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The '''discounted cash flow''' ('''DCF''') analysis, in [[financial analysis]], is a method used [[Valuation (finance)|to value]] a [[security (finance)|security]], project, company, or [[financial asset|asset]], that incorporates the [[time value of money]]. | The '''discounted cash flow''' ('''DCF''') analysis, in [[financial analysis]], is a method used [[Valuation (finance)|to value]] a [[security (finance)|security]], project, company, or [[financial asset|asset]], that incorporates the [[time value of money]]. | ||
Discounted [[cash flow]] analysis is widely used in investment finance, [[real estate developer|real estate development]], [[corporate financial]] management, and [[patent valuation]]. Used in industry as early as the 1800s, it was widely discussed in financial economics in the 1960s, and U.S. courts began employing the concept in the 1980s and 1990s. <!-- Related is the [[carbon discounted cash flow]], which integrates [[climate change|climate-related]] considerations. --> | Discounted [[cash flow]] analysis is widely used in investment finance, [[real estate developer|real estate development]], [[corporate financial]] management, [[actuarial science]], and [[patent valuation]]. Terminal value often represents a large share of total value and is highly sensitive to growth and discount rate assumptions. Enterprise DCF commonly uses free cash flow to the firm and a continuing value beyond the explicit forecast horizon.Used in industry as early as the 1800s, it was widely discussed in financial economics in the 1960s, and U.S. courts began employing the concept in the 1980s and 1990s. <!-- Related is the [[carbon discounted cash flow]], which integrates [[climate change|climate-related]] considerations. --> | ||
==Application== | ==Application== | ||
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On a very high level, the main elements in valuing a corporate by Discounted Cash Flow are as follows; see [[Valuation using discounted cash flows]], and graphics below, for detail: | On a very high level, the main elements in valuing a corporate investment by Discounted Cash Flow are as follows; see [[Valuation using discounted cash flows]], and graphics below, for detail: | ||
* '''Free Cash Flow Projections:''' Projections of the amount of Cash produced by a company's business operations after paying for operating expenses and capital expenditures.<ref name=":0">{{Cite web|url=http://www.streetofwalls.com/finance-training-courses/investment-banking-technical-training/discounted-cash-flow-analysis/|title=Discounted Cash Flow Analysis {{!}} Street of Walls|website=streetofwalls.com|access-date=2019-10-07}}</ref> | * '''Free Cash Flow Projections:''' Projections of the amount of Cash produced by a company's business operations after paying for operating expenses and capital expenditures.<ref name=":0">{{Cite web|url=http://www.streetofwalls.com/finance-training-courses/investment-banking-technical-training/discounted-cash-flow-analysis/|title=Discounted Cash Flow Analysis {{!}} Street of Walls|website=streetofwalls.com|access-date=2019-10-07}}</ref> | ||
* '''Discount Rate:''' The cost of capital (Debt and Equity) for the business. This rate, which acts like an interest rate on future Cash inflows, is used to convert them into current dollar equivalents. | * '''Discount Rate:''' The cost of capital (Debt and Equity) for the business. This rate, which acts like an interest rate on future Cash inflows, is used to convert them into current dollar equivalents. | ||
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==Discount rate== | ==Discount rate== | ||
The act of discounting future cash flows asks "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?" | The act of discounting future cash flows asks "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?"<ref name="Damodaran2012" /> In other words, discounting returns the [[present value]] of future cash flows, where the rate used is the cost of capital that ''appropriately'' reflects the risk, and timing, of the cash flows.<ref name="BerkDeMarzo" /> | ||
This " | This "required return" thus incorporates: | ||
# [[Time value of money]] ([[Risk-free interest rate|risk-free rate]]) – according to the theory of [[time preference]], investors would rather have cash immediately than having to wait and must therefore be compensated by paying for the delay. | # [[Time value of money]] ([[Risk-free interest rate|risk-free rate]]) – according to the theory of [[time preference]], investors would rather have cash immediately than having to wait and must therefore be compensated by paying for the delay.<ref name="Mishkin" /> | ||
# [[Risk premium]] – reflects the extra return investors demand because they want to be compensated for the risk that the cash flow might not materialize after all. | # [[Risk premium]] – reflects the extra return investors demand because they want to be compensated for the risk that the cash flow might not materialize after all.<ref name="Brealey" /> | ||
Mathematically, the required return on equity ($r_e$) is most commonly determined via the [[Capital Asset Pricing Model]] (CAPM): | |||
