Discounted and the levered method. The former (the most

Discounted Cash FlowINTRODUCTIONIn business practice there are different methods ofcompany valuation but one more used in practice is discounted cash flow, whichis part of the financial methods which are considered among the most rationalin order to evaluate a company as they make their own the logic with whichfinancial assets are “priced”. Discounted cash flow analysis is partof the financial methods. This method tends to determine the value of a companythrough the sum of the prospective cash flows of the same, discounted using aspecial rate. The merit of the financial methods, is to highlight the company’sability to estimate to make available to investors those monetary flows, thatthey remain after having made investments in working capital and fixed assetsnecessary to guarantee the continuation of the same in terms of economy.

Thefinancial methods can be divided into two distinct categories. The unleveredmethod and the levered method. The former (the most used) are based ondiscounting the cash flows available to all those who make financial resourcesin the company (holders of ordinary, preference, ordinary or convertible bonds,banks and lenders). Available cash flows are calculated gross of interestpayable and discounted at the Weighted Average Cost of Capital (WACC). On theother hand, the latter are based on the discounting of dividends and other cashflows available to shareholders, discounted at a rate that reflects the degreeof risk (different from that used for unlevered methods).

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Cash flows arecalculated net of interest expense (which constitutes the remuneration offinancial creditors). The “Discounted Cash Flow Analysis” determinesthe value of a company on the basis of the present value of the cash flows thatit is expected to generate in future years. Discounted cash flow is one of themain methods for evaluating the company and is particularly indicated in theevaluation of individual business areas of the company, capable of generatingindependent cash flows. The discounted cash flow analysis can be carried outwith different approaches that usually lead to the same result.

     CHAPTERONE1.      DiscountedCash Flow: What is it?Discounted cash flow method is one of the main, if notthe most important, among the various methods that can be used in companyvaluations. This relevance has been acquired, because the value functions basedon expected cash flows are considered by the majority of the practice and thedoctrine the only ones that are always acceptable, regardless of the valuationpurpose.

There are three methods for the valuation of a company using theDiscounted cash flow model. 1.     Unlevereddiscounted cash flow approach2.     ADVapproach3.

     EquityapproachIn all cases only operational surpluses and anythingthat does not concern are taken into consideration the core business, ornon-operating assets, is valued separately. The final sum, generates what isthe market value of capital. This model is based on three mainsteps: 1.     Planfor short-term cash flows 2.     Calculatethe company value after the planned period (Terminal Value) 3.

     Convertthe future values ??obtained into a single current valueThe process of valuing a company with the DiscountCash Flow methods contains different steps. In the first step is to predict thefuture free cash flows (FCF) for the next five to ten years. After that, an appropriatediscount rate, the Weighted Average Cost of Capital (WACC) has to be determinedto discount all future Free Cash Flows to calculate their Net Present Value (NPV).In the next step the Terminal Value (TV) has to be identified. The Terminal Valueis the net present value of all future cash flows that accrue after the timeperiod that is covered by the analysis. In the last step the net present valuesof the cash flows are summed up with the terminal value. Freecash flow:The main and essential elements needed to calculateCash Flow are:·        salesfor the past years. Future ones are calculated as a product among the sales ofthe past year and the rate of sales growth, which is deducted from pastperformances of the sector to which the company belongs·        operatingprofit margins, are expressed as sales percentages·        futuretax rates·        growthrate of fixed and circulating capitalAs previously stated, the Discounted Cash Flow modelsees the initial phase of the Free Cash Flow estimate.

Free cash flow (FCF) is a measure of a company’s financial performance, calculatedas operating cash flow minus capitalexpenditures. Free Cash Flowrepresents the cash that a company is able to generate after spending the moneyrequired to maintain or expand its asset base.The Discounted Cash Flow Model method plans to planfuture years, for a maximum of 5/7, and then calculate the Terminal Value,which is the value that would appear after the period already scheduled.Although the three approaches are different, they have multiple points incommon, all leading to the same result, as well as for all we must plan theshort and long-term and all must then be discounted, even if with differentdiscount rates.As for the Terminal Value, its calculation is commonto all approaches.

