Managment Engineer - Investment banking

1 - Valuation methods

Divided by topic

Contenido 1. Introduction ................................ ................................ ................................ ................ 2 2. Asset based method ................................ ................................ ................................ .... 3 3. Earnings based method ................................ ................................ ............................... 5 4. Discounted Cash Flows method (DCF) ................................ ................................ .......... 7 1. Free Cash Flow to Firm (FCFF) ................................ ................................ ................... 7 2. Free Cash Flow to Equity (FCFE) ................................ ................................ ................ 8 3. Terminal va lue ................................ ................................ ................................ ......... 8 5. Mixed method with goodwill ................................ ................................ ...................... 10 6. Economic Value Added method (EVA) ................................ ................................ ......... 11 7. Relative Valuati on methods (RV) ................................ ................................ ................. 12 1. Comparables selection ................................ ................................ ............................ 12 2. Locating the financia l information ................................ ................................ ........... 13 3. Multiple selection ................................ ................................ ................................ ...13 4. Benchmark the comparables and va lue calculat ion ................................ .................. 15 8. Multi -business companies: Sum Of The Parts (SOTP) ................................ ................... 17 9. Annexes ................................ ................................ ................................ ..................... 18 1. Balance sheet reclassification ................................ ................................ .................. 18 2. Reclassificat ion of the Profit and Loss statement (P&L) ................................ ............. 19 3. Weighted Average Cost of Capital (WACC) ................................ ............................... 20 4. Capital Asset Pricing Model (CAPM): estimation of cost of equity ............................. 20 5. FCFF and FCFE: deduction of the formulas ................................ ............................... 21 1. Introduction Valuation methods can be divided between those that focus on the market value of similar companies, which are the relative valuation approaches; and those that focus on the company itself (either its assets, cashflows, or profit), which are the other 3 approaches. The two most popular methods are traded multiples and discounted cash flows (DCF), which are always used and compared against each other, but the others can also be useful in par ticula r situations, depending on the company, its business model, its market, … If we are doing the valuation from inside the company we will be able to do it using internal information, and thus obtain much more precision. If we are outside of it we will h ave to use publicly disclosed information: using internal information would be illegal, even if we managed to find it. When using valuation methods, we will probably have to make some assumptions . It would make no sense to think that our assumptions will be 100% correct, so we will create a range of values for each guessed parameter, associating a probability to each value inside the range. This will result on us not obtaining a single EV for the company, but a range of possible Enterprise V alues (ideally we would get a probability distribution, so we can know which values of the range are more probable than the others). We will use different methods to compare the different ranges of values, and t he range in which they “overlap” will most likely be the real value of the company. We also must take into account the possible impact of our assumptions being wrong : if changing a variable doesn’t have much of an impact on the final result we can probab ly leave it however we estimated it, but if it has a big impact, we must make sure our assumptions are properly backed by theoretical and empirical data. The two most popular ways to perform this analysis is through a regular sensitivity analysis (changing the value of the variables one by one) and through a Monte Carlo simulation (changing the value of many variables at the same time). 2. Asset based method When using this method we assume that the core value of the corporation is its assets , and its future p erformance will be based on it. Of course this method should only be applied to companies in which th is assumption is close to be true: banks, insurance, real estate,… This method is based on the definition of the Book Value of Equity (also known as shareh olders equity) : � = ����� ������ − ����� ����������� The first thing we need to do in order to apply this method is to obtain the balance sheet (although we can use internal information if we are working inside the company). The problem is that the book value (the one registered in the balance sheet) corresponds to the historical value of the asset, that is, the price for which it was purchased, not its real, actual value. In order to correct this we will have to add up every pot ential gains or losses in value for each asset and liability in the balance sheet (depreciation, reparations, improvements,…) ��� .