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In
finance Finance is a term for the management, creation, and study of money In a 1786 James Gillray caricature, the plentiful money bags handed to King George III are contrasted with the beggar whose legs and arms were amputated, in the left corn ...

finance
, discounted cash flow (DCF) analysis is a method of valuing a
security Security is freedom from, or resilience against, potential Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics Physics is the natural science that studies matter, its El ...
, project, company, or
asset In financial accounting Financial accounting is the field of accounting Accounting or Accountancy is the measurement, processing, and communication of financial and non financial information about economic entity, economic entities such a ...
using the concepts of the
time value of money The time value of money is the widely accepted conjecture that there is greater benefit to receiving a sum of money Money is any item or verifiable record that is generally accepted as payment for goods and services and repayment of debts, ...
. Discounted
cash flow A cash flow is a real or virtual movement of money Money is any item or verifiable record that is generally accepted as payment for goods and services and repayment of debts, such as taxes, in a particular country or socio-economic contex ...
analysis is widely used in investment finance,
real estate development Real estate development, or property development, is a business process, encompassing activities that range from the renovation and re-lease of existing buildings to the purchase of raw Real Estate, land and the sale of developed land or parcel ...
, corporate financial management and
patent valuationIntellectual property Intellectual property (IP) is a category of property that includes intangible creations of the human intellect. There are many types of intellectual property, and some countries recognize more than others. The most well-know ...
. It was used in industry as early as the 1700s or 1800s, widely discussed in financial economics in the 1960s, and became widely used in U.S. courts in the 1980s and 1990s.


Application

To apply the method, all future cash flows are estimated and
discounted Discounting is a financial mechanism in which a debtor A debtor or debitor is a legal entity (legal person) that owes a debt Debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another p ...
by using
cost of capital In economics Economics () is a social science Social science is the branch A branch ( or , ) or tree branch (sometimes referred to in botany Botany, also called , plant biology or phytology, is the science of plant l ...
to give their
present value In economics Economics () is a social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behavi ...
s (PVs). The sum of all future cash flows, both incoming and outgoing, is the
net present value The net present value (NPV) or net present worth (NPW) applies to a series of cash flows occurring at different times. The present value of a cash flow depends on the interval of time between now and the cash flow. It also depends on the discount ra ...
(NPV), which is taken as the value of the cash flows in question; see
below Below may refer to: *Earth *Ground (disambiguation) *Soil *Floor *Bottom (disambiguation) *Less than *Temperatures below freezing *Hell or underworld People with the surname *Fred Below (1926–1988), American blues drummer *Fritz von Below (1853â ...
. For further context see valuation overview; and for the mechanics see
valuation using discounted cash flows Valuation using discounted cash flows (DCF valuation) is a method of estimating the current value of a company based on projected future cash flows adjusted for the time value of money The time value of money is the widely accepted conjecture ...
, which includes modifications typical for
startup
startup
s,
private equity Private equity (PE) typically refers to investment funds, generally organized as limited partnerships, that buy and restructure companies that are not publicly traded. Private equity is a type of equity and one of the asset classes consisti ...
and
venture capital Venture capital (VC) is a form of private equity Private equity (PE) typically refers to investment funds, generally organized as limited partnerships, that buy and restructure companies that are not publicly traded. Private equity is a ty ...
,
corporate finance Corporate finance is the area of finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money and investments. Savers a ...
"projects", and
mergers and acquisitions In corporate finance Corporate finance is the area of finance that deals with sources of funding, the capital structure of corporations, the actions that managers take to increase the Value investing, value of the firm to the shareholders, ...
. Using DCF analysis to compute the NPV takes as input cash flows and a discount rate and gives as output a present value. The opposite process takes cash flows and a price (present value) as inputs, and provides as output the discount rate; this is used in bond markets to obtain the
yield Yield may refer to: Measures of output/function Computer science * Yield (multithreading) is an action that occurs in a computer program during multithreading * See generator (computer programming) Physics/chemistry * Yield (chemistry), the amou ...
.


