Darmodaran approach to company valuation

 

From the analysis above it can be seen that 2008-2009 comes to be the most complicated as this period is climax of crisis. Moreover, these calculations prove that it is necessary to consider several years because aggregate figure shows much less equity reinvestment. In addition, if we take the part 2008-2009 it becomes absolutely irrelevant as both equity reinvestment ratio and net income are negative. However, aggregate analysis eliminates this error.

 

For prolongation of my analysis I make the following calculations:

Year	Net Income	Equity	ROE
2010-2011	6,029	36,373	17%
2009-2010	4,674	39,624	12%
2008-2009	-2,644	30,261	-9%
aggregate	8,059	106,258	8%

 

Therefore, the expected growth in Net Income= 51.85%*8%= 3.93%.

Then I can estimate the value of the equity. First of all I will calculate cost of equity for my discount rate. Taking data for beta for Daimler AG and risk-free rate for German market from reuters.com, I will get: 3%+1.94(8%-3%) =12.7%. I will calculate FCFE for the following 4 years and on the 5^th year I will calculate the Terminal Value.

Therefore, I got the following results:

Daimler AG	2012	2013	2014	2015
Expected FCFE	6266.11336	6512.5521	6768.683	7034.887
Equity Reinvestment Rate	51.86%	51.86%	51.86%	51.86%
FCFE	1,569	1,688	1,811	1,939
Cost of Equity	12.70%	12.70%	12.70%	12.70%
PV of FCFE	1392.27851	1497.556	1606.974	1720.695

 

Then the Terminal Value will be: (7034.887*(1+3.96%)*(1-51.86%))/(12.7%-3.96%)=40282.7

And the Value of the  equity will be: ∑PV of FCFE+Teminal Value =46500.155(mil euros).

 

On the day of my last valuation day there were 1,066,345,732 stocks. Therefore, the price per share is 43.6 euro. As the market price for December 2011 was 51 euro per share that mean that Daimler’s stock is overpriced.

2.4.3. FCFF approach

The third approach of valuation is Free Cash Flow to Firm where operating assets of the firm and its generated cash flows are out concern. The cash flow to the firm can be measured in two ways. One is to add up the cash flows to all of the different claim holders in the firm. Thus, the cash flows to equity investors are added to the cash flows to debt holders (interest and net debt payments) to arrive at the cash flow to the

firm. The other approach to estimating cash flow to the firm, which should yield

equivalent results, is to estimate the cash flows to the firm prior to debt payments but

after reinvestment needs have been met (endnote 3):

EBIT (1 - Tax Rate)– (Capital Expenditures – Depreciation)– Change in Noncash Working Capital= Free Cash Flow to the Firm. Or alternatively and similarly to the previous model:

Reinvestment Rate =(Capital Expenditures - Depreciation + Δ Working Capital) )/EBIT (1- tax)

Free Cash Flow to the Firm = EBIT (1 – t)(1 – Reinvestment Rate).

 

Further logic is the same as described above. There is just another precision that expected growth in EBIT is estimated as: Reinvestment rate*Return on Capital, where the latter is EBIT(1-t)/(BV of Equity +BV of Debt - Cash). Damodaran points out here that if the firm has expanded significantly it is better to use industry average for reinvestment rate than the firm’s one as historical factor will likely to be higher than the expected future rate.

Any firm that earns a return on capital greater than its cost of capital is earning an excess return. These excess returns are the result of a firm’s competitive advantages or barriers to entry into the industry. High excess returns locked in for very long periods imply that a firm has a permanent competitive advantage (endnote 4).

 

In case it is necessary to come from Firm Value to Equity Value it is not only necessary to substract all debts but also keep in mind three items which might be not clearly defined. These are deferred tax, unfunded pension and healthy plans and law suits. If there is a court process it is obligatory to diminish equity value by the product of probability and the sum of possible fine. If a firm has not put aside enough resources for pension it will be pushed to meet these obligations. Deferred tax obligations must be eliminated from the value when a firm is supposed to come to stable growth.

 

The principal advantage of FCFF method over FCFE is that it does not demand calculating new debt issues and repayments if changes frequently arise.

 

If we make some assumptions it is quite easy to get an equity value from a firm value. However, in reality two results may be different as interest rate may vary if old debt exists in book-entry; non-operating income takes place.

 

I will make up the following simple example. Let’s say that there is a firm with EBIT of 200 million and a tax rate of 20%. It has a leverage of 3/7 with equity 300 millions and 700 millions. Cost of equity is 19% and cost of debt is 10%. Therefore, wacc= 19%*0.3+10%*0.7*0.8=11.3%. The Value of the Firm= 200*0.8/0.113= 1415.929. Then Value of equity is 1415.929-700=715.929

 

Estimating directly equity value we get: Net income= (200-0.10*700)*0.8=104. Then, equity value =104/0.19=547.36. In result, even this simplified example shows that outcomes may not be equal.