In fact, the life span of a company is notoriously unknown,and for this reason an infinite life is presumed for it. As a solution, notbeing able to determine only the value of the company based on an infinitelife, the whole cycle is divided into two parts:-         3-5years with precise and accurate forecasts;-         theperiod after 3-5 years through the so-called terminal value.In this way the sum of the two current values ??obtainedshows the net present value company.In the levered formulation, the criterion in questionreaches the estimate of the economic value of the company’s net capital on thebasis of the evolution prospects of the discounted cash flows pertaining to theshareholders. Given the focus on financial flows destined to shareholders, itis customary to state that this criterion arises from an “equityside” valuation perspective: the process of discounting future cash flowsprovides, directly, the estimate of the economic value pertaining to capital ofrisk.1.1Unlevered discounted cash flowThe approach that sees the use of the WACC as adiscount rate is the most used valuation method. The discount rate used toobtain the current value, called the Weighted Avarage Cost of Capital (WACC),can be estimated as a weighted average of two rates that represent the expectedreturn on equity for investors and the expected return for bondholders.

Theweighting factors are represented by the percentages of equity and debt overtotal existing capital. In particular, in the WACC approach liquidity flows areconsidered relevant for all types of investors, both those relating to equityand those concerning financial debts. For this reason a mixed discount rate isused which includes the cost of equity as well as the cost of debt. Moreover,the respective costs of capital are calculated by proportioning them to therelative share of capital invested. In this case, weighting is not based onaccounting values, but on market values, as they are the only ones thatactually represent investor claims. 1Where:Re = cost of equityRd = cost of debtE = market value of the firm’s equityD = market value of the firm’s debtV = E + D = total market value of the firm’s financing (equity and debt)E/V = percentage of financing that is equityD/V = percentage of financing that is debtTc = corporate tax rateIt is important to underline that the cost of the debtdoes not include the costs deriving from non-financial debts, as these expensesare included among the costs of the material, and therefore also included inthe estimate of the Cash Flow.In this model it is usually expected that the discountrate will be constant throughout the life of the company, and this implies thatin addition to the cost of equity and debt, which must remain constant, thecapital structure must also stay constant.

The ratio between equity and debt,at market values, must therefore remain constant throughout the life of thecompany. In this regard, it is therefore necessary to estimate the market valueof debt and equity for each planned year.To obtain the operating Free Cash Flow (oFCF), usefulfor the WACC approach, it is necessary to start from EBIT and to deduct theadjusted taxes that are calculated by applying the corporate tax rate on EBIT.

At this point we obtain the NOPLAT (Net operating profit less adjusted) whichrepresents the operating income that a company can generate in the absence ofdebt. After making the correct adjustments, with regard to amortization andfuture adjustments, gross cash flows are obtained, ie the amount available toall investors without counting any changes to the capital relating to expensesor dividends.Changes in the values ??of working capital over aperiod, show the amount that the company has invested or disinvested, in thesame period, in the net working capital. Operating Free Cash Flow does notinclude any cash flow as well as interest costs or changes in financial debt;corporate taxes are also determined without taking into account the taxdeductibility of interest expenditure. The market value of total capital iscalculated using the net present value of operating Free Cash Flow, and thisvalue only satisfies equity investors and interest bearing debt holders.The approach that provides for the use of the WACC asa discount rate differs from the others by the fact that it already considerswithin the Cash Flow the so-called interest tax shield which, therefore, mustnot be calculated in the WACC rate.Market value of the debtTo know the market value of the debt we must firstdistinguish the two types of debt present, or those debt items whose value canbe deduced simply from the market price (think of the bonds) and those forwhich it is not. For the latter we proceed in two different ways:-         ifthe interest rate initially agreed corresponds to the current conditions of market,then the book value of the analyzed component can be used;-         ifthere are large differences between the conditions initially established andthe current market conditions, the flows relating to future payments must bediscounted (by calculating interest and principal).

The discount rate to beapplied must contain the potential risk inherent in this component, ie a rateis used that contains a similar risk, for similar conditions, to those takeninto consideration (terms and conditions must be as similar as possible).Market value of the equityIn order to calculate the market value of the equity,however, it is sufficient to discount the Cash Flow through the use of theWACC, but this creates the so-called circularity problem, usually starting fromthe market value of the equity to reach the capital structure. and calculatingthe WACC, but as we have just said, the WACC is also used to calculate themarket value of the equity, which then performs both the input and outputfunctions.To try to avoid the problem of circularity, inpractice, we calculate the market value of equity through a series ofmathematical iterations.

As a first step, the value of the equity is calculatedand, based on this estimate, an approximate WACC discount rate is set and thecompany’s net present value is calculated. Thus a preliminary value of theequity is obtained. In the second step we need to delineate a value that isbetween the initial estimate of the equity and the value obtained following thefirst discount.

