Darmodaran approach to company valuation

RUSSIAN PLEKHANOV UNIVERSITY OF ECONOMICS

 

 

INTERNATIONAL BUSINESS SCHOOL

 

 

COURSEWORK IN CORPORATE FINANCE

DAMODARAN’s APPROACH TO VALUATION

 

 

 

 

 

 

Student: Dodonova Anastasia

Master Degree, 1^st year 

Supervisor: I.V.Sokolnikova 

 

 

 

 

 

Moscow

2011

Contents

 

 

 

 

Introduction 3

1. Basis of Valuation notions according to Damodaran 4

2. DCF model 6

2.1. DCF and notion of growth stages 6

2.2. Cost of equity 9

2.2.1 CAPM and risk premium for country risk 9

2.2.2 Implied risk premium 12

2.3 Value of equity 13

2.3.1. Dividend model 13

2.3.2. Calculation of growth rates 14

2.4. From FCFE to FCFF 17

2.4.1. Cost of capital 17

2.4.2. FCFE approach 17

2.4.3. FCFF approach 20

3. Relative Valuation 22

4. Equity as an Option 24

4.1. Definition and Application 24

4.2 Advantages and Drawbacks  of the Option approach 26

Conclusion 28

Endnotes 29

Bibliography 30

Appendix 31

 

 

 

 

 

 

Introduction

Valuation is an inseparable part of any investment activity, whether it concerns buying a whole company, just one particular kind of fixed or current asset, bonds or intellectual property.  Despite a tremendous crisis and post-recession period, demand on valuation services cannot be underappreciated. Therefore, valuation is a basis for fundamental decisions, operational development and strategic one, from behalf of investors and management.

In this coursework I will describe Damodoran’s approach to valuation. This person has contributed a lot to valuation’s technic. He is an author of two books on Corporate Finance, Investment Management, Valuation and The Dark Side of Valuation, and his works were published in such magazines as Journal of Financial and Quantitative Analysis, The Journal of Finance, The Journal of Financial Economics и The Review of Financial Studies. In addition, he is a professor in Stern School Business in New York on MBA. Such a remarkable specialist described and contributed a lot to valuation technics whose works are used both in theory in universities and in practice among businessmen and valuation specialist.

There are quite a few disputes which valuation methods should be implemented: revenue approach, expense approach or comparison of similar enterprises and which methods should be implemented for each of them. However, Damodaran used explanation for a lot of technics and his advices and new approaches are one of the most referred and frequently used.

This is why I have chosen the topic of Damodaran’s Approach to value management.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. Basis of Valuation notions according to Damodaran

In one of his works Damodaran cites the words of Henry Blodget, Merrill Lynch Equity Research Analyst in January 2000, who said in a report on Internet Capital

Group, which was trading at $174 then: “Valuation is often not a helpful tool in determining when to sell hyper-growth stocks”. There were and still are many persons in financial market who have argued that market prices are determined by this factor, perceptions of buyers and sellers, but not by cashflows, earnings and different calculations. Certainly, Damodaran cannot but agree partially that perceptions are quite important. However, “bigger fool”, which says that an investor may buy questionable securities without any regard to their quality and quickly sell them off to another investor (or the greater fool), who might also to dispose of them quickly afterwards, does not the one thing to figure out asset pricing. Unfortunately, speculative bubbles always blast sooner or later that ends up with a rapid depreciation in share price due to constant selling. For example, the price of shares of the above mentioned Internet Capital Group fell down to $3 in one year.

Certainly, the valuation is not panacea for investment decisions. There are some misconceptions about valuation. First of all, a valuation is not an objective search for “true” value. There is not true and precise value. Furthermore, all valuations are biased. The only questions are how much and in which direction it is so. The direction itself and the magnitude of the bias in your is directly proportional to who pays you and how much you are paid. To expand on this myth, Damodaran gave an example of a recent company acquisition. According to him, the buyer hired a valuation firm to determine the value of the intended acquisition while the seller hired their own firm to do the same thing. When the two firms came back they presented significantly different results. In the end a third party was brought in and conveniently landed with a number right in the middle of the first firms numbers¹.

