Discounted Cash Flow

INTRODUCTION

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.

CHAPTER

ONE

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.

1.

Unlevered

discounted cash flow approach

2.

ADV

approach

3.

Equity

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

steps:

1.

Plan

for short-term cash flows

2.

Calculate

the company value after the planned period (Terminal Value)

3.

Convert

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.

Free

cash flow:

The main and essential elements needed to calculate

Cash Flow are:

·

sales

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

·

operating

profit margins, are expressed as sales percentages

·

future

tax rates

·

growth

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:

–

3-5

years with precise and accurate forecasts;

–

the

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

risk.

1.1

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.

1

Where:

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:

–

if

the interest rate initially agreed corresponds to the current conditions of market,

then the book value of the analyzed component can be used;

–

if

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

functions.

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

WACC.

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

where:

ra = expected return on a security

rrf = the rate of return for a

risk-free security

rm = the broad market’s expected rate of

return

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.

The

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:

1.2.

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:

1.

Estimate

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).

2.

Calculation

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.

3.

Sum

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

is:

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.

CONCLUSION:

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.

We

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

company.