The following analysis is derived from the research and development $($R&D$)$ section of ZAR Sdn$.$ Bhd$.$

ZAR Sd$.$ Bhd$.$ is considering the purchase of a packaging machine. The purchase price of the machine is RM$80,000,$ plus an additional RM$1,500$ to ship and RM$25,000$ to install. The new machine will have a $5-$year useful life and will be depreciated using the $3-$year MACRS class $($Depreciation in Year $133\%$; Year $245\%$; Year $315\%$; and, Year $4-7\%$ on costs$).$

The machine is expected to generate new sales of RM$40,000$ per year and is expected to save RM$15,000$ per year on labour expenses over the next $5$ years. However, the production costs will also go up by RM$3,000$ every year. Upon buying the machine, it requires inventories to increase by RM$20,000$ and accounts payable increase by RM$10,000.$ The change in Net Operating Working Capital is expected to be fully recovered at year $5.$ The machine is expected to have a disposal value of RM$30,000.$ ZAR Sdn$.$ Bhd$.$ uses a $12\%$ discount rate for capital budgeting purposes and the firm's income tax rate is $40\%.$

Required:

a$.$ Should ZAR proceed with the new project?

b$.$ Using the Payback Period Method and Discounted Payback Period Method, calculate the number of years needed to recover the initial cash outlay.

c$.$ Explain relevant and irrelevant cash flow by giving $2$ examples respectively.