Value estimates are predicted with “everything is going to go as planned” in mind. There is no way to say whether some events will affect value in some specific time. There is always a lack of information and a level of uncertainty. So valuation professionals cannot ever be wrong even if their original forecasts are far from the final one.

In addition, there is another myth that if a model is more complicated and quantitative it is better. However, complex systems lead to more intricate results and confusion.

There are three main approaches to valuation:

• Discounted cashflow valuation, relates the value of an asset to the present value of expected future cashflows on that asset.
• Relative valuation estimates the value of an asset by looking at the pricing of “comparable” assets relative to a common variable like earnings, cashflows, book value or sales.
• Contingent claim valuation uses option pricing models to measure the value of assets that share option characteristics

The basis for all them is to find assets which overvalued or undervalued. It is considered that markets are inefficient and may make errors and, therefore, it is necessary to find how to find and correct these mistakes. If there is an efficient market the price is supposed to be the best estimate of value. Hence, valuation has to prove that.

 

 

 

 

 

 

 

 

 

 

 

 

2. DCF model

2.1. DCF and notion of growth stages

Concerning DCF method it has such a philosophical Basis that every asset has an intrinsic value that can be estimated, based upon its characteristics in terms of cash flows, growth and risk. In order to perform this method it is necessary to calculate:

• the life of the asset

• the cash flows during the life of the asset

• the discount rate to apply to these cash flows to get present value

The most familiar and simple formula is Value =∑CFt/∑( 1 +r)t

where CFt is the cash flow in period t, r is the discount rate appropriate given the riskiness of the cash flow and t is the life of the asset. The discount rate can be taken as the rate of inflation, weighted average cost of capital rate, interest rate etc.

 

From this we can make some reasoning that for an asset to have value, the expected cash flows have to be positive some time over the life of the asset. Assets that generate cash flows early in their life will be worth more than assets that generate cash flows later due to time value of money; the latter may, however, have greater growth and, therefore, higher cash flows to make lower inputs in the beginning.

 

Applying this method I would like to show examples of just equity and the whole firm valuation.

For the former the value of equity is obtained by discounting expected cashflows to equity, that is the residual cashflows after meeting all expenses, tax obligations and interest and principal payments which connected with the cost of equity: ∑CF to Equityt/∑(1+ ke )t

Where, CF to Equity t = Expected Cashflow to Equity in period t

ke = Cost of Equity

Hence, the dividend discount model is a specialized case of equity valuation, and, vice versa, the value of a stock is the present value of expected future dividends.

 

For the latter The value of the firm is obtained by discounting expected cashflows to the firm, i.e., the residual cashflows after meeting all operating expenses and taxes, but prior to debt payments, discounted at the weighted average cost of capital, which is the cost of the different components of financing used by the firm, weighted by their market value proportions:

∑CF to Firm t/ ∑(1+WACC)t

Logically it is possible to get equity value from firm value. For doing so it is necessary to subtract out the value of all debts and subtract the value of all non-equity claims in the firm that are included in the cost of capital calculation. Also it is often argued that equity valuation requires more assumptions than firm valuation, because cash flows to equity require explicit assumptions about changes in leverage whereas cash flows to the firm are pre-debt cash flows and do not require assumptions about leverage. Certainly it is very important not to mix cash flows and discount rates in valuation because if we use wacc for equity valuation we will have overestimated value (as wacc is based on leverage ration).

For a listed company, the life may be endless as we can always issue new stock. Therefore, cashflows are also infinite. Though, we know production life cycle and firm’s cycle. There is a growth period, maturity and decline. In addition, if a firm issues new stock, the value of the firm will decrease. This is why we estimate cash flows for a “growth period” and then estimate a terminal value, to get the value at the end of the period: ∑CFt/∑(1+r)t+Terminal Value/(1 + r)N

 

In order to calculate cash flows at a growth period we have to understand if it grows at a constant rate. If it is do we can calculate the value with the following formula: Value = Expected Cash Flow Next Period / (r - g)

where,

r = Discount rate (Cost of Equity or Cost of Capital)

g = Expected growth rate

A company can grow at high level but after some period of time it achieve stable growth rate and the terminal value can calculated by this formula. According to Damodaran the stable growth rate cannot be higher than growth of the economy of a country. However, in reality it can happen sometimes. For example, Gazprom have achieved several times higher growth than Russia itself. Though, it happens quite rarely at not for a long period.

