DCF Modelling

The build, in order

Start with free cash flow to the firm: after-tax operating profit, plus depreciation, less capital expenditure, less the increase in working capital. Note that interest is excluded — the cash flow belongs to all providers of capital, which is why the discount rate is the WACC and why the answer is an enterprise value. Mixing a levered cash flow with a WACC, or an unlevered one with a cost of equity, is the most common structural error in a model. Project it for a forecast period long enough to reach a steady state — five to ten years for most businesses, longer for one still growing fast. Then discount each year at the WACC. Add the terminal value, which represents everything after the forecast window, computed as the final year’s cash flow grown at a perpetual rate and divided by the WACC minus that rate. Discount the terminal value back as well, because it arrives at the end of the window and not today. Then bridge to equity. The result is an enterprise value, so subtract net debt, subtract any minority interests and add back non-operating assets, and divide by diluted shares to get a value per share. That bridge is where most of the practical errors hide — a forgotten pension deficit, a convertible counted in the share count but not in the debt, or a stake in a listed company left inside the enterprise value. Read a published valuation backwards through this bridge before you trust its conclusion. The build, with the numbers — Free cash flow, last year: $100m · Years 1 to 5 at 8%: $108m, $116.6m, $126.0m, $136.0m, $146.9m · Discounted at 9%: $486.4m together · Terminal value, discounted: $1,505.9m ← · Enterprise value, then equity value, then per share: $1,992.4m ÷ 10m shares = $199.20 Terminal growth above long-run nominal GDP growth implies the company eventually becomes the economy. It is the assumption most often stretched to make a model produce a target, and the easiest one for a reader to attack.

Why the model is fragile, and what to do about it

The terminal value carries most of the answer, and it is computed from two inputs nobody can observe: a perpetual growth rate and a discount rate that will hold for decades. A tenth of a point of growth or a point of WACC moves the value by tens of percent. The arithmetic is not wrong; the honest conclusion is that a single-number output overstates how much you know. The remedy is not to abandon the model but to change what you ask of it. Build a sensitivity table over the two inputs that matter, so the output is a grid rather than a point, and check that the shares are attractive across most of the grid rather than in one cell. State which assumptions the conclusion is most sensitive to and how you would know if they are wrong. And run a scenario set rather than a table where the risk is structural: a base case, a case where the business loses its pricing power, and a case where the growth continues — each with its own cash flows, rather than one cash flow with three discount rates. Then use the model the way professionals actually do, which is backwards. Instead of forecasting cash flows and reading a value, take the price as given and solve for the cash flows or the growth it requires — the reverse DCF in F21. That reframes the exercise from prediction, where you will be wrong, to judgement about whether a specific set of expectations is reasonable, where you can be right. The output of a good DCF is a sentence like "the price assumes this business grows 15% for a decade" rather than a price target, because the sentence can be argued with and the number cannot. Two cross-checks keep a model honest. Value the same company on a multiple of the terminal year’s earnings or EBITDA, and see whether the DCF’s implied multiple is one you would accept from a peer. And compute the implied return — the discount rate that makes the present value equal to today’s price — which is the number you can compare with other uses of the money.

The consistency rules that break most models

A discounted cash flow has four inputs and one arithmetic identity, and most broken models are broken by mixing two conventions rather than by a wrong forecast. These are the mismatches worth checking before you look at the output. **Cash flow and discount rate must describe the same claim.** Free cash flow to the firm — before interest, available to every capital provider — must be discounted at WACC. Free cash flow to equity, after interest, must be discounted at the cost of equity. Mix the two and you have discounted one group of cash flows at another group’s required return, which produces a number that looks plausible and means nothing. **Nominal with nominal, real with real.** Forecast in the dollars you will actually receive and discount at a nominal rate that includes expected inflation, or forecast in today’s purchasing power and use a real rate. A 7% nominal discount rate applied to cash flows stated in today’s dollars quietly assumes zero inflation for a decade. **And the currency has to match the cash flows.** A euro-denominated forecast discounted at a dollar cost of capital is a forecast of the exchange rate you never made and cannot defend. Four mismatches and what each one does to the answer — FCFF discounted at the cost of equity: systematically too low — the wrong claim · FCFE discounted at WACC: too high — equity cash flows at a blended rate ← · Nominal forecast at a real discount rate: too high, by roughly the inflation rate compounded · Euro cash flows at a dollar WACC: invented a currency view you never wrote down · All four consistent: a number you can now argue about ← Write the convention at the top of the model: which cash flow, which rate, which currency, nominal or real. It takes one line and it stops the most common class of valuation error before it happens.

