon growth model. It is so named because it assumes that future cash flows will grow forever at the same rate of growth, and the required rate of return will not change.
Therefore, the Gordon model is best suited for valuing stocks that have stable cash flow growth rates.
For example, you have found a stock that has been paying dividends for a very long time and consistently, and that they grow by about 5% year on year.
Over the past year, dividends amounted to 5 rubles, which means that next year they will be 5 * 1.05 = 5.25, in the second year 5.25 * 1.05 = 5.5125 and so on. If you want a 12% return on your investment, then use this interest rate as your discount rate.
As you can see on the graph, dividends tend to an infinitely large value (blue bars), their discounted value, on the contrary, decreases (orange bars), and their amount tends to some finite value (the red line reaches a plateau):
To make it clearer, I will explain more specifically: the present value of dividends in the next year is 4.6875, and in the year 100 0.007872. That is, the farther away, the lower the present value, which in the end can be neglected, because its impact on the total amount of discounted cash flows will only decrease over time.
In the end, we come to a simple Gordon formula, with which you can calculate the value of a share.
Share price: P = D1 / (k-g),
where D1 is the amount of cash flow in the next year, which is calculated as D0*(1+g),
g - the growth rate of future cash flows,
k - discount rate.
In the above example, the price of a share would be 75 rubles.
If cash flows do not grow, then the formula is converted to the form P = D/k.
Both dividends and earnings per share (EPS) can act as cash flows.This technique is used by Warren Buffett, calculating r, he compares it with the current yield on long-term government bonds. If r is less, then the stock is overvalued; if it is greater, the stock is undervalued.
Flaws
- The first drawback of the Gordon model is that it can only be based on a constant growth rate of cash flows, that is, it is a single-phase model, which means it is not suitable for evaluating companies whose cash flows will vary greatly. For such companies, the multi-phase model is best suited.
- For Gordon's formula to make sense, g cannot be greater than the discount rate k, which is another shortcoming of the model.
- In addition to these limitations, the Gordon model has all the other disadvantages of the discounted cash flow model, i.e.:
- sensitive to input
- does not take into account the buyback of shares (when EPS can grow, while the company's profit falls),
- change in dividend policy and others.
It follows from this that such a model is best suited for valuing large mature companies that have already exhausted their growth potential.
For example, EPS of Wells Fargo, one of the largest US banks, has grown by an average of 7% per year over the past 10 years, Coca-Cola by 5%, IBM by 9%. As you can see, their profits do not grow by more than 10% per year.
Moreover, growth rates should be close to the average growth rates of the economy, since no company can grow at a high rate forever, sooner or later it will hit the ceiling.
Therefore, when using this model, it is imperative to use a margin of safety.
Source: "activeinvestor.pro"
Features of business and investment valuation
When evaluating an investment project, specialists find out the circumstances that affect its attractiveness:
- Can a business project be implemented - compliance with legislative, organizational and technological nuances in the proposed project.
- Availability of sufficient financial component.
- Investor protection from the risk of losing financial resources.
- The effectiveness of the project is the size of the expected profit from the implementation of the project.
- Acceptable risks are determined.
On this basis, the standard data is calculated:
- Discounted payback period (PBP).
- Net current value (NPV).
- Internal rate of return (IRR).
Such a set is the basis in the process of evaluating a business idea. It is he who is reflected in the conclusions to the business plan, showing its tempting side. However, the use of only these indicators is not always convenient and correct. The calculation is based on the NPV indicator, which has its own disadvantages:
- It is often unjustified to make a detailed forecast of the entire period, taking into account the expected investment investments.
As a result, part of the income is not taken into account. This is clearly seen when creating directions that can work almost endlessly (in theory).
- Focusing on NPV, it is difficult to judge the benefit of an investor - a participant in a particular project, and to understand what his minimum contribution should be.
What are its goals:
- Assess the return on capital (meaning equity).
- Estimate the cost of capital owned by the company.
- Estimate the discount rate of the investment project.
What is meant by discount rate? When analyzing future investments, they use calculations that take into account the discounting of the cash flow in the future. To carry out this calculation, you need to determine the amount of the bet. Then one can understand what the impact of monetary value is. For example, the source of funding for a project is Bank loan. This means that the rate in the discounted version should be equal to the lending rate.