 

DCF model implies that there are assumptions that the firm 1) can be in the stage of no high growth, 2) there will be high growth for a period, at the end of which the growth rate will drop fast to the stable growth rate, 3) and when there will be high growth for a period, at the end of which the growth rate will decline gradually to a stable growth rate.

 

The duration of high growth will vary depending on industry, economic situation, country etc but there are main factors that determine it:

• the size of the firm. The larger firm will have shorter high growth periods because it is more difficult to mobilize all the resources and keep up with the previous high growth stage.

• current growth rate . If it is high then there will be longer high growth period.

• barriers to entry and differential advantages. In case of high advantages there will be again longer growth period.

 

Graphically it can be represented by the following pictures:

 

1. Stable growth                     2-stage growth                              3-stage growth

 

Damodaran in his work demonstrate real-life examples of this growth patterns.

Resource: Aswath Damodaran-Valuation (http://pages.stern.nyu.edu)

Now I would like to switch to another component which determination is extremely important to find: discount rate. For equity it is based on risk and return model and a dividend-growth model. The former works on the principal of CAPM which gives estimation of cost of equity applying a beta of the firm.

2.2. Cost of equity

2.2.1 CAPM and risk premium for country risk

As it is highly known formula of Sharp САРМ = Rf + ß * (Rm-Rf) which also quite easy to use and very logical; as a holder of more risky assets should get risk premium. Damodaran introduced a new approach for calculation of risk premium for developing market. Damodaran used a new variable called relative equity market standard deviation which is calculated as Standard deviation of country X/ Standard deviation of US.

This model is easy to use because it starts with the U.S. risk-free rate and the U.S. equity premium. It is also useful if the local country has a viable equity market and the government debt is issued in U.S. dollars.

The model’s theory is to utilize the country default spread as adjusted for the standard deviation of the local equity market to the local bond market. This adjusted default spread is then added to the U.S. CAPM.

To estimate the long-term country default spread, the practitioner should start with the country credit rating and compare that to the country credit rating of a mature market, such as the U.S. The difference in the ratings can be measured in points, arriving at the default spread. The standard deviation of the local equity market and the local bond market can be calculated if both markets have adequate history. For situations where there is not enough history to develop standard deviations or if markets are in such turmoil that current calculations may not be deemed representative of the long term, a benchmark such as 1.5, may be appropriate. The model is applied to net cash flows expressed in U.S. dollars, and exchange risk must still be considered.

For illustration I have decided to introduce the table of countries with default spread of Latin America in 2012; risk premium calculations of countries will be explained later. Default Spread is the spread difference between dollar-denominated bonds issued by this country and the U.S. Treasury bond rate (resource: moodys.com).

Country	Local Currency Rating	Default Spread
Argentina	B3	600
Belize	B3	600
Bolivia	B1	400
Brazil	Baa2	175
Chile	Aa3	70
Colombia	Baa3	200
Costa Rica	Baa3	200
Ecuador	Caa2	850
El Salvador	Ba2	275
Guatemala	Ba1	240
Honduras	B2	500
Mexico	Baa1	150
Nicaragua	B3	600
Panama	Baa3	200
Paraguay	B1	400
Peru	Baa3	200
Uruguay	Ba1	240
Venezuela	B1	400

 

That is the 1^st step for risk premium calculation with a country risk.

So according to Damodaran country equity risk premiums can be calculated either by means of default spread on country bond, relative equity market approach or comparison of default of country’s bond and equity. This a following step.

