An investor is considering investing in a capital project. The project requires an outlay of $ $150,000$ at outset and further payments $ $100,000$ per annum throughout the year for $2$ years. The project is expected to provide the year end annual income starting at a rate of $ $20,000$ from first year for next $25$ years. Each annual income rise by $8\mathrm{.}00\%$ per annum. Rate of interest is $8\mathrm{.}00\%$ convertible by semi$-$annually.

$($a$)$ Compute NPV$.$

$($b$)$ Compute PI$.$

$($c$)$ Compute MIRR.