DCF valuation: calculating enterprise value from free cash flows
DCF valuation (discounted cash flow) estimates the value of a company as the present value of its future free cash flows. It forces you to state every assumption: growth, margin, investment, cost of capital and what comes after the forecast period. Here you work through a complete model for the fictitious Sample Corp. step by step, see which assumption moves the value the most, and read from the share price what the market is pricing in.
What a DCF measures
A company is worth as much as the money it can pay out to its investors in the future, discounted to today. The DCF method puts this idea into practice in three steps: it forecasts free cash flows in detail for a few years, sums up the period after that in a terminal value, and discounts both at the cost of capital. The basics and a first short example are in the article Fundamental analysis; this one covers a complete model and the pitfalls.
Two variants are common. The entity approach discounts the cash flows to all providers of capital (before interest) at the weighted average cost of capital and gives the enterprise value; net debt is then subtracted. The equity approach discounts only the cash flows to shareholders (after interest and debt repayment) at the cost of equity. Done correctly, both lead to the same equity value. In practice the entity approach dominates because it does not depend on the financing of individual years; textbooks such as Damodaran (2012) and Koller et al. (2020) cover both in detail. For banks and insurers, where debt is part of the business, you use the equity approach or a dividend model.
From earnings to free cash flow
In the entity approach, free cash flow starts with operating income (EBIT). Subtract the taxes an unlevered company would pay; the result is called NOPAT (net operating profit after taxes). Depreciation and amortization cost no cash and are added back; capital expenditures and additional working capital are subtracted.
- free cash flow to all providers of capital (free cash flow to the firm)
- tax rate on operating income
- spending on property, plant, equipment and software (capital expenditures)
- increase in inventories and receivables minus accounts payable
The fictitious Sample Corp. had revenue of $1,000 million and an EBIT margin of 15% in its last fiscal year, so EBIT of $150 million. The plan: revenue growth of 8% in the first year, falling by one percentage point each year to 4%, a constant EBIT margin of 15%, a tax rate of 25%, depreciation of 4% and capex of 5% of revenue, and 10 cents of additional working capital for each additional dollar of revenue. Capex above depreciation funds the growth.
| $ million | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
|---|---|---|---|---|---|
| Revenue | 1,080.0 | 1,155.6 | 1,224.9 | 1,286.2 | 1,337.6 |
| EBIT (15%) | 162.0 | 173.3 | 183.7 | 192.9 | 200.6 |
| minus taxes on EBIT (25%) | −40.5 | −43.3 | −45.9 | −48.2 | −50.2 |
| NOPAT | 121.5 | 130.0 | 137.8 | 144.7 | 150.5 |
| plus depreciation (4%) | 43.2 | 46.2 | 49.0 | 51.4 | 53.5 |
| minus capex (5%) | −54.0 | −57.8 | −61.2 | −64.3 | −66.9 |
| minus working capital (10% of added revenue) | −8.0 | −7.6 | −6.9 | −6.1 | −5.1 |
| Free cash flow | 102.7 | 110.9 | 118.6 | 125.7 | 132.0 |
| Discount factor at 8.5% | 0.9217 | 0.8495 | 0.7829 | 0.7216 | 0.6650 |
| Present value | 94.7 | 94.2 | 92.9 | 90.7 | 87.8 |
The sum of the present values is $460.2 million (calculated with unrounded values, hence small rounding differences in the table).
Cost of capital: the WACC
Cash flows are discounted at the weighted average cost of capital (WACC). It blends shareholders' required return with the after-tax interest rate on debt, weighted at market values, not book values. The cost of equity usually comes from the CAPM: the risk-free rate plus beta times the equity risk premium.
- market value of equity and financial debt (target structure)
- cost of equity
- pre-tax cost of debt
- risk-free rate
- beta of the stock
- market risk premium
For Sample Corp.: a risk-free rate of 2.5%, a beta of 1.2 and a market risk premium of 6.0% give a cost of equity of 2.5% + 1.2 × 6.0% = 9.7%. Debt costs 5.0%, or 3.75% after 25% tax. With 80% equity and 20% debt, the WACC is 0.8 × 9.7% + 0.2 × 3.75% = 8.51%, rounded to 8.5%. Each of these inputs is an estimate; the research section shows how uncertain even the cost of equity of an entire industry is.
Terminal value: perpetual growth or exit multiple
After year 5, nobody forecasts year by year anymore. The terminal value sums up all later cash flows, usually as a perpetuity with constant growth g following the model of Gordon (1959). Growth must be below the WACC and in the long run no higher than nominal growth of the economy; otherwise the company would eventually become larger than the economy.
- terminal value at the end of year T
- long-term growth after year T
- return on newly invested capital after year T
The second form, the value driver formula from Koller et al. (2020), makes visible what often stays hidden: growth costs investment. A company that grows at 2% and earns 10% on new capital has to reinvest one fifth of its NOPAT. Instead of the perpetuity, some use an exit multiple, such as eight times EBITDA in year 5. That is convenient, but it brings the market prices of comparable firms into a model that is supposed to be independent of the market. In the example below, the terminal value equals 8.1 times EBITDA in year 5; this cross-check is worth doing for every model.