Formula and calculation example
For the Gordon model to work, it is necessary to know a number of specific indicators necessary for calculations. You can’t do without the amount of current dividends, the discount rate, the planned size of dividends, and so on.
Then it is possible to make an estimate of the net profit growth and get an idea of the company's profitability.
Estimating the growth of dividends from shares according to the Gordon model - what is implied in this model:
- The company currently pays dividends, their size is indicated by the value D.
- It is planned to increase the amount of dividends, while the rate does not change and is equal to the value of g.
- The size interest rate shares (discount rates) constant, equals k.
In this case, you can calculate the current stock price P:
P \u003d D x (1 + g / k - g)
The value of the P share is subject to adjustment - this is the result of the influence of many factors (the size of the company has increased and other factors). Therefore, a simplified formula is used:
P0 \u003d D1 x / (k - g)
In this case, D1 is the dividend forecast for the coming year. His calculation is: D1= D0 (1 + g)
Thus, knowing the discount rate and the amount of current dividends, one can estimate the growth of dividends in the future.Evaluation of the profitability of the company - to estimate what profitability will bring equity capital, you can use the formula:
r = (D1 / P0) + g,
where r is the return on capital;
D1 - expected dividends for the next year;
D0 – dividends of the current period;
P0 - current price stock;
g is the average value of the growth rate of dividends paid out.
The formula will look a little different if it is complicated by calculating future dividends:
D1= D0 (1 + g), so r = (D0 (1 + g) / P0) + g
Suppose we consider the profitability of a company:
- The increase in the growth rate of dividends paid out over four years is on average 0.3.
- The amount of dividends in the current year is 0.1.
- The share price at the current moment is 150 rubles.
r = (0.1 (1 + 03) / 150) + 0.3 = 0.3
In other words, the yield for the next year will be 30%. You can rely on a period of 12 years. The calculations will require statistical data provided by official sources.
Pros and cons
How to find out the figure that determines the value of any company? By studying (analyzing) its assets or by comparing similar companies.
One of the variants of the approach is income analysis, which is what makes Gordon's model remarkable. However, this model has its limitations.
The Gordon model is not acceptable in the following cases:
- The stability of the situation in the economic sphere has been disrupted.
- When a company is characterized by stable volumes of goods produced along with stable sales.
- The credit resource is always available.
- The discount rate is greater than the increase in dividend payments.
The market must be stable against the backdrop of constant economic growth. Then we can talk about an adequate analysis of future profits and business value using the Gordon method.
The model has been successfully applied to largest companies relating to the oil and gas or raw materials industries. If the market is in the development stage, the result will be distorted.
Source: "crediti-bez-problem.ru"
Gordon's formula in excel for estimating future returns on stocks and businesses
For cost estimation own funds and return on common stock, the Gordon model is applied. It is also called the formula for calculating constant growth dividends, since the growth of its value depends on the rate of increase in dividend payments of an enterprise.
The task of the model is to evaluate the cost of own funds, their profitability, and the discount rate for an investment project.The Gordon formula applies only in the following cases:
- the economic situation is stable;
- the discount rate is greater than the growth rate of dividend payments;
- the enterprise has a steady growth (volume of production and sales);
- the firm is free to access financial resources.
The formula for evaluating the return on equity according to the Gordon model is an example of calculation:
where r is the return on equity of the enterprise, the discount rate;
D1 - dividends in the next period;
P0 is the share price at this stage of the company's development;
g is the average growth rate of dividend payments.
To find the size of dividends for the next period, they need to be increased by the average growth rate. The formula becomes: r = (D0 * (1 + g))/P0 + g
Let's evaluate the profitability of the shares of OJSC Mobile TeleSystems using the Gordon model. Let's make a table where the first column is the year of payment of dividends, the second is dividend payments in absolute terms:
Gordon's formula "works" under certain conditions. Therefore, we first check that the values of dividends obey the exponential distribution law. Let's build a graph:
To check, let's add a trend line with the approximation confidence value. For this:
Now it is clearly seen that the data of the "Dividends" range obey the exponential distribution law. Reliability - 77%.
