What it means
A dollar in five years is worth less than a dollar today, for two reasons: today's dollar can be invested to grow, and the future dollar may not arrive. Discounting captures both.
A discount rate is chosen that represents the return an investor could earn on an alternative of similar risk, and each future cash flow is divided by one plus that rate raised to the power of the number of years away, which shrinks distant and risky cash flows more than near and safe ones. The result is the amount that, invested today at the discount rate, would grow to the future cash flow: its present value.
Adding up the present values of all the cash flows an investment will produce gives what the investment is worth today, which can be compared with what it costs. The cash flows are the first input, and they must be cash, not profit: the actual money that will come in and go out, after tax, after the capital expenditure needed to sustain the business, and after the working capital it will absorb.
For a project, they are the incremental cash flows the project causes, ignoring sunk costs and allocated overheads that would exist anyway. For a business, the usual measure is free cash flow, the cash available to all providers of capital after operating costs, tax and reinvestment.
Forecasting them requires assumptions about volumes, prices, costs and investment, and the quality of a DCF depends entirely on the quality of those assumptions; the arithmetic is the easy part. The discount rate is the second input.
For a project of the same risk as the company's existing business, it is the company's weighted average cost of capital, the blended after-tax cost of its debt and equity. For a project of different risk, it is adjusted.
For valuing the equity of a business directly from the cash flows to shareholders, it is the cost of equity. The rate is an estimate, built from market data and judgement, and a difference of one percentage point can change a valuation by 10% to 20%, which is why analysts present sensitivities rather than a single number and why the choice of rate is argued over in every negotiation.
Most businesses do not stop after the forecast period, so a business valuation adds a terminal value at the end of the explicit forecast, representing all the cash flows beyond it. The commonest approach assumes the final year's cash flow grows at a constant rate forever and values it as a perpetuity: cash flow next year divided by the discount rate less the growth rate.
An alternative applies an exit multiple to the final year's earnings. The terminal value is discounted back like any other cash flow, and it typically accounts for more than half of the total value, sometimes far more, which means the valuation rests heavily on two assumptions, the long-term growth rate and the discount rate, about a period nobody has forecast in detail.
DCF's strength is that it forces explicit thinking about what an investment will actually produce and when, and it produces a value grounded in cash rather than in accounting conventions or market moods. Its weakness is that it is only as good as its inputs, that small changes in assumptions produce large changes in value, and that a spreadsheet full of precise numbers can lend false authority to guesses.
Used well, with cash flows built up carefully, a discount rate chosen with care, sensitivities shown honestly, and the result cross-checked against market multiples and comparable transactions, it is the best tool available. Used badly, it is a way of producing whatever answer was wanted.
In practice
Real-world examples.
Example
A retailer evaluates a new store by discounting its forecast cash flows over a ten-year lease at the company's cost of capital, and rejects it because the net present value is negative once the fit-out and working capital are included.
Example
An investment bank values an acquisition target by DCF at $180,000,000 to $220,000,000 across a range of discount rates and growth assumptions, and cross-checks the range against comparable company multiples.
Example
A pharmaceutical company values a drug candidate by discounting its expected cash flows, weighted by the probability of passing each clinical trial stage, at a rate reflecting the risk of the sector.
Think of it
“DCF is like calculating today's price for a series of future lottery payments. You figure out what future payments are worth right now.
Formula
Calculation
Present value of a cash flow = Cash flow in year t / (1 + Discount rate) to the power of t
Net present value = Sum of present values of all cash flows minus Initial investment
Terminal value (perpetuity growth) = Final year cash flow x (1 + Growth rate) / (Discount rate minus Growth rate)
Enterprise value = Sum of discounted forecast free cash flows + Discounted terminal value
Equity value = Enterprise value minus Net debt
Worked example: a project. A company considers investing $5,000,000 in equipment expected to generate after-tax cash flows of $1,200,000, $1,500,000, $1,800,000, $1,800,000 and $1,500,000 over five years. Its cost of capital is 10%.
