A DCF run at a textbook WACC rarely reproduces the price a buyer actually paid. The gap is information, and calibration carries it into every later mark.
Solve for the discount rate at which the DCF returns the price actually paid, measure its gap to the market WACC, and carry that gap into every later valuation. On an illustrative company bought for 172.0, the implied rate is 11.15 per cent against a 10.0 per cent WACC: a calibration premium of 1.15 points. A year later, with WACC at 10.5 per cent, the calibrated rate of 11.65 per cent values the business at 166.0. The same DCF at the bare WACC says 190.4, 14.7 per cent too high.
Worked in full in The Private Markets Valuation Specialist by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A fund buys a fictional private company at arm's length. The valuation team builds a DCF on the management case and a market-derived WACC. All figures are illustrative.
| Input | Value |
|---|---|
| Enterprise value paid | 172.0 |
| Free cash flow, years 1 to 5 | 12.0, 13.5, 15.0, 16.2, 17.0 |
| Terminal growth | 2.5% |
| WACC from a market build-up | 10.0% |
Run the model at the transaction date with the WACC. It returns 199.2. The fund paid 172.0. If the model were used as it stands, the investment would be marked up by 27.2, or 15.8 per cent, on the day it was bought, with nothing having happened. Under fair value standards an orderly arm's length price is the best evidence of value on that date, so the gap says the model disagrees with the market, not that the fund got a bargain.
Find r such that Σ FCFt / (1 + r)t + FCF5 × (1 + g) / (r − g) / (1 + r)5 = 172.0
Goal Seek on the rate cell, or a bisection, gives r = 11.15%
Present value of the five forecast years = 53.3; terminal value 201.4, worth 118.7 today; total 172.0
Calibration premium = 11.15% − 10.0% = 1.15 points
Excel: Data > What-If Analysis > Goal Seek: set the EV cell to 172 by changing the rate cell
| Year | Free cash flow | Discount factor at 11.15% | Present value |
|---|---|---|---|
| 1 | 12.0 | 0.8997 | 10.80 |
| 2 | 13.5 | 0.8094 | 10.93 |
| 3 | 15.0 | 0.7282 | 10.92 |
| 4 | 16.2 | 0.6552 | 10.61 |
| 5 | 17.0 | 0.5894 | 10.02 |
| Terminal value 201.4 | 0.5894 | 118.7 | |
| Enterprise value | 172.0 |
The 1.15 points are what the buyer charged for everything the WACC does not capture: a management forecast more optimistic than a market participant would accept, a customer concentration, a key-person risk, the illiquidity of a private stake. The calibration does not need to say which; it needs to be recorded, so that later changes to it are deliberate. Note that 69 per cent of the value sits in the terminal value, so the calibrated rate matters far more than any single forecast year, a point developed in what percentage of a DCF the terminal value should be.
One year on, market rates have risen and the WACC build-up gives 10.5 per cent. The company has delivered close to plan and management has rolled the forecast: 13.0, 14.4, 15.6, 16.5 and 17.2. Net debt is 80.0.
Calibrated rate = 10.5% + 1.15 = 11.65%
EV = 54.9 of forecast value + 111.0 of discounted terminal value (192.7 undiscounted) = 166.0
Equity = 166.0 − 80.0 = 86.0
The movement from the 172.0 paid explains itself in three pieces. Rolling the original forecast forward a year at the original rate adds 7.2: the unwinding of one year's discount, net of the year 1 cash that has left the enterprise and now sits in net debt. The higher market rate takes off 9.9. The slightly lower forecast takes off 3.3. Together that is the fall of 6.0, and each piece can be shown to an auditor with its own evidence.
| Discount rate | g 2.0% | g 2.5% | g 3.0% |
|---|---|---|---|
| 10.65% | 178.7 | 186.8 | 196.0 |
| 11.15% | 168.7 | 175.8 | 183.8 |
| 11.65% | 159.7 | 166.0 | 173.0 |
| 12.15% | 151.6 | 157.2 | 163.3 |
| 12.65% | 144.3 | 149.3 | 154.7 |
Half a point of rate is worth about 9 of value either way on average, roughly 5.6 per cent of enterprise value and 10.8 per cent of the 86.0 of equity. That is why the premium has to be held deliberately. Dropping it quietly, for instance because the deal team now feels more confident, would lift the mark by 24.4 with no new evidence at all.
Running the DCF at the textbook WACC and treating the result as fair value. Here it gives 190.4 at the second date. Against the calibrated 166.0 that overstates enterprise value by 24.4, 14.7 per cent, and because net debt is fixed the equity by 28.4 per cent: 110.4 against 86.0. The overstatement is the day-one gain carried forward, a gain the market never offered. The opposite error is calibrating once and then letting the premium drift each quarter to land on a number someone wanted. The market-approach version of the same discipline, with the entry multiple's discount to peers carried forward, is in how to calibrate a private company valuation to the entry price; when the two approaches disagree after calibration, the disagreement itself is worth investigating.
The book's income approach, with the terminal value computed both ways and the rate and growth grid live, is in the free workbook for this case; a blank version of the model is the DCF terminal value template.
The internal rate of return that equates the forecast cash flows and terminal value with the price paid. On an illustrative 172.0 acquisition with five years of free cash flow and 2.5 per cent terminal growth it is 11.15 per cent. It is found with Goal Seek or a bisection, since the terminal value formula makes the equation non-linear.
Because the forecast or the rate does not match what market participants actually priced. In the illustrative case the management forecast at a 10.0 per cent WACC gives 199.2 against a price of 172.0, a 15.8 per cent gain on the day of purchase. An arm's length price is the best evidence of fair value on that date, so the model, not the price, needs adjusting.
It is the starting assumption, not a rule. It should change when the reason for it changes: the business plan is de-risked, a customer concentration falls away, or the forecast is rebased. Each change should be named and evidenced. Holding 1.15 points of premium for no stated reason is as arbitrary as dropping it.
The income approach and the weight of its terminal value are worked in chapter 6 of The Private Markets Valuation Specialist. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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