Now let's find out the current value of an ordinary share of Mobile TeleSystems OJSC. This is 215.50 rubles.
Thus, the expected return on shares of OJSC Mobile TeleSystems is 38%.
Model Based Business Valuation Method
The cost of an investment object at the beginning of the next period, according to the Gordon formula, is equal to the sum of current and all future annual cash flows. The amount of annual income is capitalized - the value of the business is formed. This is important to consider when evaluating the value of a company.
The calculation of the capitalization rate according to the Gordon model in Excel is carried out according to a simplified scheme:
FV = CF (1+n) / (DR - t)
The essence of the formula in assessing the value of a business is almost the same as in the case of calculating the future profitability of a share. To determine the value of a business, several other indicators are taken:
- FV - the amount of equity capital;
- CF (1+n) – expected cash flows;
- DR - discount rate;
- t is the growth rate of cash flows in the residual period.
The difference in the denominator of the equation (DR - t) is called the capitalization rate. Sometimes the letter g is used to denote the long-term growth rate of cash flows.
- t = price growth rate * rate of change in production volumes;
- DR is taken equal to the return on equity;
- 1/(DR - t) - coefficient to income.
To evaluate a business using the Gordon model, you need to find the product of income and the coefficient.
The model formula is used to evaluate investment objects and businesses in a sustainable economic growth. The domestic market is characterized by volatility, due to which the application of the model leads to a distortion of the results.
Source: exceltable.com
Estimated return on capital
The Gordon Growth Model is used to estimate the cost of equity and the return on a company's common stock.
This model is also called the constant growth dividend model, since the key factor that determines the growth of the company's value is the growth rate of its dividend payments. The Gordon model is a variation of the dividend discount model.
The purpose of estimating the Gordon model: estimating the return on equity, estimating the cost of a company's equity, estimating the discount rate for investment projects.The model has a number of limitations on applicability and is used when:
- stable economic situation;
- the product sales market has a large capacity;
- the company has a stable volume of production and sales of products;
- there is free access to financial resources (loan capital);
- the growth rate of dividend payments must be less than the discount rate.
In other words, the Gordon Model can be used to value a company if it has sustainable growth, which is expressed by stable cash flows and dividend payments.
Return on equity based on the Gordon model
You can similarly rewrite the formula for dividend payments in the next year by increasing them by the size of the average growth rate:
where r is the return on equity of the company (discount rate);
D1 - dividend payments in the next period (year);
D1 - dividend payments in the current period (year);
P0 – share price at the current time (year);
g is the average growth rate of dividends.
Evaluation example in EXCEL
Consider, for example, the assessment of the future profitability of OAO Gazprom using the Gordon model.
OAO Gazprom was taken for analysis because it is the key national economy, has a variety of sales and production channels, i.e. has a fairly stable vector of development. At the first stage, it is necessary to obtain data on dividend payments by years.
To get statistics on the size of dividend payments, you can use the InvestFuture website and the Stocks → Dividends tab. So the period from 2000 to 2013 was taken for the shares of OAO Gazprom. The figure below shows the statistics of the size of dividends per ordinary share:
Data for calculating stock returns using the Gordon model
It should be noted that for the correct application of the Gordon model, dividend payments must increase exponentially.
At the next stage, it is necessary to obtain the current value of a Gazprom share on the stock market; for this, you can use the Finama service:
Determination of the current value of OAO Gazprom shares
The current value of a Gazprom share is 150.4 rubles. Next, we calculate the average growth rate of dividends and the expected return.
CAGR =(B20/B7)^(1/13)-1
Expected stock return =B20*(1+D7)/E7+D7
Calculation of expected return using the Gordon model in Excel
The expected return on OAO Gazprom shares for 2014 is expected to be 48%. This model is well applicable for companies that have a close relationship between the growth rate of dividends and the value in the stock market.
As a rule, this is observed in a stable economy without major crises. The domestic market is characterized by instability, low liquidity and high volatility; all this leads to the difficulty of using the Gordon model to assess the return on equity.
The Gordon Model is an alternative to the CAPM (Capital Asset Pricing Model) and allows you to estimate the future profitability of a company or its market value in an overall sustainable economic growth. Applying the model to emerging capital markets will distort the results. The model can be adequately applied to large national companies from the oil and gas and raw materials industries.