The following table represents relation of cash flows and different claimers.

Claimholder	Cash flows to claimholder
Equity Investors	Free Cash flow to Equity
Debt Holders	Interest Expenses (1 - tax rate)+ Principal Repayments- New Debt Issues
Preferred Stockholders	Preferred Dividends
Firm+ Equity Investors+ Debt Holders+ Preferred Stockholders	Free Cash flow to Firm =Free Cash flow to Equity + Interest Expenses (1- tax rate)+ Principal Repayments- New Debt Issues+ Preferred Dividends

Resource: Valuation presentation/Damodaran p24

 

To end up with this method I would like to underline Damodaran’s interesting emphasis on valuation of private companies. It implies the same technics but we have to apply higher risk rates because private businesses are usually undiversified or less diversified and private companies have limited life. Therefore, value of private firms will be remarkably less. Damodaran explains that some firms go private in order to correct existing problems and then they go public again.

 

 

3. Relative Valuation

Comparing to discounted cash flow approach, relative valuation has the objective to value assets, based on how similar assets are currently priced in the market. In order to do so some steps must be undertaken.

 

First of all it is necessary to standardize values of assets concerning earnings and revenues they generate, their book value, their replacement value². Such indicators may be outstanding as Price/earning, Price/book value, Price/replacement cost ratios, Price or Value/sales ratios. The last ration is not based on accounting measures, rules and standards and, therefore, it is the most comfortable way to compare different markets.

 

For obtaining, analyzing these multiplies and what cause changes in the value we take simplest discounted cash flow model Value of Equity = Dividend(1+g)/(costequity- gn)and the following steps are made:

1. Divide both sides by the earnings per share, we obtain: Valueeq/ Earnings/#Shares)=(D(1+g)/(r-g))*Earnings/#shares)=> P/E=payout ratio(1+g)/(ke-g)
2. Divide both sides by the book value of equity, we can estimate the price/book value ratio for a stable-growth firm: P/BV=ROE*(Payout ratio*(1+g)/(ke-g)
3. Divide by the sales per share then we will get:P/Sales=Net Profit Margin * Payout Ratio *(1+ gn)/(ke –gn)

 

The same logic is applied to FCFF approach:Value=FCFF/(kc-g) => Value/FCFF=1/(kc-g).

Therefore we get : Value/EBITDA=(1- t)/(kc – g)+Depr (t)/EBITDA/(Kc-g)-CEx/EBITDA/

(kc – g)- (DWorking Capital/EBITDA)/(kc – g)

 

Applying this formula we can understand why certain price of a stock is than the one of another. For example, P/E of two stocks can be 1.3 and 1.1. Therefore, it does not just tell that the first is more expensive but also that it has higher return on equity etc.

 

Then, comparing the multiples of a company with average multiples for the industry we can say whether certain equity or a firm has more potential growth, ROE, payout ratio etc or it is just overvalued. Comparable companies may be chosen preferably concerning their size, similar cash flows, risk and growth or just all the companies in the industry if there are not many companies in the market or there are not so similar firms. However, if more than one variables are different it is necessary to run regression model of if relationship between variables and multiples are stable there are large number of firms. If this is not sufficient we can take similar firms from other industries applying regression as well.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4. Equity as an Option

1. Definition and Application

The third for valuation according to Damodaran concerns option approach. It can seem that equity, actually, does not have anything in common with option. However, the professor explains in the following way. The equity has two main characteristics. Investors have rights to control the business and to sell their assets. However, they are the last who gets anything in case of liquidation of the firm. Despite this negative fact, investors will not lose more than the amount of their investments, that is, their liabilities are limited. This situation is similar to call option.

 

Therefore, the equity can be regarded as call option on the firm. It means that for exercising it, liquidation of the firm is needed and all the debts must be paid off. Then, it will be clear whether option will be used or not when all the debts are to be paid. Moreover, it implies that the firm itself is underlying asset.

The graph of such mentioned model of option looks like classical option on securities or goods.

                                                    Net pay-offs on equity

 

 

 

Face value of the debt

                                             Value of the firm

Comparing to a classical concept, face value of debt must be reimbursed just like the usual premium on option is paid at any case. Net pay-off on equity will obviously depend on the Value of the firm. The equity will not be worthless if Value < Debt because firm value may change in time before the debt come due. However, that logic works only before the exploding storm. In case of the real liquidation net pay-offs will be positive only if the value of a firm is more than debt.

 

By means of this approach we can estimate equity from the firm value and estimate which interest rate should correspond exactly the company with this certain value and at this amount of debt.