� = ���� � + Δ������ − Δ����������� In order to calculate the potential gains and losses on the assets we should take into account, among other factors: - Depreciation/Amortization. - The current market price of the owned asset, as well as the market price of a new one. - The cost of setting up a new one (th at is, purchase + transport + installation + …). - The money invested in the currently owned one (repairs, improvements,…). The “real” value of the asset should be estimated taking these points into account (not necessarily all of them, just the most appropr iate ones). As a general rule, we can calculate the adjusted value of an asset as: ������ ����� − ������������ − ��������� ������ + ��������� ����� − ���� ����� − ����� With depreciation being calculated as the depreciation rate times the year since the asset was purchased. We should also take into account the expected losses when working with trade receivables, and, for bonds, we can calculate the current value (and use it as “market value” in the previous equation) as the NPV of all future cashflows. In practice we will have to look at each asset individu ally and never forget taxes , calculated as (1 -t)*gross potential gain. If the gross potential gain is negative (that is, a potential loss), we will get a tax shield from it. It is important to not e that, if we use the method to update our book value and we end up having an increase in the company’s value, we will have to pay taxes without having created any real value. This is why value of an asset on the balance sheet is usually updated only if the company is planning to sell it. Potential gross gain/loss There are two versions of the method: • Simple asset based method : only the tangible assets and liabilities included in the balance sheet are considered (tangible assets). • Complex asset based method : it includes not only the assets and liabilities in the balance sheet, but also the intangible ones. It can be performed on two levels: ➢ First level : only the intangible assets present in the balance sheet are considered (trademark, licenses, concessions, p atents,…) ➢ Second level : the off -balance intangible assets are also considered. Only those assets that could be transferred independently are taken into account (like sales network, but, for example, market share, image, or customers can not be valued separ ately). Depending on the relevance of the intangible assets we will choose one of the previous methods. Of course, deciding whether those intangibles are relevant or not can be difficult a priori. For example, an easy way to check if the value of the compa ny is mainly based on its products is to compare the price of its products with other equivalent ones in the same market: if the price is higher and they manage to have a significant market share anyway, the trademark is probably a relevant asset (like Coc a Cola against other cola drinks). There are 2 approaches we can use to value intangible goods : • Analytical , based on rational hypotheses, explained and documented on each item: ➢ Sum of the historical costs needed to obtain that good (“discounted” from the past to the present to express its equivalent actual value). ➢ Sum and discounting of the costs the company would have if it had to replace the good. ➢ Sum and discounting of additional incomes and benefits created by the ownership of the good. ➢ Sum and discount ing of the losses the company would have in case it didn’t have the good anymore. • Empirical , based on the application of real -world observations by experts. In each situation we must choose the most appropriate valuation technique. Overall, the main pros a nd cons of the method are: 3. Earnings based method This method estimates the value by considering the cashflows the company will be able to generate in the future. This way, the fundamental value drivers are considered to be the cash flows themselves, the time at which they occur, and the discounting rate (which represents the risk profile of the company). This method is basically a simplified DCF, so it is not used often, unless maybe for stable companies in financial equilibrium. Earnings based methods can be classified in 2 categories: • Analytical methods : cashflows are estimated for each year of the forecasting horizon. After the forecasting horizon is reached, we can calculate a terminal value (TV) by estimating a cash flow that will stay cons tant indefinitely for t>T (R TV) and add it as a perpetuity. We will usually forecast the cash flows until we reach a point in the future in which we expect the company to remain “stable” and have a constant growth rate (which could be 0). The value of the firm will be calculated as: � = ∑ � � (1 + �)� � �=1 + � �� (�− �) ∗ (1 + �)�+1 With: - W = value (can be EV or equity value). - R = cash flow (usually EBITDA, EBIT, or NP). - i = discount rate (WACC or k E). - t = time [years]. - T = end of forecasting horizon [years]. - RTV = cash flow for t=T+1. - g = annual growth of R TV [%]. If no growth is expected, we can just set g=0. • Synthetic methods : the idea is the same, but we will not estimate the cash flows for each year of the forecasting horizon. Instead , we will ju st estimate an average cash flow (R avg ) and assume it grows constantly with a rate g (which might be 0). That is, we will basically calculate a terminal value with T=0. If we want to calculate the value the company would have if it kept generating cash flo ws indefinitely we will use a perpetuity (left), while, if we want to consider the cashflows to stop after n years, we will use an annuity (right). � = ������������������� ������−������ � = ������������������� ������−������ ∗ (1 − (1+������)������ (1+�)������) These formulas can be used to calculate both EV and Equit y value, depending on the cash flows and discounting rate we use (see annexes on kE and WACC ). Value Cash flow Discount rate EV EBITDA (or EBIT) WACC E Net Profit Cost of equity (kE) TV The implementation of the method requires the following steps: 1) Definition of the analytical forecasting horizon (from t=1 to t=T). Usually the end of the forecasting horizon will be set at a point in the future in which the company is supposed to stabilize its performance, that is, it will have a constant, perpetual growth (from there on we will calculate the terminal value). This might range from ~5 years to ~ 10, depending on the specific company and its situation. 