Source: "finzz.ru"
Treating a stock like a bond with ever-increasing coupon rates
In parallel with my research on company selection, I decided to look at the "Gordon model" and, in general, approach the stock as "a bond with an ever-growing coupon." Interesting topic.
Why is this approach interesting?
The reason is that when conducting research according to my methodology, which has a mostly “Graham” bias, I almost always exclude from the shortlist companies that fit Buffett’s criteria (buys or holds Buffett even taking into account expensive prices on them), - Coca-Cola, Gillette, American Express, McDonald's, Walt Disney, etc., but Graham's filters do not pass at all.
Although they have stable income and there is no doubt about their future, but for me they are very “expensive”, and most importantly, they continue to rise in price! Paradox or norm? Nonsense, but it looks like it will continue. I wrote about this earlier, why this happens in the understanding of Warren Buffett - "You pay a high price for an entrance ticket just to cross the threshold."
I decided to take a closer look at stock valuation in terms of dividend payouts, not just equity growth and net income growth.
It is “Dividends” that can be considered the very “coupon” of a share, and in Russia, by the way, skeptics of fundamental analysis pay more attention to dividends in calculations than equity and the net profit that remains in the company.
Dividends are a real cash flow to the shareholder, and if you are going to hold the stock forever (like Buffett), then it will be more like a bond investment, not a stock, but only an order of magnitude more interesting.
In the classical course of fundamental analysis (which is taught in all universities of the world), there is a method for valuing stocks with a uniformly increasing dividend, which is called the Gordon model.
Gordon Model
If the initial value of the dividend is D, while increasing annually with the growth rate g, then the present value formula is reduced to the sum of the members of an infinitely decreasing geometric progression:
PV = D*(1+g)/(1+r) + D*(1+g)^2/(1+r)^2 + D*(1+g)^2/(1+r)^ 2… = D*(1+g)/(rg),
where PV is the present value,
r is the rate of return used to discount future receipts.
But in this case, I was interested in what can be obtained from this formula (Gordon) - knowing the current value of the share, the last dividend for 12 months and the rate of increase in the dividend (at least approximately) - you can find the rate r:
r = (D*(1+g)/PV + g)*100
That is, to find the very rate of return that is used to discount future receipts. Thus, we reduce the weak point of any analysis to the maximum - forecasting the future.
We start from a bet already priced in and analyze how likely it is that the status quo will continue for a long time.
By the way, I studied one study a few years ago about investments in companies that paid dividends and those that did not. What do you think, which group turned out to be better in terms of profitability? Of course, companies that paid dividends! Maybe the companies that did not pay dividends in that study, and could not pay them in principle due to their weak financial position.
Of course, dividends are a derivative of net profit, but in any case, dividends paid and growing year by year are very good!
But there is another opinion about the payment of dividends from the same Buffett, his company Berkshire Hathaway does not pay dividends, and here's why - this year's letter to shareholders is well described. It is interesting to get along two approaches in one person - he does not pay dividends for his company, but he likes to receive dividends for investments ...)Let's return to the Gordon formula, and to the question of how you can buy even "expensive" companies. The question of the quality of the business, the brand, the "safety moat" - you can read a lot about this in Buffett, but how can all this be translated into objective numerical values?
I will try to analyze the application of the Gordon formula (it is very well applicable for Buffett's investments - he owns shares forever).
- Firstly, in order for a company to be calculated at all according to this formula, it must pay dividends stably and they must grow (respectively, net profit, otherwise the growth of dividends will rest against the net profit indicator). Which already greatly reduces the number of such companies.
- And secondly, you need to have great confidence in the continuation of this situation. Most likely, these will be companies from the consumer sector (due to the greater predictability of financial results and business growth rates) than the commodity sector, where such stability is more difficult to achieve.
Coca-Cola example
I will give a classic example of such a company - Coca-Cola, and an example of a successful investment in an "expensive company".
In June 1988, the Coca-Cola Company's share price was approximately $2.50 per share (taking into account the stock split over the entire 25 years). Over the next ten months, Buffett bought 373,600 shares at an average price of $2.74 per share, which was fifteen times the profit and twelve times the cash receipts per share and five times more book value shares.
