Acquisition Mathematics


There are many reasons to buy a small business. Individual buyers list reasons like independence, freedom and financial rewards. Strategic buyers (companies in the same or related industries to the target company) can derive many additional benefits from acquisitions, in addition to the basic earnings of the company: strategic buyers can benefit from economies of scale, cost synergies and access to new markets, for example.

But strategic buyers have one other important incentive for buying other companies which might not be immediately obvious: the valuation multiple. Because of the way valuation multiples work, growing via acquisition can be a powerful way to add value.

Valuation Multiple Mathematics for Strategic Buyers

In business valuation the size of a company has the greatest impact on its valuation multiple. A publicly listed company may trade at 15 x earnings, a mid-market company in the same industry (with revenues of say £20m) might be valued at 7 x earnings and a small business in this industry might be valued at 2-4 x earnings, depending on its exact size and the other factors that affect its valuation.

Let’s say the small business has revenues of £1m, EBITDA of £200,000 and is valued at a 3x multiple of EBITDA (£600,000). The mid-market company mentioned above has revenues of £20m and pre-tax earnings of £4m. With a 7 x valuation multiple the company would be valued at £28m. Now if the mid-market company acquired the small business, it would add £1m to its revenue and £200k to its earnings. This would make it an £8m revenue company, with £4.2m earnings. Based on its 7x valuation multiple, the company would now be worth £29.4m – in other words, it has added £1.4m in value through a £600,000 acquisition.

Remember that this is before any cost synergies are rinsed out, economies of scale are realised, or other strategic benefits achieved. Successful acquisitions will boost profits further through these means, and increase the acquirer’s value even more, via its favourable valuation multiple.

Acquirers can also sometimes increase their own valuation multiple through acquisition. As companies grow in size their valuation multiple rises. The owner of a £900k turnover company will be aware of the fact that growing revenues to above the £2m mark will typically result in an increased valuation multiple (eg: the multiple might currently be 2.5, but companies in this industry with revenues over £2m might trade at a 4 x multiple). In order to get to the £2m turnover mark the company will have to more than double in size – a difficult task through organic growth alone. However, growth through acquisition is much faster. The owner might be able to acquire some smaller competitors turning over £300k, £400k and £500k respectively, bringing the total turnover of the combined company up to £2.1m. Once the company is integrated and stable its valuation should be based on the higher multiple.


Remember that this is before any cost synergies are rinsed out, economies of scale realised, or other strategic benefits achieved


How would the mathematics of a case like this work? Using example figures for now, we’ll say that in each of these companies EBITDA was 20% of turnover. So the original company would have had an EBITDA of £180k and the EBITDA of the acquisitions would have been £60k, £80k and £100k respectively. The valuation multiple of the original company was 2.5, so based on its EBITDA of £180k the valuation would have been £450k. The smaller acquisitions might have had valuation multiples of between 1.5 and 2.5: let’s say an average of 2. Therefore these businesses would have been acquired for £120k, £160k and £200k respectively – a total cost of £480k. This would have added £240k per annum EBITDA to the total company, bringing its EBITDA to £420k and its total revenue to £2.1m. Based on these numbers alone, (note again that this is before cost synergies, economies of scale and other benefits are realised), using the new valuation multiple of 4, the value of the total combined company would be £1.68m (£420k x 4 = £1.68m). So the company has added £1.23m to its value by spending £420k on acquisitions. In this case the bulk of the benefit was achieved by moving the total company up to a higher valuation multiple.

Financial Buyers (Private Equity)

Private equity investors don’t buy the genuinely small (<£2m businesses) that are our core interest and the subject of this blog. But no summary of acquisition mathematics would be complete without mentioning financial buyers and what motivates them.

The last example focused on the benefit achieved by acquiring a business at one multiple and revaluing it at another. This “PE multiple arbitrage” is the primary driver behind a particular acquisition strategy sometimes used by private equity buyers, called a “roll-up”. In a roll-up, several businesses in the same industry are acquired and amalgamated to form one business. The final entity is much larger than any of the individual acquisitions, and is therefore valued using a higher valuation multiple. If four or five companies within the £2-5m turnover range can each be acquired at (say) a 4 x multiple and the combined entity sold at a 7 x multiple, this PE multiple arbitrage alone will generate an outstanding return. As with all acquisitions by “financial buyers” (who intend to sell the acquisitions again within a short time frame), timing the economic cycle is critical: valuation multiples are influenced by the whim of the business cycle so buying during a boom and selling the combined entity in a downturn will make things difficult. But PE multiple arbitrage provides a powerful incentive.

Since strategic buyers can typically derive more benefit from a given acquisition than financial buyers can, and can therefore afford to pay more, how do financial buyers compete? One way is to use leverage.

Let’s say a target company is turning over £5m with net earnings of £1m. The appropriate valuation multiple for this business will be dependent on its industry, the economic cycle and other factors, but let’s say it is a multiple of 4, giving a valuation of £4m. Assuming no growth, an acquisition at this price would give a return on equity of 25% to the private equity buyer. On the other hand, a strategic buyer, understanding the cost synergies, economies of scale and other benefits it can achieve through the acquisition, might be willing to pay £5m for the same company. How does the private equity firm compete? Leverage: it incorporates some debt into the capital structure for the acquisition, allowing it to generate the same return on equity while paying a higher price. Rough guideline figures might be as follows. The private equity fund could pay £5.2m for the acquisition, funded via £3.2m equity and £2m debt (a combination of debt structures with a combined interest rate of 10%). The earnings of the business would now be £0.8m after interest payments, giving a 25% return on the £3.2m equity. Strategic buyers can use debt in capital structures too of course, but this kind of acquisition is more typically associated with financial buyers.


The value created by an acquisition is often largely driven by its impact on the valuation multiple of the final entity. In addition to these mathematically-derived benefits, strategic buyers can benefit in other ways from acquisitions, and can usually pay more than other buyers as a result.