2) Normalization of the accounting results . This defines an average income adjusted for all the extraordinary components, which are supposed to be non -recurrent and unrelated to normal operations, and thus they could artificially increase or decrease the cash flows. This adjustment operations eliminate: ➢ Extraordinary components (gains and losses) which are not recurring. ➢ Unrelated components to the normal operations (capital contribution,…). ➢ Effects from intangible resources (if the income is strictly influenc ed by the result of the investments produced by intangibles, it is appropriate to distribute the costs borne for the investments in intangibles during time). ➢ Apparent income components (like artificial incomes reached in periods with high inflation) 3) Defin ition of the expected incomes . This is done using: ➢ Historical data discounted to its NPVs, with a maximum usability timeframe of approximately 5 years. ➢ Forecasted results which express the expectations for the future. 4) Definition of the discounting rate . It has to be coherent with the cash flows used and the value we want to calculate (WACC and EBIT or EBITDA for EV, k E and NP for equity value). The way to calculate these rates is shown in the annexes. 4. Discounted Cash Flows method (DCF) DCF is basically an improved version of the earnings based method. The main difference is that, while earnings based relied too much on earnings, DCF is focused on cash flows in general. It is not uncommon for lots of companies to have negative earnings du ring long periods of time (in order to invest in the company and make it grow, to avoid taxes,…). Like the earnings based method, DCF will be specially useful when calculated the value of limited duration projects and when valuing stable businesses, with l imited growth and/or foreseeable results. However, DCF is used in most company valuations , usually in combination with, at least, the relative valuation method. In the exact same way as w hat was shown in the previous method, DCF can be calculated from the asset side to obtain EV, or from the equity side to obtain equity. The difference is that now, instead of EBITDA, we will use Free Cash Flows to Firm (FCFF), and instead of NP, we will use Free Cash Flows to Equity (FCFE). The discounting rates will still be WACC for the asset side and k E for the equity side . Given that EV=E+NFP, the calculations can be performed from both sides with equal results, but it is strongly advised to first calculate EV from the asset side and then use the NFP to calculate E . FCFE are usually calculated from FCFF, so it is also more convenient to do it that way. 1. F r ee Cash Flow to Firm (FCFF) FCFF are cashflows available to all investors, both debt holders and equity holders. It is usually calculated as: ���� = ��������� ∗(1− �������)+ �&� − Δ��� − ����� • EBIT is calculated as Sales – OpEx – D&A. • Taxes are calculated as t*EBIT , not as t*EBT. This is done in order to “ignore” tax shields (they are taken into account, but not as “negative taxes”, but in the financial structure of the company). The term EBIT*(1 -t) is also referred to as EBIAT. • D&A : here we must include amortization of intangible assets (patents, license s,…), provisions for employee termination indemnities, and other provisions . • ΔNWC : the net working capital represents the sum of current assets minus the sum of total liabilities, without taking into account cash. It can be seen as the amount of cash the c ompany needs to have “permanently invested” in order to fund its operations on an ongoing basis. We can calculate its variation as ΔNWC= ΔAR+ ΔINV -ΔAP . • Capex : it represents investment in physical assets ( maintenance, expansion, acquisitions ,…). The cash infl ows due to disinvestments have to be deducted. Once FCFF for each period are calculated, EV is obtained as: �� = ∑ ��� �� (1+ ���� )� � �=1 + �� �� (1+ ���� )�+1 2. F r ee Cash Flow to Equity (FCFE) FCFE are cashflows available only for shareholders, and thus net of all flows related to non - operating activities (financial structure, variations in debt or equity,…). It is calculated as: ���� = ���� ± ��� .��� /��� ± Δ�ℎ��� ������� ± Δ��� ���� • Financial revenues and expenses (net of taxes) : both financial revenues and expenses have to be reported net of taxes, that is, multiplied by (1 -t). This will cause financial expenses to create a tax shield. • Increase in share capital : we can calculate it as Capital increase – Di vidends , with capital increase being caused by selling new shares. • Net debt variation : new loans will make more cash available to shareholders, while debt refunds will have the opposite effect. Once FCFE for each period are calculated, the equity value can be obtained as: � = ∑ ��� �� (1+ ��)� + �� � (1+ ��)�+1 � �=1 3. Ter m inal value With DCF we encounter the same problem we found with the earnings based method: it is not possible to forecast all future cashflows for an infinite time, so we will have to fo recast them for a number of years (usually 5 to 10 years ) until we reach a point in which the company behaves in a stable way (supposedly), and calculate the terminal value (TV) from there. There are 2 possible ways to calculate the terminal value: • Perpetu al growth : we assume that, after the forecasted horizon, the company will remain stable and its growth will stay constant (with a value that could be 0). It is a risky approach, as companies don’t really tend to grow forever with a steady rate, no matter h ow “stable” their situation is. Given that the last cash flow we estimated was the FCF t=T and that the TV begins at T+1, depending on whether we are looking at the asset side or equity side, the TV will be: ���� = ��� �������∗(1+������) ��������� −������ ��� = ��� �������∗(1+������) �������−������ • Exit multiples : the terminal value is calculated as: �� = ����������� ∗ �������� Where the fundamental is a cash flow of some kind (usually sales, EBIT or EBITDA if calculating EV, and NP if calculating E) and the multiple is a proportion between a cashflow and a firm’s value (like EV/sales, EV/EBIT, EV/EBITDA, E/NP, P/EPS,…). Of course, the fundamental and the multiple must be coherent and both must involve the same cash flow. The fundamental used can be a cas h flow from the last analytica l period (t=T), while the multiple typically depend on the industry or market of the firm. TV is calculated for t=T+1, which is why it has to be discounted when calculating EV or E. It can be seen that both methods for calcula ting TV are really simple, but the amount of assumptions about the future that have to be made in order to calculate it are so many that any attempt to increase precision would just make the calculations more complex without any real positive effects. In t he end, the banker’s experience and his knowledge about the method, the firm, and the market in which it operates will be far more important than any mathematical model (kind of a “half -art -half -science” situation). TV usually represents a very relevant p ortion of the company’s value (between 60% and 90%), so it is important to be as precise as possible when calculating it and make sure we can back all the assumptions made. Of course, the longer the analytical period (forecast period) the lower the weight of TV, but that wouldn’t help much as a general rule, given that, the farther away from the present, the more imprecise our projections on cash flows will be. In the end it will be around 5 -10 years (maybe more for companies involved in long economic cycle s, long term investments, and multi -year concessions; maybe less for very unstable industries). When using this method it is specially important to perform some kind of sensitivity analysis to identify the most relevant variables, and thus the most relevan t assumptions, in order to make sure that they are properly backed by theory and evidence. One variable that will probably have a big weight in the final result will be the discount rate (either WACC or k E). The way of calculating both is showed in the ann exes. 5. Mixed method with goodwill Mixed method, together with EVA, are the two valuation methods based on the economic profit approach . Mixed method focuses on calculating the Equity value, while EVA calculates EV. These approaches are based on the idea that the economic capital is dependent on: • The value of the company operations (equity or assets). • The value of the incomes minus the exp ected return of such operations. The idea being that, if the income generated is lower than the expected return of the assets (or equity), there is no economic profit. The equity value will be calculated as: � = � + ∑ ���− ��,�∗� (1+ ��,�)� � �=1 Being E the equity value, K the adjusted equity (calculated in the asset based method), and G the goodwill (return of the company minus its expected return). As long as the goodwill is positive, the value calculated with the mixed method will always be bet ween the one calculated with the asset based method (which would be only the adjusted equity, and thus the lower bound) and the one calculated with the earnings based method (which would take into account all the return generated, not just the goodwill, th us being the upper bound) . On the formula on the right KE,H accounts for the historical return on equity, while K E,F is the estimated future cost of equity. It should be bigger than the historical one, as it accounts for the risk associated with a higher i ncome. This method can be applied with limited or unlimited compounding , depending on whether the forecasting horizon has a limit or not. Of course estimating infinite cashflows is not feasible, and assuming a constant growth rate and calculating it as a p erpetuity would not make sense either, as we would be assuming that the goodwill will always be positive, that is, that the company will always outperform the “expected” return on equity for its assets. Calculating a terminal value would not make sense for the same reason: by definition the company is supposed to remain “stable” after the forecasting horizon is finished, so at that point the goodwill should be 0 . This method is suitable for stable companies , where it is useful to consider the ability of respecting shareholders profitability requirements considering the investments done . 6. Economic Value Added method (EVA) This method can be considered equivalent to the mixed method , but it looks at enterprise value instead of equity value . The equivalent to goodwill will be the EVA: �� ��= ���� ��− ���∗���� With CE being the capital employed, and NOPAT being the Net Operating Profit After Taxes, also known as EBIAT, and calculated as NOPAT = EBIT*(1 -t). EV will be calculated as the sum of the Market Value Added (MVA) and Adjusted Capital Employed (ACE): �� = ��� + ��� Once EV has been calculated, we can obtain the equity value as EV = E + NFP. ACE is calculated with the asset based method : to do it, we must remember that: �� = ����� ������ − ������� ����������� = �� + ��� − �� ℎ�� ��� .���� . MVA is calculated as: ��� = ∑ ���� ��− (���� ∗��� )� (1+ ���� )� � �=1 = ∑ �� �� (1+ ���� )� � �=1 As it occurred with the mixed metho d, estimating the length of the forecasting period (T) will be difficult and important, as well as estimating the cash flows and the discounting rates (we might calculate a different WACC for each future year) . This method is usually suitable for companies with high growth rates . 