- Year 1: $1,200,000 / 1.10 = $1,090,909
- Year 2: $1,500,000 / 1.21 = $1,239,669
- Year 3: $1,800,000 / 1.331 = $1,352,367
- Year 4: $1,800,000 / 1.4641 = $1,229,425
- Year 5: $1,500,000 / 1.61051 = $931,382
- Sum of present values = $5,843,752; net present value = $5,843,752 minus $5,000,000 = $843,752, so the project adds value and should be accepted
Worked example: a business. A company's free cash flows are forecast at $2,000,000, $2,200,000, $2,400,000, $2,600,000 and $2,800,000 over five years, growing 2% a year thereafter. Its weighted average cost of capital is 9%, and it has net debt of $8,000,000.
- Present values at 9%: $1,834,862; $1,851,696; $1,853,232; $1,841,918; $1,819,804; total $9,201,512
- Terminal value at end of year 5 = $2,800,000 x 1.02 / (0.09 minus 0.02) = $2,856,000 / 0.07 = $40,800,000
- Present value of terminal value = $40,800,000 / 1.09 to the power of 5 = $40,800,000 x 0.6499 = $26,517,000
- Enterprise value = $9,201,512 + $26,517,000 = about $35,700,000; equity value = $35,700,000 minus $8,000,000 = about $27,700,000
- The terminal value is 74% of enterprise value
Sensitivity. At a 10% discount rate with the same growth: present values of the forecast cash flows total $8,953,943; terminal value = $2,856,000 / 0.08 = $35,700,000, present value $22,167,000; enterprise value about $31,100,000; equity value about $23,100,000. One percentage point on the discount rate reduces the equity value by 17%.Case study
Seen in the real world.
The owners of a specialist engineering company received an offer from a trade buyer and engaged an adviser to value the business. The adviser's DCF, built on management's five-year plan of 8% annual growth, a 9% cost of capital and a 3% terminal growth rate, gave an equity value of $42,000,000.
The buyer's DCF, built on the same historical figures but with growth of 4% a year, a 10% cost of capital and 2% terminal growth, gave $26,000,000. Both were internally consistent; the gap of $16,000,000 was entirely a difference of assumptions, and the terminal value was more than 70% of the answer in both.
The negotiation therefore became a negotiation about assumptions rather than about the number. The buyer challenged the 8% growth as above anything the company had achieved in the past five years (the average had been 5%); the sellers challenged the 10% cost of capital as reflecting the buyer's view of risk rather than the market's. On terminal growth, the sellers conceded that 3% assumed the business would grow faster than the economy forever, which nobody believed.
Each side rebuilt its model with the assumptions it could defend: growth of 5% to 6%, a cost of capital of 9.5%, and terminal growth of 2%. The two models then produced values of $33,000,000 and $31,000,000, and a deal was done at $32,000,000 with an earn-out linked to the growth the sellers had claimed.
The sellers' adviser noted afterwards that the DCF had not determined the price; the assumptions had, and the DCF had been the framework that made the assumptions explicit enough to argue about. The buyer's finance director made a related point: the model's precision, to the dollar, had disguised a range of plausible values from $26,000,000 to $42,000,000, and the honest output of a DCF is a range with the sensitivities shown, not a number. Both agreed that the exercise had been more useful than a multiple of earnings, because it had forced both sides to say what they believed about the company's future.
Watch out
Common mistakes.
- Discounting profit rather than cash, or forgetting the capital expenditure and working capital the business needs to sustain the forecast, which overstates the cash available and the value.
- Presenting a single value without sensitivities, when a one-point change in the discount rate or the terminal growth rate moves the answer by 15% or more and the terminal value dominates.
- Including sunk costs and allocated overheads in a project's cash flows, or excluding the cannibalisation of existing sales; only incremental cash flows caused by the decision are relevant.
Questions
People also ask.
What discount rate should be used?
For a project of the same risk as the existing business, the company's weighted average cost of capital; for a project of different risk, a rate adjusted for that risk; for valuing equity directly, the cost of equity. The rate should reflect the return investors could earn on an alternative of similar risk.
Why is the terminal value so large?
Because a going concern generates cash indefinitely, and the explicit forecast covers only a few years. The terminal value captures everything beyond, and even after discounting it usually exceeds the forecast period's value. It should be tested against the implied exit multiple for reasonableness.
How does DCF compare with valuation multiples?
DCF values the business on its own forecast cash flows; multiples value it by reference to what similar businesses trade or sell for. DCF is more rigorous and more assumption-dependent; multiples are simpler and market-based. Good practice uses both and reconciles the results.
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