:<math>r_e = r_f + \beta \cdot (r_m - r_f)</math> | |||
where: | |||
* <math>r_f</math> is the risk-free rate (e.g., the yield on government bonds); | |||
* <math>\beta</math> (Beta) measures the asset's sensitivity to market movements; | |||
* <math>r_m - r_f</math> is the [[equity risk premium]], the expected excess return of the market over the risk-free rate. | |||
For an entire firm or project, the discount rate is typically the [[Weighted Average Cost of Capital]] (WACC): | |||
<math display=block>\mathrm{WACC}=\frac{E}{D+E} r_e + \frac{D}{D+E} r_d (1-T)</math> | |||
where <math>E</math> and <math>D</math> are the market values of equity and debt, <math>r_e</math> is the [[cost of equity]], <math>r_d</math> is the cost of debt and <math>T</math> is the corporate tax rate.<ref name="BerkDeMarzo2024" /> | |||
For the latter, various [[economic model|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 {{slink|Capital asset pricing model|Asset-specific required return}} and {{slink|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]], 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". | |||
The terminology "expected return", although formally the [[expected value|mathematical expected value]], is often used interchangeably with the above, where "expected" means "required" or "demanded" by investors. | |||
The method may also be modified by industry, for example various formulae have been proposed when choosing a discount rate [[healthcare economics|in a healthcare setting]];<ref>Lim, Andy; Lim, Alvin (2019). "Choosing the discount rate in an economic analysis". Emergency Medicine Australasia.</ref> similarly in a [[mining]] setting, where risk-characteristics can differ (dramatically) by [[mineral rights|property]].<ref>Queen's University minewiki. "Discount rate".</ref> | |||
==Methods of appraisal of a company or project== | ==Methods of appraisal of a company or project== | ||
For these [[Valuation (finance)|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]] of the company. However the assumptions used in the appraisal (especially the equity discount rate and the [[cash flow forecast|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]] 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.) | For these [[Valuation (finance)|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]] of the company. However the assumptions used in the appraisal (especially the equity discount rate and the [[cash flow forecast|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]] 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.) | ||
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** Advantages: Overcomes the requirement for debt capital finance to be earmarked to particular projects | ** 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. | ** 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) | * [[Total cash flow]] approach (TCF) | ||
** Discount the total cash flows to the firm, with the [[tax shield]] on debt interest included in the cash flows rather than the discount rate | |||
** 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. | ** 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.<ref>{{cite book | ** 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.<ref>{{cite book | ||
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{{Further|Dividend discount model#Problems with the constant-growth form of the model}} | {{Further|Dividend discount model#Problems with the constant-growth form of the model}} | ||
The following difficulties are identified with the application of DCF in valuation: | 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.<ref>{{Cite work|last1=Chan|first1=Louis K.C.|last2=Karceski|first2=Jason|last3=Lakonishok|first3=Josef|date=May 2001|title=The Level and Persistence of Growth Rates|location=Cambridge, MA|doi=10.3386/w8282|doi-access=free}}</ref> (See [[Stock valuation#Growth rate]] and [[Sustainable growth rate#From a financial perspective]].) <br/>In other terms, using DCF models is problematic due to the [[problem of induction]], 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.<ref>{{Cite web|url=https://www.sec.gov/fast-answers/answersmperfhtm.html|title=SEC.gov {{!}} Mutual Funds, Past Performance|publisher=U.S. Securities and Exchange Commission|access-date=2019-05-08}}</ref><br/>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: | # '''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.<ref>{{Cite work|last1=Chan|first1=Louis K.C.