7. Relative Valuation methods (RV) The idea behind the relative valuation approach is not to focus on the past or the future of a company, but rather on the value of other companies similar to it (comparables). The main advantage of this method is that it takes into account the market price s of companies like the one we are valuating , the main problem is that the method is as good (or as bad) as the comparables we choose: if they are not truly similar to our company the method won’t work at all, and selecting those comparables is not easy. Also, it can be affected by market volatility. RV methods are not usually used as the main valuation method , but rather as a sanity check for other methods (usually DCF) to make sure that the result is consistent with market valuations . RV approach is used on 2 valuation methods: traded multiples (also known as comparable companies) and comparable transactions . The main difference is that traded multiples focuses on the cash flows of the comparable companies with respect to their value, while comparable tran sactions looks at the ratio between those cash flows and the price for which the comparable companies were sold in the past (mainly in M&As). In this notes we will focus on the traded multiples method, but most of its characteristics can be applied to the other one, given their many similarities. The traded multiples method is performed through 5 steps : 1) Select the universe of comparable companies. 2) Locate the necessary financial information. 3) Spread key statistics, ratios, and trading multiples. 4) Benchmark th e comparable companies. 5) Determine valuation. 1. C o m parables selection Selecting the comparable companies is by far the most difficult part of the method. As it was said before, if the companies are not truly comparable the method will be useless, so it is better to choose few but really comparable companies . Competitors are usually a good starting point, but not always (example: Porsche is considered a luxu ry company and thus compared against luxury companies (LVMH,…) rather than automotive manufacturers like Renault or Volkswagen). Some of the parameters we can look at when selecting comparable companies are: - Industry or sector. - Geographical location (count ry, continent,…). - Size (assets, Capital Employed (CE), cashflows,…). - Profitability (ROE, ROCE, operative margins,…). - Financial structure and risk profile. - Maturity, stability and/or age. - Business model and value driver (maybe the most important one). 2. Lo ca ting the financial information Finding the financial information we need of the comparable companies can be relatively easy if they are listed companies, but it can be difficult, or even impossible, if they are private. If we assume them to be listed compa nies the information should be publicly disclosed; howe ver, we should also decide which years we should take into account. The main idea is to never use historical data , only estimations of the future. The first year of the budget or of the prospective est imation could be a good choice; we could also use the average of more than one year to cancel cyclical effects, or focus on stationary years (those that are not subject of positive/negative trends of growth). This choice will probably change on each specif ic case. 3. M u ltiple selection We should choose the multiple which better suits the characteristics of the target company. However, some industries tend to use specific multiples, and it might be difficult to find information about other multiples, so it can be better to just use the most accepted in the sector. Multiples take the form of a ratio in which the numerator is the EV or Equity value, and the denominator is a key value driver of the company. That value driver is usually a cash flow (EBITDA, NP, FCFF,…), but it can also be an indicative of the company’s size (assets, capital employed, book value of equity,…), or even something completely different from financial and accounting parameters (users for big data companies, raw materials reserves for mi ning companies,…). Of course the numerator and the numerator must be coherent: that is, NP, FCFE and BV go with Equity value, while EBITDA, EBIT, FCFF, assets, CE and sales go with EV. Non -traditional parameters (nº of users, raw material reserves,…) are usually paired with EV, as they tend to be a value driver of the entire company. Some of the multiples that can be used are: • EV/EBITDA : it is the most popular multiple , and it can be useful in most situations, as long the companies have similar business mo dels (internal production vs outsourcing,…). It is used for industrial companies, but it is not suitable for companies with very flexible structures and business models based on outsourcing, as they will have little to no D&A costs ( for outsourcing compan ies it is better to use EBIT ). Another advantage is that, unlike other cash flows, the EBITDA multiple can be computed for companies that are reporting net losses , since EBITDA is usually positive. It is also more appropriate than P/E ratio for companies i n industries that require high investment in infrastructure and long gestation periods . It allows for the comparison of companies with different leverage , as it ignores distinctions in the quality of cash flows resulting from different accounting policies. Some variations of the multiple are: ➢ EV/EBITDAR: EBITDA before rentals (leasing), used for the valuation of airlines. ➢ EV/EBITDAg: EBITDA discounted by its future growth. The lower the multiple, the higher the growth, and thus the more convenient it is to buy the company. • EV/EBIT : used for industrial companies, especially useful for those that are asset -ligth . For very much all other situations EBITDA is commonly used, as it is an overall better proxy of cash flows. • EV/FCFF : FCFF is also known as OFCF (Ope rative Free Cash Flow). It is used for telecom companies , and it has the advantage of being the most similar to the DCF method, but FCFF can often be difficult to obtain. • EV/sales : typically used for start -ups , as they usually have very low margins and neg ative EBITDA. The big problem of this multiple is that it does not take into account margins and profitability, so it may cause over -valuation in many situations. It is not really a good multiple overall, and it is not clear whether it makes sense to use t raded multiples