Discounted cash flow: the intuition before the spreadsheet

The one sentence underneath every model

A business is worth the cash it will hand its owners over its remaining life, adjusted for the fact that cash arriving later is worth less than cash arriving now, and adjusted again for the fact that the later cash might not arrive at all.

That is the whole idea. Every discounted cash flow model, however many tabs it has, is an attempt to put numbers on that sentence.

It is worth noticing that this is not a niche investing technique. Present value reasoning is embedded in financial reporting itself. Companies are required to test assets and goodwill for impairment, and one of the permitted measures is value in use, which is calculated by projecting future cash flows and discounting themSource^source. Present value techniques also appear in the standard that governs fair value measurement, which explicitly frames such techniques as requiring assumptions about future amounts, their timing and the risk attached to themSource^source. When a company writes down goodwill, somebody inside that company has run a discounted cash flow and concluded the answer is lower than the carrying value.

So the method is not exotic. What is exotic is the confidence with which its output is sometimes quoted.

Why later cash is worth less

There are three separate reasons a payment of 100 next year is worth less than 100 today, and collapsing them into one number is the single largest simplification in the method.

**Opportunity.** If you had the 100 today you could put it somewhere and have more than 100 next year. Whatever that alternative return is, it sets a floor on what waiting must compensate you for. Benchmark rates are not a constant of nature. They are set and changed over time by monetary authorities, which means the floor itself movesSource^source.

**Uncertainty.** A promised 100 next year might arrive as 80, or as nothing. The further out the promise, the wider the range of what actually shows up.

**Preference.** Even setting aside the first two, most people and institutions prefer resources now to resources later, because plans, obligations and lives are lived in the present.

A DCF handles all three with a single discount rate. That is a real limitation, not a technicality. When you raise a discount rate from 8 to 10 per cent because a business feels risky, you are not modelling the risk. You are applying a uniform annual haircut that happens to punish distant cash flows far more than near ones, whether or not that matches the actual shape of the risk. A business with a genuine chance of failing in year two and a strong outcome otherwise is not well described by a slightly higher constant rate.

Building a present value by hand

Do this once with three numbers and the spreadsheet will never intimidate you again.

Suppose a small business will produce exactly 100 of free cash at the end of each of the next three years, and then cease to exist. Suppose you require a 10 per cent annual return to bother.

• Year one's 100 is divided by 1.10, giving about 91.
• Year two's 100 is divided by 1.10 twice, giving about 83.
• Year three's 100 is divided by 1.10 three times, giving about 75.

Add them and you get about 249. That is the value of the business under those assumptions. If someone offers it to you at 200, your return will exceed 10 per cent. At 300, it will fall short.

Now change one thing. Require 15 per cent instead of 10, and the same three payments are worth about 87, 76 and 66, totalling about 229. A five point change in the required return moved the answer by roughly 8 per cent over a three year horizon.

Hold that observation, because the horizon is where it becomes dramatic. The same five point change applied to cash flows twenty or thirty years out cuts their present value by more than half. A DCF of a mature business with a long tail of assumed cash flows is enormously sensitive to a rate that you essentially chose.

The three inputs, and which one actually moves the answer

Every model has the same three ingredients.

1. **The cash flows.** Usually free cash flow, meaning the cash the business generates from operations after the capital spending needed to keep generating it. Definitions vary, which is why building it yourself from the published statements is safer than importing a number of unknown construction.
2. **The discount rate.** The return required to compensate for opportunity, uncertainty and waiting. Often built from a risk-free rate plus a risk premium, and blended across debt and equity if you are valuing the whole enterprise.
3. **The terminal value.** What the business is assumed to be worth at the end of your explicit forecast period, standing in for every year you did not model individually.

Here is the uncomfortable part. In a typical model with a ten year forecast, the terminal value routinely accounts for somewhere between half and three quarters of the total present value. The ten years of carefully researched forecasts, the segment revenue build, the margin ramp, the working capital schedule, frequently determine a minority of the answer. The majority is decided by two numbers in the terminal value formula that were chosen in a few seconds.

If you take one habit from this article, take this one. Before reading anyone's DCF conclusion, find out what percentage of the total value sits in the terminal value. If it is above roughly two thirds, the model is mostly an assertion about perpetuity, dressed as a forecast.

The terminal value problem

The usual terminal value method assumes the business grows at a constant rate forever and computes the value of that perpetual stream. The formula divides the final year's cash flow, grown by one year, by the difference between the discount rate and the perpetual growth rate.

The trouble is visible in the arithmetic. If your discount rate is 9 per cent and your perpetual growth rate is 2 per cent, you divide by 0.07. Raise perpetual growth to 4 per cent and you divide by 0.05. The same cash flow is now worth 40 per cent more, from a change most people would describe as a rounding adjustment.

