At the seller's projection every earn-out shape pays in full, so the shape can only be priced on the range of outcomes around it.
Price each shape on a range of outcomes, not on the seller's projection, because at the projection every shape pays in full. On a €12.00 million earn-out over two years, with a €16.0 million threshold, an €18.0 million target and EBITDA projected at the target with a standard deviation of €1.5 million, a cliff is worth €6.00 million, a straight line from threshold to target €8.79 million, and a line from zero €11.60 million. The cliff is half the headline before anything goes wrong.
Worked in full in Closing the Deal by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Earn-out shape is usually negotiated as a drafting point and conceded as one. The seller's model shows the business at its target, the cliff pays €12.00 million in that model, and the concession looks free. It is free only in the one outcome that is least likely to happen exactly. The calculation below puts a value on each shape, then checks it against what a business that narrowly missed actually received.
| Term | Value |
|---|---|
| Enterprise value at completion | 118.0 |
| Earn-out period, years | 2 |
| Threshold: nothing paid below this EBITDA | 16.00 |
| Target: full annual payment at or above | 18.00 |
| Maximum a year | 6.00 |
| Maximum in total, 10.2% of enterprise value | 12.00 |
| Seller's projection, EBITDA each year | 18.00 |
| Standard deviation of annual EBITDA (illustrative) | 1.50 |
The three shapes on the table: a cliff pays 6.00 in a year if EBITDA reaches 18.00 and nothing otherwise. A straight line pays nothing at 16.00, 6.00 at 18.00, and pro rata between, so each euro of EBITDA inside the band is worth 3.00 of price. Linear from zero pays EBITDA divided by 18.00, times 6.00, capped at 6.00, so each euro is worth 0.33. The standard deviation of 1.50 is 8.3 per cent of the target; take it from the business's own monthly or annual history, not from a guess.
Payment in a year = MIN(cap, MAX(0, slope × (EBITDA − start)))
Expected payment = slope × (C(start) − C(start + cap ÷ slope)), where C(k) = (m − k) × N(z) + s × n(z) and z = (m − k) ÷ s
Cliff: expected payment = cap × (1 − N((target − m) ÷ s))
m is the projected EBITDA, s its standard deviation, N and n the normal distribution and density. In Excel, with m in B1, s in B2 and k in B3: =(B1-B3)*NORM.S.DIST((B1-B3)/B2,TRUE)+B2*NORM.S.DIST((B1-B3)/B2,FALSE) gives C(k). The straight line uses a start of 16.00 and a slope of 3.00, so it reaches the cap at 18.00 of EBITDA; the line from zero uses a start of 0 and a slope of 0.33.
Step 1, the cliff. The projection sits exactly on the target, so the chance of reaching it in any year is 50.0 per cent. The expected payment is 6.00 × 50.0 per cent = 3.00 a year, 6.00 over the two years. Both years pay in full only 25.0 per cent of the time, and neither year pays 25.0 per cent of the time.
Step 2, the straight line. The business clears the threshold in 90.9 per cent of years, and in most of them lands somewhere inside the band, where it is paid pro rata. The expected payment is 4.40 a year, 8.79 over two.
Step 3, linear from zero. There is no threshold for a bad year to fall below, and a shortfall of a few per cent costs a few per cent of the payment. The expected payment is 5.80 a year, 11.60 over two, 96.7 per cent of the maximum.
| Shape | In the seller's projection | Expected, s = 1.50 | % of maximum | What happened: 16.90 and 17.40 |
|---|---|---|---|---|
| Cliff at the target | 12.00 | 6.00 | 50.0 | 0.00 |
| Straight line, threshold to target | 12.00 | 8.79 | 73.3 | 6.90 |
| Linear from zero, capped | 12.00 | 11.60 | 96.7 | 11.43 |
The projection column is why the shape gets conceded: it reads 12.00 three times. The expected column is the price of the concession. Accepting a cliff instead of a straight line gives up 2.79 of expected value; accepting a straight line instead of a line from zero gives up another 2.81. Together, 5.60, close to half the headline earn-out, changed hands on a drafting point.
