Finance Decide

Discounted Cash Flow

Discounted cash flow values a business from the present value of the cash it is expected to produce.

The questionWhat is this business worth today, given the cash it can be expected to produce and the return investors require?

DCF. This note covers the enterprise version, which discounts free cash flow at WACC.

Formula · Irving Fisher and John Burr Williams, 1930s

Equity value What shareholders own

Enterprise value Sum of discounted cash

PV of forecast FCF Each year discounted at WACC

PV of terminal value Value after the forecast, discounted

−

Net debt Plus other prior claims

Simplified bridge from forecast cash to equity value in the enterprise version of DCF.

When to use it

A client is considering an acquisition, divestiture, or large investment and needs a value the board can argue about one assumption at a time.
A business plan has to be tested for what it implies about value, such as what growth and margin the current price requires.
Comparable multiples are unavailable or unreliable because the business is unusual or the comparables are mispriced.
Management wants to compare strategic options, such as invest or harvest, on one basis.

When to avoid it

There is no basis for a forecast, as with an early-stage company with no history. A range of scenarios or a multiple of something observable is more honest, and the DCF would mostly restate the founders' hopes.
Someone will take the single output and defend it. Terminal value and the discount rate drive the answer, so only a range is defensible.
The sponsor has already chosen the number and wants a model that produces it. A DCF is easy to tune, and the work is better spent on a transparent comparison with market multiples.
You need a quick comparison across many companies. Multiples do that faster and with fewer assumptions to argue over.

Overview

A discounted cash flow valuation estimates what a business is worth today as the sum of the free cash flow it is expected to generate, each year’s cash reduced by a discount rate that reflects the risk. It supports decisions about buying, selling, or investing: what price can be justified, and what the forecast must deliver to justify a quoted one.

In a five-year model most of the value usually sits in the terminal value, so small changes in the discount rate or long-run growth move the answer a lot. Report a range with the assumptions behind it. A single figure to the nearest million overstates what the inputs support.

The pieces

Free cash flow forecast

Operating profit after tax, plus depreciation, minus capital spending, minus the increase in working capital, for each year of an explicit forecast, usually five to ten. It is cash available to every provider of capital, before any interest.

Discount rate

For enterprise cash flows, the weighted average cost of capital, which reflects the risk of the cash flows and the mix of debt and equity. See the WACC note for how it is built and where it is weak.

Terminal value

The value at the end of the forecast of all later cash flows. The perpetuity growth method takes the final year's cash flow, grows it once at a long-run rate, and divides by the discount rate minus that growth rate. The exit multiple method applies an observed multiple instead.

Bridge to equity value

Enterprise value minus net debt and other claims that rank ahead of shareholders, such as pension deficits and minority interests, gives equity value. If non-operating assets are not in the cash flows, add them back here.

The steps

Fix the purpose and the perimeter

State what is being valued, as of what date, in what currency, and on what basis, with or without synergies. A stand-alone value for a seller and a value including the buyer's synergies are different numbers for different purposes.
Forecast free cash flow

Build it from a few operating drivers such as volume, price, margin, capital spending, and working capital, each tied to evidence. Cover five to ten years. Check that the reinvestment in each year supports the growth in that year. The output is a yearly unlevered free cash flow line.
Set the discount rate

Take the WACC that fits the risk of these cash flows, which may differ from the company's own. Keep its range as well as its point value, because it will be needed in the last step.
Estimate terminal value

Use perpetuity growth with a rate at or below long-run economic growth, and check the multiple it implies against comparable businesses. Or use an exit multiple and check the growth rate it implies. In either case, make sure the terminal-year investment is enough to fund the growth you assume.
Discount, sum, and bridge to equity

Discount each year and the terminal value, and add them to get enterprise value. Subtract net debt and other prior claims, and add non-operating assets not already in the cash flows. Show each bridge item and its source.
Show the range

Vary the discount rate and terminal growth together in a table, and vary the two or three operating drivers that matter most. Report the terminal value as a share of enterprise value. The output is a range with the assumptions at each end.

