MarketValuation using discounted cash flows
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Valuation using discounted cash flows

Valuation using discounted cash flows 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 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".

Basic formula for firm valuation using DCF model
for a typical DCF valuation, with each step detailed in the text (click on image to see at full size) valuation, using free cash flows to estimate the stock's fair value, and displaying sensitivity to WACC and perpetuity growth (click on image to see at full size) Value of firm = \sum_{t=1}^n \frac{FCFF_t}{(1+WACC_{t})^t} + \frac{\left[\frac{FCFF_{n+1}}{(WACC_{n+1}-g_{n+1})}\right]}{(1+WACC_{n})^n} where • FCFF is the free cash flow to the firm (essentially operating cash flow minus capital expenditures) as reduced for tax • WACC is the weighted average cost of capital, 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 (i.e. its market value as distinct from market price); for corporate finance valuations, this represents the project's net present value 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 instead of WACC which incorporates the cost of debt. Free cash flows to the firm are those distributed among – or at least due to – all securities holders of a corporate entity (see ); to equity, are those distributed to shareholders only. Where the latter are dividends then the dividend discount model can be applied, modifying the formula above. == Use ==
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; 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; often these are based on management's assumptions re COGS, payroll, and other expenses. 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, 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" (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. 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. 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 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. 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. For a discussion of the risks and advantages of the two methods, see . 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 Its implied exit multiple can then act as a check, or "triangulation", on the perpetuity derived number. (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. • Analysts in private equity and corporate finance often also generate scenario-based valuations, • 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 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, see . But, again, in the venture capital context, it is not often applied, seen as adding "precision but not accuracy" (and requiring knowledge of the underlying distributions); 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. 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... [then] depending on the plausibility of the cash flows, decide whether the stock is worth its going price." More extensively, using a DCF model, investors can "estimat[e] the expectations embedded in a company's stock price.... [and] then assess the likelihood of expectations revisions." 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. 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==
Literature
Standard textsRichard Brealey, Stewart Myers, Franklin Allen (2013). Principles of Corporate Finance. Mcgraw-Hill • Aswath Damodaran (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley • Tim Koller, Marc Goedhart, David Wessels (McKinsey & Company) (2020). Valuation: Measuring and Managing the Value of Companies (7th ed.). John Wiley & Sons. • • • 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 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 (Includes a review of basic valuation models, including DCF and CAPM) • Campbell Harvey (1997). Equity Valuation (Valuation of Cash Flow Streams). Duke University Fuqua School of BusinessInternational Federation of Accountants (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 • R. S. Ruback. (1995) An Introduction to Cash Flow Valuation Methods (Case # 295-155). Harvard Business School • 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) • Ivo Welch (2022). Pro Forma Financial Statements and Valuation. Chapter 21 in Corporate Finance: 5th Edition Resources • Valuation spreadsheets, Aswath Damodaran • discounted cash flow valuation spreadsheet , Alfred Rappaport and Michael J. Mauboussin ("Expectations Investing") • DCF Valuation Sheet, Danielle Stein Fairhurst ("Financial Modeling in Excel For Dummies")
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