The last column is the case that actually happened. Meridian earned 16.90 and 17.40, short of the target by 6.1 and 3.3 per cent. The straight line paid (16.90 − 16.00) ÷ 2.00 × 6.00 = 2.70 and then 4.20, 6.90 in total. Under a cliff the same performance pays nothing at all. Linear from zero pays 5.63 and 5.80, 11.43. Each euro of EBITDA inside a band 2.00 million wide is worth 3.00 of price, which is also why the band is where buyer adjustments do their damage, as what buyer adjustments cost an earn-out shows on the same deal.
| Standard deviation | Cliff | Straight line | From zero | Straight line less cliff |
|---|---|---|---|---|
| 0.50 | 6.00 | 10.80 | 11.87 | 4.80 |
| 1.00 | 6.00 | 9.66 | 11.73 | 3.66 |
| 1.50 | 6.00 | 8.79 | 11.60 | 2.79 |
| 2.00 | 6.00 | 8.21 | 11.47 | 2.21 |
| 3.00 | 6.00 | 7.54 | 11.20 | 1.54 |
With the projection on the target, a cliff is worth half the maximum whatever the volatility, because the business is above or below the line with equal odds. The straight line loses value as volatility rises, since the bad years are capped at zero and the good years at the maximum. Compare the band with the volatility: a band of 2.00 is 11.1 per cent of the target, against a standard deviation of 8.3 per cent. A band narrower than one standard deviation behaves almost like a cliff.
| Projected EBITDA | Cliff | Straight line | From zero |
|---|---|---|---|
| 16.50 | 1.90 | 4.54 | 10.92 |
| 17.00 | 3.03 | 6.00 | 11.18 |
| 17.50 | 4.43 | 7.46 | 11.41 |
| 18.00 | 6.00 | 8.79 | 11.60 |
| 18.50 | 7.57 | 9.89 | 11.75 |
| 19.00 | 8.97 | 10.72 | 11.85 |
If the buyer believes 17.00 rather than 18.00, the straight line is worth 6.00 to it and the cliff 3.03. A buyer who prices the earn-out on its own forecast, and a seller who prices it on the projection, can both think they won the shape argument. Only one of them computed it.
Valuing the earn-out at the projection. Every shape pays 12.00 when EBITDA is exactly 18.00, so the model that the price was agreed on cannot tell a cliff from a line. The difference only appears when the outcome is spread out, which it always is. Run the payment formula over a distribution, or at the very least over a downside, base and upside, before agreeing any threshold, target or cliff. The expected values above are before discounting and before the buyer's credit risk; the fair value treatment is worked in how to calculate the fair value of an earn-out.
A seller who must accept a threshold should ask for the band to be at least as wide as one standard deviation of the business's EBITDA, and for a catch-up in year two if year one falls short. Both turn a coin toss back into a price.
The shape of an earn-out is a price, not a drafting preference. Here the same terms are worth 6.00, 8.79 or 11.60 depending on one sentence, and the business that missed its target by a few per cent received 0.00, 6.90 or 11.43. The free workbook for this case runs the three shapes on the same performance, with a dropdown to read each on the projection and on the case that happened.
A cliff, or all-or-nothing, earn-out pays the full annual amount if the metric reaches the target and nothing if it falls short by any amount. On an €18.0 million EBITDA target with €6.00 million a year at stake, a business earning €17.40 million, 3.3 per cent short, receives nothing, where a straight line from a €16.0 million threshold would pay €4.20 million for the same year.
Subtract the threshold from the actual metric, divide by the width of the band between threshold and target, multiply by the annual maximum, and cap between zero and that maximum. With a €16.0 million threshold, an €18.0 million target and €6.00 million a year, EBITDA of €16.90 million pays (16.90 minus 16.00) divided by 2.00, times 6.00, which is €2.70 million.
Less, for a capped straight line projected at its target, because shortfalls are floored at zero and upside is capped. On the illustrative terms the straight line is worth €10.80 million at a standard deviation of €0.5 million, €8.79 million at €1.5 million and €7.54 million at €3.0 million. A cliff projected exactly at the target stays at €6.00 million, half the maximum.
This article is one calculation from Closing the Deal. 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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