Wonder Works Pte Ltd $($WW$)$ produces hair curlers. The equipment for this task cost WW $$70,000$ four years ago. The reduced book value now stands at $$45,000.$ An improved version of the machine is currently available for $$139,350.$ The new machine has a useful life of five years. The disposal value at that point in time is estimated to be $$20,000.$The new machine is expected to increase unit sales by $6,000$ curlers per annum. The estimated unit selling price is $$35$ for the first year.$$The following table provides the unit costs for the first year:

$$$Direct labour, $5$ hours at $$2$ per hour$10$

Direct materials$7$

Fixed costs including depreciation$11$

Total$28$

WW is short of production workers due to the COVID$-19$ pandemic in Singapore. It has decided to divert some labour from another project to the new project. These workers earn a contribution of $$2$ per direct labour hour in their original department. The fixed overhead cost would be $$2\mathrm{.}20$ per hour and this is expected to remain unchanged.The sales agreement for the curlers allows the selling price to rise at the rate of $10$ percent per year after the first year. The unit costs, except for fixed costs, is expected to increase at the same rate as the selling price.

Working capital requirements are expected to be $$15,000$ in the first and second years, increasing to $$18,000$ in the third year and is expected to remain at this level till the end of the project. All the amounts of working capital will be recovered at the time of project termination.$$WW enjoys a tax holiday for the next five years. The required return for projects of this risk class is $27$ percent per annum.

Required:

a$.$ Derive the yearly net cash flows for the project. $($using a tabel$)$

b$.$ Make a reasoned recommendation as to whether WW should proceed to purchase the new machine.$($NPV method$)$

c$.$ Conduct sensitivity analysis on the cost of capital to achieve a net present value of $$30,000.$ Utilize the IRR approach with the r trial values of $18\%$ and $22\%.$