$($a$)$ Acacia Ltd is considering investing in the following projects and details of these projects are as follows:

Project Initial outlay Present value of cash flows

$$\text{'}000$ $$\text{'}000$

AB $2,0002,780$

CD $2,100$ See details below

EF $8002,100$

GH $2,2003,600$

The annual cash flows $($in current price terms$)$ of Project CD are as follows:

Year $1234$

$$\text{'}000$ $$\text{'}000$ $$\text{'}000$ $$\text{'}000$

Revenue $1,0871,1471,327918$

Costs $217252303141$

The revenue inflation and costs inflation are expected to be $6\%$ and $5\%$ respectively. Acacia Ltd has an after$-$tax cost of capital $12\%($nominal$)$ and the company pays tax at the rate of $15\%$ in the same year.

Acacia Ltd has only $ $4$ million $($capital$)$ to invest in the above$-$mentioned projects. All of the above projects are divisible and none can be delayed or repeated. The present value table of $12\%$ is as follows:

Year $1234$

Present value $0\mathrm{.}89290\mathrm{.}79720\mathrm{.}71180\mathrm{.}6355$

$($i$)$ Calculate the Net Present Value $($NPV$)$ of Project CD$.$

$[12$ Marks$]$

$($ii$)$ Calculate the NPV using the Profitability Index methodology taking into consideration the capital constraint of the company.

$[12$ Marks$]$