|last2=Karceski|first2=Jason|last3=Lakonishok|first3=Josef|date=May 2001|title=The Level and Persistence of Growth Rates|location=Cambridge, MA|doi=10.3386/w8282|doi-access=free}}</ref> (See [[Stock valuation#Growth rate]] and [[Sustainable growth rate#From a financial perspective]].) <br/>In other terms, using DCF models is problematic due to the [[problem of induction]], 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.<ref>{{Cite web|url=https://www.sec.gov/fast-answers/answersmperfhtm.html|title=SEC.gov {{!}} Mutual Funds, Past Performance|publisher=U.S. Securities and Exchange Commission|access-date=2019-05-08}}</ref><br/>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 [[Real estate appraisal#The income approach|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.<ref>{{Cite book|last1=Reilly|first1=Robert F.|last2=Schweihs|first2=Robert P.|date=2016-10-28|title=Guide to Intangible Asset Valuation|doi=10.1002/9781119448402|isbn=9781119448402|s2cid=168737069 }}</ref> | #* Real Estate: Investors use DCF models [[Real estate appraisal#The income approach|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.<ref>{{Cite book|last1=Reilly|first1=Robert F.|last2=Schweihs|first2=Robert P.|date=2016-10-28|title=Guide to Intangible Asset Valuation|doi=10.1002/9781119448402|isbn=9781119448402|s2cid=168737069 }}</ref> | ||
#* Early-stage Technology Companies: [[Startup company#Valuations|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 | #* Early-stage Technology Companies: [[Startup company#Valuations|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 most 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.<ref>{{Citation|chapter=Measuring and Managing Value in High-Tech Start-ups|date=2015-09-12|pages=285–311|publisher=John Wiley & Sons, Inc.|isbn=9781119200154|doi=10.1002/9781119200154.ch18|title=Valuation for M&A}}</ref> | ||
# '''Discount rate estimation''': Traditionally, DCF models assume that the [[capital asset pricing model]] 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.<ref>{{Cite journal|last1=Fama|first1=Eugene F.|last2=French|first2=Kenneth R.|date=2003|title=The Capital Asset Pricing Model: Theory and Evidence|journal=SSRN Working Paper Series|doi=10.2139/ssrn.440920|s2cid=12059689 |issn=1556-5068|url=https://bibliotecadigital.fgv.br/ojs/index.php/rae/article/view/36903 }}</ref> various other models are proposed (see [[asset pricing]]), although all are subject to some theoretical or empirical criticism. | # '''Discount rate estimation''': Traditionally, DCF models assume that the [[capital asset pricing model]] 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.<ref>{{Cite journal|last1=Fama|first1=Eugene F.|last2=French|first2=Kenneth R.|date=2003|title=The Capital Asset Pricing Model: Theory and Evidence|journal=SSRN Working Paper Series|doi=10.2139/ssrn.440920|s2cid=12059689 |issn=1556-5068|url=https://bibliotecadigital.fgv.br/ojs/index.php/rae/article/view/36903 }}</ref> various other models are proposed (see [[asset pricing]]), 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]]." Small changes in inputs can result in large changes in the value of a company. This is especially the case with [[Terminal value (finance)|terminal values]], which make up a large proportion of the Discounted Cash Flow's final value. | # '''Input-output problem''': DCF is merely a mechanical valuation tool, which makes it subject to the principle "[[garbage in, garbage out]]." Small changes in inputs can result in large changes in the value of a company. This is especially the case with [[Terminal value (finance)|terminal values]], which make up a large proportion of the Discounted Cash Flow's final value. | ||
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==References== | ==References== | ||
{{ | <references> | ||
<ref name="BerkDeMarzo2024">{{cite book |last1=Berk |first1=Jonathan |last2=DeMarzo |first2=Peter |title=Corporate Finance, Global Edition |edition=6th |publisher=Pearson |date=2024 |isbn=978-1292740522 |url=https://www.pearson.com/en-gb/subject-catalog/p/corporate-finance-global-edition/P200000009910/9781292740522 |access-date=30 January 2026}}</ref> | |||
</references> | |||
==Further reading== | ==Further reading== | ||
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<!-- *[http://www.wacc.biz Monography about DCF (including some lectures on DCF)]. extremely technical--> | <!-- *[http://www.wacc.biz Monography about DCF (including some lectures on DCF)]. extremely technical--> | ||
*[https://web.archive.org/web/20080110115513/http://www.thestreet.com/university/personalfinance/10385275.html Getting Started With Discounted Cash Flows]. ''[[TheStreet.com|The Street]]''. | *[https://web.archive.org/web/20080110115513/http://www.thestreet.com/university/personalfinance/10385275.html Getting Started With Discounted Cash Flows]. ''[[TheStreet.com|The Street]]''. | ||
*[https://wacc.info/ Open educational material (videos and book)] on Discounted Cash Flow. | |||
{{Corporate finance and investment banking}} | {{Corporate finance and investment banking}} | ||