Your brother, Sam, has approached you with ideas of venturing into business as per two options below. He has a capital rationed budget of N$$260,000$ obtainable from a local bank at the open market interest rate of $18\%$ p$.$a$.$ compound calculated daily.

Option $1$ Invest in one of two investment opportunities namely, a floor tiles manufacturing business $($hereinafter Project A$),$ or a brick$-$making business $($hereinafter Project B$).$ The two projects require initial capital outlays of N$$200,000$ and N$$260,000$ and have residual values of N$$50,000$ and N$$60,000,$ respectively. Profits are projected as follows:

Year $12345$

Project A: $40,00055,00065,00050,00045,000$

Project B: $50,00065,00075,00080,00055,000$

Option $2$: Investing in a portfolio comprising both businesses. However, since he is operating under conditions of capital rationing to the sum of N$$260,000,$ he is considering investing N$$100,000$ in Project A and N$$160,000$ in Project B$.$

Calculate and make an informed choice $($i$.$e$.$ giving reasons for your choice$)$ on the project to undertake based on the following:

a$.$ Net Present Value $(2$ x $10=20$ marks$)$

b$.$ Discounted Payback Period $(2$ x $10=20$ marks$)$

c$.$ Profitability Index $(2$ x $3=6$ marks$)$

d$.$ Internal Rate of Return $(2$ x $15=30$ marks$)$