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Valuation using discounted cash flows (DCF valuation) is a method of estimating the current value of a company based on projected future
cash flow A cash flow is a real or virtual movement of money: *a cash flow in its narrow sense is a payment (in a currency), especially from one central bank account to another; the term 'cash flow' is mostly used to describe payments that are expected ...
s adjusted for 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 now rather than an identical sum later. It may be seen as an implication of the later-developed concept of time preference. The ...
. The cash flows are made up of those within the “explicit” forecast period, together with a continuing or terminal value that represents the cash flow stream after the forecast period. In several contexts, DCF valuation is referred to as the "income approach". Discounted cash flow valuation was used in industry as early as the 1700s or 1800s; it was explicated by
John Burr Williams John Burr Williams (November 27, 1900 – September 15, 1989) was an American economist, recognized as an important figure in the field of fundamental analysis, and for his analysis of stock prices as reflecting their " intrinsic value". He is ...
in his ''
The Theory of Investment Value John Burr Williams (November 27, 1900 – September 15, 1989) was an American economist, recognized as an important figure in the field of fundamental analysis, and for his analysis of stock prices as reflecting their " intrinsic value". He is ...
'' in 1938; it was widely discussed in financial economics in the 1960s; and became widely used in U.S. courts in the 1980s and 1990s. This article details the mechanics of the valuation, via a worked example; it also discusses modifications typical for
startup A startup or start-up is a company or project undertaken by an entrepreneur to seek, develop, and validate a scalable business model. While entrepreneurship refers to all new businesses, including self-employment and businesses that never intend t ...
s,
private equity In the field of finance, the term private equity (PE) refers to investment funds, usually limited partnerships (LP), which buy and restructure financially weak companies that produce goods and provide services. A private-equity fund is both a ty ...
and
venture capital Venture capital (often abbreviated as VC) is a form of private equity financing that is provided by venture capital firms or funds to startups, early-stage, and emerging companies that have been deemed to have high growth potential or which hav ...
, corporate finance "projects", and
mergers and acquisitions Mergers and acquisitions (M&A) are business transactions in which the ownership of companies, other business organizations, or their operating units are transferred to or consolidated with another company or business organization. As an aspec ...
, and for sector-specific valuations in financial services and mining. See
Discounted cash flow The discounted cash flow (DCF) analysis is a method in finance of valuing a security, project, company, or asset using the concepts of the time value of money. Discounted cash flow analysis is widely used in investment finance, real estate devel ...
for further discussion, and for context.


Basic formula for firm valuation using DCF model

Value of firm = \sum_^n \frac + \frac where * ''FCFF'' is the
free cash flow In corporate finance, free cash flow (FCF) or free cash flow to firm (FCFF) is the amount by which a business's operating cash flow exceeds its working capital needs and expenditures on fixed assets (known as capital expenditures). It is that porti ...
to the firm (essentially
operating cash flow In financial accounting, operating cash flow (OCF), cash flow provided by operations, cash flow from operating activities (CFO) or free cash flow from operations (FCFO), refers to the amount of cash a company generates from the revenues it brings in ...
minus
capital expenditures Capital expenditure or capital expense (capex or CAPEX) is the money an organization or corporate entity spends to buy, maintain, or improve its fixed assets, such as buildings, vehicles, equipment, or land. It is considered a capital expenditure ...
) as reduced for tax * ''WACC'' is the
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. Importantly, it is dictated by t ...
, combining the cost of equity and the after-tax cost of debt * ''t'' is the time period * ''n'' is the number of time periods to "maturity" or exit * ''g'' is the sustainable growth rate at that point In general, "Value of firm" represents the firm's
enterprise value Enterprise value (EV), total enterprise value (TEV), or firm value (FV) is an economic measure reflecting the market value of a business (i.e. as distinct from market price). It is a sum of claims by all claimants: creditors (secured and unsecured) ...
(i.e. its
market value Market value or OMV (Open Market Valuation) is the price at which an asset would trade in a competitive auction setting. Market value is often used interchangeably with ''open market value'', ''fair value'' or ''fair market value'', although the ...
as distinct from
market price A price is the (usually not negative) quantity of payment or compensation given by one party to another in return for goods or services. In some situations, the price of production has a different name. If the product is a "good" in the ...
); for corporate finance valuations, this represents the project's
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 ...
or NPV. The second term represents the continuing value of future cash flows beyond the forecasting term; here applying a "perpetuity growth model". Note that for valuing equity, as opposed to "the firm", free cash flow to equity (FCFE) or dividends are modeled, and these are discounted at the
cost of equity In finance, the cost of equity is the return (often expressed as a rate of return) a firm theoretically pays to its equity investors, i.e., shareholders, to compensate for the risk they undertake by investing their capital. Firms need to acquire cap ...
instead of WACC which incorporates the cost of debt.
Free cash flow In corporate finance, free cash flow (FCF) or free cash flow to firm (FCFF) is the amount by which a business's operating cash flow exceeds its working capital needs and expenditures on fixed assets (known as capital expenditures). It is that porti ...
s to the firm are those distributed among – or at least due to – all
securities A security is a tradable financial asset. The term commonly refers to any form of financial instrument, but its legal definition varies by jurisdiction. In some countries and languages people commonly use the term "security" to refer to any for ...
holders of a corporate entity (see ); to equity, are those distributed to
shareholder A shareholder (in the United States often referred to as stockholder) of a corporation is an individual or legal entity (such as another corporation, a body politic, a trust or partnership) that is registered by the corporation as the legal ow ...
s only. Where the latter are dividends then the
dividend discount model In finance and investing, the dividend discount model (DDM) is a method of valuing the price of a company's stock based on the fact that its stock is worth the sum of all of its future dividend payments, discounted back to their present value. In o ...
can be applied, modifying the formula above.


