Jide Enterprises is considering investing in new equipment for two projects: Project X and Project Y$.$ Both projects have a lifespan of $5$ years. The company requires a minimum rate of return of $10\%$ on its investments.

Cost of Investment:

Project X: $5,000,000$

Project Y: $3,000,000$

The following are the cash flows:

Year Project X $()$ Project Y $()$

$1|1,000,000|800,000|$

$2|1,500,000|1,200,000|$

$3|1,200,000|1,500,000|$

$4|800,000|1,000,000|$

$5|500,000|700,000|$

You are required to:

$1.$ Evaluate both projects using the following techniques:

a$)$ Payback Period: Calculate the number of years it takes for each project to recover the initial investment.

b$)$ Net Present Value $($NPV$)$: Determine the NPV of each project considering the $10\%$ required rate of return.

$2.$ Based on your analysis, recommend which project Jide Enterprises should choose and justify your answer