The problem is that if the money is raised from a loan, then the direct cost might be only 8% but the increased gearing will mean that the shareholders will require a higher return (because they have more risk). If we do not give them a higher return then the share price is going to fall.
So….the return required from the project must be enough to pay the interest on the load plus the extra dividend needed for shareholders. With some assumptions, this is what the weighted average is measuring.