Use

The diagram aside shows an overview of the process of company valuation. All steps are explained in detail below.


Determine forecast period

The initial step is to decide the forecast period, i.e. the time period for which the individual yearly cash flows input to the DCF formula will be explicitly modeled. Cash flows after the forecast period are represented by a single number; see § Determine the continuing value below. The forecast period must be chosen to be appropriate to the company's strategy, its market, or industry; theoretically corresponding to the time for the company's ( excess) return to "converge" to that of its industry, with constant, long term growth applying to the continuing value thereafter; although, regardless, 5–10 years is common in practice (see for discussion of the economic argument here). For
private equity In the field of finance, the term private equity (PE) refers to investment funds, usually limited partnerships (LP), which buy and restructure financially weak companies that produce goods and provide services. A private-equity fund is both a ty ...
and
venture capital Venture capital (often abbreviated as VC) is a form of private equity financing that is provided by venture capital firms or funds to startups, early-stage, and emerging companies that have been deemed to have high growth potential or which hav ...
investments, the period will depend on the investment timescale and exit strategy.


Determine cash flow for each forecast period

As above, an explicit cash flow forecast is required for each year during the forecast period. These must be "
Free cash flow In corporate finance, free cash flow (FCF) or free cash flow to firm (FCFF) is the amount by which a business's operating cash flow exceeds its working capital needs and expenditures on fixed assets (known as capital expenditures). It is that porti ...
" or
dividend A dividend is a distribution of profits by a corporation to its shareholders. When a corporation earns a profit or surplus, it is able to pay a portion of the profit as a dividend to shareholders. Any amount not distributed is taken to be re-in ...
s. Typically, this forecast will be constructed using historical internal accounting and sales data, in addition to external industry data and economic indicators (for these latter, outside of large institutions, typically relying on published surveys and industry reports). The key aspect of the forecast is, arguably, predicting revenue, a function of the analyst's forecasts re market size, demand, inventory availability, and the firm's
market share Market share is the percentage of the total revenue or sales in a market that a company's business makes up. For example, if there are 50,000 units sold per year in a given industry, a company whose sales were 5,000 of those units would have a ...
and
market power In economics, market power refers to the ability of a firm to influence the price at which it sells a product or service by manipulating either the supply or demand of the product or service to increase economic profit. In other words, market powe ...
. Future costs, fixed and variable, and investment in PPE with corresponding capital requirements, can then be estimated as a function of sales via "common-sized analysis". At the same time, the resultant line items must talk to the business' operations: in general, growth in revenue will require corresponding increases in
working capital Working capital (WC) is a financial metric which represents operating liquidity available to a business, organisation, or other entity, including governmental entities. Along with fixed assets such as plant and equipment, working capital is consi ...
, fixed assets and associated financing; and in the long term, profitability (and other financial ratios) should tend to the industry average, as mentioned above; see , and . Approaches to identifying which assumptions are most impactful on the value – and thus need the most attention – and to model "calibration" are discussed below (the process is then somewhat iterative). For the components / steps of business modeling here, see , as well as financial forecast more generally. There are several context dependent modifications: *Importantly, in the case of a