For example,

• Brazil was rated B2 by Moody’s and the default spread on the Brazilian dollar denominated C.Bond at the end of August 2004 was 6.01%. (10.30%-4.29%)
• Brazil’s index Bovespa had standard deviation of 34.56, S&P 500’s one was 19.01 and the premium of the US was 4.82%. Therefore, Total risk premium for Brazil = 4.82% (34.56%/19.01%) = 8.76% and, subsequently, country equity risk premium for Brazil = 8.76% - 4.82% = 3.94%
• Country ratings measure default risk. While default risk premiums and equity risk premiums are highly correlated, one would expect equity spreads to be higher than debt spreads.

            Then, we get Brazil’s Equity risk premium = Default spread on country bond* σBovespa/σBrazil’s Bond=

=6.01% (34.56%/26.34%) = 7.89%

Applying this to our previous table we will get such results:

Country	Total Risk Premium	Country Risk Premium
Argentina	15.00%	9.00%
Belize	15.00%	9.00%
Bolivia	12.00%	6.00%
Brazil	8.63%	2.63%
Chile	7.05%	1.05%
Colombia	9.00%	3.00%
Costa Rica	9.00%	3.00%
Ecuador	18.75%	12.75%
El Salvador	10.13%	4.13%
Guatemala	9.60%	3.60%
Honduras	13.50%	7.50%
Mexico	8.25%	2.25%
Nicaragua	15.00%	9.00%
Panama	9.00%	3.00%
Paraguay	12.00%	6.00%
Peru	9.00%	3.00%
Uruguay	9.60%	3.60%
Venezuela	12.00%	6.00%

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

Calculating total risk premium, Damodaran added 6% rate for mature markets (obtained from the index S&P 500).

 

Calculation of the finite return will depend on the following approaches:

1. If it is assumed that every company in the country is equally exposed to country risk E(Return) = Rf  + Country risk premium+ ß(US premium). In comparison we can say this is assumed that the local

Government’s dollar borrowing rate is taken as a riskf rate. This formula implies that  specific firm also has its specific risk.

2. Assume that a company’s exposure to country risk is similar to its exposure to other market risk.

E(Return) = Riskf + Beta (US premium + Country risk premium).

3. Country risk is taken as a separate risk factor and firms are to have different exposures to country risk which may be taken as a proportion of their revenues come from non-domestic sales.

            E(Return)=Riskf + ß(US premium) + αCountry risk premium. This approach is usually most preferred as a company may have less exposure to country risk if it has more international activity. α may be found as a proportion: % in local market/%in international activity.

However, in order to calculate ß we have to use a long historical data. We have to look at the historical premium earned by stocks over default-free securities during long time periods. Therefore, this approach cannot be used in all the countries but only in those which have diversified stock market and long history of equity returns and government securities.

Some experts consider that it is not necessary to take a very long-term prospectus for calculation of standard deviation. However, Damodaran opposes to this introducing standard error. For example, standard deviation of risk premiums is 20% for various time ranges. Therefore, we will get the following table:

Estimation Period  Standard Error of Risk Premium

5 years                        20%/ √5 = 8.94%

10 years                      20%/ √10 = 6.32%

25 years                     20% / √25 = 4.00%

50 years                     20% / √50 = 2.83%

Source:http://www1.worldbank.org/finance/assets/images/Equity_Risk_Premiums.pdf, page 6

Therefore, we can see that for a short period standard error is quite large and can highly affect the end results. Moreover, there is another problem of the historical approach in the assumption that during the studied period the investors’ risk premium and risk remained the same. Moreover, even if we have substantial historical period we have another problem of “survivor markets”. For example, if we take the period of commencing from 1920-es it is obvious that some countries investments will be much larger than in the others. Therefore, for the second group earnings will be diminished and expected premiums will be larger in the first group.