History

Discounted cash flow calculations have been used in some form since money was first lent at interest in ancient times. Studies of ancient
Egyptian Egyptian describes something of, from, or related to Egypt. Egyptian or Egyptians may refer to: Nations and ethnic groups * Egyptians, a national group in North Africa ** Egyptian culture, a complex and stable culture with thousands of years of r ...
and
Babylonian mathematics Babylonian mathematics (also known as ''Assyro-Babylonian mathematics'') denotes the mathematics developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the centuries following the fall of Babylon in 539 BC. Bab ...
suggest that they used techniques similar to discounting of the future cash flows. Modern discounted cash flow analysis has been used since at least the early 1700s in the UK coal industry. Discounted cash flow valuation differentiated between the accounting
book value In accounting, book value is the value of an asset according to its balance sheet In financial accounting Financial accounting is the field of accounting Accounting or Accountancy is the measurement, processing, and communication of fin ...
, which is based on the amount paid for the asset. Following the
stock market crash of 1929 The Wall Street Crash of 1929, also known as the Great Crash, was a major American stock market crash that occurred in the autumn of 1929. It started in September and ended late in October, when share prices on the New York Stock Exchange T ...
, discounted cash flow analysis gained popularity as a valuation method for
stock In finance, stock (also capital stock) consists of all of the shares In financial markets A financial market is a market in which people trade financial securities and derivatives at low transaction costs. Some of the securities i ...

stock
s.
Irving Fisher Irving Fisher (February 27, 1867 – April 29, 1947) was an American economist An economist is a professional and practitioner in the social science Social science is the branch The branches and leaves of a tree. A branch ( or , ...

Irving Fisher
in his 1930 book ''The Theory of Interest'' and
John Burr Williams John Burr Williams (November 27, 1900 – September 15, 1989) was an American economist An economist is a practitioner in the social sciences, social science discipline of economics. The individual may also study, develop, and apply theories ...
's 1938 text ''
The Theory of Investment Value John Burr Williams (November 27, 1900 – September 15, 1989) was an American economist An economist is a professional and practitioner in the social science Social science is the Branches of science, branch of science devoted to the s ...
'' first formally expressed the DCF method in modern economic terms.


Mathematics


Discounted cash flows

The discounted cash flow formula is derived from the present value formula for calculating the time value of money :DCF = \frac + \frac + \dotsb + \frac and
compounding In the field of pharmacy, compounding (performed in compounding pharmacies) is preparation of a custom formulation of a medication to fit a unique need of a patient that cannot be met with commercially available products. This may be done for med ...

compounding
returns: :FV = DCF \cdot (1+r)^n. Thus the discounted present value (for one cash flow in one future period) is expressed as: :DPV = \frac where * ''DPV'' is the discounted present value of the future cash flow (''FV''), or ''FV'' adjusted for the delay in receipt; * ''FV'' is the
nominal value In economics Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods ...
of a cash flow amount in a future period (see Mid-year adjustment); * ''r'' is the
interest rate An interest rate is the amount of interest In and , interest is payment from a or deposit-taking financial institution to a or depositor of an amount above repayment of the (that is, the amount borrowed), at a particular rate. It is disti ...
or discount rate, which reflects the cost of tying up
capital Capital most commonly refers to: * Capital letter Letter case is the distinction between the letters Letter, letters, or literature may refer to: Characters typeface * Letter (alphabet) A letter is a segmental symbol A symbol ...
and may also allow for the risk that the payment may not be received in full; * ''n'' is the time in years before the future cash flow occurs. Where multiple cash flows in multiple time periods are discounted, it is necessary to sum them as follows: :DPV = \sum_^ \frac for each future cash flow (''FV'') at any time period (''t'') in years from the present time, summed over all time periods. The sum can then be used as a
net present value The net present value (NPV) or net present worth (NPW) applies to a series of cash flows occurring at different times. The present value of a cash flow depends on the interval of time between now and the cash flow. It also depends on the discount ra ...
figure. If the amount to be paid at time 0 (now) for all the future cash flows is known, then that amount can be substituted for ''DPV'' and the equation can be solved for ''r'', that is the
internal rate of return Internal rate of return (IRR) is a method of calculating an investment Investment is the dedication of an asset to attain an increase in value over a period of time. Investment requires a sacrifice of some present asset, such as time, money, ...
. All the above assumes that the interest rate remains constant throughout the whole period. If the cash flow stream is assumed to continue indefinitely, the finite forecast is usually combined with the assumption of constant cash flow growth beyond the discrete projection period. The total value of such cash flow stream is the sum of the finite discounted cash flow forecast and the
Terminal value (finance) In finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money and investments. Savers and investors have money availabl ...
.