Let’s consider the following example using Black-Scholes pricing option model which look like:

Where:

The variables are:

S = stock price 
X = strike price 
t = time remaining until expiration, expressed as a percent of a year 
r = current continuously compounded risk-free interest rate 
v = annual volatility of stock price (the standard deviation of the short-term returns over one year). See below for   
ln = natural logarithm 
N(x) = standard normal cumulative distribution function 
e = the exponential function

Then we assume that we have a firm with standard deviation 50%. Then the Value of the underlying asset = S = Value of the firm = $ 200million, Exercise price = K = Face Value of outstanding debt = $ 150 million, Life of the option = t = Life of zero-coupon debt = 10 years, Variance in the value of the underlying asset = Variance in firm value = 0.25 Riskless rate = r = Treasury bond rate corresponding to option life = 10%

Having made my calculations I received:

d1 = 1,015073 N(d1) = 0.8438

d2 = 0,515073 N(d2) = 0.6950

Value of the call = 200 (0.8438)– 150 e-(.10)(10) (0.6950) = $130,4 million and the value of the debt is 38,35143. Therefore, the interest rate on debt must be = (150/38,35)^0,1=14,61%. Hence, the risk premium must be equal to 4,61%.

This model is also different in the fact that when in DCF the value of firm will not be sufficient to cover debt, the equity will have this value. For example, let’s say that the value of the firm dropped from 200 to 120 mln. Therefore, the equity value will be 94,92-34,3066=60,6134

 

 

 

 

 

4.2 Advantages and Drawbacks of the Option approach

In addition, there is also one remarkable difference between DCF and option approaches. In the former increasing risk automatically decreases the equity value. In the latter, however, this is not the case. With a reference to the mentioned model of Black-Scholes, we can say that with standard deviation, the value of the equity increases (as well as probability of default and premium for risk).

However, we should always keep in mind that not everything is so simple and straightforward in the model. In order to accomplish the calculation, the following four assumptions are made:

• There are only two claimholders in the firm - debt and equity. Elimination of preferred stocks makes calculation much easier.
• There is only one issue of debt outstanding and it can be retired at face value what add similarity to the strike price.
• The debt has a zero coupon and no special feature; coupon payments might push equity holders to exercise the option earlier if there is a lack of cash.
• The value of the firm and the variance in that value can be estimated.

Option approach may seem redundant because it is easier to subtract market value of the debt from the firm value if the debts are listed. However, when the debt of a firm is not publicly traded, option pricing may be the alternative way. In addition, debts can be inadequately priced and, therefore, option calculation can be reasonable.  And, eventually, redistributive effect of value between debt and equity is the outstanding one.

 

Certainly, it will be much more difficult to implement this model with all the four assumptions and to get more accurate results at the same time because not a lot of firms will meet these requirements. Then we can use two first approaches and then apply option model for determining redistributive effect. It represents one of the ways out. However, values will differ a lot.

 

Another solution is to convert various bonds issues and coupon payments into one equivalent zero-coupon bond. For this we will calculate durations of all the bonds and apply their weighted average which will be our conductor of time expiration for the option.

 

The same thing concerns the face value of the debt. It is possible to sum up all the principals and apply it to the calculated duration. There is a drawback of this approach. A firm will have to pay out interests at the specific periods concerning every bond in reality. Another way is to calculate in another order: firstly, we sum up all the expected interest payments and come to the face value. The third way is to calculate the face value of the debt and the interest payment each according to the percentage of the whole firm value. That means that during its existence the firm will gradually lose its value each year.

 

From the mentioned analysis and explanation it is obvious that the option approach gives additional variables for consideration. It states that not only margins are important for business but also duration of the bond and variance of the firm are crucial.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Conclusion

 

In my work I described and explained Damodaran’s approach to valuation. It can seem that there is something controversial in his three approaches. Choosing different approaches we can get different results and, furthermore, these values may differ a lot.

 

Such a phenomenon can be explained by the fact that DCF model consider a firm for the long-term period and implies that the market has time to correct its errors. By contrast, relative valuation states that, on average, firms on the market are priced correctly whereas it may be not.

 

DCF demands finding expected growth, cash flow, the time period for valuation, terminal value and discount rate. It requires understanding when firm is to be at the high growth state and at the stable. It emphasize on the importance of profitability and growth.

 

Relative valuation implies to find standardized measure of value. It finds out important multiples for valuation and, hence, has a deeper analysis. For example, it gives understanding that a certain stock is higher priced due to its high ROE.

 

Eventually, the third approach assumes that equity investors own the option to liquidate the firm’s assets and claim the difference between asset value and debt outstanding for themselves.

 

It is clear that valuation states somehow subjective but we can choose proper valuation approach for a certain case. The last approach is best for high-leveraged and in financially difficult situation firms. Whereas, the relative approach is suitable in case of presence of many similar firms on the market which are correctly priced. At long last DCF approach is the simplest one and may be used when the stage of growth is certain and when two others are not applicable.

 

 

 

 

 

 

 

 

Endnotes

1. Aswath Damodaran/ Corporate Finance, page 815
2. Aswath Damodaran/ Corporate Finance, page 819
3. Aswath Damodaran/ Corporate Finance, page 849
4. Aswath Damodaran/ Corporate Finance, page 852