D'Chillies Berhad is currently considering buying a new grinding machine at a cost of $$40,000$ excluding the cost of installation and transportation of $$5,500$ and $$4,500$ respectively. The capital cost of the machine is $13$ percent. The annual cash flow after tax that will be generated by the machine is as follows:

$\backslash$table$[[$Year$,$Cash Flows $($$$)],[1,15000],[2,15000],[3,15000],[4,15000],[5,15000]]$

Calculate,

a$)$ Payback Period $($PP$)(5$ marks$)$

b$)$ Net Present Value $($NPV$)(6$ marks$)$

c$)$ Profitability Index.

$(4$ marks$)$

d$)$ Specify the machine must be purchased or otherwise based on the net present value an payback period methods if the period of time to obtain a return on capital set by th management is $4$ years.