Continuous cash flows

For continuous cash flows, the summation in the above formula is replaced by an integration: :DPV= \int_0^T FV(t) \, e^ dt = \int_0^T \frac \, dt\,, where FV(t) is now the ''rate'' of cash flow, and \lambda = \ln(1+r).


Discount rate

The act of discounting future cash flows answers "how much money would have to be invested currently, at a given rate of return, to yield the forecast cash flow, at its future date?" In other words, discounting returns the
present value In economics Economics () is a social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behavi ...
of future cash flows, where the rate used is the cost of capital that ''appropriately'' reflects the risk, and timing, of the cash flows. This "required return" thus incorporates: #
Time value of money The time value of money is the widely accepted conjecture that there is greater benefit to receiving a sum of money Money is any item or verifiable record that is generally accepted as payment for goods and services and repayment of debts, ...
(
risk-free rate The risk-free rate of return, usually shortened to the risk-free rate, is the rate of return of a hypothetical investment with scheduled payment(s) over a fixed period of time that is assumed to meet all payment obligations. Since the risk-free ...
) – according to the theory of
time preference In economics, time preference (or time discounting, delay discounting, temporal discounting, long-term orientation) is the current relative valuation placed on receiving a good In most contexts, the concept of good denotes the conduct that ...
, investors would rather have cash immediately than having to wait and must therefore be compensated by paying for the delay. #
Risk premium Overview A risk premium is a measure of excess return that is required by an individual to compensate them for being subjected to an increased level of risk. It is used widely in finance and economics with the general definition being the expec ...
– reflects the extra return investors demand because they want to be compensated for the risk that the cash flow might not materialize after all. For the latter, various
models
models
have been developed, where the premium is (typically) calculated as a function of the asset's performance with reference to some macroeconomic variable - for example, the CAPM compares the asset's historical returns to the " overall market's"; see Capital asset pricing model#Asset-specific required return and Asset pricing#General Equilibrium Asset Pricing. An alternate, although less common approach, is to apply a "fundamental valuation" method, such as the " T-model", which instead relies on accounting information. (Other methods of discounting, such as
hyperbolic discounting In economics Economics () is a social science Social science is the Branches of science, branch of science devoted to the study of society, societies and the Social relation, relationships among individuals within those societies. ...
, are studied in academia and said to reflect intuitive decision-making, but are not generally used in industry. In this context the above is referred to as "exponential discounting".) Note that the terminology "
expected return The expected return (or expected gain) on a financial investment To invest is to allocate money Image:National-Debt-Gillray.jpeg, In a 1786 James Gillray caricature, the plentiful money bags handed to King George III are contrasted with th ...
", although formally the mathematical expected value, is often used interchangeably with the above, where "expected" means "required" or "demanded" in the corresponding sense. The method may also be modified by industry, for example different formulae have been proposed when choosing a discount rate in a healthcare setting.


