Discounted and the levered method. The former (the most

Discounted Cash Flow


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In business practice there are different methods of
company valuation but one more used in practice is discounted cash flow, which
is part of the financial methods which are considered among the most rational
in order to evaluate a company as they make their own the logic with which
financial assets are “priced”. Discounted cash flow analysis is part
of the financial methods. This method tends to determine the value of a company
through the sum of the prospective cash flows of the same, discounted using a
special rate. The merit of the financial methods, is to highlight the company’s
ability to estimate to make available to investors those monetary flows, that
they remain after having made investments in working capital and fixed assets
necessary to guarantee the continuation of the same in terms of economy. The
financial methods can be divided into two distinct categories. The unlevered
method and the levered method. The former (the most used) are based on
discounting the cash flows available to all those who make financial resources
in the company (holders of ordinary, preference, ordinary or convertible bonds,
banks and lenders). Available cash flows are calculated gross of interest
payable and discounted at the Weighted Average Cost of Capital (WACC). On the
other hand, the latter are based on the discounting of dividends and other cash
flows available to shareholders, discounted at a rate that reflects the degree
of risk (different from that used for unlevered methods). Cash flows are
calculated net of interest expense (which constitutes the remuneration of
financial creditors). The “Discounted Cash Flow Analysis” determines
the value of a company on the basis of the present value of the cash flows that
it is expected to generate in future years. Discounted cash flow is one of the
main methods for evaluating the company and is particularly indicated in the
evaluation of individual business areas of the company, capable of generating
independent cash flows. The discounted cash flow analysis can be carried out
with different approaches that usually lead to the same result.







1.      Discounted
Cash Flow: What is it?

Discounted cash flow method is one of the main, if not
the most important, among the various methods that can be used in company
valuations. This relevance has been acquired, because the value functions based
on expected cash flows are considered by the majority of the practice and the
doctrine the only ones that are always acceptable, regardless of the valuation
purpose. There are three methods for the valuation of a company using the
Discounted cash flow model.

discounted cash flow approach



In all cases only operational surpluses and anything
that does not concern are taken into consideration the core business, or
non-operating assets, is valued separately. The final sum, generates what is
the market value of capital. This model is based on three main

for short-term cash flows

the company value after the planned period (Terminal Value)

the future values ??obtained into a single current value

The process of valuing a company with the Discount
Cash Flow methods contains different steps. In the first step is to predict the
future free cash flows (FCF) for the next five to ten years. After that, an appropriate
discount rate, the Weighted Average Cost of Capital (WACC) has to be determined
to 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 Value
is the net present value of all future cash flows that accrue after the time
period that is covered by the analysis. In the last step the net present values
of the cash flows are summed up with the terminal value.

cash flow:

The main and essential elements needed to calculate
Cash Flow are:

for the past years. Future ones are calculated as a product among the sales of
the past year and the rate of sales growth, which is deducted from past
performances of the sector to which the company belongs

profit margins, are expressed as sales percentages

tax rates

rate of fixed and circulating capital

As previously stated, the Discounted Cash Flow model
sees the initial phase of the Free Cash Flow estimate. Free cash flow (FCF) is a measure of a company’s financial performance, calculated
as operating cash flow minus capital
expenditures. Free Cash Flow
represents the cash that a company is able to generate after spending the money
required to maintain or expand its asset base.

The Discounted Cash Flow Model method plans to plan
future 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 in
common, all leading to the same result, as well as for all we must plan the
short and long-term and all must then be discounted, even if with different
discount rates.

As for the Terminal Value, its calculation is common
to 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, not
being able to determine only the value of the company based on an infinite
life, the whole cycle is divided into two parts:

years with precise and accurate forecasts;

period after 3-5 years through the so-called terminal value.

In this way the sum of the two current values ??obtained
shows the net present value company.