From enterprise value to a share price: the bridge that eats the errors

A discounted cash flow produces one number — the value of the operating business, before the claims on it are settled. Turning that into a share price is a separate step with its own set of decisions, and it is where most of the avoidable error in a valuation is introduced, because the arithmetic is easy and the choices are quiet. The bridge runs in a fixed order: subtract **net debt** (total debt less cash and equivalents), subtract any minority interest at value, subtract preferred stock, and then divide by the diluted share count rather than the basic one. Get the ordering wrong and the value moves without anything looking wrong on the page. The two steps that are most often mishandled are the cash and the share count. Not all cash is the same: cash held in a country where it cannot be repatriated, or cash that is required as working capital in a regulated business, is not available to a shareholder and subtracting it in full flatters the equity value. On the share count, options and other convertible instruments are not shares but will become them. The standard treatment counts the shares that would be issued if the instruments were exercised, net of the shares the company could buy back with the proceeds — which means the addition rises with the share price and falls with it, so a valuation done at a high price must include more dilution than the same valuation done at a low one. The bridge also produces the number to compare with, and that comparison is the point of the exercise. A valuation that ends at thirty dollars against a market price of twenty is a claim that the market is wrong by a third, and the honest response is to ask which assumption has to move to close that gap rather than to assume the model is right. If the answer is that the value only holds with a growth rate the business has never achieved, the model has told you something about your own optimism. If the answer is that the difference is explained by the market applying a discount rate two points above yours, the disagreement is about the cost of capital, which is a disagreeable but legitimate position to hold — and one worth writing down before the price moves. • Bridge in order: enterprise value, less net debt, less minority interest and preferred, divided by diluted shares. • Not all cash is distributable — trapped cash and regulatory capital are not equity value. • Dilution from options rises with the share price, so the share count depends on the valuation. • End by asking which single assumption closes the gap to the market, not by assuming the model is right.

Discounting the calendar: mid-year, stubs and the terminal-value check

A discounted cash flow is a sum of discounted numbers, and the discount factor is a function of *when* each number arrives — so the calendar convention is a real modelling choice with a real effect on the answer, and it is the one most often left at the default. Discounting a full year of cash flow at a whole-year factor treats the entire year as if it arrived on the last day, which understates its value, because cash generated in March could have been invested or distributed. The convention most practitioners use instead is the **mid-year convention**: discount each period at half a period earlier, on the reasoning that cash arrives roughly evenly through the year. The effect is a simple multiple — the present value rises by a factor of the square root of one plus the discount rate, about two percent at a nine percent rate — which sounds small until you remember that it applies to every year of a fifteen-year forecast and to the terminal value as well. The rule is not which convention you choose but that it is stated, and that the explicit period and the terminal value use the same one, because mixing them shifts value between the two halves of the model without changing anything real. The **stub period** is the second calendar problem, and it is the one that bites in a live model. A valuation built in September for a company with a December year-end has a first period of four months, not twelve. Two things have to follow. The first period’s cash flow must be the four months actually forecast, and its discount factor must be four months of a year, not a whole one. And the terminal value must begin after the last full period of the forecast rather than after the last calendar year, or the model will double-count or omit a stretch of time. The error is easy to make and invisible in the output, because a stub discounted as a full year simply moves value from the explicit period into the terminal — and since the terminal typically carries two-thirds to four-fifths of the total, that is where the mistake compounds. The third piece is the check that catches the most common terminal-value error, and it comes from the relationship the expectations lesson used in the other direction. **Growth equals the return on invested capital multiplied by the reinvestment rate**, so a terminal value that assumes perpetual growth while setting free cash flow equal to after-tax operating profit has assumed a business that grows forever without spending anything. The repair is arithmetic: at a terminal growth rate of two and a half percent and a terminal return on capital of nine percent, the reinvestment rate must be about twenty-eight percent of profit, so the terminal free cash flow is seventy-two percent of terminal profit. A model that ignores it overstates the terminal value by a third or more, which is the same as overstating the whole valuation by a fifth. Two further constraints sit alongside it: a terminal growth rate above the long-run growth of the economy is a claim that the company eventually becomes the economy, so it is normally held below long-run nominal growth, and the implied terminal return on capital should be checked against the company’s own history, because a terminal return above anything it has ever earned is a forecast rather than an assumption. Three calendar checks before reading the output — Mid-year convention: Discount at t − 0.5 and apply it to the terminal value too — about a 2% uplift at a 9% rate · Stub period: A September valuation has a four-month first period, discounted as four months ← · Terminal reinvestment: Reinvestment rate = g ÷ ROIC = 2.5% ÷ 9% ≈ 28% of terminal profit ← · Terminal growth ceiling: Below long-run nominal growth, because the company cannot become the whole economy The pair of checks worth running in this order: does the terminal cash flow leave room for the reinvestment that its own growth rate requires, and does the implied terminal return on capital look like anything the business has achieved before? A model that passes both can still be wrong about the business, but it is at least not wrong about the arithmetic.

Sources

• Free cash flow to the firm, and the two-stage DCFDamodaran, "Investment Valuation"; Koller, Goedhart & Wessels, "Valuation" (McKinsey)
• Terminal value and the Gordon growth formGordon (1959); standard valuation practice
• The enterprise-value-to-equity bridge: net debt, minorities and optionsStandard valuation practice; CFA Institute equity curriculum
• Sensitivity and scenario analysis as the honest output of a modelStandard modelling practice; Koller et al., "Valuation"