Wonder Works Pte Ltd $($WW$)$ produces ceramic hair curlers to sell to department stores. The production equipment costs WW $$70,000$ four years ago. Currently, the net book value stands at $$45,000.$ An improved version of the equipment is available now 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$

Required:

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

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

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 $22\%.$