# Valuation using discounted cash flows

Year 1 Year 2 Year 3 Year 4 Year 5 Forward Discount Rate MedICT is a medical ICT startup that has just finished its business plan. Its goal is to provide medical professionals with bookkeeping software. Its only investor is required to wait for five years before making an exit. Therefore, MedICT is using a forecast period of 5 years. The forward discount rates for each year have been chosen based on the increasing maturity of the company. Only operational cash flows (i.e. Free cash flow to firm) have been used to determine the estimated yearly cash flow, which is assumed to occur at the end of each year (which is unrealistic especially for the year 1 cash flow; see comments aside re mid year adjustments). Figures are in $thousands: Revenues +30 +100 +160 +330 +460 Personnel -30 -80 -110 -160 -200 Car Lease -6 -12 -12 -18 -18 Marketing -10 -10 -10 -25 -30 IT -20 -20 -20 -25 -30 Cash Flow -36 -22 +8 +102 +182 Risk Group Seeking Money Early Startup Late Start Up Mature (22) (10) 3 28 42 This gives a total value of 41 for the first five years' cash flows. MedICT has chosen the perpetuity growth model to calculate the value of cash flows beyond the forecast period. They estimate that they will grow at about 6% for the rest of these years (this is extremely prudent given that they grew by 78% in year 5), and they assume a forward discount rate of 15% for beyond year 5. The terminal value is hence: (182*1.06 / (0.15-0.06)) × 0.229 = 491. (Given that this is far bigger than the value for the first 5 years, it is suggested that the initial forecast period of 5 years is not long enough, and more time will be required for the company to reach maturity; although see discussion aside.) MedICT does not have any debt so all that is required is to add together the present value of the explicitly forecast cash flows (41) and the continuing value (491), giving an equity value of$532,000.

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.[1] The cash flows are made up of the cash flows within the forecast period together with a continuing or terminal value that represents the cash flow stream after the forecast period.

Discounted Cash Flow valuation was used in industry as early as the 1700s or 1800s; it was publicly explicated by John Burr Williams in his The Theory of Investment Value 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.[2]

This article details the mechanics of the valuation, via a worked example; but see Discounted cash flow for further discussion, and Valuation (finance) #Valuation overview for context.

## Basic formula for firm valuation using DCF model

Value of firm = ${\displaystyle \sum _{t=1}^{n}{\frac {FCFF_{t}}{(1+WACC_{t})^{t}}}+{\frac {\left[{\frac {FCFF_{n+1}}{(WACC_{n}-g_{n})}}\right]}{(1+WACC_{n})^{n}}}}$

where

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 Corporate finance #Capital structure); 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.

## Using the DCF Method

The diagram 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 fixed number. The forecast period must be chosen to be appropriate to the company's strategy, its market, and/or the features of the investment itself; see under Forecast period (finance), as well as #Determine the continuing value below.

### 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" or dividends.

Typically, this forecast will be constructed using historical internal accounting and sales data, in addition to external industry data and economic indicators. The key aspect of the forecast is, arguably, predicting revenue; future costs, fixed and variable, as well as capital, can then be estimated as a function of sales via "common-sized analysis".

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. [3]

Importantly, in the case of a start-up, 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.

For the components / steps of business modeling here, see the list for "Equity valuation" under Outline of finance #Discounted cash flow valuation; as well as financial forecast and Financial modeling #Accounting more generally. Alternate approaches to 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.[4]

### 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:

1. For the cost of equity, the analyst will apply a model such as the CAPM most commonly; see Capital asset pricing model #Asset-specific required return and Beta (finance). An unlisted company’s Beta can be based on that of a listed proxy as adjusted for gearing, ie debt, via Hamada's equation. (Other approaches, such as the "Build-Up method" or T-model are also applied here.)
2. The cost of debt may be calculated for each period as the scheduled after-tax interest payment as a percentage of outstanding debt; see Corporate finance #Debt capital.
3. 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 period, each year's discount factor will be compounded over the rates to that date.

By contrast, for venture capital and private equity valuations - and particularly where the company is a startup, as in the example - the discount factor is often set by funding stage, as opposed to modeled (hence, "Risk Group" in the example). [5] 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: Private equity #Investment timescales; Venture capital #Financing stages. 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; or via probability-weighting these as in rNPV.

### 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.

### Determine the continuing value

The continuing value, or terminal value, is the estimated value of the cash flows after the forecast period. Typically the approach is to model the values using a "perpetuity growth model", essentially returning the value of the future cash flows modeled as 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 Sustainable growth rate #From a financial perspective and Stock valuation #Growth rate. The alternative, exit multiple approach, 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 at the rate 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, 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 gains or price appreciation.[6] Its implied exit multiple can then act as a check on the perpetuity derived number. Given this dependence on terminal value, analysts will often establish a "valuation range", 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 Terminal value (finance) #Comparison of methodologies.

### Determine equity value

The equity value is the sum of the present values of the explicitly forecast cash flows, and the continuing value; see Equity (finance) #Market value of equity stock and Intrinsic value (finance) #Equity. 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.

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 various of the following (see Corporate finance #Quantifying uncertainty for general discussion of these):

• Most commonly, they will produce a valuation range, especially based on different terminal value assumptions as mentioned. They may also carry out a sensitivity analysis 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 variables that "really drive value", reducing the need to estimate dozens of variables.[7]
• Analysts 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; see First Chicago Method. Note that in practice the required probability factors are usually too uncertain to do this.
• 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 probability that the investment will have at least a particular value, or will generate a specific return. But again this is not often applied, seen as adding “precision but not accuracy”; the investment in time (and software) here is then seen as unlikely to be warranted.

• Further discussion:
• Private equity / venture capital specific techniques:
• Economic profit approaches:

## References

1. ^ Pablo Fernandez (2015). Valuing Companies by Cash Flow Discounting: Ten Methods and Nine Theories
2. ^ Simkovic, Michael (2017). "The Evolution of Valuation in Bankruptcy". American Bankruptcy Law Journal. SSRN 2810622.
3. ^ Chris Haynes (N.D.). Mid-Year Discount Definition
4. ^ Pablo Fernandez (2004). Equivalence of ten different discounted cash flow valuation methods. IESE Research Papers. D549
5. ^ Sanjai Bhagat (2013). Why do venture capitalists use such high discount rates?. The Journal of Risk Finance, Vol. 15 No. 1, 2014
6. ^
7. ^ Aswath Damodaran (2016). Musings on Markets; Myth 3

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