for start -ups in the first place (by definition they are somehow “different”, so it is difficult to find other companies comparable to them. A better alternative for valuating start -ups is to use the comparable transactions method and look at what prices where paid for similar companies in past M&As, but this information can be difficult to find, as it is often private. • EV/CE : it is used in the luxury sector . It is a multiple strictly related to the value creation, but it ca n be difficult to calculate the “real” value of assets. EV/assets would be an alternative, but it is better to use CE. • P/E : it refers to the share price divided by EPS, and it is the same as net profit divided by equity value. Share price and EPS are easie r to find than equity value and net profits, which is why P/E is used. It can also be calculated as market capitalizatio n divided by earnings. It is, together with EV/EBITDA, the most popular multiple, used in all sectors . It has the big advantage of being easy to use and understand , while having the disadvantage of being affected by leverage , which doesn’t really change the real value of the company. Some variations of the multiple are: ➢ P/E adjusted: adjusted by the non -recurring components. ➢ P/FCFE. ➢ P/Eg: EPS are discounted by their estimated future growth. As it happened with EV/EBITDAg, the lower the multiple, the higher the growth, and the more convenient it is to buy. • P/BV : also referred to as “market to book” (M/B), it is calculated as market capitaliz ation divided by shareholders equity . It shows the premium investors are willing to pay when compared with the “real” value of the assets of the company, and can be applied to companies with negative earnings. The main problem is that when using BV we don’ t have any information about the cash flows generated by the equity invested, so it can be combined with ROE to solve that. It is used for banks and the real estate sector . • Other multiples referred to EV : EV divided by: ➢ Access lines, fiber length or route length [km]: telecommunications. ➢ Broadcast Cash Flow (BCF): media and telecommunications. ➢ EBITDA before rent expense: used for casinos, restaurants, and retail sector. ➢ EBITDA before exploration expenses: used for oil, gas, and natural reso urces extraction companies. ➢ Population: telecommunications. ➢ Production or production capacity: resource mining companies (oil, gas, metals, paper and forest products, …). ➢ Reserves: Reserves: resource mining companies (oil, gas, metals, …). ➢ Subscribers or u sers: media, telecommunications, big data companies. ➢ Square footage: real estate and retail sector. • Other multiples of equity value (or share price) : E divided by (if using P, the values are divided by the number of shares) : ➢ Cash available for distribution : real estate. ➢ Discretionary cash flow: natural resources. ➢ Funds from operations: real estate. ➢ Net asset value: financial institutions and real estate. 4. B en chmark the comparables and value calculation Once we have the multiples of all the comparable compan ies we could just calculate their mean (or median), multiply that value by the cash flow of our company (or whatever we are using in the denominator), and obtain the firm’s value. However, this is a very limited approach: a much better choice is to use a correlation analysis . This way we wouldn’t just focus on the multiple itself, but also on a third variable (usually the growth or margin of the cash flow we used, or the return if we used some measurement of the value of the assets). We would plot all the c ompanies in a graph in which one axis is the multiple and the other is that third value, and, with a correlation, use the third variable of our company to obtain its multiple, and from there its value. An example can be seen below. We should look at the R2 to see if there is any correlation between the multiple and the third value, but we don’t necessarily need high values: an R 2 of 0.2 or 0.3 might be enough to work with. The correlation does not have to be necessarily linear. Some of the third variable s used for the different multiples are: • EV/Sales v.s. sales growth. • EV/EBITDA v.s. EBITDA growth or margin. • EV/EBIT v.s. EBIT growth or margin. • P/E v.s. EPS growth. • P/BV v.s. ROE. • EV/CE v.s. ROCE. 8. Multi -business companies: Sum Of The Parts (SOTP) If we have a company with multiple business units, or a holding with multiple companies, we will value the entire company/holding using the Sum Of The Parts (SOTP) method. That is, each unit’s value will be estimated separately using the most appropriate method , and then they will be summed up to calculate the value of the entire group. The method goes as follows: 1) Identify the EV of each b.u. using the most appropriate method (if possible, taking into accoun t synergies between business units). 2) Identify central costs for the entire company. 3) Calculate EV of the entire company as the sum of the EV of each b.u. minus the central costs. 4) Calculate the NFP of the entire company and substract it from the EV to obtai n the equity value of the entire company . It is important to note that the WACC will be different for each business unit : • The leverage used is that of the entire company, so it is the same for each b.u. • The cost of debt is the same for each b.u. because the interest (spread) and the tax shield (and tax rate) depend on the entire company, while the risk free rate depends on the entire market. • The cost of equity will be different for each b.u.: even though the market risk premium depends on the entire mark et, beta will be different in each situation , as it has to reflect the operative risk of each b.u. 9. Annexes 1. B a lance sheet reclassification Traditional balance sheets (BS) identify total assets (current and non -current) as opposed to total liabilities (shareholder’s equity, financial and non -financial debt, and provisions). BS reclassification requires highlighting of : • Capital employed , which reflects the level of capital used by the business to finance operating assets and working capital. • Total sources of funding through which the company finances its ordinary and extra - ordinary operations. Capital employed (CE) is defined as: �� = ��� .