To do this, the mathematical iteration is used until the valueof the equity obtained from the actualization does not correspond to the valuethat was estimated at the beginning for the calculation of the approximateWACC.  The cost of equity This turns outto be the most complex component to calculate. The difficulties in estimatingthe cost of equity are that it is not a certain figure, such as the interestpayable on the debt, but a “opportunity cost” (the opportunity toinvest differently). The cost of own capital can be determined with referenceto different economic models, such as CAPM (Capital Asset Pricing Model),market multiples or APT (Arbitrage Pricing Theory). Using the uni-periodicalmodel of the CAPM, the expected return of a security (or an investment project)is tied to its significant risk component, ie not further eliminated byresorting to portfolio diversification. At the basis of the CAPM there is infact the assumption of operating in highly organized markets and that havecharacteristics of liquidity of the investment such as to allow the investor maximumdiversification of the portfolio. In such markets, rational investors are ableto obtain an effective diversification of the portfolio they hold so as toneutralize a portion of the risk related to the individual investments made; asa consequence, only the risk that cannot be eliminated through diversificationmust be remunerated by the market.

Although not exempt from theoreticalcriticism and applicative difficulties as regards, for example, the univocaldefinition of the beta, the market premium and even the risk free rate, theCAPM is nevertheless the most widely accepted approach.With CAPM, the cost of equity is determined as the sumbetween the return of risk-free securities and a risk premium which in turndepends on the systematic risk of the company being valued, measured by a”beta” coefficient. The CAPM formula is as follows:ra = rrf + Ba (rm-rrf)2where:ra = expected return on a securityrrf = the rate of return for arisk-free security rm = the broad market’s expected rate ofreturn Ba = beta of the assetFor returns at zero risk, long-term government bondyields are usually considered.

However, it should be remembered that the ratesof government bonds are not risk-less rates: yield is not certain, but depends,to a small extent, on the performance of the stock market. The market riskpremium (MRP) is intended as a higher return expected from the equity market(Km) compared to an investment in debt securities without risk (Kf = risk freerate). This is why often the MRP is also indicated by the expression (Km – Kf).As a general rule, Km is represented by the share index consisting of thelargest number of securities traded on the market relating to the country inwhich the company being analyzed is located. Here we simply recall that theestimation of MRP involves numerous methodological problems. Finally, the betacoefficient measures the specific risk of a single company; in other words, itis the amount of risk that the investor endures by investing in a given companyrather than in the stock market as a whole.

The beta is only an expression ofthe systematic and therefore non-diversifiable risk of the investment in thecompany. Indicates the way in which, on average, returns on a stock vary asmarket returns vary. Statistically, the beta is equal to the covariance betweenthe expected returns of the stock and those of the market, divided by thevariance of the expected return on the market.

The beta are directly connected to the activity of thecompany being analyzed. There are two macro drivers: the volatility ofoperating cash flows and the degree of leverage. If the company is not listed,it is not possible to calculate the beta starting from the market observations,but we must proceed differently. Some authors suggest using industry beta orsimilar companies (peers). Once the beta of the companies belonging to thesector has been calculated or obtained from another source, it is necessary topurify it from the financial risk of the individual companies, thus making itan indicator of only operational risk (beta unlevered). In fact, the betacalculated for a company (equity beta) reflects two components: the businessrisk (associated with the underlying base of company loans) and the financialrisk (associated with the company’s financial structure). With the calculationof the unlevered beta it “purifies” the beta from the component offinancial risk, highlighting the beta of only business risk. Once the unleveredbeta of the companies of a given sector is obtained, it is possible, by makingthe weighted average for the market value of each, to calculate the unleveredbeta of the sector.

The choice of the most correct beta is fundamental indetermining the cost of equity, given that, as evidenced by the CAPM formula,the beta behaves as a multiplier of the risk premium. It is often possible tostate that the determination of the WACC is carried out in a much deeper way asmore work has been devoted to identifying the beta; usually, those who have fewelements available, end up assigning a value of 1 to the beta, that is to saythe average market risk. Ultimately, the choice of the beta is anything buteasy, especially for those who do not have access to specialized databases.Thecost of debt.The cost of debt is necessary, as is clear from theWACC formula previously exposed, for the determination of the same discountrate.

In this case it is not based on the data historical interest ratesapplied in the past, used to calculate the market value of debt, but you mustadopt a current discount rate that has the same level of risk reported by theanalyzed debt component. As the cost of the equity also the cost of debtconsists of two factors, the risk-free interest rate and the risk premiummultiplied by the factor ?. The formula for obtaining the enterprise value byadopting the WACC approach results therefore be the following: 1.2.Adjusted Present Value Approach The “adjusted present value” method, aims asthe first objective, to determine the value of the company in question. Thecharacteristic of this approach sees the delineation of equity value in threesteps main: 1.     Estimateof the current value of the company in the absence of debt.