Methods of appraisal of a company or project

For these valuation purposes, a number of different DCF methods are distinguished today, some of which are outlined below. The details are likely to vary depending on the
capital structure Capital structure in corporate finance Corporate finance is the area of finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and manag ...

capital structure
of the company. However the assumptions used in the appraisal (especially the equity discount rate and the projection of the cash flows to be achieved) are likely to be at least as important as the precise model used. Both the income stream selected and the associated
cost of capital In economics Economics () is a social science Social science is the branch A branch ( or , ) or tree branch (sometimes referred to in botany Botany, also called , plant biology or phytology, is the science of plant l ...
model determine the valuation result obtained with each method. (This is one reason these valuation methods are formally referred to as the Discounted Future Economic Income methods.) The below is offered as a simple treatment; for the components / steps of business modeling here, see the list for "Equity valuation" under Outline of finance#Discounted cash flow valuation.


Equity-approach

*
Flows to equity In corporate finance, free cash flow to equity (FCFE) is a metric of how much cash can be distributed to the equity shareholders of the company as dividends or Share repurchase, stock buybacks—after all expenses, reinvestments, and debt repayments ...
approach (FTE) ** Discount the cash flows available to the holders of equity capital, after allowing for cost of servicing debt capital ** Advantages: Makes explicit allowance for the cost of debt capital ** Disadvantages: Requires judgement on choice of discount rate


Entity-approach

* Adjusted present value approach (APV) ** Discount the cash flows before allowing for the debt capital (but allowing for the tax relief obtained on the debt capital) ** Advantages: Simpler to apply if a specific project is being valued which does not have earmarked debt capital finance ** Disadvantages: Requires judgement on choice of discount rate; no explicit allowance for cost of debt capital, which may be much higher than a
risk-free rate The risk-free rate of return, usually shortened to the risk-free rate, is the rate of return of a hypothetical investment with scheduled payment(s) over a fixed period of time that is assumed to meet all payment obligations. Since the risk-free ...
*
Weighted average cost of capital The weighted average cost of capital (WACC) is the rate that a company is expected to pay on average to all its security holders to finance its assets. The WACC is commonly referred to as the firm's cost of capital In economics Economics ...
approach (WACC) ** Derive a weighted cost of the capital obtained from the various sources and use that discount rate to discount the cash flows from the project ** Advantages: Overcomes the requirement for debt capital finance to be earmarked to particular projects ** Disadvantages: Care must be exercised in the selection of the appropriate income stream. The net cash flow to total invested capital is the generally accepted choice. * Total cash flow approach (TCF) ** This distinction illustrates that the Discounted Cash Flow method can be used to determine the value of various business ownership interests. These can include equity or debt holders. ** Alternatively, the method can be used to value the company based on the value of total invested capital. In each case, the differences lie in the choice of the income stream and discount rate. For example, the net cash flow to total invested capital and WACC are appropriate when valuing a company based on the market value of all invested capital.


