Monte Carlo simulation for the earn-out valuation: distribution assumptions and thresholds

Earn-outs are variable purchase price components that are frequently used in corporate transactions to compensate for the uncertainty regarding the future performance of a company. By linking part of the purchase price to future results, sellers have the opportunity to receive additional payments if the company performs well, while buyers can minimise their risk if expectations are not met. Earn-outs are based on various performance indicators such as revenue or EBIT(DA) and extend over a certain period of time after the transaction has been completed. In addition, threshold values are often part of the agreement in order to manage both the risk and the opportunities for both parties. A floor is a minimum amount of the earn-out that is paid regardless of whether the earn-out milestones are achieved. A more restrictive variant is a so-called cliff, where a minimum level of the agreed milestone must be reached before a payment is made. A cap, on the other hand, sets the maximum amount of an earn-out payment at the upper end. In order to model the earn-out agreement correctly, a precise understanding of the earn-out mechanism is necessary.

The valuation of earn-outs requires a precise modelling of the uncertainty with regard to the future development of the company. A proven method for a path-dependent simulation to be able to include agreed threshold values in the valuation is the Monte Carlo simulation. This stochastic method is based on the repeated random generation and simulation of future scenarios. At least 10,000 repetitions of the random experiment are required to obtain a meaningful result, in order to obtain a distribution of the earn-out underlying, i.e. sales or EBIT(DA), for example. In a typical scenario, probability distributions are defined for relevant financial key figures such as sales or sales growth or EBITDA or EBITDA margins, and the future corporate performance is simulated on the basis of these distributions. This allows uncertainties and fluctuations to be realistically modelled in order to properly evaluate the possible payments from an earn-out.

The underlying distribution assumptions play a crucial role in the Monte Carlo simulation. When selecting the appropriate distribution, a distinction is regularly made between normal distribution and log-normal distribution. Normal distribution is suitable for underlying values that can take on both positive and negative values and scatter symmetrically around a mean value. It is described by two parameters: the mean (µ), which indicates the expected value of the underlying, and the standard deviation (σ), which captures the uncertainty around this mean. When deciding between a normal distribution and a log-normal distribution for EBITDA (earnings before interest, taxes, depreciation and amortisation), the normal distribution is considered more suitable because EBITDA can take on both positive and negative values. In contrast, the log-normal distribution is suitable for underlying values that can only take on positive values and have an asymmetrical risk profile. It is also described by mean and standard deviation, but with a limitation of the simulated values to the positive spectrum resulting from the nature of the logarithm. This makes the log-normal distribution a suitable choice for revenue-dependent earn-out milestones. In principle, however, both distributions can be converted into one another. If the resulting revenue distribution is assumed to be log-normally distributed, the simulation can be carried out over time assuming a normally distributed log revenue growth.

In practice, a Monte Carlo simulation is carried out in several steps. First, the relevant input variables that determine the earn-out, such as sales or EBITDA, are defined. A distribution assumption is then made for each of these variables, whereby the normal or log-normal distributions described are used as standard. The distribution parameters are calibrated and the development of the corresponding earn-out base value over time is simulated. When simulating the EBITDA, it makes sense in practice not to focus directly on the change in the EBITDA, but rather to simulate the sales growth using a log-normal distribution in the first step and to derive the EBITDA on the basis of the resulting normally distributed sales figure and a simulation of normally distributed EBITDA margins. The simulations are repeated thousands of times and it is checked for each simulation path whether an agreed threshold has been reached. The path-dependent earn-out payment is then calculated and the resulting mean value across all simulation paths is discounted to the valuation date.

The calibration of the distribution parameters is crucial for the accuracy of the Monte Carlo simulation. The mean (µ), which represents the expected value of the underlying key figure, and the standard deviation (σ), which captures the uncertainty around this mean, are of central importance here. The expected value can usually be derived from the business plan for financial variables. In other words, if the simulation is calibrated correctly, the mean value must match the management's business plan in the form of the planned revenue or EBITDA. An understanding of business planning is important in order to assess whether the planned values are actually expected values. In practice, volatility can be derived from comparable companies or market data. In this context, the historical and expected earnings of the peer group companies, derived from analysts' estimates, are regularly used. The corresponding time series of revenue or EBITDA figures provides the basis for calculating the volatility of the changes over time.

Caps, cliffs and floors do not influence the underlying distribution assumptions of the earn-out base value, but they do influence the payment profile of the earn-out payments. In this case, all values above the cap (based on the base value of the earn-out, i.e. sales, for example) are limited to the maximum earn-out payment, and values below the floor (again based on the base value) are raised to a minimum earn-out payment, whereby base values below the cliff do not result in any earn-out payments. Overall, these thresholds lead to a reduced spread of the resulting payments, as extreme deviations are excluded. Accordingly, the histogram of the resulting earn-out payments shows an accumulation at the cap or floor and a reduction below the cliff:

As a result, the expected earn-out payment will be consistently lower (higher) if a cap or cliff (floor) is agreed compared to an agreement without a cap or cliff (floor). 

Earn-outs are an effective instrument for balancing out uncertainties in corporate transactions by linking part of the purchase price to the future development of the company. They enable sellers to receive additional payments if performance is good, while buyers limit their risk if expectations are not met. Monte Carlo simulations are a common method for valuing earn-outs because they make it possible to simulate numerous future scenarios and their uncertainties. The choice of distribution assumptions, such as normal or log-normal distribution, as well as the calibration of parameters such as mean and volatility, are crucial. Caps, cliffs and floors influence the payment profile of the earn-out, whereby the fundamental incentive effect of the earn-out can be further fine-tuned.