������ − ������� ���� .= �� − ��� − ��� .�������� − ���� ���� . With : • �� = �� &� + ��������������� �� + ��������� �� • ��� = �� + �������� − �� ± �� ℎ�� ������� ��� ��� /����������� NWC is defined as the difference between current assets and current liabilities. • ���= ���−1+ ���� ��− �&�� • Ideally we would receive AR faster than we pay AP: that is, DPO (Days Payables Outstanding) higher than DSO (Days Sales Outstanding): ��� = ������������������ .������� ��������������� ∗365 ��� = ������������������ .������� ���� ∗365 �������� = ������������������ .�������� ���� (�� ��������������� )∗365 Sources of funding are defined as the sum of debt capital, equity capital, and retained earnings. They can be calculated as: ������� �� ������� = ��� + �ℎ��� ℎ������ ������ With: • ��� = ���� − ��� ℎ & ����������� • �ℎ� = ����� ������ − ����� ����������� �ℎ.� = �ℎ��� ������� + �������� + �������� �������� + �������� ��������� Receivables from shareholders should be reclassified as a re duction in Sh.E. • �ℎ.��= �ℎ.��−1+ ���− ������� ��+ ��� .������������ �� Shareholders’ equity is defined as total assets minus total liabilities . It is also referred to as book value of Equity . 2. R eclassification of the Profit a nd Loss statement (P& L) P&L reclassification is about calculating measures of profitability (e.g. EBITDA, EBIT, net income, etc ) which requires not only a review of the numerical financial data, but also a review of the written management discussion and analysis of the financ ial data. The calculations are done as follows: 3. W eig hted Average Cost of C apital (WACC) WACC is the discounting rate generally used for cash flows directed to the entire company, as opposed to cost of equity, which is used to discount cash flows towards shareholders; and cost of debt, used for cash flows directed towards debt holders. This is done because WACC considers cost of equity ( kE), cost of debt ( kD), tax rate ( tc), and leverage ( L=D/E =Debt/Equity). As such, WACC is exa ctly what its name indicates. It is calculated as: ���� = ��∗ � � + � + ��∗(1− �������)∗ � � + � The term kD(1-tc) reflects the net cost of capital, net of tax shield s. KD is the weighted average of the cost of the different loans the company has. It will alwa ys be lower than k E (unless the company is close to default), as the risk undertaken by debt holders (banks) is usually lower than that undertaken by equity holders (in case of bankruptcy they get nothing, while debt holders might have collaterals backing their debt). Many times we will not know the values of E and D , but only the leverage L. The formula of WACC can be applied anyway: knowing that L=D/E, we can transform the formula into: ���� = ��∗ 1 1+ �+ ��∗ � 1+ �∗(1− �������) The cost of capital k D and the tax rate t c are usually easy to know, while the cost of debt is calculated through the Capital Asset Pricing Model (CAPM). 4. C a p ital Asset Pr icing Model (CAPM) : estimation of cost of equity CAPM allows to estimate the cost of equity with the follow ing formula: ��= ��+ �������∗(�� − ��) Where: - kE = cost of equity . - rF = risk free rate of return . - rM = market return. - (rM – rF) = market risk premium. - ΒL = beta levered of the investment. The risk free rate is the return that an investor would get from a zero -risk investment (in Europe, German y’s 10 year bonds’ return is usually used), while the market return is the return rate of the overall market. The market risk premium (the difference between the 2) is the compensation investors receive for undertaking risks, and is usually estimated as a value between 4 and 6%. Beta levered indicates how risky (that is, how volatile) the returns expected from the specific company are, when compared to the risk of the m arket as a whole. The higher its value, the higher the risk, and thus the higher the expected average return for the investment to be worth the risk (and vice versa). Beta levered can take values lower than 1 for specially safe companies (safer than the ma rket overall), but never lower than 0, as that would indicate a risk lower than the risk free rate, and negative risk does not make sense. Beta levered indicates the risk of a company (that is, the volatility of its value). T heoretically, that risk can be expressed as a function of the company’s leverage, the tax rate, and the risk of the market in which it operates. That last term is expressed with another variable called beta unlevered ( βU), which can be calculated as: β�= β�∗(1+ (1− �������)∗� �) If we are studying a listed company we could calculate beta levered by comparing its stock return against the market’s return, by consulting specialized publications, or it could even be estimated by the company itself. If we are looking a t an unlisted company, a possible way to calculate beta levered (and thus k E) would be: 1) Find a sample of listed comparable companies. 2) Calculate beta unlevered for each company. 3) Compute the average beta unlevered, which will be the one of the target company . 4) Use it to compute the target’s beta levered (assuming we know its leverage and tax rate). 5) If necessary, take into account company size (huge companies are often perceived as having a smaller risk, or, in other words, start -ups and small companies are per ceived to have a higher risk than the one estimated with CAPM). 