startup A startup or start-up is a company or project undertaken by an entrepreneur to seek, develop, and validate a scalable business model. While entrepreneurship refers to all new businesses, including self-employment and businesses that never intend t ...
, substantial costs are often incurred at the start of the first year – and with certainty – and these should then be modelled separately from other cash flows, and not discounted at all. (See comment in example.) Forecasted ongoing costs, and capital requirements, can be proxied on a similar company, or industry averages; analogous to the "common-sized" approach mentioned. *For corporate finance projects, cash flows should be estimated incrementally, i.e. the analysis should only consider cash flows that could change if the proposed investment is implemented. (This principle is generally correct, and applies to all (equity) investments, not just to corporate finance; in fact, the above formulae do reflect this, since, from the perspective of a listed or private equity investor ''all'' expected cash flows are incremental, and the full FCFF or dividend stream is then discounted.) *For an M&A valuationW. Brotherson, K. Eades, R. Harris, R. Higgins (2014)
Company Valuation in Mergers and Acquisitions: How is Discounted Cash Flow Applied by Leading Practitioners?
''Journal of Applied Finance'', Vol. 24;2.
the free cash flow is the amount of cash available to be paid out to all investors in the company after the necessary investments under the business plan being valued. Synergies or strategic opportunities will often be dealt with either by probability weighting / haircutting these, or by separating these into their own DCF valuation where a higher discount rate reflects their uncertainty. Tax will receive very close attention. Often each business-line will be valued separately in a sum-of-the-parts analysis. *When valuing financial services firms,Aswath Damodaran (2009)
''Valuing Financial Service Firms''
Stern, NYU
Doron Nissim (2010)
''Analysis and Valuation of Insurance Companies''
Columbia Business School Columbia Business School (CBS) is the business school of Columbia University, a private research university in New York City. Established in 1916, Columbia Business School is one of six Ivy League business schools and is one of the oldest bus ...
FCFE or dividends are typically modeled, as opposed to FCFF. This is because, often, capital expenditures, working capital and debt are not clearly defined for these corporates ("debt... is more akin to raw material than to a source of capital"), and cash flows to the ''firm'', and hence
enterprise value Enterprise value (EV), total enterprise value (TEV), or firm value (FV) is an economic measure reflecting the market value of a business (i.e. as distinct from market price). It is a sum of claims by all claimants: creditors (secured and unsecured) ...
, cannot then be easily estimated. Discounting is correspondingly at the
cost of equity In finance, the cost of equity is the return (often expressed as a rate of return) a firm theoretically pays to its equity investors, i.e., shareholders, to compensate for the risk they undertake by investing their capital. Firms need to acquire cap ...
. Further, as these firms operate within a highly regulated environment, forecast assumptions must incorporate this reality, and outputs must similarly be "bound" by regulatory limits. ( Loan covenants in place will similarly impact corporate finance and M&A models.) Alternate approaches within DCF valuation will more directly consider economic profit, and the definitions of "cashflow" will differ correspondingly; the best known is EVA. With the cost of capital correctly and correspondingly adjusted, the valuation should yield the same result, for standard cases. These approaches may be considered more appropriate for firms with negative free cash flow several years out, but which are expected to generate positive cash flow thereafter. Further, these may be less sensitive to terminal value. See .