2.2.2 Implied risk premium

This approach is alternative to cases when there is no sufficient historical data. We then will use above-mentioned formula Value=Dividend/r-g if there is a constant growth. For example, we have equity price of a company X 1496 in 14 December 2012. We can assume that the yield on this index is 2%. The forecast growth of equity is 7%. Therefore, we will get 1496=0,2*1496/(r-7) => r=27% this  will be our expected revenue for the equity X. The risk free rate will be taken as index RTS which is equal to 8%. Then we can find implied risk premium for the company. It will be equal to 27-7=20%. Such a calculation may be fulfilled if there is a constant growth. If there is not then we will use the formula of DCF.

For example for a company X we will have such cashflows and yields.

 

Year	Cash Flow on Index	Yield
1	=1496*4%=59.84	4%
2	50.86	3.4%
3	29.92	2%
4	48.62	3.25%
5	74.8	5%

 

Therefore we will get: 1496=59.84/1+r + 50.86/(1+r)^2+29.92/(1+r)^3+48.62/(1+r)^4+74.8/(1+r)^5+74.8*(1.07)/((r-0.07)*1,07^5). Therefore, r=

 

Concerning US market we can see dynamics of ERP and t-bons rate from 1961 to 2005. The ERP varies from 2.5 to 7 % and the total expected return from 5 to 20%.

(ESP. ASwath Damodaran)

 

 

 

2.3 Value of equity

2.3.1. Dividend model

Above I mentioned Damodaran’s approach to cost of equity in valuation. As it may be clear from the formula, we also need to choose the right cash flows for our valuation. We can choose dividends flow and FCFE. The first one is much more conservative as firms very often pay insignificant part of their net income as dividends. However, retained earnings have a great value for equity as that means that the company is going to develop and grow. This is why FCFE is more frequently used and “the value of equity, based on the FCFE, will therefore yield a more realistic estimate of value for equity, especially in the context of a takeover, since the acquirer can lay claim to the entire FCFE rather than just the dividends”(endnote 1).

The third method is FCFF. It is similar to FCFE and both of them must have similar results. However, as FCFE must take into account Financial leverage which may change quite often over time, FCFF may be easier.

Still It is necessary to discuss all discount models.

An investor expects two different cash flows from equity: these are dividends and a finite price when he or she sells the shares. The more dividends are paid the more is the price of a share. Therefore, dividend flows is the one to be used in one model.

Damodaran says that “the value of a stock in the dividend discount model is the present value of the expected dividends on the stock in perpetuity” (endnote 2) => Value per share of stock = ∑Expected Dividends in period t/ ∑(1+Cost of Equity)t   It is comprehensive that in reality we cannot actually calculate equity’s value in perpetuity. This is why it is necessary to determine the rate of a stable growth as it was described in earlier section. In the very beginning, a firm is supposed to grow more rapidly with some slowdowns. However, we need to calculate annually the growths of dividends and discount them until a firm reaches a presumed stable growth with which it is possible to calculate the terminal value: Value0 =∑E(Dividends)t/∑(1+r)t  +Terminal Valuen/(1+r)n where Terminal Valuen =E(Dividends)n +1/(rn - gn ).

 

The Risk free rate must be lower than the growth rate. This is explained by the fact that a firm usually cannot overrun the growth rate of the economy. As a risk free rate contains factors of inflation and interest rate, the growth cannot be larger than the risk free rate. High-growth companies may grow much faster than the whole economy at some period of time and once again this is the reason that the Terminal Value can be calculated only at stable growth. This notion of the Terminal Value is also known as Gordon’s formula.

 

Making judgments, this is quite easy to get that another obstacle is a determination the period of this high-growth. Certainly, high-growth term will come to an end sooner or later. When a firm grows, it earns more return on investments, that is ROE, which is also higher that the cost of capital. If this difference is substantial, excessive earnings will draw attention of competitors (if there are sufficient conditions for fair market economy). The latter will pretend the company from high-growth.

2.3.2. Calculation of growth rates

Three options exist for calculation the growth rates. The first one is to use historical growth rate in earnings. For doing so it is necessary to determine how large the time range will be and whether to use arithmetical or geometrical average. As the latter represents average of growth rates compounded over years, it shows more informative results. The second choice is to look at similar stocks and apply their grow rates. The last choice is to use ROE and retention ratio.

