Buying small and selling large is the most repeatable part of buy-and-build, and the most overstated, because the usual arithmetic forgets the price.
Multiple arbitrage is the add-on EBITDA times the gap between the platform's exit multiple and the multiple paid, less the cost of integrating it. On an illustrative buy-and-build, 6.0 million of add-on EBITDA bought at a blended 5.0x and sold inside a platform valued at 9.0x creates 21.0 million of net arbitrage, not the 54.0 million a value creation deck usually prints. The arbitrage disappears at an exit multiple of 5.5x.
Worked in full in The Private Equity Operating Partner by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Buy-and-build rests on a simple observation: small companies change hands at lower multiples than large ones, so EBITDA bought small and sold large is revalued on the day it is bolted on. That revaluation is real, and it is the most repeatable part of the strategy. It is also the part most often overstated, because the arithmetic that shows it is one subtraction short.
| Add-on | EBITDA | Multiple paid | Price |
|---|---|---|---|
| A | 2.0 | 4.0x | 8.0 |
| B | 2.0 | 5.0x | 10.0 |
| C | 2.0 | 6.0x | 12.0 |
| Total | 6.0 | 5.0x | 30.0 |
The platform carries 20.0 million of EBITDA and is expected to exit at 9.0x, the same multiple it was bought at, so that nothing in this calculation comes from market re-rating. Integration costs 3.0 million, one-off. The add-ons are bought three years before exit and funded half with acquisition debt. Integration also produces 1.0 million of cost synergies, which are kept separate below.
Gross arbitrage = add-on EBITDA × (exit multiple − entry multiple)
Net arbitrage = gross arbitrage − integration costs
Break-even exit multiple = (price paid + integration costs) ÷ add-on EBITDA
In Excel: =SUMPRODUCT(EBITDA,Exit_Multiple-Entry_Multiple)-Integration, which handles add-ons bought at different multiples in one line.
| Add-on | Price | Value at 9.0x | Arbitrage |
|---|---|---|---|
| A, at 4.0x | 8.0 | 18.0 | 10.0 |
| B, at 5.0x | 10.0 | 18.0 | 8.0 |
| C, at 6.0x | 12.0 | 18.0 | 6.0 |
| Total | 30.0 | 54.0 | 24.0 |
| Less integration costs | −3.0 | ||
| Net arbitrage | 21.0 |
Each add-on contributes its EBITDA times the spread between the 9.0x exit and its own entry multiple: 2.0 × 5, 2.0 × 4 and 2.0 × 3 turns, or 10.0, 8.0 and 6.0. Together, 24.0 million, the same as 6.0 of EBITDA times the 4.0-turn spread to the blended 5.0x entry. Integration takes 3.0, leaving 21.0 million.
The 33.0 million deployed (30.0 of price and 3.0 of integration) is worth 54.0 million at exit, a 1.64x unlevered multiple and a 17.8 per cent annual return over three years, counting the exit value only: the cash the add-ons earn in the meantime and any operating improvement come on top. With half the price borrowed, the equity put in is 18.0 million and the equity value at exit is 39.0 million, 2.17x before interest and, again, before the add-ons' own cash generation. That is the honest case for buy-and-build: a mechanism a buyer can verify and continue.
The 1.0 million of synergies, worth 9.0 million at the exit multiple, is a separate line. It is operating work: purchasing, overlapping sites, shared back office. Mixing it into the arbitrage hides the one thing the next owner most wants to know, which is how much of the value came from paying less and how much from running better.
Add-on by add-on, the table also shows where the programme's discipline lies. Add-on A, bought at 4.0x, produces 10.0 of arbitrage on 8.0 of price; add-on C, at 6.0x, produces 6.0 on 12.0. Paying two turns more for the same EBITDA cut the arbitrage by 40 per cent. In a competitive add-on market the entry multiple drifts upward deal by deal, and the arithmetic says each of those turns comes straight out of the thesis.
| Exit multiple | Bought at 4.0x | Bought at 5.0x | Bought at 6.0x |
|---|---|---|---|
| 7.0x | 15.0 | 9.0 | 3.0 |
| 8.0x | 21.0 | 15.0 | 9.0 |
| 9.0x | 27.0 | 21.0 | 15.0 |
| 10.0x | 33.0 | 27.0 | 21.0 |
Every turn on either side is worth 6.0 million, one turn times the add-on EBITDA. A turn saved at entry is worth exactly as much as a turn gained at exit, and only the first is in the buyer's control. The break-even is (30.0 + 3.0) ÷ 6.0 = 5.5x: below that exit multiple the add-ons destroy value even if they perform exactly to plan.
The arbitrage is hostage to the platform multiple. At exit the combined business carries 27.0 million of EBITDA: the platform's 20.0, the add-ons' 6.0 and 1.0 of synergies. One turn of contraction on that base costs 27.0 million, more than the whole 21.0 of net arbitrage. A buyer who sees an unintegrated collection of small businesses will not pay the platform multiple for it, which is why integration is the condition of the arbitrage and not an optional extra.
The common mistake is to attribute the add-ons' full exit value to acquisitions: 6.0 × 9.0 = 54.0 million. That figure ignores the 30.0 million paid and the 3.0 spent integrating, cash that would otherwise have repaid debt. It overstates the contribution by 157 per cent, and the overstatement does not vanish: it reappears as a deleveraging bucket that looks too small, because the cash went into the add-ons instead. A value creation bridge that reconciles to zero forces the price back in. The second mistake is to present the arbitrage as a growth story. It is a pricing story, and a buyer will pay for it only if the exit multiple applies to the whole, which is a statement about integration, not about the deal count.
Compute arbitrage as EBITDA times the multiple spread, net of integration, add-on by add-on, and quote the break-even exit multiple beside it. Keep synergies on their own line. The bridge in the free workbook for this book shows the same correction on the Vireo case, where add-ons bought at 4.0x inside a platform at 10.2x are worth far less net than gross. For the split that sits next to it in any bridge, see how to split EBITDA growth and multiple expansion, and for the leverage side, whether leverage dilutes the operating contribution.
It is the value created by buying EBITDA at a lower multiple than the one at which it is eventually sold, typically by bolting small add-ons onto a larger platform. In the illustrative case, 6.0 million of EBITDA bought at 5.0x and sold inside a 9.0x platform creates 24.0 million before integration costs and 21.0 million after 3.0 of integration.
No. Multiple expansion is the platform itself re-rating between entry and exit, which no one in the deal controls. Arbitrage holds the platform multiple constant and comes from the price paid for the add-ons. In the illustrative case the platform enters and exits at 9.0x, so all 21.0 million of net value is arbitrage and none is expansion.
At the price plus integration costs divided by the add-on EBITDA. Three add-ons with 6.0 million of EBITDA bought for 30.0 million and integrated for 3.0 break even at an exit multiple of 5.5x. Each turn either side moves the result by 6.0 million, and one turn of contraction on the combined 27.0 million of EBITDA erases more than the whole arbitrage.
This article is one calculation from The Private Equity Operating Partner. 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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