Also, in ITP, we talked about the model for "rational experimentation", that is to say the formula which describes the logic between probability of successful outcomes versus the risk and initial investment required (looks suspiciously similar to an NPV calculation because it uses the same mathematical components with probability of success superimposed on the cash flow, similar to how the CFA teaches to account for risk).

With my last post on M&A and splitting synergies with the target's share holders, this got me thinking about what would be "rationally" fair in M&A negotiations. I thought about it and decided it might be a good idea to integrate the thoughts from the post below with the idea of a Sharpe Ratio (or more exactly, Roy’s Safety First Criterion – where we use a “minimum return” rather than risk free rate).

S = (E[R] - Rf) / sigma

Where:

- E[R] is the expected return of the project
- Rf is the risk free rate (or in Roy's SFC, minimum return)
- sigma is the standard deviation of the investment

I would propose that the Sharpe ratio calculation can be used in an analogous manner for an M&A deal with synergies. For example:

- Expected Returns --> Synergies
- Risk Free Rate --> Premium
- Sigma --> some sort of volatility related to success of M&A deals to achieve expected returns

In fact, you can take this a step further and get:

- Synergies / EV as a proxy for M&A incremental ROA
- Premium / EV as a proxy for M&A minimum return

S = (Synergies – Premium) / (EV * sigma)

The formula would then calculate something very similar to marginal excess ROA or value creation per unit risk by the deal. Besides helping you understand your BATNA, this metric might also help you select acquisition targets from a financial perspective.

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