December 17, 2012

It's rational to pay far more

A while back I read a post by Chris Dixon where he lays out the logic for "build vs. buy" and argues that it may be rational for a big company to pay quite a lot to get their hands on a hot new product.

His argument goes something like this:
Big company estimates that hot product can boost its market cap by $500M, and that they'd have a 50% chance of building it for $50M. The alternative is to acquire little startup that has already built it. Assume there are no second chances and ignore time, then the upper bound of what big company would rationally pay to acquire would be $100M.
As Chris points out an M&A group at a real "big company" would of course have a much more sophisticated model anyway, taking all kinds of things into account. With that said, I think it's interesting to note that (even) in this simplistic example it is rational to pay 3x more than what Chris thinks.

Why? Well, big company only really has one choice: acquire little startup or don't. Now what is the expected outcome if they do acquire little startup? Easy, it's a boost in market cap of $500M - X, where X is the cost of acquisition. What's the outcome if they don't acquire little startup and instead try to build the product themselves? That depends. If they succeed then the gain is a whopping $450M, but if they fail they've spent $50M for nothing. Since the probability of outcomes is 50/50 the expected value is just $200M. This means that if big company buys little startup for anything less than $300M they can expect to do better than if they try to build. Don't believe me? Draw the decision tree.

This is a very simplistic model, but the result indicates a principle that in my mind bears generalization: the acquisition valuations are dominated by opportunity cost, not development cost. In other words; opportunity cost is what drives valuations of little startups.

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