Journal number 2 ∘ Givi Lemonjava ∘
Business Valuation Financial Models

DOI kodi: 10.52340/ekonomisti.2026.02.09

Annotation.  This paper presents an analysis and evaluation of DCF models and the parameters included in the model, which determine the accuracy of the models valuation. Such parameters include: cash flows (CF), discount rate (r), and length of valuation periods (n). The paper discusses three ways to use this model: 1) the dividend discount model (DDM); 2) the free cash flow of equity (FCFE) discount model; and 3) the free cash flow of the firm (FCFF) discount model. They estimate the intrinsic value of a company, which is based on the companys ability to generate cash. According to these models, the value of a company is a function of its future cash flows, the weighted average cost of capital (WACC), and the growth rate (g). The business valuation process determines the current value of a business, investment, or asset, using objective measures, and evaluating all aspects of the business.

Keywords: DCF model, Dividend Discount Model (DDM), Gordon Growth Model (GGM), The Free Cash Flow (FCF) Discount Model, Terminal Value (TV), WACC.    

Inroduction

A business valuation is the process of determining the economic value of a business. During the valuation process, all parties of a business are considered to determine its worth. The business valuation process determines the current value of a business, investment, or asset, using objective measures, and evaluating all aspects of the business. Valuation is an important exercise since it can help identify mispriced securities or determine what projects a company should invest. Some of the main reasons for performing a valuation are: buying or selling a business; strategic planning; Capital financing; and Securities investing.

When valuing a company as a going concern, there are three main valuation techniques used by industry practitioners: (1) DCF analysis, (2) comparable company analysis, and (3) precedent transactions. Market approach(public company comparables or precedent transactions), income approach(discount free cash flow discount(DCF) or residual income - Economic value added), and assets approach(replacement cost or cost to build) -  these are the most common methods of valuation used in investment banking, equity research, private equity, corporate development, mergers & acquisitions (M&A), leveraged buyouts (LBO), and most areas of finance. The paper aims to study these methods and ways of their use. 

DCF ModelStucture

DCF model values a company by forecasting its cash flow and discounting it to determine current value. This is a model which is widely used in both academia and practice. It estimates a company’s intrinsic value which is based on a company’s ability to generate cash flow. According to this model, the value of the company function of its future cash flow, weighted average cost of capital(WACC), and growth rate (g). 

The value of any operating asset/investment is equal to the present value of its expected future economic benefit stream. The reliability of these benefit streams is different from asset to asset and from entity to entity. The risk accompanies benefit streams is assessed and measured as a  “cost of capital”.

There are two methods to calculate the cash flows generated by business: one – unlevered cash flow and second – levered cash flow. The first ignores capital structure and makes companies comparable; the second calculates the money that is left to shareholders after all non-equity related claims have been removed.

DCF method is similar to the capitalized cash flow method. Their theoretical precept is the same. Pigure 1 shows the generic form of DCF model. 

Figure 1

There are three ways to use this model: 1) dividends discount model (DDM) [3,5]; 2) free cash flow to equity (FCFE[1])[1,4] discount model; and 3) free cash flow to the firm (FCFF[2])[1,4].

DDM is the simplest model for valuing equity. Where the value of a stock is the present value of expected dividends on it. Now let\s consider these models in detail.

 I.       Dividend Discount Models(DDM)

Three variants of this model are known: a) the Gordon Growth Model (GGM)[3,5], b) One-period dividend discount model, and c) the multi-period dividend discount model. 

a) The Gordon Growth Model (GGM)

This model is a quantitative method of valuing a company’s stock price based on the assumption that the current fair price of a stock equals the sum of all of the company’s future dividends discounted back to their present value[3,5]; it used to find the intrinsic value of a companys stock.

         

The GGM is based on the assumption that the stream of future dividends will grow at some constant rate in the future for an infinite time. The model is helpful in assessing the value of stable businesses with strong cash flow and steady levels of dividend growth. It generally assumes that the company being evaluated possesses a constant and stable business model and that the growth of the company occurs at a constant rate over time - shortly, its use is limited to firms that are growing at a stable rate comparable to or lower than the nominal growth in the economy and which have well established dividend payout policies that they intend to continue into the future. 

The stable levels of dividend growth expected to last forever and the firms other measures of performance (including earnings) can also be expected to grow at the same or lower rate as dividend do. One more other issue is what a stable growth rate should be. Based on several arguments[3], it would not be unreasonable to assume that it can be the growth rate of the economy in which the firm operates. If a firm has an average growth rate that is close to a stable growth rate, the model can be used with little real effect on value. Thus, a cyclical firm that can be expected to have year-to-year swings in growth rates, but has an average growth rate that is 5%, can be valued using the Gordon growth model, without a significant loss of generality.

