Price is an equity value metric, meaning that it only accounts for the equity value and does not account for the debtholders. It represents either stock price or market capitalization.
EBITDA is an enterprise value metric, meaning that it goes to both equity holders and debt holders. This is EBITDA is before interest, so we have not accounted for payments to debt holders.
You can’t use an equity value metric in the numerator and enterprise value metric in the denominator because it’s not apples-to-apples.
Price / Earnings makes sense because we are taking an equity metric (stock price) and dividing it by another equity metric (earnings per share).
EV / EBITDA makes sense because we are taking the enterprise value and dividing it by another enterprise metric, EBITDA.
Price / EBITDA is like dividing two numbers with different units; it won’t work mathetmatically because the numerator is an equity value metric and the denominator is an enterprise value metric.