A firm is considering whether to finance a new project with debt or equity. Will the choice of financing affect the WACC the firm uses to discount the project?

Yes. The resulting WACC after the finance choice will be affect investment evaluation and hence discount of the project.

Explanation:

The Weighted Average Cost of Capital or WACC is the return that is required by the providers of long term sources of finance.

WACC is used to evaluated Capital Investment Projects against their Return. A project will be accepted if it gives a return greater than the WACC (Cost of Capital).

So the finance used on the project will greatly alter the existing WACC and the resulting WACC will later be used to evaluate the Investment or Project. This will as well affect discount of the cash flow from the project.

i might look it up later.