Let’s consider an illustrative example of this model, which value the XY company that in   2025 had following background information. In 2024, company X&Y paid dividends per share of $2.35 on earnings per share of $2.45; the dividend payment ratio is 95.92% ($2.35/$2.45); the firm had a return on equity of 14.22%; average beta = 0.85; risk free rate = 4.2%; equity risk premium = 4.5%; cost of equity = 4.2% + 0.85 x 4.5% = 8.03%; and Expected growth rate = (1- 0.9592) (0.1422) = 0.58%.

 

If this value for XY is different from the market price, there are three possible explanations for this deviation. One is that this valuation is right and the market is wrong, or the second - that the market is right and you are wrong, or the third – these two   explanations do not hold because the difference is too small to draw any conclusions.

We can to examine the magnitude of the difference between the market price and our estimate of value, we can hold the other variables constant and change the growth rate in your valuation until the value converges on the price equals $31.75 and find corresponding to this price implied growth rate. 

The Gordon growth model has some limitations [2].  In particular, it is extremely sensitive to the inputs for the growth rate (see figure 2); when as the growth rate converges on the discount rate, the value goes to infinity; end if the growth rate exceeds the cost of equity, the value per share becomes negative. It doesnt take into account factors unrelated to dividends, which would likely undervalue the share price.

As figure 2 shows, as the growth rate approaches the cost of equity, the value per share approaches infinity. If the growth rate exceeds the cost of equity, the value per share becomes negative.

 

The growth rate in the firm is comparable to the nominal growth rate in the economy, applies for the terminal growth rate (gn) in this model as well. The payout ratio[4] has to be consistent with the estimated growth rate. If the growth rate is expected to drop significantly after the initial growth phase, the payout ratio should be higher in the stable phase than in the growth phase. A stable firm can pay out more of its earnings in dividends than a growing firm.

The two-stage model works best for firms: 1) which are in high growth and expect to maintain that growth rate for a specific period, after which the sources of the high growth are expected to disappear; 2) which have modest growth rates in the initial phase; 3) which maintain a policy of paying out most of the residual cash flows.

There are three serious limitations of the two-stage dividend discount model:

• The first practical problem is in defining the length of the extraordinary growth period. Since the growth rate is expected to decline to a stable level after this period, the value of an investment will increase as this period is made longer.
• The second problem with this model lies in the assumption that the growth rate is high during the initial period and at the end of the period is suddenly become a lower stable rate. Such sudden change assumption is not very realistic, because it is more likely to happen gradually over time.
• If there are firms that are paying less dividends than can afford, the model would be skewed estimates of value for such firms.  

Next illustration shows Valuing the P&L firm with the two-stage dividend discount model. P&L in 2023 had following background information:

1. Earnings per share = $3.00
2. Dividends per share = $1.37
3. Payout ratio = $1.37/$3.0 = 45.67
4. ROE = 29.37%

We should make following estimates:

1. Cost of equity = riskfree rate + beta(risk Premium) =  5.4% + 0.85 (4%) = 8.8%
2. Expected growth rate = Retention ratio * Return on Equity = (1 – 0.4567)(0.25) = 13.58%
3. Cost of equity in stable growth = 5.4% + 1 (4%) = 9.40%,
4. Retention ratio in stable growth = g/ROE =5%/15% = 33.33%
5. Payout ratio in stable growth = 1 -33.33% = 66.67%. 

 

 Figure 3: Expected Growth in the H Model

The model assumptions:   1) the earnings growth rate starts at a high initial rate (ga) and declines linearly over the extraordinary growth period (which is assumed to last 2H periods – twice of high growth period) to a stable growth rate (gn); 2) the dividend payout and cost of equity are constant over time, they are not affected by the shifting growth rates.

This estimation model can be written as follows: 

 

Where: P0 = Value of the firm now per share, DPSt = DPS in year t, ke= Cost of equity, ga = Growth rate initially gn = Growth rate at end of 2H years, applies forever afterwards. 

This model used for firms which are growing rapidly right now, but where the growth is expected to decline gradually over time as the firms get larger and the differential advantage they have over their competitors declines. The assumption that the payout ratio is constant, however, makes this an inappropriate model to use for any firm that has low or no dividends currently. Thus, the model, by requiring a combination of high growth and high payout, may be quite limited in its applicability. 

This model avoids the problems associated with the growth rate dropping very quickly from the high growth to the stable growth phase, but doing this comes at a cost. First, the decline in the growth rate is expected to follow the strict the model’s structure. It  drops in linear increments each year based upon the initial growth rate, the stable growth rate and the length of the extraordinary growth period. While small deviations from this assumption do not affect the value significantly, large deviations can cause problems. Second, the assumption that the payout ratio is constant through both phases of growth does not seem very realable, because usually when the growth rate decreases, the share of payments must be increase. 

d) Three-stage Dividend Discount Model

The three-stage dividend discount model[5] (Damodaran) combines the features of the two-stage model and the H-model. It allows for an initial period of high growth, a transitional period where growth declines and a final stable growth phase. It is the most general of the models because it does not impose any restrictions on the payout ratio.