Determine discount factor / rate

A fundamental element of the valuation is to determine the ''appropriate'' required rate of return, as based on the risk level associated with the company and its market. Typically, for an established (listed) company: #For the
cost of equity In finance, the cost of equity is the return (often expressed as a rate of return) a firm theoretically pays to its equity investors, i.e., shareholders, to compensate for the risk they undertake by investing their capital. Firms need to acquire cap ...
, the analyst will apply a model such as the CAPM most commonly; see and
Beta (finance) In finance, the beta (β or market beta or beta coefficient) is a measure of how an individual asset moves (on average) when the overall stock market increases or decreases. Thus, beta is a useful measure of the contribution of an individual a ...
. An unlisted company’s Beta can be based on that of a listed proxy as adjusted for gearing, ie debt, via
Hamada's equation In corporate finance, Hamada’s equation is an equation used as a way to separate the financial risk of a levered firm from its business risk. The equation combines the Modigliani–Miller theorem with the capital asset pricing model. It is used ...
. (Other approaches, such as the "Build-Up method" or T-model are also applied.) #The cost of debt may be calculated for each period as the scheduled after-tax interest payment as a percentage of outstanding debt; see . #The value-weighted combination of these will then return the appropriate discount rate for each year of the forecast period. As the weight (and cost) of debt could vary over the forecast, each period's discount factor will be compounded over the periods to that date. By contrast, for
venture capital Venture capital (often abbreviated as VC) is a form of private equity financing that is provided by venture capital firms or funds to startups, early-stage, and emerging companies that have been deemed to have high growth potential or which hav ...
and
private equity In the field of finance, the term private equity (PE) refers to investment funds, usually limited partnerships (LP), which buy and restructure financially weak companies that produce goods and provide services. A private-equity fund is both a ty ...
valuations – and particularly where the company is a
startup A startup or start-up is a company or project undertaken by an entrepreneur to seek, develop, and validate a scalable business model. While entrepreneurship refers to all new businesses, including self-employment and businesses that never intend t ...
, as in the example – the discount factor is often ''set'' by funding stage, as opposed to modeled ("Risk Group" in the example).Kubr, Marchesi, Ilar, Kienhuis (1998). ''Starting Up''. McKinsey & Company In its early stages, where the business is more likely to fail, a higher return is demanded in compensation; when mature, an approach similar to the preceding may be applied. See: ; . (Some analysts may instead account for this uncertainty by adjusting the cash flows directly: using certainty equivalents; or applying (subjective) "haircuts" to the forecast numbers, a " penalized present value"; or via probability-weighting these as in rNPV.) Corporate finance analysts usually apply the first, listed company, approach: here though it is the risk-characteristics of the project that must determine the cost of equity, and not those of the parent company. M&A analysts likewise apply the first approach, with risk as well as the target capital structure informing both the cost of equity and, naturally, WACC. For the approach taken in the mining industry, where risk-characteristics can differ (dramatically) by
property Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on the nature of the property, an owner of property may have the right to consume, alter, share, r ...
, see: .


Determine current value

To determine current value, the analyst calculates the current value of the future cash flows simply by multiplying each period's cash flow by the discount factor for the period in question; see
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 now rather than an identical sum later. It may be seen as an implication of the later-developed concept of time preference. The ...
. Where the forecast is yearly, an adjustment is sometimes made: although annual cash flows are discounted, it is not true that the entire cash flow comes in at the year end; rather, cash will flow in over the full year. To account for this, a "mid-year adjustment" is applied via the discount rate (and not to the forecast itself), affecting the required averaging. For companies with strong seasonality — e.g. retailers and holiday sales,
agribusiness Agribusiness is the industry, enterprises, and the field of study of value chains in agriculture and in the bio-economy, in which case it is also called bio-business or bio-enterprise. The primary goal of agribusiness is to maximize profit w ...
with fluctuations in working capital linked to production, Oil and gas companies with weather related demand — further adjustments may be required; see.


Determine the continuing value

The continuing, or "terminal" value, is the estimated value of all cash flows after the forecast period. *Typically the approach is to calculate this value using a "perpetuity growth model", essentially returning the value of the future cash flows via a
geometric series In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms. For example, the series :\frac \,+\, \frac \,+\, \frac \,+\, \frac \,+\, \cdots is geometric, because each suc ...
. Key here is the treatment of the long term growth rate, and correspondingly, the forecast period number of years assumed for the company to arrive at this mature stage; see and . *The alternative, exit multiple approach, (implicitly) assumes that the business will be sold at the end of the projection period at some multiple of its final explicitly forecast cash flow: see Valuation using multiples. This is often the approach taken for venture capital valuations, where an exit transaction is explicitly planned. Whichever approach, the terminal value is then discounted by the factor corresponding to the final explicit date. Note that this step carries more risk than the previous: being more distant in time, and effectively summarizing the company's future, there is (significantly) more uncertainty as compared to the explicit forecast period; and yet, potentially (often) this result contributes a significant proportion of the total value. Here, a very high proportion may suggest a flaw in the valuation (as commented in the example); but at the same time may, in fact, reflect how investors make money from equity investments – i.e. predominantly from
capital gain Capital gain is an economic concept defined as the profit earned on the sale of an asset which has increased in value over the holding period. An asset may include tangible property, a car, a business, or intangible property such as shares. ...
s or price appreciation. Its implied exit multiple can then act as a check, or "triangulation", on the perpetuity derived number. Given this dependence on terminal value, analysts will often establish a "valuation range", or sensitivity table (see graphic), corresponding to various appropriate – and internally consistent – discount rates, exit multiples and perpetuity growth rates. For a discussion of the risks and advantages of the two methods, see . For the valuation of mining projects (i.e. as to opposed to listed mining corporates) the forecast period is the same as the "life of mine" – i.e. the DCF model will explicitly forecast all cashflows due to mining the reserve (including the expenses due to mine closure) – and a continuing value is therefore not part of the valuation.


