Using Proxies: M&A Accretion or Dilution

Another phenomenal question that was asked at the Rotman stock pitch was this:
Company A is trading at a PE of 10.
Company B is trading at a PE of 15.
Company A acquires B using only debt at an after tax rate of 5%.

Is the deal accretive or dilutive?

This was a brilliant question and the trick was this:

PE is calculated as EPS / Price per Share and is a per share approximation of NI / E which is a proxy for cost of capital. This is the same result as when I was wondering about PEG ratios to find an appropriate discount rate for equity.

So using PE, the reciprocal of 15 is 6.67%. If the deal is paid entirely in debt at a kd(1-t) of 5%, then the cost of capital raised is cheaper than the return on capital used (the returns from the investment instrument we are buying outstrip the costs of the investment instrument we use to raise capital). Think of profiting from a financing transaction.

Another way of thinking of it is that (assuming that equity is always more expensive than debt) is that the change to the capital structure in this transaction is that the two entities are being combined and there is more debt being added to the capital strucure (more leverage, ceteris paribus).

In this case, the deal is accretive. This was absolutely a brilliant question.

A variation of this question could have been: "What if only equity was used to raise capital?"

Then the cost of capital for this incremental deal would be the ke of the acquiring company (Company A). The cost of capital would be the inverse of a PE of 10 or 10%. 10% is greater than the 6.67% of Company B and would therefore be dilutive.

Logically, the next question that follows would be: "Why would a company ever do a deal that's dilutive?"

One possible solution is that we're looking at the original formula for PE and PEG, a company that trades at a high PE ratio (keeping most other characteristics constant and assuming perfectly efficient markets) may have some growth build into the price.

For instance, Company B could be a young upstart company with a really strong product with potential for growth, whereas Company A is more mature but with good distribution networks. Company A might acquire Company B to have access to it's high growth product which it can distribute on it's network for high earnings growth (synergies).

In this case, a short term dilutive transaction might lead to much stronger future earnings growth for the combined entity.