Shortcomings

The following difficulties are identified with the application of DCF in valuation: # Forecast reliability: Traditional DCF models assume we can accurately forecast revenue and earnings 3–5 years into the future. But studies have shown that growth is neither predictable nor persistent. (See Stock valuation#Growth rate and Sustainable growth rate#From a financial perspective.)
In other terms, using DCF models is problematic due to the
problem of induction The problem of induction is the philosophical Philosophy (from , ) is the study of general and fundamental questions, such as those about existence Existence is the ability of an entity to interact with physical or mental reality ...
, i.e. presupposing that a sequence of events in the future will occur as it always has in the past. Colloquially, in the world of finance, the problem of induction is often simplified with the common phrase: past returns are not indicative of future results. In fact, the SEC demands that all mutual funds use this sentence to warn their investors.
This observation has led some to conclude that DCF models should only be used to value companies with steady cash flows. For example, DCF models are widely used to value mature companies in stable industry sectors, such as utilities. For industries that are especially unpredictable and thus harder to forecast, DCF models can prove especially challenging. Industry Examples: #* Real Estate: Investors use DCF models to value commercial real estate development projects. This practice has two main shortcomings. First, the discount rate assumption relies on the market for competing investments at the time of the analysis, which may not persist into the future. Second, assumptions about ten-year income increases are usually based on historic increases in the market rent. Yet the cyclical nature of most real estate markets is not factored in. Most real estate loans are made during boom real estate markets and these markets usually last fewer than ten years. In this case, due to the problem of induction, using a DCF model to value commercial real estate during any but the early years of a boom market can lead to overvaluation. #* Early-stage Technology Companies: In valuing startups, the DCF method can be applied a number of times, with differing assumptions, to assess a range of possible future outcomes—such as the best, worst and mostly likely case scenarios. Even so, the lack of historical company data and uncertainty about factors that can affect the company's development make DCF models especially difficult for valuing startups. There is a lack of credibility regarding future cash flows, future cost of capital, and the company's growth rate. By forecasting limited data into an unpredictable future, the problem of induction is especially pronounced. # Discount rate estimation: Traditionally, DCF models assume that the
capital asset pricing model In finance Finance is a term for the management, creation, and study of money In a 1786 James Gillray caricature, the plentiful money bags handed to King George III are contrasted with the beggar whose legs and arms were amputated, i ...
can be used to assess the riskiness of an investment and set an appropriate discount rate. Some economists, however, suggest that the capital asset pricing model has been empirically invalidated. various other models are proposed (see
asset pricing :'' This article is theory focused: for the corporate finance Corporate finance is the area of finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned wit ...
), although all are subject to some theoretical or empirical criticism. # Input-output problem: DCF is merely a mechanical valuation tool, which makes it subject to the principle "
garbage in, garbage out In computer science, garbage in, garbage out (GIGO) is the concept that flawed, or nonsense input (computer science), input data produces nonsense input/output, output or "garbage". Sometimes the term rubbish in, rubbish out (RIRO) is used. The pri ...
." Small changes in inputs can result in large changes in the value of a company. This is especially the case with terminal values, which make up a large proportion of the Discounted Cash Flow's final value. # Missing variables: Traditional DCF calculations only consider the financial costs and benefits of a decision. They do not include the environmental, social and governance performance of an organization. This criticism, true for all valuation techniques, is addressed through an approach called "IntFV" discussed below.


Integrated Future Value

To address the lack of integration of the short and long term importance, value and risks associated with natural and social capital into the traditional DCF calculation, companies are valuing their environmental, social and governance (ESG) performance through an
Integrated Management Integration may refer to: Biology *Modular integration, where different parts in a module have a tendency to vary together *Multisensory integration *Path integration * Pre-integration complex, viral genetic material used to insert a viral genome ...
approach to reporting, that expands DCF or Net Present Value to Integrated Future Value (IntFV). This allows companies to value their investments not just for their financial return but also the long term environmental and social return of their investments. By highlighting environmental, social and governance performance in reporting, decision makers have the opportunity to identify new areas for value creation that are not revealed through traditional financial reporting. As an example, the
social cost of carbon The social cost of carbon (SCC) is the marginal cost of the impacts caused by emitting one extra tonne of greenhouse gas ( carbon dioxide equivalent) at any point in time, inclusive of 'non-market' impacts on the environment and human health. Th ...
is one value that can be incorporated into Integrated Future Value calculations to encompass the damage to society from greenhouse gas emissions that result from an investment. This is an integrated approach to reporting that supports Integrated Bottom Line (IBL) decision making, which takes
triple bottom line The triple bottom line (or otherwise noted as TBL or 3BL) is an accounting Accounting or Accountancy is the measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), ...
(TBL) a step further and combines financial, environmental and social performance reporting into one balance sheet. This approach provides decision makers with the insight to identify opportunities for value creation that promote growth and change within an organization.