They come thenCalculated the Free Cash Flow calculated as if it were financed only fromequity, with the cost of unlevered equity (the formula of the CAPM for thecalculation of the cost of equity by adopting the ?unlevered factor). 2.     Calculationof the expected tax benefit from the holding of debt (produced between the taxrate and the presumed debt in each planned period) discounted to moment ofevaluation.

The discount rate used is the cost of debt.3.     Sumof the values ??obtained in points 1 and 2The mathematical formula for obtaining enterprisevalue is: One of the peculiarities of the APV Approach thatdifferentiates it from the WACC Approach is the greater ease that allows totrack down the value of the debt distinct from that of equity, but at the sametime it is one of the least used methods at present. The reason basic is thefact that to calculate the value of the company in the absence of debt muststart from basic and purely theoretical assumptions.1.3. Equity ApproachThe equity approach is also less used than theAdjusted Present Value Approach. There main feature of this procedure is thatit also includes all aspects directly into cash flows that in this case aredefined as cash Flow to Equity (CF to Equity).

Starting from EBIT, the grosscash flows are obtained at net interest income, as in the Cash Flow calculationwith the WACC Approach. In this case however, only capital expenditures and sumof changes in capital are not deducted circulating, but also the positive andnegative variations of the position are added financial. This allows thecreation of CF to Equity which are discounted exclusively with the cost ofequity as, as mentioned, the cost of debt has already been introduced in theCash Flow. The mathematical formula for obtaining enterprise valueis:  2.

Vantageand disadvantage of DCF modelThe Discounted Cash Flow valuation model isparticularly suitable for companies characterized by investments that produceconstant and positive net operating cash flows or rising cash flows at aconstant rate. The unlevered Discounted Cash Flow does not require any explicitforecast of cash flows related to debt capital (on the opposite, these cashflows linked to financial assets and liabilities must be taken into account inthe estimate of cash flows to shareholders). This is an important feature whenthe leverage is particularly high or when it is expected to suffer significantchanges over time, due to the complexity of the estimate of debt capital issuesand related future repayments. This also represents an important element forthe comparison of companies characterized by markedly different levels ofleverage. However, the unlevered DCF requires information on the debt / equityratio and on interest rates to estimate the WACC. On the other hand, DCF does not work in the presence of companies thatare growing investments because FCF does not express the concept of addedvalue, but rather the concept of investment (or liquidation). It confuses inparticular investments with investment payoffs; when a company invests moreliquidity in transactions than it gets, the FCF decreases even if theinvestment has a positive NPV), vice versa if the company decreases itsinvestments the FCF increases (even if a company is worth more and not less ifit invests profitably). This happens because in DCF the income from investmentsis usually recorded in the following periods compared to the date on which theinvestment is made.

 In addition, there are problems related to the highsubjectivity due to the assumptions necessary for the timely estimate of thecash flows available during the explicit forecast period, as well as thelimited reliability of the cash flow forecast process available over a certainnumber of years. CONCLUSION:In the present work, we arrive at the achievement of agoal, that is to explain the functioning, the limits and the merits of one ofthe most used, in practice, evaluation methods of a company, the Discountedcash flow. The discounted cash flow method (DCF) is based on the determinationof the present value of the cash flows expected from a specific asset. The flowcan be represented not only by cash flow but also by dividends. Valuation basedon discounted cash flows is a function of three fundamental elements: theamount of cash flow, the distribution over time of flows and the discount rate.Wefocused on the evaluation model, which is now considered among the mostprofitable. At the same time this model presents three approaches, respectivelythe WACC Approach, the Adjusted Present Value Approach and the Equity Approach,and although in theory it is advisable to use them at the same time, in realityalmost exclusively WACC uses it. The main reason that favours the WACC rate isthe possibility of forecasting changes in the relationship between equity anddebt.

At the same time, the WACC Approach introduces the problem ofcircularity, therefore causing greater difficulties in calculating the cost ofequity. The Adjusted Present Value, on the other hand, highlights the problemof having to evaluate, as a first step, a company that is apparently not indebt, therefore having to start from theoretical bases and hypotheses. Lastly,the Equity Approach, which also includes the aspects of debt in the final CashFlow, does not allow to easily divide the values ??deriving from equity andthose deriving from the financial portion. Later in this work we focused on the advantages andthe possible problems concerning the use of these methods of evaluation of thecompany.