This model assumes an initial period of stable high growth, a second period of declining growth and a third period of stable low growth that lasts forever. Figure 4 graphs the expected

growth over the three time periods. 

Figure 4: Expected Growth in the Three-Stage DDM

 

According to this structure, the value of the stock is: 

 

The advantage of this model is that it avoids many of the limitations of previous models, but it requires many more inputs - payout ratios by years, growth rates and betas. But it should be taken into account that the probability of input errors in the evaluation process increases, which can overshadow the benefits obtained from its advantages. 

This model removes many of the constraints imposed by other versions of the dividend discount model[2]. In return, however, it requires a much larger number of inputs - year-specific payout ratios, growth rates, and betas. For firms where there is substantial noise in the estimation process, the errors in these inputs can overwhelm any benefits that accrue from the additional flexibility in the model. This threat is especially great for firms that are in a noisy environment during the evaluation process. 

II. The Free Cashflow Discount Model

a)      Free cash flow to equity (FCFE) Discount Model

FCFE is a measure of how much cash is available to the equity shareholders of a company after all expenses, reinvestment, and debt are paid. FCFE is a measure of equity capital usage. The formula of FCFE is:

FCFE=Cash from operations – Capex + Net debt issued      

    = Net Income - (Capital Expenditures - Depreciation) - (Change in Non-cash Working Capital) + (New Debt Issued - Debt Repayments)                          

First, Capital expenditures are subtracted from the net income, since they represent cash outflows. Depreciation and amortization, on the other hand, are added back in because they are non-cash charges. The difference between capital expenditures and depreciation is referred to as net capital expenditures and is usually a function of the growth characteristics of the firm. Secound, Increases in working capital drain a firm’s cash flows, while decreases in working capital increase the cash flows available to equity investors. Firms that are growing fast, in industries with high working capital requirements (retailing, for instance), typically have large increases in working capital. Finally, equity investors also have to consider the effect of changes in the levels of debt on their cash flows. Repaying the principal on existing debt represents a cash outflow; but the debt repayment may be fully or partially financed by the issue of new debt, which is a cash inflow. 

The  value of the firms equity is calculated using the following formula:

  

Table 1  shows the estimation results of this model, where g=5% and . K_e = 25% 

b)      Free cash flow to Firm (FCFF) Discount Model

The free cash flow to the firm is the sum of the cashflows to all claim holders in the firm, including stockholders, bondholders, and preferred stockholders. There are two ways of measuring the free cash flow to the firm (FCFF):

One:

FCFF = Free Cashflow to Equity + Interest Expense (1 - tax rate) + Principal Repayments - New Debt Issues + Preferred Dividends              

Second:

FCFF = EBIT (1 - tax rate) + Depreciation - Capital Expenditure - Δ Working Capital 

Table 1: Estimates of Free Cashflow to Equity for firm X&Y

Year	Net Income	Depreciation	Capital spending	Change in non-cash working capital	Net debt issued	FCFE	Discounted value
1	9,000	9,000	11,000	1,000	2,000	8,000	6,400
2	9,450	9,450	11,550	1,050	2,100	8,400	5,376
3	9,923	9,922	12,127	1,102	2,205	8,821	4,516
Terminal Value						46,310	23,711
Value of Equity							40,003

In this example, the firm has $40,000 in cash. Mint, WACC = 15.24%, equity ratio = 60%, growth rate = 5%,  tax rate = 15%, and cash plus cash equivalents = 0.

Based on these parameters, the value of the firm calculated by formula (8) is given in Table 2. 

 

 

The cost of capital has a big influence on company valuation result. As can be seen from the Figure 1, It is one of the aggregates of WACC, as well as another -  is Cost of Debt. Interest rate, market and specific risk, and financial market conditions and  the aviability of capital are factors  which are reflected in both components of WACC.

 The  CAPM formula is:

CAPM = (Risk  Free Rate) + (Beta) x (Capital Market Risk Premium )    (7)

The analysis and calculation of the factors involved in the model will be done on the example of the small Georgian gas distribution company Varketair. Rumored primary data are given in the upper left corner of Figure 7. The rest of Figure 7 presents the output data of the WACC.xlsm program.

Risk – Free Rate

The risk-free rate represents the interest an investor would expect from an absolutely risk-free investment over a specified period of time. This rate should correspond to the country where the investment is being made, and the maturity of the bond should match the time horizon of the investment. In practice, the risk-free rate is commonly considered to be equal to the interest paid on a 10-year highly rated government Treasury bond(5.00% - see Figure 2), because it’s the most heavily quoted and most liquid bond.

