M&A - P/E Multiple vs. Cost of Debt

Can someone help me understand in the simplest of terms the connection between P/E multiple and cost of debt in terms of which you would choose to use to fund an acquisition? i.e. what P/E multiple makes sense to issue stock vs. raising debt to fund an acquisition given an interest rate?

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the absolute simplest way is to flip P/E and instead take E/P. That gives you the "earnings yield" on the current stock price. Now you have two comparable %'s to line up against each other. Then line up earnings yield vs. the cost of debt and see what is cheaper. Then choose the cheaper option.

If you follow the logic through, the higher P/E ratio you have, the lower earnings yield your stock price and therefore it becomes "cheaper" to finance with stock the higher the P/E goes. 

This is obviously over-simplistic vs. the real world, but this is how it should be thought about in terms of interview questions and back-of-the-napkin math. 

 

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