See also

* Adjusted present value *
Capital asset pricing model In finance Finance is a term for the management, creation, and study of money In a 1786 James Gillray caricature, the plentiful money bags handed to King George III are contrasted with the beggar whose legs and arms were amputated, i ...
*
Capital budgeting Capital most commonly refers to: * Capital letter Letter case (or just case) is the distinction between the letters that are in larger uppercase or capitals (or more formally ''majuscule'') and smaller lowercase (or more formally ''minusc ...
*
Cost of capital In economics Economics () is a social science Social science is the branch A branch ( or , ) or tree branch (sometimes referred to in botany Botany, also called , plant biology or phytology, is the science of plant l ...
*
Debt ratio Debt Ratio is a financial ratio A financial ratio or accounting ratio is a relative magnitude of two selected numerical values taken from an enterprise's financial statement Financial statements (or financial reports) are formal records of the ...
*
Economic value added #REDIRECT Economic value added#REDIRECT Economic value added In corporate finance, as part of fundamental analysis, economic value added is an estimate of a firm's economic profit, or the value created in excess of the Required rate of return, requi ...
*
Enterprise valueEnterprise value (EV), total enterprise value (TEV), or firm value (FV) is an economic measure reflecting the market value Market may refer to: *Market (economics) A market is a composition of system A system is a group of Interaction, intera ...
*
Financial modeling Financial modeling is the task of building an abstraction, abstract representation (a mathematical model, model) of a real world finance, financial situation. This is a mathematical model designed to represent (a simplified version of) the perfor ...
*
Flows to equity In corporate finance, free cash flow to equity (FCFE) is a metric of how much cash can be distributed to the equity shareholders of the company as dividends or Share repurchase, stock buybacks—after all expenses, reinvestments, and debt repayments ...
* Forecast period (finance) *
Free cash flow In corporate finance Corporate finance is the area of finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money and ...
*
Internal rate of return Internal rate of return (IRR) is a method of calculating an investment Investment is the dedication of an asset to attain an increase in value over a period of time. Investment requires a sacrifice of some present asset, such as time, money, ...
*
Market value added Market value added (MVA) is the difference between the current market value of a firm and the capital contributed by investors. If MVA is positive, the firm has added value. If it is negative, the firm has destroyed value. The amount of value a ...
*
Net present value The net present value (NPV) or net present worth (NPW) applies to a series of cash flows occurring at different times. The present value of a cash flow depends on the interval of time between now and the cash flow. It also depends on the discount ra ...
*
Patent valuationIntellectual property Intellectual property (IP) is a category of property that includes intangible creations of the human intellect. There are many types of intellectual property, and some countries recognize more than others. The most well-know ...
* Present value of growth opportunities * Residual income valuation *
Terminal value (finance) In finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money and investments. Savers and investors have money availabl ...
*
Time value of money The time value of money is the widely accepted conjecture that there is greater benefit to receiving a sum of money Money is any item or verifiable record that is generally accepted as payment for goods and services and repayment of debts, ...
*
Valuation using discounted cash flows Valuation using discounted cash flows (DCF valuation) is a method of estimating the current value of a company based on projected future cash flows adjusted for the time value of money The time value of money is the widely accepted conjecture ...
*
Weighted average cost of capital The weighted average cost of capital (WACC) is the rate that a company is expected to pay on average to all its security holders to finance its assets. The WACC is commonly referred to as the firm's cost of capital In economics Economics ...


References


Further reading

* * * * * *


External links


Calculating Intrinsic Value Using the DCF Model
wealthyeducation.com
Calculating Terminal Value Using the DCF Model
wealthyeducation.com
Continuous compounding/cash flows
ocw.mit.edu

''
Motley Fool The Motley Fool is a private financial and investing To invest is to allocate money in the expectation of some benefit/return in the future. In other words, to invest means owning an asset or an item with the goal of generating income from the i ...
''.
Getting Started With Discounted Cash Flows
'' The Street''. {{Authority control Cash flow Engineering economics Corporate finance Valuation (finance)