You are evaluating a project that requires an investment of $$$$98$ today and garantees a single cash flow of $$$$123$ one year from now. You decide to use $100\%$ debt$$ financing, that$$ is$,$ you will borrow $$$$98.$ The$$ risk$-$free rate is $4\%$ and the tax rate is $31\%.$ Assume that the investment is fully depreciated at the end of the$$ year, so without leverage you would owe taxes on the difference between the project cash flow and the$$ investment, that$$ is$,$$$25.$

a$.$ Calculate the NPV of this investment opportunity using the APV method.

b$.$ Using your answer to part $($a$),$ calculate the WACC of the project.

c$.$ Verify that you get the same answer using the WACC method to calculate NPV$.$

d$.$Finally$,$ show that$$ flow$-$to$-$equity method also correctly gives the NPV of this investment opportunity.