In the levered formulation, the criterion in question
reaches the estimate of the economic value of the company’s net capital on the
basis of the evolution prospects of the discounted cash flows pertaining to the
shareholders. Given the focus on financial flows destined to shareholders, it
is customary to state that this criterion arises from an “equity
side” valuation perspective: the process of discounting future cash flows
provides, directly, the estimate of the economic value pertaining to capital of

Unlevered discounted cash flow

The approach that sees the use of the WACC as a
discount rate is the most used valuation method. The discount rate used to
obtain the current value, called the Weighted Avarage Cost of Capital (WACC),
can be estimated as a weighted average of two rates that represent the expected
return on equity for investors and the expected return for bondholders. The
weighting factors are represented by the percentages of equity and debt over
total existing capital. In particular, in the WACC approach liquidity flows are
considered relevant for all types of investors, both those relating to equity
and those concerning financial debts. For this reason a mixed discount rate is
used 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 the
relative share of capital invested. In this case, weighting is not based on
accounting values, but on market values, as they are the only ones that
actually represent investor claims.


Re = cost of equity
Rd = cost of debt
E = market value of the firm’s equity
D = market value of the firm’s debt
V = E + D = total market value of the firm’s financing (equity and debt)
E/V = percentage of financing that is equity
D/V = percentage of financing that is debt
Tc = corporate tax rate

It is important to underline that the cost of the debt
does not include the costs deriving from non-financial debts, as these expenses
are included among the costs of the material, and therefore also included in
the estimate of the Cash Flow.

In this model it is usually expected that the discount
rate will be constant throughout the life of the company, and this implies that
in addition to the cost of equity and debt, which must remain constant, the
capital structure must also stay constant. The ratio between equity and debt,
at market values, must therefore remain constant throughout the life of the
company. In this regard, it is therefore necessary to estimate the market value
of debt and equity for each planned year.

To obtain the operating Free Cash Flow (oFCF), useful
for the WACC approach, it is necessary to start from EBIT and to deduct the
adjusted taxes that are calculated by applying the corporate tax rate on EBIT.
At this point we obtain the NOPLAT (Net operating profit less adjusted) which
represents the operating income that a company can generate in the absence of
debt. After making the correct adjustments, with regard to amortization and
future adjustments, gross cash flows are obtained, ie the amount available to
all investors without counting any changes to the capital relating to expenses
or dividends.

Changes in the values ??of working capital over a
period, show the amount that the company has invested or disinvested, in the
same period, in the net working capital. Operating Free Cash Flow does not
include any cash flow as well as interest costs or changes in financial debt;
corporate taxes are also determined without taking into account the tax
deductibility of interest expenditure. The market value of total capital is
calculated using the net present value of operating Free Cash Flow, and this
value only satisfies equity investors and interest bearing debt holders.

The approach that provides for the use of the WACC as
a discount rate differs from the others by the fact that it already considers
within the Cash Flow the so-called interest tax shield which, therefore, must
not be calculated in the WACC rate.

Market value of the debt

To know the market value of the debt we must first
distinguish the two types of debt present, or those debt items whose value can
be deduced simply from the market price (think of the bonds) and those for
which it is not. For the latter we proceed in two different ways:

the interest rate initially agreed corresponds to the current conditions of market,
then the book value of the analyzed component can be used;

there are large differences between the conditions initially established and
the current market conditions, the flows relating to future payments must be
discounted (by calculating interest and principal). The discount rate to be
applied must contain the potential risk inherent in this component, ie a rate
is used that contains a similar risk, for similar conditions, to those taken
into consideration (terms and conditions must be as similar as possible).

Market value of the equity

In order to calculate the market value of the equity,
however, it is sufficient to discount the Cash Flow through the use of the
WACC, but this creates the so-called circularity problem, usually starting from
the market value of the equity to reach the capital structure. and calculating
the WACC, but as we have just said, the WACC is also used to calculate the
market value of the equity, which then performs both the input and output

To try to avoid the problem of circularity, in
practice, we calculate the market value of equity through a series of
mathematical iterations. As a first step, the value of the equity is calculated
and, based on this estimate, an approximate WACC discount rate is set and the
company’s net present value is calculated. Thus a preliminary value of the
equity is obtained. In the second step we need to delineate a value that is
between the initial estimate of the equity and the value obtained following the
first discount. To do this, the mathematical iteration is used until the value
of the equity obtained from the actualization does not correspond to the value
that was estimated at the beginning for the calculation of the approximate