Determine equity value

The equity value is the sum of the present values of the explicitly forecast cash flows, and the continuing value; see and . Where the forecast is of free cash flow to firm, as above, the value of equity is calculated by subtracting any outstanding debts from the total of all discounted cash flows; where free cash flow to equity (or dividends) has been modeled, this latter step is not required – and the discount rate would have been the cost of equity, as opposed to WACC. (Some add readily available cash to the FCFF value.) The accuracy of the DCF valuation will be impacted by the accuracy of the various (numerous) inputs and assumptions. Addressing this, private equity and venture capital analysts, in particular, apply (some of) the following. With the first two, the output price is then market related, and the model will be driven by the relevant variables and assumptions. The latter two can be applied only at this stage. *The DCF value is invariably "checked" by comparing its corresponding P/E or EV/EBITDA to the same of a relevant company or sector, based on share price or most recent transaction. This assessment is especially useful when the terminal value is estimated using the perpetuity approach; and can then also serve as a model "calibration". The use of traditional multiples may be limited in the case of startups – where profit and cash flows are often negative – and ratios such as price/sales are then employed. *Very commonly, analysts will produce a valuation range, especially based on different terminal value assumptions as mentioned. They may also carry out a
sensitivity analysis Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. A related practice is uncertainty ana ...
– measuring the impact on value for a small change in the input – to demonstrate how " robust" the stated value is; and identify which model inputs are most critical to the value. This allows for focus on the inputs that "really drive value", reducing the need to estimate dozens of variables. *Analysts in private equity and corporate finance often also generate scenario-based valuations, based on different assumptions on economy-wide, "global" factors ''as well as'' company-specific factors. In theory, an " unbiased" value is the probability-weighted average of the various scenarios (discounted using a WACC specific to each); see First Chicago Method and expected commercial value. Note that in practice the required probability factors are usually too uncertain to do this.Guillaume Desaché (ND)
''How to value a start-up?''
HEC Paris HEC Paris (french: École des hautes études commerciales de Paris) is a business school, and one of the most prestigious and selective grandes écoles, located in Jouy-en-Josas, France. HEC offers Master in Management, MSc International Fi ...
*An extension of scenario-based valuations is to use Monte Carlo simulation, passing relevant model inputs through a spreadsheet risk-analysis add-in, such as ''@Risk'' or ''Crystal Ball''. The output is a
histogram A histogram is an approximate representation of the distribution of numerical data. The term was first introduced by Karl Pearson. To construct a histogram, the first step is to " bin" (or "bucket") the range of values—that is, divide the ent ...
of DCF values, which allows the analyst to read the expected (i.e. average) value over the inputs, or the probability that the investment will have at least a particular value, or will generate a specific return. The approach is sometimes applied to corporate finance projects,International Federation of Accountants (2008). ''Project Appraisal Using Discounted Cash Flow'' see . But, again, in the venture capital context, it is not often applied, Frank Fabozzi, Sergio M. Focardi, Caroline Jonas (2017). ''Equity Valuation – Science, Art, or Craft?''.
CFA Institute The CFA Institute is a global, not-for-profit professional organization that provides investment professionals with finance education. The institute aims to promote standards in ethics, education, and professional excellence in the global investme ...
Research Foundation
seen as adding " precision but not accuracy"; and the investment in time (and software) is then judged as unlikely to be warranted. The DCF value may be applied differently depending on context. An investor in listed equity will compare the value per share to the share's traded price, amongst other stock selection criteria. To the extent that the price is lower than the DCF number, so she will be inclined to invest; see Margin of safety (financial), Undervalued stock, and
Value investing Value investing is an investment paradigm that involves buying securities that appear underpriced by some form of fundamental analysis. The various forms of value investing derive from the investment philosophy first taught by Benjamin Graham ...
. The above calibration will be less relevant here; reasonable and robust assumptions more so. A related approach is to " reverse engineer" the stock price; i.e. to "figure out how much cash flow the company would be expected to make to generate its current valuation...
hen Hen commonly refers to a female animal: a female chicken, other gallinaceous bird, any type of bird in general, or a lobster. It is also a slang term for a woman. Hen or Hens may also refer to: Places Norway * Hen, Buskerud, a village in Ringe ...
depending on the plausibility of the cash flows, decide whether the stock is worth its going price."Ben McClure (2015)
''Evaluate Stock Price With Reverse-Engineering DCF''
/ref> More extensively, using a DCF model, investors can "estimat the expectations embedded in a company's stock price.... ndthen assess the likelihood of expectations revisions." Alfred Rappaport and Michael Mauboussin (2003). ''Expectations Investing'', Harvard Business Review Press. Corporations will often have several potential projects under consideration (or active), see . NPV is typically the primary selection criterion between these; although other investment measures considered, as visible from the DCF model itself, include ROI, IRR and payback period. Private equity and venture capital teams will similarly consider various measures and criteria, as well as recent comparable transactions, "Precedent Transactions Analysis", when selecting between potential investments; the valuation will typically be one step in, or following, a thorough
due diligence Due diligence is the investigation or exercise of care that a reasonable business or person is normally expected to take before entering into an agreement or contract with another party or an act with a certain standard of care. It can be a ...
. For an M&A valuation, the DCF may be one of the several results combined so as to determine the value of the deal; note that for early stage companies, however, the DCF will typically not be included in the "valuation arsenal", given their low profitability and higher reliance on revenue growth.


