$[4$ marks$].$ The Table $1$ shows the capital costs and net savings of two energy$-$saving measures.

$($a$)$ For a discount rate of $16\%,$ calculate the Net Present Value $($NPV$),$ Profitability Index $($PI$)$ of each project.

$($b$)$ Calculate the Internal Rate of Return $($IRR$)$ for each project.

$($c$)$ Which project would you choose and why? Explain.

Table $1.$

$\backslash$table$[[,$Project $1,$Project $2],[$Capital Cost $($$$)$:$,20,000,20,000],[$Net Annual savings $($$$)$:$,,],[$Year $1,7,000,8,500],[$Year $2,7,000,8,000],[$Year $3,7,000,7,500],[$Year $4,7,000,7,000],[$Year $5,7,000,6,500],[$Year $6,7,000,6,000],[$Year $7,7,000,5,500]]$