6) Use beta levered to calculate the cost of equity, and use k E to calculate the WACC. 5. F C F F and FCFE: d eduction of the formulas The "Free" in FCFF means "available" for the company to be used. In FCFE (in which equity refers to equity holders), it refers to the cash available for shareholders to use at some point in time. It is critical to know well the sources of cashflows to and from the company. Some will be: Cash -ins: -Customers (revenue) -Shareholders capital -Financial revenue -Bonds and similar financial sources of money -Loans Cash -outs: -Taxes -Operative costs -Suppliers (of material and labour , aka workers) -Dividends for shareholders -Interests for banks FCFF: +Revenues (the "actual" one, without account receivables - AR) -OPEX -Taxes -CAPEX ->Financial structure is not taken into account in FCFF (where the cash comes from is not taken into account). Initial formula: FCFF=Revenue -taxes -OPEX -CAPEX In FCFF the financial elements and profits are not taken into account. Revenues are not considered financial, but economic. There are two reasons for this: account receivables (AR) and inventories (INV). Account receivables (AR) are an amount of money "owed" by the customer, for a service/product it has obtained from the company but hasn't paid yet. As they are not paid, they are subtracted from the revenues . But, as they have to be paid within one year (otherwise they wouldn't be considered receivables and thus current assets), the receivables of the last year have to be added to the revenue . Thus, the term corresponding to the revenue in the FCFF equation is: Rev -AR+AR[ -1] In a P&L, revenues are not based on what is sold but on what is produced, as that's what you pay taxes for. That is why inventories (INV) have to be subtracted from the revenues in the FCFF formula, as the total "revenue" includes everything that was produced (for accounting reasons), and the inventory is the par t of it that wasn't sold. In t he same way as account receivables, inventories are considered current assets, not fixed ones, which means that they have to be sold within one year. Thus, the inventories of last year (INV[ -1]) must be added to the FCFF . Accounts payable (AP): cash that we still haven't paid to suppliers/workers, similar to account receivables. They are current liabilities, so they have to be paid within one year. That means that, while AP of this year are subtracted from the OPEX costs, AP of last year are added to it. This leaves the formula as: OPEX=OPEX -AP+AP[ -1] From the previous notes, the following quantities are defined: -Change of account receivables : ΔAR=AR -AR[ -1] -Change of inventories : ΔINV=INV -INV[ -1] -Change of account payables : ΔAP=AP -AP[ -1] These 3 are related to Net Working Capital (NWC), which is the difference between a companies current assets and current liabilities. NWC=AR+INV -AP -> ΔNWC=ΔAR+ΔINV -ΔAP The final formula for FCFF is: FCFF=(Rev -ΔAR -ΔINV) -t-(OPEX -ΔAP) -CAPEX It can also be expressed as: FCFF=EBITDA -ΔNWC Revenues -OPEX, with all the details given in the previous notes, constitutes the EBITDA. That means: EBITDA'=(Rev -ΔAR -ΔINV) -(OPEX -ΔAP) -> FCFF=EBITDA' -t-CAPEX It can also be expressed as: FCFF=EBITDA -ΔNWC -CAPEX -Taxes P&L: EBITDA -DA=EBIT EBIT -Financial Expenses=EBT EBT -TAXES=NP (TAXES=t*EBT) BUT these taxes and the ones in the FCFF formula are not the same In accounting: -TAXES= -t*EBT= -t*(EBIT -Fin.Exp)= -t*EBIT+t*Fin.Exp.= -t*(EBITDA -DA)+t*Fin.Exp= -t*EBITDA+t*(DA+Fin.Exp) There is a tax shield on Depreciations and Amortizations (sort of an "incentive" for companies to invest) and on financial expenses (in order to help companies get enough capital). In finance, tax shields are not included under taxes. This means that the "taxes" in the formula of FCFF are: TAXES=t*EBIT The tax shield is taken into account, but not as taxes, but as part of the financial structure of the company. Regarding CAPEX : If we are inside the company , we know the invested amount first hand. But if we are outside, we will have to calculate it from the accounting data. CAPEX are investments that increase the fixed assets' (FX) value. BUT fixed assets lose value with time (depreciate), so we can't calcu late CAPEX_t=FX_t -FX_(t -1). Instead, we have to calculate the value that fixed assets from the year t -1 would have in the year t after applying the discount rate (d), let's call them: FX'_t=FX_(t -1)*(1 -d) Thus, the CAPEX will be calculated as: CAPEX_t = FX_t - (1-d)*FX_(t -1) From the asset side, the value of the company would be calculated as: ∑ ��� �� (1+ ���� )� � Equity side : FCFE In this approach the focus is on the cash flows to/from shareholders, rather than the company itself. The financial structure of the company has to be checked in order to see where the difference between FCFF and FCFE is coming from (if there is such dif ference). Starting from FCFF, FCFE can be calculated as: FCFF +New loan (if any) -Loan repayment -(1-t)*Financial expenses =FCFE In case of having financial revenues instead of financial expenses: FCFF +New loan (if any) -Loan repayment +(1 -t)*Financial revenue =FCFE The term (New loan - Loan repayment) can be written as ΔD. The term (1 -t)*Fin.Exp. can be written as Fin.Exp_net, and the same can happen with financial revenue. To sum things up, the elements regarding banks have an influence on FCFF that can be calculated as : ΔD -(1-t)*Fin.Exp, or ΔD+(1 -t)*Fin.Rev . When it comes to shareholders, the following elements have to be taken into account: -Dividends +Shareholders capital These are the cashflows related to the shareholders, bu t from the point of view of the company. That is why dividends are negative and SH capital is positive. The final formula would be: FCFE=FCFF+ΔD -(1-t)*Fin.Exp. -DIV+SH Capital From the equity side, the value of the company would be calculated as: ∑ ��� �� (1+ ��)� � The problem with this method is that, in order to make the calculations, we need to know the future dividends and the variations in SH capital . This is problem for two reasons: 1 - They are difficult to estimate 2 - They are released in extra ordinary situations, which makes them even harder to predict (kind of an oxymoron). Also, if you know the company will need to raise more capital in the future, it means it has problems now For this, it is advised to always use the Assets side method