Terminology

Accretive M&A transaction

An M&A transaction is accretive (i.e. EPS of the combined company > EPS of the acquiring company) if the acquirer’s P/E ratio > target’s P/E ratio.

This is for the situation where the full consideration is paid by issuing new shares in the acquirer. This also assumes that the earnings of the combined company is simply the sum of the separate earnings of the acquirer and the target (i.e. no additional earnings due to synergies, cost cuts, etc.).

Proof:

original EPS = earnings of acquirer / original number of shares
final EPS = (earnings of acquirer + earnings of target) / (original number of shares + new shares issued)

final EPS > original EPS
=> (earnings of acquirer + earnings of target) / (original number of shares + new shares issued) > (earnings of acquirer / original number of shares)
=> (earnings of acquirer + earnings of target) > earnings of acquirer + (new shares issued * (earnings of acquirer / original number of shares))
=> earnings of target > (new shares issued * (earnings of acquirer / original number of shares))
=> original number of shares / earnings of acquirer > new shares issued / earnings of target
=> acquirer P/E > target P/E

Note:

Acquirer P/E = original number of shares * share price / earnings of acquirer
Target P/E = new shares issued * share price / earnings of target

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