The cost of equity

 This turns out
to be the most complex component to calculate. The difficulties in estimating
the cost of equity are that it is not a certain figure, such as the interest
payable on the debt, but a “opportunity cost” (the opportunity to
invest differently). The cost of own capital can be determined with reference
to different economic models, such as CAPM (Capital Asset Pricing Model),
market multiples or APT (Arbitrage Pricing Theory). Using the uni-periodical
model of the CAPM, the expected return of a security (or an investment project)
is tied to its significant risk component, ie not further eliminated by
resorting to portfolio diversification. At the basis of the CAPM there is in
fact the assumption of operating in highly organized markets and that have
characteristics of liquidity of the investment such as to allow the investor maximum
diversification of the portfolio. In such markets, rational investors are able
to obtain an effective diversification of the portfolio they hold so as to
neutralize a portion of the risk related to the individual investments made; as
a consequence, only the risk that cannot be eliminated through diversification
must be remunerated by the market. Although not exempt from theoretical
criticism and applicative difficulties as regards, for example, the univocal
definition of the beta, the market premium and even the risk free rate, the
CAPM is nevertheless the most widely accepted approach.

With CAPM, the cost of equity is determined as the sum
between the return of risk-free securities and a risk premium which in turn
depends 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)2


ra = expected return on a security

rrf = the rate of return for a
risk-free security 

rm = the broad market’s expected rate of

Ba = beta of the asset

For returns at zero risk, long-term government bond
yields are usually considered. However, it should be remembered that the rates
of 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 risk
premium (MRP) is intended as a higher return expected from the equity market
(Km) compared to an investment in debt securities without risk (Kf = risk free
rate). 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 the
largest number of securities traded on the market relating to the country in
which the company being analyzed is located. Here we simply recall that the
estimation of MRP involves numerous methodological problems. Finally, the beta
coefficient measures the specific risk of a single company; in other words, it
is the amount of risk that the investor endures by investing in a given company
rather than in the stock market as a whole. The beta is only an expression of
the systematic and therefore non-diversifiable risk of the investment in the
company. Indicates the way in which, on average, returns on a stock vary as
market returns vary. Statistically, the beta is equal to the covariance between
the expected returns of the stock and those of the market, divided by the
variance of the expected return on the market.

The beta are directly connected to the activity of the
company being analyzed. There are two macro drivers: the volatility of
operating 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 or
similar companies (peers). Once the beta of the companies belonging to the
sector has been calculated or obtained from another source, it is necessary to
purify it from the financial risk of the individual companies, thus making it
an indicator of only operational risk (beta unlevered). In fact, the beta
calculated for a company (equity beta) reflects two components: the business
risk (associated with the underlying base of company loans) and the financial
risk (associated with the company’s financial structure). With the calculation
of the unlevered beta it “purifies” the beta from the component of
financial risk, highlighting the beta of only business risk. Once the unlevered
beta of the companies of a given sector is obtained, it is possible, by making
the weighted average for the market value of each, to calculate the unlevered
beta of the sector. The choice of the most correct beta is fundamental in
determining 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 to
state that the determination of the WACC is carried out in a much deeper way as
more work has been devoted to identifying the beta; usually, those who have few
elements available, end up assigning a value of 1 to the beta, that is to say
the average market risk. Ultimately, the choice of the beta is anything but
easy, especially for those who do not have access to specialized databases.

cost of debt.

The cost of debt is necessary, as is clear from the
WACC formula previously exposed, for the determination of the same discount
rate. In this case it is not based on the data historical interest rates
applied in the past, used to calculate the market value of debt, but you must
adopt a current discount rate that has the same level of risk reported by the
analyzed debt component. As the cost of the equity also the cost of debt
consists of two factors, the risk-free interest rate and the risk premium
multiplied by the factor ?.

