Why is normal profit an opportunity cost?

This is a great question, because on the surface, profit seems to contradict the analysis of perfectly competitive markets. However, the "zero economic profit" outcome of perfectly competitive markets embeds the assumption that all capital has an opportunity cost.

If normal profit were zero -- or if perfectly competitive markets actually had zero profit -- we would see that firms would not attract the capital necessary to fund themselves. We can also see that money has a time value, and that investors correlate their expectations of profit with their perceived risk of any investment.

We can also view this from the internal perspective of a firm deciding how to allocate its capital. This is very common. Firms decide on which projects to fund on a regular basis. Such decisions should incorporate the firm's required rate of return as a cost of capital.

If the firm invests in a project that does not meet it's required rate of return, then the firm's shareholders will discover that their share of the firms profits is not providing them with their expected returns, and they will either sell their shares (depressing the share price) or seek to replace the firm's management through the shareholder governance process. In any case, the investors will believe that they could have earned higher returns through alternative investment opportunities (and that brings us back to opportunity cost!).