Multiple Arbitrage Explained: Why Private Equity Pays More Than the Math Suggests

Multiple arbitrage is the cleanest way to explain why a private equity firm can buy a company, run it competently but not extraordinarily, and still produce returns far above what the underlying business growth would predict.

The core idea is simple. Different sized companies trade at different multiples of their earnings. If a buyer can purchase smaller businesses at low multiples and combine them into a larger business that sells at a higher multiple, the difference is pure profit, even if nothing else about the operations improves.

The numbers, in plain English

EBITDA is the standard earnings measure for private companies. It stands for earnings before interest, taxes, depreciation, and amortisation, and it approximates the cash a company generates before financial structure decisions.

When private equity firms or strategic buyers value a company, they typically express the price as a multiple of EBITDA. A four times multiple on a company doing $2 million in EBITDA means a purchase price of $8 million. The same company at eight times would be $16 million.

The multiple a particular business commands depends on a long list of factors, but the most important is size. Larger companies sell for higher multiples. A representative table for a stable, recurring-revenue services industry might look like this:

• Under $500,000 EBITDA: 2 to 4 times.
• $500,000 to $2 million EBITDA: 3 to 5 times.
• $2 to $5 million EBITDA: 5 to 7 times.
• $5 to $20 million EBITDA: 7 to 9 times.
• $20 to $75 million EBITDA: 8 to 11 times.
• $75 million-plus EBITDA: 10 to 14 times, often higher for high-growth segments.

These ranges shift with the credit cycle and the industry, but the directional pattern is permanent. Bigger trades higher.

Why the spread exists

The multiple gap is not arbitrary. It reflects genuine differences in the risk profile and the buyer pool for businesses of different sizes.

The buyer pool is larger. A $20 million EBITDA business can be acquired by hundreds of private equity firms, dozens of public strategic buyers, and a handful of large family offices. A $1 million EBITDA business has a much smaller universe of qualified buyers, mostly local investors, individual operators, and search funds. More competition for the same earnings stream pushes the multiple up.

Customer concentration is lower. A $1 million EBITDA business often has its top three customers contributing more than half of revenue. Losing one of them is an existential threat. A $20 million EBITDA business almost always has a more diversified revenue base, which means lower volatility, which means a higher multiple.

Management depth is greater. A $1 million EBITDA business is usually run by its founder. If the founder leaves, the business is at risk. A $20 million EBITDA business has a chief financial officer, a head of sales, and a chief operating officer. The institution survives the people.

Access to debt is better. Banks and credit funds compete to lend against $20 million EBITDA companies. They charge thinner margins, demand fewer covenants, and accept lower equity tickets. Cheaper debt lets a buyer pay a higher multiple while still hitting their return targets.

Operational systems are professional. Larger companies tend to have real accounting, real customer relationship management software, real inventory controls, and audited financial statements. A buyer pays less for messy financials.

Each of these is a real risk. The multiple gap is the market’s accurate pricing of them.

How rollups exploit this

A rollup is the most direct way to capture the multiple arbitrage. A private equity sponsor buys a platform company in a fragmented industry, then bolts on dozens of smaller targets at the smaller multiples. Each tuckin enters the platform at, say, four times EBITDA. Once integrated, the platform’s combined earnings trade at eight or nine times EBITDA, because the platform itself has the size and the systems of a mid-market business.

A simple example. A sponsor buys an HVAC platform with $5 million of EBITDA for $35 million (seven times). Over three years, the sponsor adds ten tuckins averaging $1 million of EBITDA each, paying four times. The total purchase cost of the tuckins is $40 million. Now the platform has $15 million of consolidated EBITDA, which sells to a larger sponsor at nine times. Sale price: $135 million.

Total purchase cost: $35 million + $40 million = $75 million. Sale price: $135 million. Gross gain on the trade: $60 million, against $75 million of invested capital.

No improvement in operations is required for this math to work. In practice, real rollups do also achieve some genuine cost savings, revenue synergies, and growth. Those add to the return. But the multiple arbitrage by itself is the structural engine.

The four ways to capture it

Multiple arbitrage is not only available to rollup investors. Any private capital strategy that buys smaller and sells larger can capture some of it.

1. Buy small, build organically. A single platform acquisition that grows from $5 million to $20 million of EBITDA over five years through pure organic growth will typically also expand its multiple from seven to nine. The multiple expansion alone adds about 30 percent to the eventual sale price.
2. Buy small, roll up. The textbook rollup strategy described above.
3. Buy mid-market, professionalise. Buying a $10 million EBITDA family-owned business with sloppy financials, installing real systems, then selling it to a larger sponsor at the institutionally appropriate multiple. The gain is in the systems-driven re-rating.
4. Carveouts. A division of a larger public company often trades at the parent’s blended multiple, which can be lower than what the division would command standalone. Buying the carveout and then selling the now-standalone business to a strategic buyer at a higher multiple is a meaningful source of return in carveout strategies.

When multiple arbitrage breaks

The strategy is durable but not bulletproof. Three failure modes recur.

Multiple compression on exit. If the credit environment tightens between entry and exit, all multiples in the relevant size bracket can fall by one to three turns. A platform that was projected to sell at nine times might exit at seven. The arithmetic still works in most cases, but the equity return is hit hard.

Overpaying on the platform. If the sponsor pays seven times for the initial platform because the auction was competitive, and then can only bolt on at four times, the blended cost of capital is much higher than a typical rollup. The exit multiple has to deliver an outsized step-up to make the strategy work.

Operational drag. Integration is real work. If the platform cannot actually run twenty branches without losing the customer service that made each of the original businesses valuable, EBITDA shrinks and the multiple shrinks with it. Many failed rollups die from integration debt, not from acquisition errors.

Industry deterioration. If the underlying industry suffers a structural shift, say, a regulatory change, a technology disruption, or a buyer-pool collapse, the exit multiple can fall further than predicted. Customer demand matters more than the financial engineering.

What this means for an aspiring buyer

If you are looking at private capital from the outside and trying to understand how returns are actually generated, multiple arbitrage is the single most important concept to internalise. Operating improvements matter, but they are often a smaller contribution to the realised return than people assume. The big lever is structural: buying at small-company multiples and selling at mid-market multiples.

This is also why the playbook is so reliably profitable across decades. The underlying mechanism is rooted in real economic differences between small and large companies, and those differences do not vanish with competition. As long as $1 million EBITDA businesses command lower prices than $20 million EBITDA businesses, the spread remains, and the patient buyer can keep capturing it.