TechXpert Ltd$.$ operates with a $12\%$ cost of capital. The company intends to make a capital investment of $7,500,000$ in a machinery project that spans five years. This machinery will facilitate the production and sale of $350,000$ units of Product Zephyr annually. The manufacturing cost for each unit is $11($variable cost$),$ while the wholesale selling price is set at $17$ per unit.

Required:

a$)$ Determine the net present value $($NPV$)$ of the given project. $(10$ Marks$)$

b$)$ Assess the sensitivity of the NPV to variations in the subsequent project parameters:

$(0)$ initial investment

$($ii$)$ Sale

$(0)$ Cost

$($iv$)$ Contribution Margin