What is the cost of equity for a company that trades at 10x P/E?

A proxy for cost of equity is the inverse of price / earnings per share, ie earnings per share / price.

You can think of this as the % of return you will get for buying one share, with the return measured as earnings per share. This expected return can be a proxy for the cost of equity.

Therefore, since P/E is 10x, cost of equity = 1/10 = 10%.