A discounted cash flow model says a business is worth the cash it will produce, adjusted for the fact that cash arriving in five years is worth less than cash arriving today. Enter your projected free cash flows, a discount rate, and a growth rate for everything beyond the forecast, and the calculator returns the value.
Open the second section and it bridges from enterprise value to equity value by taking off debt and adding back cash, then divides by shares outstanding to give a fair value per share. Add the current market price and it tells you how far the two are apart.
What a DCF actually does
Every other valuation method is a shortcut. A multiple is shorthand for a cash flow expectation someone else already formed. A discounted cash flow model skips the shorthand and states the expectation directly.
The logic runs in three steps. Forecast the cash the business will generate. Discount each year back to today at a rate that reflects what capital costs and how risky the cash is. Add a terminal value for everything beyond the forecast horizon, because businesses do not stop at year five.
The output is an enterprise value: what the whole operating business is worth to everyone with a claim on it, lenders included. Getting from there to what shareholders own takes one more step, which the calculator handles.
The DCF formula
Value of the firm = Σ (FCFF_t ÷ (1 + WACC)^t) + (Terminal value ÷ (1 + WACC)^n)
The first term discounts each projected year's free cash flow. The second discounts the terminal value, which is calculated with the perpetuity growth method:
Terminal value = FCFF_n × (1 + g) ÷ (WACC − g)
Where g is the rate at which cash flow grows forever after the forecast period ends, and n is the final projected year.
Then the bridge from firm to shareholders:
Equity value = Enterprise value − Debt + Cash
Fair value per share = Equity value ÷ Shares outstanding
Two constraints are structural rather than optional. The discount rate must exceed the perpetual growth rate, or the terminal value formula divides by zero or turns negative. And free cash flow to the firm must be discounted at WACC rather than the cost of equity, because that cash belongs to lenders and shareholders together.
A worked example
A company projects five years of free cash flow: $90,000, $100,000, $108,000, $116,200, and $123,490. Its weighted average cost of capital is 9.94% and its cash flow is expected to grow at 4.48% in perpetuity.
Terminal value = $123,490 × 1.0448 ÷ (0.0994 − 0.0448) = $2,363,047
Discounting the five years back gives about $402,300. Discounting the terminal value back five years gives about $1,471,300. Together the enterprise value is $1,873,574.
The company has $900,000 of debt and $100,000 of cash, so net debt is $800,000 and the equity is worth $1,073,574. Across 100,000 shares, that is a fair value of $10.74 a share. If the stock trades at $5.00, the model says it is undervalued by 114.7%.
Now look again at the composition. The terminal value contributes $1,471,300 of the $1,873,574, which is 78.5% of the total. Four fifths of this valuation rests on a single assumption about growth after year five.
Terminal value is where the valuation actually lives
This is not a quirk of the example. In most discounted cash flow models the terminal value accounts for somewhere between 60% and 80% of the total, and in high-growth cases it can exceed 90%. The five years of carefully forecast cash flow, the part that takes all the work, is usually the minority of the answer.
Two consequences follow.
First, the perpetual growth rate deserves far more scrutiny than it gets. A business cannot grow faster than the economy forever, because it would eventually become the economy. Analysts generally hold g somewhere between long-run inflation and nominal GDP growth, which in most developed markets means roughly 2% to 3%. The 4.48% in the example above is aggressive, and it is doing an enormous amount of work.
Second, the sensitivity is brutal. Take the same $123,490 of final-year cash flow at a 9.94% discount rate:
Perpetual growth | Terminal value |
|---|---|
2.0% | $1,586,000 |
3.0% | $1,833,000 |
4.0% | $2,162,000 |
5.0% | $2,625,000 |
A three point range in a number nobody can verify moves the terminal value by 65%. This is why experienced analysts present a range of values rather than a point estimate, and why a discounted cash flow that arrives at a suspiciously precise figure should be read as a negotiating position.
Where the inputs come from
Free cash flow to the firm is operating cash flow after tax and after capital expenditure, before any payments to lenders. It is the cash the business genuinely throws off, not accounting profit. A company can report healthy earnings and produce no free cash flow at all if it is reinvesting everything into equipment or working capital.
