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A bunch of reasons, but the answer that the interviewer is probably looking for is "Leverage." P/E ignores leverage since it is an equity-based valuation, but EBITDA values the enterprise value. If you lever up a whole bunch to increase earnings, that doesn't actually increase the value of the company / asset, it just makes the earnings more volatile, indicating that the earnings should warrant a lower P/E multiple. So one should generally avoid P/E multiples since they are distorted by the effects of leverage and utilize an EBITDA multiple or some other multiple that gives enterprise value versus equity value.

 
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I'd say "capital structure" not "leverage" because an excess of cash on the balance sheet (especially in a low rate environment) is also going to cause PE and EBITDA valuations to diverge.

Your answer also kind of suggests that debt is free, but it creates interest expense, which of course depresses EPS, until/unless the company is converting the debt to earnings at a rate in excess of the debt's cost.

(All that said, I realize this was a WSO comment, not a PhD dissertation).

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