 

As a primary goal of a financial manager is to maximize stockholder’s wealth we need to maximize either the value of the firm or minimize wacc. Further, it is obligatory to estimate growth rate for the firm or equity which may be a challenge. Expected growth in earnings is the most popular. For the equity we will forecast growth in net income and earnings per share whereas for a firm we will predict increase in operating income.

 

Therefore,: gEPS = Retained Earningst-1/ NIt-1 * ROE= Retention Ratio * ROE

Retention ratio is used because it is the most reliable and important source of growth. As it may be seen from the formula the expected growth rate in earnings for a company cannot exceed its return on equity in the long term.

 

For demonstration I decided to analyze 3 extremely important companies in our country:

 

30 June 2012,rur	Lukoil	TNK-BP	Gazprom
net income	269 989 458 000,00	84 986 000 000,00	306 702 000 000,00
retained profit	206 295 469 000,00	30 731 325 000,00	277 065 000 000,00
shares	1 701 126 510 000,00	1 152 638 642 828,00	118 367 564 500,00

 

 

Having made calculations I received the following results:

30 June 2012	Lukoil	TNK-BP	Gazprom
Retention ratio	76,41%	36,16%	90,34%
ROE	15,87%	7,37%	25,91%
Expected growth	12,13%	2,67%	23,41%

 

From this we can see again that retention ration is very important for growing earnings for a company. In addition not a distinctive growth in TNK-BP may be explained due to quite difficult period of internal affairs.

ROE ratio has a relation with leverage as well. Otherwise, it can be expressed as: ROE = Return on Capital+D/E (ROC - i (1-t))

where, ROC = (Net Income + Interest (1 - tax rate)) / BV of Capital= EBIT (1- t) / BV of Capital

D/E = BV of Debt/ BV of Equity

i = Interest Expense on Debt / BV of Debt

t = Tax rate on ordinary income

Damodaran states that historical option may be not so reliable because past growths and future ones do not show high correlation. Concerning analytical comparison, it may be worthwhile to use this information; however, it does not reflect activities of a specific company studied. The last option takes into consideration the performance of the company and what the company actually does. Therefore, Damodaran mostly relies on the third variant. The best way to calculate the growth rate with this approach is to calculate average net income during several years. Damodaran explains by the fact that if we take only one year for our net income factor it may be biased; that may happen if that particular year is post-year of the slowdown that will result in a comparative boom or vice versa that period might show very low numbers due to recession.

 

He demonstratively justifies his logic by means of the following example with Deutsche bank. Taken historical approach for 4 years from 2003 to 2007 he got the expected growth of more than 47% for the bank: Compounded Earnings Growth Rate = (Net Income2007/Net Income 2003)^1/4 -1 = (6510/1365)^1/4-1=47,78%. Whereas taken ROE approach for 2007 he attained the figure of more than 19%: ROE= Net Income2007/BV of Equity2006=6510/33475=19.45%. Therefore, g= Retention Ratio * ROE = 0.6703 * 0.1945 =13.04%. Eventually, analyzing years 2003-2007 he got: Normalized ROE =Average Net Income2003-07/BV of Equity2006 = 3,954/33,475=11.81%; g = Retention Ratio * ROE = 0.4572 * 0.1181 =5.40%

 

Obviously, the results are very different and this is explained by very low-income period in 2001-2003 for the bank. However, “black-swan” factors should not be forgotten. As 2008 appeared to be a severe crisis, net income for Deutsche bank was negative. That underlines once more that valuation is not “solve all” panacea and it is not accurate.

 

Dividend Discount Model may seem to be restricted because of dividend’s limit comparable to the whole net income. However, FCFE might be difficult to calculate as operating income and capital expenditures are not always definitely defined. This model is also very useful to estimate which shares undervalued or overvalued.