The discount rate is normally the weighted average cost of capital, blending the cost of equity and the after-tax cost of debt by their weights in the capital structure. Higher risk means a higher rate and a lower valuation.
The forecast horizon is conventionally five to seven years. Shorter, and too much value falls into the terminal calculation. Longer, and you are forecasting a business you cannot see.
The perpetual growth rate should reflect a mature business in a mature market, not the company's current trajectory. The whole point of the terminal period is that the growth phase is over.
Where DCF misleads
It manufactures precision. The output has decimal places. The inputs are guesses. Nothing about the arithmetic improves the quality of the forecast that went into it.
Small input changes swing the answer enormously. A point on the discount rate and a point on terminal growth, both entirely defensible, routinely move a valuation by 30% or more.
It is easy to reverse engineer. Analysts under pressure to justify a price can find a combination of growth and discount rate that produces it, and every individual assumption will look reasonable in isolation.
It assumes the business survives. The terminal value treats the company as a going concern in perpetuity. Businesses in structurally declining markets do not get perpetuities.
It struggles with early-stage companies. Negative cash flows for years, followed by a hockey stick, put essentially all the value in the terminal calculation, which is another way of saying the model is not telling you anything you did not already assume.
It ignores optionality. A business with a valuable but unexercised strategic option, a land bank, a patent, a platform that could be monetised differently, is worth more than its projected cash flows suggest.
How to use the number honestly
Run a range, not a point. Vary the discount rate and terminal growth by a point in each direction and look at the four corners. If the investment case only works in one corner, there is no investment case.
Check what share the terminal value takes. The calculator above reports it. Above about 80%, you are not valuing a cash flow forecast, you are valuing an opinion about the far future.
Sanity check against a multiple. Divide your enterprise value by current EBITDA. If the implied multiple is far outside what comparable businesses trade at, the model needs an explanation, not a defence.
Use conservative terminal growth by default. If the valuation only works at 5% perpetual growth, it does not work.
Model the cash, not the profit. Capital expenditure and working capital swings are exactly what separate a business that generates cash from one that only reports earnings.
Further reading from Revenue Memo
FAQs
How do I calculate discounted cash flow?
Project free cash flow for each year of your forecast, divide each year's figure by one plus the discount rate raised to the power of that year, and add the results. Then calculate a terminal value for everything beyond the forecast, discount that back as well, and add it in. The calculator above does all of it from five cash flow figures, a discount rate, and a growth rate.
What discount rate should I use in a DCF?
Use the weighted average cost of capital when you are discounting free cash flow to the firm, because that cash belongs to lenders and shareholders together. If you are discounting free cash flow to equity instead, use the cost of equity alone. Higher risk justifies a higher rate, and a higher rate produces a lower valuation.
What is a good perpetual growth rate?
Something between long-run inflation and nominal economic growth, which usually means 2% to 3%. No company can grow faster than the economy forever, so a terminal growth rate above nominal GDP is an arithmetic impossibility dressed up as optimism.
Why is terminal value such a large part of a DCF?
Because the forecast period is short and the business is assumed to continue indefinitely afterwards. Everything past year five is compressed into one number, and that number typically carries 60% to 80% of the total value. It is the reason terminal assumptions matter more than the detailed forecast.
Can the discount rate equal the growth rate?
No. The terminal value formula divides by the difference between them, so equal rates produce a division by zero and a growth rate above the discount rate produces a negative value. If your model is heading that way, one of the two assumptions is wrong.
Can I use negative cash flows in a DCF?
Yes, in the projected years, and it is normal for businesses investing heavily. But the final year and the terminal period must be positive, or the model returns a negative value for the business, which is not a meaningful answer.
What is the difference between enterprise value and equity value in a DCF?
Discounting free cash flow to the firm gives enterprise value, the worth of the whole operating business. Subtract debt and add cash to get equity value, which is what shareholders own. Divide that by shares outstanding for the fair value per share.