Discounted cash flow

A discounted cash flow model values a company as the cash it will produce for its owners, adjusted for the fact that cash arriving in ten years is worth less than cash arriving today. Free cash flow is forecast for a set number of years, each year is divided by a discount rate compounded over the distance, and the results are added together.

At a 10% discount rate, $100 arriving in a year is worth $90.91 today, and the same $100 arriving in ten years is worth $38.55. That compounding is what makes the near years count for so much more than the far ones.

Every DCF comes down to four assumptions, and the argument about a valuation is always an argument about one of them. The starting cash flow, usually free cash flow for the last twelve months. The growth rate applied across the explicit forecast. The discount rate. And the terminal assumption covering everything after the forecast ends.

The first is the only one taken from the accounts. The other three are judgements, and the model gives no indication of which are reasonable: it will produce a clean, precise-looking number from assumptions that could not all hold at once.

A forecast cannot run indefinitely, so a DCF projects five or ten years explicitly and adds a terminal value covering everything after that. There are two conventions for it.

A perpetuity terminal value takes the final forecast year and assumes it grows at a fixed rate forever, dividing by the discount rate less that growth rate. It is the standard academic form, and it is sensitive in an awkward way: the denominator is a difference between two numbers that are usually within a few points of each other, so small changes to either move the result sharply. The growth rate also cannot exceed long-run economic growth without implying the company eventually becomes the economy.

An exit multiple terminal value instead assumes the business is worth some multiple of its earnings or cash flow at the end of the forecast, which is how an acquirer or a private equity buyer would frame it. It replaces an assumption about growth forever with an assumption about what a buyer pays, which is easier to sanity-check against actual transactions and harder to defend as a first-principles valuation.

Either way the terminal value usually dominates. In the worked example below it is between 47% and 64% of the total, and its share rises as the discount rate falls, so most of the answer comes from the years that were never modelled.

The discount rate represents the return required for taking the risk, and in a full model it is the weighted average cost of capital: the cost of equity and the after-tax cost of debt, weighted by how much of each the company uses.

The cost of equity is itself an estimate, conventionally built from a risk-free rate, an equity risk premium and a beta measuring how much the share moves relative to the market. Each of those is contested, and beta in particular is a measure of past volatility being used as a proxy for future risk.

In practice many analysts skip the derivation and pick a rate that reflects the return they require, which is more honest about what the number is. What matters is knowing how much of the answer that choice is deciding.

The table takes one company and changes nothing except the discount rate and the terminal growth rate. The forecast is identical in every cell: $100m of free cash flow growing 5% a year for ten years, with a perpetuity terminal value.

The range across the grid is $1,396m to $2,414m, a spread of about 73% from the lowest cell to the highest, and every cell is a defensible set of assumptions. Moving the discount rate alone from 9% to 10% at 2.5% terminal growth takes the value from $1,904m to $1,639m, a fall of 14%.

This is the reason a DCF output is read as a range rather than as a price, and the reason two analysts modelling the same company from the same accounts can land far apart without either having made an error.

The more testable use is to enter the current price and solve for the growth and margins the market must be assuming. That turns an unfalsifiable forecast into a question that can be assessed: has this company ever grown at that rate, and for how long.

Run that way the model stops producing a target and starts describing the consensus, which is the part worth disagreeing with.

The tool on each company page is a five-year model with an exit multiple rather than a perpetuity, and it is worth knowing exactly what it does before reading its output. It takes a per-share figure, either EPS or free cash flow per share for the last twelve months, grows it for five years at a growth rate, applies a multiple to the fifth year, and discounts that back to today at a discount rate.

It seeds the growth rate and the multiple with the company's own five-year medians, so the default case is what the business has recently done rather than a blank sheet, and every field is editable with the result recalculating as it changes.

What it does not do is model the cash flows year by year or derive a cost of capital, so it is a structured way to test the assumptions behind a price rather than a full valuation. Its most useful setting is the reverse one: change the growth rate until the output matches the current price, and read off what the market is assuming.

Banks and insurers, where borrowing is the raw material of the business rather than a financing choice, so free cash flow as normally defined does not describe them. They are valued on equity cash flows or on book value instead.

Companies with no earnings and no visibility on when they will have any. The model still returns a number, and essentially all of it comes from the terminal assumption.

Deep cyclicals, where the last twelve months of cash flow is a point on a cycle rather than a run rate, and any growth rate applied to it compounds the error.

Any situation where the answer is being used to justify a decision already taken. A DCF is easier to reverse-engineer to a desired number than any other valuation method, because three of its four inputs are opinions.