Cost of capital
The two numbers that move a DCF most are the two you cannot look up
In a standard two-stage model, one point on the discount rate moves the answer about three times as far as one point on the five-year forecast. Both of the inputs that matter are estimates.
By Javier SanzPublished
Founder of ValueScreener. Built and sold Ninety Nine, a retail brokerage, and ran operations at Alpaca, the brokerage API. Built an earlier version of this product that did everything and earned nothing.
Most of the work in a discounted cash flow goes into the forecast. Revenue, margin, capital expenditure, working capital, year by year for five years. It is the part that feels like analysis, and it is the part that moves the answer least.
Here is the arithmetic, on a model simple enough to check by hand.
Start with free cash flow of 100. Grow it at 8 percent for five years. After that, assume it grows forever at 2 percent. Discount everything at 9 percent.
| Year | Free cash flow | Discounted at 9% |
|---|---|---|
| 1 | 108.00 | 99.08 |
| 2 | 116.64 | 98.17 |
| 3 | 125.97 | 97.27 |
| 4 | 136.05 | 96.38 |
| 5 | 146.93 | 95.50 |
The five explicit years are worth 486. The terminal value is 146.93 x 1.02 / (0.09 - 0.02), which is 2,141, discounted back five years to 1,392. Total: 1,878.
Three quarters of the answer is a number nobody forecast
Of that 1,878, the terminal value is 1,392. That is 74 percent of the valuation sitting in a single line that no part of the forecast produced. The five years of work account for the other quarter.
This is not a quirk of the inputs. It is what the Gordon growth formula does. The terminal value divides by the difference between the discount rate and the perpetual growth rate, and that difference is small. Here it is 7 percentage points. A small denominator makes a large quotient, and it makes that quotient extremely sensitive to anything that moves the denominator.
What each input is actually worth
Change one input at a time and leave the rest alone.
| Discount rate | Valuation | Change |
|---|---|---|
| 7% | 2,651 | +41.2% |
| 8% | 2,200 | +17.2% |
| 9% | 1,878 | base |
| 10% | 1,637 | -12.9% |
| 11% | 1,449 | -22.8% |
| 12% | 1,299 | -30.8% |
Now the forecast, the part the evening went into.
| Five-year growth | Valuation | Change |
|---|---|---|
| 6% | 1,728 | -8.0% |
| 7% | 1,801 | -4.1% |
| 8% | 1,878 | base |
| 9% | 1,957 | +4.2% |
| 10% | 2,039 | +8.6% |
One percentage point on the discount rate is worth 12.9 percent of the valuation. One percentage point on the five-year growth forecast is worth 4.2 percent. The rate moves the answer about three times as far as the forecast does, for the same one-point change.
The third input is worse.
| Perpetual growth | Valuation | Change |
|---|---|---|
| 1% | 1,692 | -9.9% |
| 2% | 1,878 | base |
| 3% | 2,126 | +13.2% |
Moving perpetual growth from 2 percent to 3 percent adds 13.2 percent to the valuation. It is a guess about the year 2100 and it is worth more than everything you concluded about the next five years.
Both of the sensitive inputs are estimates
The forecast is at least anchored to something. You built it from filed revenue, filed margins and filed capital expenditure, and a reader can argue with you about each of them against a document.
The discount rate is not. If you build it as a weighted average cost of capital, two of the five inputs are read out of filings, one is a share price, one is derivable, and the cost of equity is an estimate on top of an estimate: it usually comes from the capital asset pricing model, whose equity risk premium is not observable at all and whose published estimates disagree with each other by more than the figure moves in a decade.
The perpetual growth rate is not anchored either. It is bounded above by the long-run growth of the economy, because a company growing faster than that forever eventually becomes the economy, and bounded below by zero if you believe the business survives. Between those two bounds it is a preference.
So the two inputs that move the answer most are the two with no document behind them, and the input with the most documentation behind it moves the answer least. That is the actual shape of a DCF, and it is not what the time spent on one would suggest.
What to do about it
Three things, none of which require abandoning the model.
Compute the range, not the point. Run the model at the top and the bottom of the discount rate you would defend, not at the middle. If the range spans a factor of two, the honest output of the exercise is a range that spans a factor of two.
Write down the rate and why. The number is a judgement, so it should be recorded as one, with the reasoning attached. A discount rate with no stated basis is the single easiest place for a valuation to be quietly rebuilt around the answer you wanted.
Check what share of the answer is terminal. If the terminal value is 90 percent of the valuation, you have not valued a business, you have valued a perpetuity with a five-year preamble. That is sometimes the right thing to do. It should be a decision rather than a surprise.
What this leaves out
Every figure above is arithmetic on invented round inputs. It is not any company's filed figures, and it is not a view on any security. Run it yourself with different inputs and the percentages change; the ordering of the three sensitivities is what the shape of the formula produces, not the particular numbers.
The sensitivities are computed one input at a time. In practice the inputs move together: a higher discount rate usually travels with a different growth outlook, and the combined effect is not the sum of the separate ones.
A two-stage free cash flow model with a Gordon growth terminal is one model among several. An exit multiple terminal value shifts the sensitivity somewhere else rather than removing it. None of this says a DCF is the right way to value a particular business, and for some businesses it is not.