See also

*Further discussion: **
Discounted cash flow The discounted cash flow (DCF) analysis is a method in finance of valuing a security, project, company, or asset using the concepts of the time value of money. Discounted cash flow analysis is widely used in investment finance, real estate devel ...
, and especially § Shortcomings ** ** ** *Private equity / venture capital related techniques: ** LBO valuation model ** Chepakovich valuation model ** First Chicago Method * Economic profit approaches: ** Market value added **
Residual income valuation Residual income valuation (RIV; also, residual income ''model'' and residual income ''method'', RIM) is an approach to equity valuation that formally accounts for the cost of equity capital. Here, "residual" means in excess of any opportunity cos ...
** Clean surplus accounting ** Adjusted present value *DCF related investment measures: ** Capital efficiency **
Return on investment Return on investment (ROI) or return on costs (ROC) is a ratio between net income (over a period) and investment (costs resulting from an investment of some resources at a point in time). A high ROI means the investment's gains compare favourably ...
**
Internal rate of return Internal rate of return (IRR) is a method of calculating an investment’s rate of return. The term ''internal'' refers to the fact that the calculation excludes external factors, such as the risk-free rate, inflation, the cost of capital, or f ...
** Modified internal rate of return ** Discounted payback period ** Equivalent annual cost ** Cut off period ** PVGO *Mergers and acquisitions related considerations: ** Pre-money valuation ** Post-money valuation ** Minority discount **
Control premium A control premium is an amount that a buyer is sometimes willing to pay over the current market price of a publicly traded company in order to acquire a controlling share in that company. If the market perceives that a public company's profit and ...
** Accretion/dilution analysis