That is, it is not necessary to argue that Buffett bought shares cheaply. He bought expensive. What did Warren Buffett do?
For 1988 and 1989 Berkshire Hathaway bought more than $1 billion worth of Coca-Cola stock, representing 35% of all common stock Berkshire owned at the time.
It was a bold move. In this case, Buffett acted in accordance with one of his main principles. investment activity: When the probability of success is very high, don't be afraid to bet big. Later, more shares were bought at a higher price - the number was increased to 400,000 thousand units (in current shares) for $1,299 million ($3.25 per share).
On the this moment this portfolio is valued at $16,600 million ($41.5 per share). Plus $4,336 million in dividends ($10.84 per share over 25 years)! Warren Buffett was willing to go for it because of his belief that real value companies are much higher. And he turned out to be right!
Share price, USD
Dividends, USD
Let's look at the numbers. What exactly inspired this confidence? I will calculate the rate r from the Gordon model and other indicators for the last 30 years. I wonder if this is a coincidence or not - but after Buffett's acquisition of shares - the r rate increased significantly due to a sharp increase in dividends (due to the growth of net profit, since the dividend payout ratio only decreased from 65.3% in 1983 to 33.6% in 1997):
Rate R, %
%
Net profit, million USD
Growth of dividends, %
Dividend payout ratio, %
The Coca-Cola Company is a company that consistently pays and increases the amount of dividends, while reducing the share of payments for dividends (!), regularly makes reasonable buy-backs, works optimally with leverage, maintains a high ROE level (about + 30-35%) , - in general, not a company, but an ideal!
And the ideal cannot be cheap, now P / E = 19, P / BV = 5.5 (in 1987 - 15 and 5).
It turns out that if an “expensive” company does a good job increasing its net profit and dividends year by year, it will remain “expensive” (and even become even more expensive), and it is safer to buy such companies than very “cheap” ones, but with vague perspectives.
Treat a stock like a bond with an ever-increasing coupon
If you look at the shares of Coca-Cola as a "bond" whose coupon yield is still growing, then over the past 25 years it has turned out to be a super "bond".
On the one hand, if we evaluate in 1988 the dividend yield for 1987 (0.0713) and the price at the end of March 1988 (2.39), then the dividend yield is 2.98% with a yield of 10T at that time 8.72% somehow not impressed, but it's only at first glance.
Coupon growth, %
Compare - buy a "stock-bond" or a 10T bond!
The declining trend in the yield of the debt market and, conversely, the expected increase in dividend payments reasonably indicated that the stock is a more promising investment, because with the growth of yield on "coupons", the face value of the "bonds" itself grows several times over a long period, since often the current dividend yield is almost constant.
But with the growth of dividends, the value of the share itself will also grow (a good “bond” - the coupon yield grows and the “bond face value” grows!).
Current dividend yield of Coca-Cola shares over the past 30 years, %
What's next
Still, it is worth noting that the situation was in 1988, different than now - inflation and yields on 10T began to fall for a long time (after rampant in the 1970s-80s).
The company's sales grew effectively (net profit grew faster sales), there was a realization of the possibility of shifting inflationary price increases to consumers, the company expanded the scope of sales (remember Fanta, when it was from a natural product in the late 80s in the USSR) to the countries of the former communist bloc and so on ...Now there are also quite a lot of opportunities for the company:
- the welfare of many "poor" countries is growing, which will also increase the consumption of Coca-Cola products (soon it will earn more simply by selling water - in countries where there are problems with water with an increase in welfare in these countries),
- “cheap” debts help to develop a highly profitable business almost for nothing,
- a possible inflationary surge would significantly reduce the real debt burden.
So Buffett, although he bought Coca-Cola shares 25 years ago, still holds them now. And most likely would have bought them today.
The R rate, dividend growth rate, ROE are all in a satisfactory state at the moment with Coca-Cola, but do you always want the least risk when investing so as not to buy "expensive" shares in 2000, when they are already expensive beyond the norm? Maybe there is a specific criterion when you still do not need to buy shares of even such a wonderful company.
