Darmodaran approach to company valuation

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