DCF and Intrinsic Value

In short

A discounted cash flow model says that a business is worth the cash it will produce, adjusted for the fact that cash arriving later is worth less than cash arriving now.

Canonical data. Figures tie to Wexford Instruments, the Pillar 22 parameters (cost of equity 9.0%), and the Pillar 25 market-data extension — an illustrative price of $12.00.

The logic is unimpeachable and the practice is treacherous, for a reason worth stating at the outset: the model is arithmetic, and arithmetic cannot be wrong. Everything that can be wrong is in the inputs — and the model presents their consequences with a precision they do not possess.

The three inputs

Cash flows. Usually free cash flow, forecast explicitly for some years. The forecast is a guess about the future dressed in decimals, and it is the least reliable part of the exercise even when done carefully.

The discount rate. Typically the cost of equity for equity flows, or a blended cost of capital for flows available to everyone. Pillar 22's canonical parameters give a market-beta cost of equity of 9.0%, and a single percentage point of movement changes a valuation by more than 12%.

The terminal value. What the business is worth at the end of the forecast, usually a growing perpetuity. This is where most of the answer comes from, which is uncomfortable because it is also the crudest assumption in the model.

Terminal value is the model

On a conventional five-year forecast, the terminal value routinely accounts for two-thirds to four-fifths of the total. On the worked example below it is 74%.

The implication deserves to be stated plainly: a reader scrutinising the five years of explicit forecasts is examining a quarter of the answer. The terminal growth rate — a single number, usually set near long-run economic growth and rarely defended in detail — determines most of it. And terminal growth must be below the discount rate or the arithmetic breaks entirely, producing a negative or infinite value, which is a useful reminder that the perpetuity formula is a convenience rather than a description of reality.

The reverse DCF

Because the inputs dominate, running the model backwards is often more useful than running it forwards. Instead of forecasting cash flows to produce a value, take the market price as given and solve for the growth rate that justifies it. The output is not a valuation but a question — is that growth rate plausible? — and questions of that shape are answerable in a way that forecasts are not.

This is the single most practical technique in the article, because it converts an argument about whether a price is right into an argument about whether an expectation is reasonable, which is where the disagreement actually lives.

Worked example

Worked example: a DCF on Wexford, and why it does not settle anything (canonical figures, USD millions). The forward model. Take free cash flow of 20.3, grow it at 8% for five years, then apply a terminal growth rate of 2%, discounting throughout at the canonical 9.0%. The explicit five years contribute 98.7 of present value; the terminal value contributes 282.5; the total is 381.2. The terminal value is 74% of the answer. Against the market. That 381.2 sits against a market capitalisation of 1,200.0 — the model produces roughly a third of the price. Sensitivity. Move the discount rate alone: at 8% the total is 446.6; at 10%, 332.2. A two-point range in one assumption moves the answer by 34%. Now reverse it. What perpetual growth would justify 1,200.0 at a 9.0% discount rate? On reported free cash flow, 7.19%. On free cash flow adjusted to a maintenance-capex basis of 56.3, 4.12%. And reversing the P/E instead gives 7.50%. What a reader should take from this. Three defensible calculations produce values from 381 to 1,200, and the honest conclusion is that this model cannot tell you what Wexford is worth. What it can tell you is precisely what the market is assuming — perpetual growth somewhere between 4% and 7.5% depending on which cash-flow basis is right — and whether that is plausible for a capital-intensive industrial manufacturer is a judgement about the business, not a calculation. This article does not make that judgement, and a model that appears to make it for you has concealed an assumption. (Canonical figures; independently verified. Cash flows are discounted at year-end; the terminal value is the year-six flow ÷ (9.0% − 2.0%), discounted five years; the reversals solve 1,200 = FCF × (1 + g) ÷ (0.09 − g).)

Frequently asked

8 questions

What is a discounted cash flow model?

A calculation that values a business as the cash it will produce, adjusted for the fact that later cash is worth less. The logic is sound; the difficulty is entirely in the inputs, whose consequences the model presents with a precision they don't possess.

What are the three inputs?

Forecast cash flows, a discount rate, and a terminal value. The forecast is the least reliable part, the discount rate is the most sensitive, and the terminal value is usually the largest.

How much does the terminal value matter?

On a conventional five-year model, typically two-thirds to four-fifths of the total — 74% on the illustration here. Which means someone scrutinising the five years of explicit forecasts is examining about a quarter of the answer.

How sensitive is a DCF to the discount rate?

Very. On the illustration, moving it from 8% to 10% changes the total by 34%. A single percentage point moves a growing-perpetuity valuation by more than 12%.

What is a reverse DCF?

Taking the market price as given and solving for the growth rate that justifies it. The output is a question — is that growth plausible? — rather than a valuation, and questions of that shape are answerable in a way forecasts aren't.

Why is the reverse version more useful?

Because it converts an argument about whether a price is right into an argument about whether an expectation is reasonable, which is where the disagreement actually lives.

Why must terminal growth be below the discount rate?

Because the perpetuity arithmetic breaks otherwise, producing a negative or infinite value. It's a useful reminder that the formula is a convenience rather than a description of reality.

What did the worked example conclude?

That three defensible calculations produce values from 381 to 1,200 — so the model can't say what the company is worth. What it can say is what the market is assuming: perpetual growth somewhere between 4% and 7.5%. Whether that's plausible is a judgement about the business, not a calculation.

References

Investor.gov (SEC) — How to Read Financial Statements —
SEC — Beginners' Guide to Financial Statements —
Investor.gov (SEC) — Investor Bulletin: Performance Claims (a projected figure is only as good as its stated assumptions) —