The formula

EV = FCF1/(1 + WACC) + FCF2/(1 + WACC)^2 + ... + FCFN/(1 + WACC)^N + TV/(1 + WACC)^N, where TV = FCFN × (1 + g) / (WACC - g)

Enterprise value is each year's free cash flow divided by one plus the discount rate, raised to the power of the year, plus the terminal value discounted the same way as the last forecast year. Equity value is enterprise value minus net debt and other claims.

FCFt: unlevered free cash flow in year t, after tax and after investment.
WACC: the discount rate, here the weighted average cost of capital.
N: the last year of the explicit forecast.
g: the long-run growth rate of free cash flow after year N. It must be below WACC, and is usually set at or below expected long-run growth of the economy.
TV: the value at the end of year N of all cash flows after year N.

In practice

Take a target with forecast free cash flow of 100, 110, 120, 130, and 140 over the next five years, in millions, a WACC of 10 percent from the finance team's calculation, and a terminal growth rate of 2 percent. The discounted cash flows are 90.9, 90.9, 90.2, 88.8, and 86.9, which sum to 447.7. Terminal value is 140 × 1.02 ÷ (0.10 - 0.02) = 1,785, and discounted five years at 10 percent it is 1,108.3. Enterprise value is 447.7 + 1,108.3 = 1,556. Terminal value is about 71 percent of it. The target has debt of 400 and cash of 100, so net debt is 300 and equity value is 1,556 - 300 = 1,256.

The team does not report 1,256. With WACC at 9 percent, enterprise value is 1,786 and equity is 1,486. With WACC at 11 percent, enterprise value is 1,377 and equity is 1,077. One point of WACC moves equity value by about 14 to 18 percent, so the board sees a range of about 1,080 to 1,490 and the assumptions that sit behind each end of it. The negotiating conversation then moves from the number to what the seller would have to show to defend the lower discount rate.

What you leave with

A yearly free cash flow forecast, with each operating assumption and its evidence listed.
Enterprise value and equity value, with each bridge item shown.
Terminal value as a share of enterprise value, and the exit multiple it implies.
A sensitivity table on the discount rate and terminal growth.
A short list of the assumptions the value depends on most, to test in diligence.

Failure points

Terminal value does the work

In the example above it is about 71 percent of enterprise value. When most of the value sits after the forecast, the model is mainly a statement about the long-run growth rate and the discount rate, and the five years of detail add little.

Rate shopping

The discount rate is adjusted at the end to arrive at the value the sponsor wants. In the example, a one-point change moves enterprise value by 11 to 15 percent, so a little pressure on the rate buys a lot of value.

Cash flows and rate that do not match

Cash flows after interest are discounted at WACC, or cash flows in nominal terms at a real rate. The model double counts the cost of debt or understates value, and the error does not show up until someone checks the pairing.

Growth without investment

Revenue grows each year while capital spending and working capital stay flat and margins rise. Free cash flow is overstated because the reinvestment that growth needs is missing.

Mistakes in the equity bridge

Pensions, leases, and minority interests are left out, or cash is counted once in the cash flows and again in the bridge. The enterprise value is right and the equity value is wrong.

The failures above are usually Commercial Acumen: the work was not tied to money, for the client and/or for you.

Origin

The idea that an asset is worth the present value of the cash it will pay is older than any single author, and Irving Fisher's The Theory of Interest (1930) set out the modern treatment of present value. John Burr Williams, in The Theory of Investment Value (1938), applied it to common stock, valuing a share on its discounted future dividends. His book is the usual reference for valuing a business on discounted future payouts.

The enterprise form used in most consulting work forecasts free cash flow to all providers of capital, discounts it at the weighted average cost of capital, and then bridges from enterprise value to equity value. Variants discount cash flow to equity directly, or separate the value of the business from the value of its financing.