The example worked to the end
Three quarters of the value lies in the terminal value, i.e. in the period after year 5. That is typical and the reason why the terminal value assumptions deserve more care than the third decimal of the forecast.
How sensitive the result is
A sensitivity table recalculates the value per share for other combinations of WACC and perpetual growth. For Sample Corp., the range runs from $22.88 to $45.54, although only two inputs change by at most one percentage point.
| WACC / perpetual growth | 1.0% | 1.5% | 2.0% | 2.5% | 3.0% |
|---|---|---|---|---|---|
| 7.5% | $32.03 | $34.56 | $37.55 | $41.15 | $45.54 |
| 8.0% | $29.25 | $31.38 | $33.87 | $36.81 | $40.33 |
| 8.5% | $26.84 | $28.65 | $30.75 | $33.19 | $36.07 |
| 9.0% | $24.74 | $26.29 | $28.07 | $30.13 | $32.53 |
| 9.5% | $22.88 | $24.23 | $25.76 | $27.51 | $29.52 |
The closer growth gets to the WACC, the more steeply the value rises: the denominator WACC − g becomes small. Figures from the example above.
Which input matters most? Changing one assumption at a time by one percentage point and keeping the rest the same gives the following for Sample Corp.:
| Assumption | Change | Value per share |
|---|---|---|
| Revenue growth, years 1 to 5 | +1 percentage point per year | +$1.23 |
| EBIT margin | +1 percentage point | +$2.81 |
| Capex | +1 percentage point of revenue | −$3.74 |
| WACC | +1 percentage point | −$4.99 |
| WACC | −1 percentage point | +$6.81 |
| Perpetual growth | +1 percentage point | +$5.33 |
| Perpetual growth | −1 percentage point | −$3.91 |
The effect is not symmetric: a lower WACC raises the value more than a higher one lowers it. And growth in the first five years matters less than perpetual growth afterward.
Reverse DCF: what the share price prices in
Instead of calculating a value from assumptions, you can ask the reverse question: which assumption is in today's share price? At $30 and a WACC of 8.5%, Sample Corp.'s share price justifies perpetual growth of 1.8% after year 5. Whether that is plausible is easier to discuss than a price target. For growth stocks, a reverse DCF often shows that decades of high margins and high growth are priced in.
The same calculation checks the terminal value for internal consistency. In the example, free cash flow in year 5 is 12.3% lower than NOPAT: that much goes into capex and working capital. If that is enough to grow 2% forever, the new capital earns 2% / 12.3% = 16.3%, far above the WACC. If you assume instead that new investments only earn their cost of capital (RONIC = WACC), growth no longer creates value, and the value per share falls to $27.22.
Advanced: beta, timing and inflation
- Converting beta: The beta measured in the market includes the company's leverage. For a different target structure, you first convert it to an unlevered beta and then relever it, using the formula from Hamada (1972): β_L = β_U × (1 + (1 − t) × D / E). Sample Corp. has a beta of 1.2 at D / E = 0.25, so unlevered 1.2 / (1 + 0.75 × 0.25) = 1.01. At D / E = 0.5 it would rise to 1.01 × (1 + 0.75 × 0.5) = 1.39 and the cost of equity to 2.5% + 1.39 × 6.0% = 10.8%.
- Mid-year convention: Cash flows arrive throughout the year, not on December 31. Discounting them to the middle of the year raises their present value by the factor 1.085^0.5, i.e. by 4.2%. With perpetual growth this also applies to all years after year 5, so the terminal value rises by the same factor and with it the whole enterprise value Koller et al. (2020); Sample Corp.'s value per share would then be $32.28.
- Nominal and real: Cash flows that include inflation belong with a WACC that includes inflation. Discounting real cash flows at nominal rates, or putting real growth into a nominal perpetuity, systematically understates or overstates the value.
- Circularity in the WACC: The weights should be market values, but the market value of equity is exactly the result. Practitioners use a target structure or iterate until the weights and the result no longer change.
- Steady state in the final year: The terminal value assumes that the company has reached a steady state in year T: a stable margin and capex in line with growth. One-off effects or an investment wave in the last forecast year get carried into the entire future by the perpetuity.
What the research shows
- Accuracy: Kaplan and Ruback (1995) compared the market values of 51 highly leveraged transactions from 1983 to 1989 with the discounted cash flow forecasts presented with the transactions. On average, the DCF values were within 10% of the actual values and performed at least as well as valuations based on comparable companies and transactions.
- Cost of capital: According to Fama and French (1997), even the cost of equity of entire industries is estimated imprecisely: standard errors of more than 3.0% per year are typical for both the CAPM and the three-factor model. For individual firms and projects, the estimates are even less certain.
- Forecasts: Chan et al. (2003) found that long-term earnings growth is hardly more persistent than chance would suggest, and analysts' growth forecasts are too optimistic. For a DCF, this means that high growth rates over many years are the exception, not the rule.