References


Literature

Standard texts * Richard Brealey, Stewart Myers,
Franklin Allen Franklin Allen, (born 6 March 1956) is a British economist and academic. Since 2014, he has been professor of finance and economics, and executive director of the Brevan Howard Centre at Imperial College London. He was the Nippon Life Prof ...
(2013). ''
Principles of Corporate Finance ''Principles of Corporate Finance'' is a reference work on the corporate finance theory edited by Richard Brealey, Stewart Myers, Franklin Allen, and Alex Edmans. The book is one of the leading texts that describes the theory and practice of c ...
''. Mcgraw-Hill *
Aswath Damodaran Aswath Damodaran (born 24 September 1957), is a Professor of Finance at the Stern School of Business at New York University (Kerschner Family Chair in Finance Education), where he teaches corporate finance and equity valuation. Background Kno ...
(2012). '' Investment Valuation: Tools and Techniques for Determining the Value of Any Asset ''. Wiley * Tim Koller, Marc Goedhart, David Wessels (McKinsey & Company) (2005). '' Valuation: Measuring and Managing the Value of Companies''. John Wiley & Sons. * * *{{cite book , author=Jerald E. Pinto , title=Equity Asset Valuation (
CFA Institute The CFA Institute is a global, not-for-profit professional organization that provides investment professionals with finance education. The institute aims to promote standards in ethics, education, and professional excellence in the global investme ...
Investment Series), publisher= Wiley Finance , year=2020, isbn=978-1119628101 Discussion * W. Brotherson, K. Eades, R. Harris, R. Higgins (2014)
Company Valuation in Mergers and Acquisitions: How is Discounted Cash Flow Applied by Leading Practitioners?
''Journal of Applied Finance'', Vol. 24;2. * Goort de Bruijn and Wout Bobbink (2019)
''Startup valuation: applying the discounted cash flow method in six easy steps''
ey.com/nl * Aswath Damodaran (ND)
''Discounted Cash Flow Valuation''
New York University Stern School of Business * Aswath Damodaran (ND)
''Probabilistic Approaches: Scenario Analysis, Decision Trees and Simulations''
New York University Stern School of Business * Frank Fabozzi, Sergio M. Focardi, Caroline Jonas (2017)
''Equity Valuation – Science, Art, or Craft?''
CFA Institute The CFA Institute is a global, not-for-profit professional organization that provides investment professionals with finance education. The institute aims to promote standards in ethics, education, and professional excellence in the global investme ...
Research Foundation * Pablo Fernandez (2004)
''Equivalence of ten different discounted cash flow valuation methods''
IESE Research Papers. D549 * Pablo Fernandez (2015)
''Valuing Companies by Cash Flow Discounting: Ten Methods and Nine Theories''
EFMA 2002 London Meetings * Edward J. Green, Jose A. Lopez, and Zhenyu Wang (2003)
''Formulating the Imputed Cost of Equity Capital''
Federal Reserve Bank of New York The Federal Reserve Bank of New York is one of the 12 Federal Reserve Banks of the United States. It is responsible for the Second District of the Federal Reserve System, which encompasses the State of New York, the 12 northern counties of New ...
(Includes a review of basic valuation models, including DCF and CAPM) * Campbell Harvey (1997)
''Equity Valuation (Valuation of Cash Flow Streams)''
Duke University Duke University is a private research university in Durham, North Carolina. Founded by Methodists and Quakers in the present-day city of Trinity in 1838, the school moved to Durham in 1892. In 1924, tobacco and electric power industrialist Jam ...
Fuqua School of Business *
International Federation of Accountants The International Federation of Accountants (IFAC) is the global advocacy organization for the accountancy profession; mainly for the financial accounting and auditing professions. Founded in 1977, IFAC has more than 175 members and associates in ...
(2008)
''Project Appraisal Using Discounted Cash Flow''
* T. Keck, E. Levengood, and A. Longfield (1998). ''Using Discounted Cash Flow Analysis in an International Setting: A Survey of Issues in Modeling the Cost of Capital'', '' Journal of Applied Corporate Finance'', Fall, pp. 82–99. * Eric Kirzner (2006
''Selected Moments in the History of Discounted Present Value''
Rotman School of Management (Archived) * Kubr, Marchesi, Ilar, Kienhuis (1998)
''Starting Up''
McKinsey & Company McKinsey & Company is a global management consulting firm founded in 1926 by University of Chicago professor James O. McKinsey, that offers professional services to corporations, governments, and other organizations. McKinsey is the oldest and ...
* R. S. Ruback. (1995
''An Introduction to Cash Flow Valuation Methods'' (Case # 295-155)
Harvard Business School Harvard Business School (HBS) is the graduate business school of Harvard University, a private research university in Boston, Massachusetts. It is consistently ranked among the top business schools in the world and offers a large full-time MBA ...
*Tham, Joseph and Tran Viet Thang (2003)
''Equivalence between Discounted Cash Flow (DCF) and Residual Income (RI)''
(Working paper; Duke University - Center for Health Policy, Law and Management) Resources

Aswath Damodaran
discounted cash flow valuation spreadsheet
Alfred Rappaport and Michael J. Mauboussin ("''Expectations Investing''") Valuation (finance) Cash flow