The formula for obtaining the enterprise value by
adopting the WACC approach results therefore be the following:

Adjusted Present Value Approach

The “adjusted present value” method, aims as
the first objective, to determine the value of the company in question. The
characteristic of this approach sees the delineation of equity value in three
steps main:

of the current value of the company in the absence of debt. They come then
Calculated the Free Cash Flow calculated as if it were financed only from
equity, with the cost of unlevered equity (the formula of the CAPM for the
calculation of the cost of equity by adopting the ?unlevered factor).

of the expected tax benefit from the holding of debt (produced between the tax
rate and the presumed debt in each planned period) discounted to moment of
evaluation. The discount rate used is the cost of debt.

of the values ??obtained in points 1 and 2

The mathematical formula for obtaining enterprise
value is:

One of the peculiarities of the APV Approach that
differentiates it from the WACC Approach is the greater ease that allows to
track down the value of the debt distinct from that of equity, but at the same
time it is one of the least used methods at present. The reason basic is the
fact that to calculate the value of the company in the absence of debt must
start from basic and purely theoretical assumptions.

1.3. Equity Approach

The equity approach is also less used than the
Adjusted Present Value Approach. There main feature of this procedure is that
it also includes all aspects directly into cash flows that in this case are
defined as cash Flow to Equity (CF to Equity). Starting from EBIT, the gross
cash flows are obtained at net interest income, as in the Cash Flow calculation
with the WACC Approach. In this case however, only capital expenditures and sum
of changes in capital are not deducted circulating, but also the positive and
negative variations of the position are added financial. This allows the
creation of CF to Equity which are discounted exclusively with the cost of
equity as, as mentioned, the cost of debt has already been introduced in the
Cash Flow.

The mathematical formula for obtaining enterprise value


2. Vantage
and disadvantage of DCF model

The Discounted Cash Flow valuation model is
particularly suitable for companies characterized by investments that produce
constant and positive net operating cash flows or rising cash flows at a
constant rate. The unlevered Discounted Cash Flow does not require any explicit
forecast of cash flows related to debt capital (on the opposite, these cash
flows linked to financial assets and liabilities must be taken into account in
the estimate of cash flows to shareholders). This is an important feature when
the leverage is particularly high or when it is expected to suffer significant
changes over time, due to the complexity of the estimate of debt capital issues
and related future repayments. This also represents an important element for
the comparison of companies characterized by markedly different levels of
leverage. However, the unlevered DCF requires information on the debt / equity
ratio and on interest rates to estimate the WACC. On the other hand, DCF does not work in the presence of companies that
are growing investments because FCF does not express the concept of added
value, but rather the concept of investment (or liquidation). It confuses in
particular investments with investment payoffs; when a company invests more
liquidity in transactions than it gets, the FCF decreases even if the
investment has a positive NPV), vice versa if the company decreases its
investments the FCF increases (even if a company is worth more and not less if
it invests profitably). This happens because in DCF the income from investments
is usually recorded in the following periods compared to the date on which the
investment is made.  In addition, there are problems related to the high
subjectivity due to the assumptions necessary for the timely estimate of the
cash flows available during the explicit forecast period, as well as the
limited reliability of the cash flow forecast process available over a certain
number of years.



In the present work, we arrive at the achievement of a
goal, that is to explain the functioning, the limits and the merits of one of
the most used, in practice, evaluation methods of a company, the Discounted
cash flow. The discounted cash flow method (DCF) is based on the determination
of the present value of the cash flows expected from a specific asset. The flow
can be represented not only by cash flow but also by dividends. Valuation based
on discounted cash flows is a function of three fundamental elements: the
amount of cash flow, the distribution over time of flows and the discount rate.
focused on the evaluation model, which is now considered among the most
profitable. At the same time this model presents three approaches, respectively
the 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 reality
almost exclusively WACC uses it. The main reason that favours the WACC rate is
the possibility of forecasting changes in the relationship between equity and
debt. At the same time, the WACC Approach introduces the problem of
circularity, therefore causing greater difficulties in calculating the cost of
equity. The Adjusted Present Value, on the other hand, highlights the problem
of having to evaluate, as a first step, a company that is apparently not in
debt, therefore having to start from theoretical bases and hypotheses. Lastly,
the Equity Approach, which also includes the aspects of debt in the final Cash
Flow, does not allow to easily divide the values ??deriving from equity and
those deriving from the financial portion. Later in this work we focused on the advantages and
the possible problems concerning the use of these methods of evaluation of the