- Complex is not more accurate: Liu et al. (2002) compared multiples with more elaborate values from simplified residual income models. In explaining stock prices, the more elaborate models brought no improvement over multiples based on forecast earnings.
Read together: a careful DCF can capture a company's value well if the forecasts are good. But the method only shifts the uncertainty into the assumptions; it does not remove it.
Limits and common mistakes
- Growth above the WACC: If g is close to or above the WACC, the terminal value becomes huge or negative. In the long run, more than nominal economic growth is not sustainable.
- Hockey sticks: Margins and growth that only rise steeply from year 3 are a warning sign. Check whether the company has ever reached such figures.
- Incomplete net debt: Lease liabilities, pension obligations and noncontrolling interests belong in the bridge from enterprise value to equity value if their costs are not already in the cash flow. Counting them twice is as wrong as forgetting them.
- Dilution: Stock options and convertible bonds increase the number of shares. Divide by the diluted share count.
- Cyclical companies: A peak year as the starting point of the perpetuity overstates the value. Use a margin over the whole cycle.
- False precision: A value of $30.75 per share sounds precise. A range from the sensitivity table is more honest.
This article explains a method; it is not investment advice and not a recommendation of individual stocks. Sample Corp. and all figures in the example are fictitious.
How Portfolio Lab calculates
The DCF calculator computes exactly this scheme: a five-year forecast with revenue growth and EBIT margin for each year, tax rate, depreciation, capital expenditure and working capital, the terminal value as a perpetuity or with an exit multiple, the WACC directly or from the CAPM and, if you like, with the mid-year convention. Sample Corp. from this article is the default. It also shows the sensitivity to WACC and growth, each assumption changed by one percentage point and the reverse DCF. For US companies it can fill the inputs from their SEC filings (methodology). You will find building blocks of the cost of capital elsewhere in the app:
- Market valuation: The Valuation page shows the Shiller CAPE of the S&P 500 since 1881 and what real returns similar valuations produced in the following years (methodology).
- Beta and factors: The Factors page estimates market beta and loadings on the Fama and French factors for funds and portfolios (methodology).
Frequently asked questions
What is a DCF valuation in simple terms?
You estimate how much cash a company can freely pay out to its investors in the coming years and beyond, and discount these amounts to today at the cost of capital. The sum is the enterprise value; after subtracting net debt, what remains is the value for shareholders.
How do you calculate free cash flow for a DCF?
EBIT times (1 minus the tax rate), plus depreciation, minus capex, minus the increase in working capital. For Sample Corp. in the first forecast year: 121.5 + 43.2 − 54.0 − 8.0 = $102.7 million.
What discount rate do you use in a DCF model?
In the entity approach, the weighted average cost of capital (WACC) from the cost of equity under the CAPM and the after-tax cost of debt, weighted at market values. In the example, a 9.7% cost of equity and a 3.75% cost of debt at 80 to 20 give a WACC of 8.5%.
How high can perpetual growth in the terminal value be?
It must be below the WACC and should not exceed nominal growth of the economy in the long run. Also check whether the assumed capex fits this growth.
Why does the terminal value make up so much of the enterprise value?
Because it covers all years after the forecast period. For Sample Corp. it is 75.0%; even one percentage point more or less growth shifts the value per share by several dollars.
What is a reverse DCF?
The reverse calculation: you look for the assumption, such as perpetual growth, at which the model gives exactly today's share price. For Sample Corp., that is 1.8% at a WACC of 8.5%.
Literature
- Chan, Louis K. C.; Karceski, Jason; Lakonishok, Josef (2003): The Level and Persistence of Growth Rates. The Journal of Finance 58 (2), pp. 643–684. doi:10.1111/1540-6261.00540
- Damodaran, Aswath (2012): Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley, 3rd edition.
- Fama, Eugene F.; French, Kenneth R. (1997): Industry costs of equity. Journal of Financial Economics 43 (2), pp. 153–193. doi:10.1016/S0304-405X(96)00896-3
- Gordon, Myron J. (1959): Dividends, Earnings, and Stock Prices. The Review of Economics and Statistics 41 (2). doi:10.2307/1927792
- Hamada, Robert S. (1972): The Effect of the Firm's Capital Structure on the Systematic Risk of Common Stocks. The Journal of Finance 27 (2), pp. 435–452. doi:10.1111/j.1540-6261.1972.tb00971.x
- Kaplan, Steven N.; Ruback, Richard S. (1995): The Valuation of Cash Flow Forecasts: An Empirical Analysis. The Journal of Finance 50 (4), pp. 1059–1093. doi:10.1111/j.1540-6261.1995.tb04050.x
- Koller, Tim; Goedhart, Marc; Wessels, David (2020): Valuation: Measuring and Managing the Value of Companies. Wiley, 7th edition (McKinsey & Company).
- Liu, Jing; Nissim, Doron; Thomas, Jacob (2002): Equity Valuation Using Multiples. Journal of Accounting Research 40 (1), pp. 135–172. doi:10.1111/1475-679X.00042
This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.