Beta: There are three approaches available for estimating these parameters. The first is to use historical data on market prices for individual investments. The second is to estimate the betas from the fundamental characteristics of the investment. The third is to use accounting data.

One way for calculation of the volatility of earnings is shown in Figure 6. Here beta equals 0.84, which is the slope of the company\\\\\\\\\'s returns relative to the stock market returns. Experience shows that the regression holds significance in cases where a four-year monthly sample is taken, or a one- or two-year weekly sample.

Figure 6

 

 

 

 

 

 

 

When the company still has assets and liabilities that do not contribute to the creation of cash flows, this valuation, about 9.3 million GEL of the company, will be adjusted by their value—assets will be added, and liabilities will be subtracted. Only such possible adjustments should be made to fair value.

As seen from the tables 5 and Figue 7 of the sensitivity analysis, the valuation shows high sensitivity to the cost of equity and growth rate. Based on this, when evaluating the company, it is necessary to pay as much attention as possible to the accuracy of the evaluation of these two factors, which can be achieved by obtaining the correct methodology and reliable data.

Figure 8

 

Conclusion

Dividend Discount Model(DDM) and the Free Cashflow Discount Models(FCDM) are a financial modeling technique, used to estimate the value of a public traded firm’s share,  a firm capital value, a firm value and an investment based on its expected future cash flows. DCF Analysis  can be used to compare different investments and help investors choose the best option.

When we buy stock in a publicly traded firm, the only cash flow we receive directly from this investment are expected dividends. The dividend discount model builds on this simple propositions and argues that the value of a stock then has to be the present value of expected dividends over time. Dividend discount models can range from simple growing perpetuity models such as the Gordon Growth model to the three-stage dividend discount model combines the features of the two-stage model and the H-model.

The cash flows to the firm are discounted at the weighted average cost of capital to obtain the value of the firm, which when reduced by the market value of outstanding debt, yields the value of equity. Since the cash flow to the firm is a cashflow before debt payments, this approach is more straightforward to use when there is significant leverage or when leverage changes over time, though the weighted average cost of capital, used to discount free cashflows to the firm, has to be adjusted for changes in leverage. Finally, the costs of capital can be estimated at different debt ratios and used to estimate the optimal debt ratio for a firm.

Analysis, based on these models, requires accurate inputs to be effective. This includes accurate estimates of future cash flows, discount rates, and growth rates. If any of these inputs are inaccurate, the results of the analysis will be unreliable. While DCF analysis is a powerful tool, it is not perfect. It relies on assumptions about future cash flows, discount rates, growth rates, and terminal values, which may not always be accurate. Additionally, it does not take into account factors such as market trends, changes in technology, or shifts in consumer behavior. Thus, in some cases, it may be justified not to make a point estimate, but to define a confidence interval for the estimated value of a company.

References

1.Aswath Damodaran (2002). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset, Second Edition 2nd Edition.

2.Issues in using the Dividend Discount Model (2002). https://pages.stern.nyu.edu/~adamodar/pdfiles/valn2ed/ch13d.pdf

3.Myron J. Gordon (1962). "The Investment, Financing, and Valuation of the Corporation," R.D. Irwin.

4.Single-Stage, Two-Stage, and Three-Stage FCFF and FCFE Models (2021): https://analystprep.com/study-notes/cfa-level-2/free-cash-flow-variations/?gad_source=1&gclid=CjwKCAjw7s20BhBFEiwABVIMrd65vKKM13Aftr16wU7XXAp9rYWUNmIjvDldj0o8J7a4rb-hn133EBoCskEQAvD_BwE/”.

5.Stern School of Business, New York University (2002). "Dividend Discount Models," pages 2-8; https://pages.stern.nyu.edu/~adamodar/pdfiles/valn2ed/ch13.pdf.

 

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¹ FCFE = cash flows after taxes, reinvestment needs and debt cash flows - levered free cash flow.

² FCFF = cash follows before debt but after reinvestment needs and taxes - unlevered free cash flow; FCFF = Free Cashflow to Equity + Interest Expense (1 - tax rate) + Principal Repayments - New Debt Issues + Preferred Dividends.

³ The growth rate of a company may not be greater than that of the economy but it can be less because  stable firms becomes smaller over time relative to the economy.

⁴ Expected Growth = Retention ratio * Return on equity; Stable Payout ratio=(Stable growth rate)/(Stable period return on equity).

⁵ https://pages.stern.nyu.edu/~adamodar/pdfiles/valn2ed/ch14d.pdf.

⁶ Capital Market Risk Premium =Market Rate of Return - Risk-Free Rate of Return

⁷ https://www.bloomberg.com/profile/company/661713Z:US.

⁸ https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/ctryprem.html

⁹ For example, Georgia: S&P – BB and Mood’s – Ba2.

¹⁰ https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/ctryprem.html

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