 

 

 

 

 

 

 

 

 

 

 

 

 

2.4. From FCFE to FCFF

2.4.1. Cost of capital

Concerning cost of capital there is another approach, where we have to know weights of debt and equity in our structure and its cost => WACC = ke (E/(D+E)) + kd (D/(D+E)). In addition, tax shield must be taken into account as debts decrease our tax burden.

To demonstrate change of cost of capital for a firm I will make up the following data.

Variant	E/(D+E)	Cost of Equity	D/(D+E)	After-tax Cost of Capital	Cost of Capital
1	90%	17%	10%	0.0900	16.2000%
2	80%	18.70%	20%	0.1050	17.0600%
3	70%	20.00%	30%	0.1150	17.4500%
4	60%	21.00%	40%	0.1200	17.4000%
5	50%	21.50%	50%	0.1310	17.3000%
6	40%	23.20%	60%	0.1350	17.3800%
7	30%	25.20%	70%	0.1400	17.3600%
8	5%	27.50%	95%	0.1680	17.3350%
9	1%	30.50%	99%	0.1700	17.1350%

 

From this we can see that how much the cost can be changed and this is obvious as well that after some point there may be optimal cost of capital and where decrease in equity do not lead reduce cost of capital. Therefore, capital structure must be studied carefully and meticulously as it has an influence on the value of the whole firm.

2.4.2. FCFE approach

In valuation there are such very important factors of Free Cash Flow to Equity and Free Cash Flow to Firm. The former is a measure of how much cash can be paid to the equity shareholders of the company after all expenses, reinvestment and debt repayment and calculated as: FCFE = Net Income – (Capital expenditures-Depreciation) - Change in Net Working Capital + New Debt - Debt Repayment. The latter is calculated as EBIT (1 - tax rate)+ Depreciation- Capital Spending- Change in Working Capital= Cash flow to the firm and which is used primary in valuation of the firm. If capex and working capital are partially financed by debt and principal repayments are made it must be taken into account. Therefore, formula will look like : FCFE = Net Income - (1– debt ratio)(Capital Expenditures – Depreciation) - (1– debt ratio)∆Working Capital.

FCFE can also be calculated in another way. Similar to retention ratio mentioned above we calculate reinvestment rate. Equity Reinvestment Rate = (Capital Expenditures - Depreciation + ∆Working Capital) (1- δ)/Net Income and therefore, FCFE = Net Income (1 – Equity Reinvestment Rate). After these calculations the equation resembles the one in Dividend Model: Value of the Stock = PV of FCFE during High Growth + PV of Terminal Price or Value0 =

∑(FCFE)t/(1+r)t+Terminal Valuen/(1+r)n.

 

There is one principal difference between two approaches. The value of dividends certainly cannot be below zero whereas the one of FCFE can be. That can happen especially during periods of establishment and development as they demand high reinvestment resources.

 

As in the previous model we have to take average capital expenditures as they can vary a lot. In addition, R&D and acquisitions and other external capital expenditures must be considered as capex as well because this kind of expenditures is used for many years. The same reason is applied to working capital expenditure.

 

In addition, expected growth is also calculated similarly to the previous model. Expected Growth in Net Income = Equity Reinvestment Rate * Return on Equity. It is different in the fact the expected growth can be negative because reinvestment rate may be less than 0 if capital investment becomes less than depreciation; it can be more than 100 percent as well and then net income will increase more than ROE but a company will be pushed to issue new shares.

 

There is as well one precision about discount of FCFE. As it contains both incomes from operation, cash and securities for more precision net income should be discounted after substraction of incomes from securities and cash and then these incomes must be added to the result.

My example of calculation will be based on the analysis of Mercedes Company. I have taken data from 2008-2011 years (appendix 1).

 

mil euros	2010-2011	2009-2010	2008-2009	Aggregate
Net income	6,029	4,674	-2,644	8,059
Depreciation	3,575	3,364	3,264	10,203
non-cash working capital	3,872	-57	-2,186	1,629
CAPEX	8187	9004	-4438	12,753
Equity Reinvestment ratio	8,484	5,583	-9,888	4,179
Equity Reinvestment rate	1.407199	1.1944801	3.7397882	0.518551