Two disciplines help.

• **Cap perpetual growth at something defensible.** A company cannot grow faster than the economy it operates in forever, because it would eventually become the economy. Long-run nominal growth of the relevant economy is a reasonable ceiling, and many practitioners use something at or below it.
• **Cross-check with an exit multiple.** Compute what your terminal value implies as a multiple of that final year's earnings or cash flow, then ask whether that multiple is plausible for a mature business of that type. If the perpetuity method implies a terminal multiple far above what mature businesses in that industry have historically commanded, the assumption is doing work it cannot support.

Neither check makes the terminal value correct. They make it explicit, which is different and more useful.

Sensitivity, or why the output should be a range

A DCF that produces a single number is presenting false precision. The inputs have ranges, so the output has a range.

The honest presentation varies the two or three inputs that matter most, typically the discount rate and the perpetual growth rate, and reports the resulting spread. Run a plausible band around each and you will commonly find the answer varies by a factor of two or more.

That result is often treated as an embarrassment. It should be treated as the finding. It tells you that the value of this particular business is genuinely uncertain and that anybody claiming to know it to the nearest per cent is not being careful. It also tells you where to concentrate your research. If the answer swings wildly on the perpetual growth rate, the research question is durability of the business, not next quarter's margin.

The version worth actually using

Forward DCF asks, "what is this worth?" It requires you to forecast, and forecasting distant cash flows is something almost nobody does reliably.

Reverse DCF asks a different and much better question. "What would have to be true for today's price to make sense?"

The procedure:

1. Start with the current market value of the business, adjusted for net debt if you are working at enterprise level.
2. Choose a discount rate you would genuinely accept, and a defensible perpetual growth rate.
3. Solve for the growth rate in the explicit forecast period that makes the model produce exactly today's price.
4. Read the answer as a claim, and interrogate it.

Suppose the answer comes back as 14 per cent annual free cash flow growth for the next decade. Now you have something falsifiable. How many businesses in this industry have sustained that? Does it require market share the industry does not contain, or margins nobody in the sector has achieved, or capital spending the balance sheet cannot fund? Does it assume competitors do not respond?

Sometimes the implied assumption is modest and the research question becomes why expectations are so low. Sometimes it is heroic. Either way you have converted a valuation exercise into a specific question about the business, which is the only kind of question research can answer.

Where the method breaks down

Banks and insurers

Debt is raw material for a bank, not financing, so the usual free cash flow construction does not translate. Valuation for these businesses typically works from equity cash flows or from returns on equity against book value, with capital requirements setting the constraint on growth.

Early stage and pre-profit companies

When near-term cash flows are negative and the entire value sits in the terminal assumption, a DCF is a perpetuity calculation wearing a forecast costume. It can still be useful in reverse form, to state what the price implies, but treating its forward output as a valuation is not defensible.

Deep cyclicals and commodity producers

Starting a forecast from a peak or trough year propagates that starting point through every subsequent line. Normalise to mid-cycle conditions before you begin, and say explicitly what mid-cycle means in your model.

Businesses with real optionality

A company with a genuine chance of a very large outcome and a meaningful chance of failure has a value distribution that a single expected path cannot represent. Scenario weighting is a partial answer, and it should be labelled as such.

Anything requiring capital you have not modelled

If growth needs new plants, new licences or new working capital, and the model grows revenue without growing the capital base, the answer is inflated by construction. Check that reinvestment scales with growth.

What a DCF is not

It is not a measurement. Nothing was measured. Every input was chosen.

It is not objective because it is quantitative. The arithmetic is objective; the assumptions are opinions, and the arithmetic obediently amplifies them.

It is not a timing tool. A model can conclude that a business is worth more than its price and be right about that for a decade while the price does nothing.

It is not a substitute for understanding the business. The inputs come from somewhere, and that somewhere is competitive dynamics, capital intensity, customer behaviour and management conduct. A model built on a business you cannot describe in plain language is arithmetic performed on guesses.

It is not a way to be certain. Its most valuable output is usually the discovery of which single assumption the answer depends on.

How to use it honestly

Build the small version first. Five years of cash flow, one discount rate, one terminal assumption, on a single page you can hold in your head. If a five line model and a fifty tab model disagree, the disagreement is almost always in an assumption, not in the detail, and the small model makes it visible.

Then do three things before believing any output. Report the share of value sitting in the terminal value. Show the answer as a range across plausible discount and growth rates rather than as a point. And run the model backwards from the market price so you can state, in one sentence, what the price already assumes.

Used that way, the discounted cash flow is not a machine that tells you what something is worth. It is a discipline that forces you to write your assumptions down where they can be argued with, which is a considerably more valuable thing.