Parker Incorporated plans to buy a new machine. The cost of the machine, payable immediately, is $$800,000$ and the machine has an expected life of five years. Additional investment in working capital of $$90,000$ will be required at the start of the operation. At the end of five years, the machine will be sold for scrap, with the scrap value expected to be $5\%$ of the initial purchase cost of the machine. The machine will not be replaced.

Production and sales from the new machine are expected to be $100,000$ units per year. Each unit can be sold for $$16$ per unit and will incur variable costs of $$11$ per unit. Incremental fixed costs arising from the operation of the machine will be $$160,000$ per year.

Parker Incorporated has an after$-$tax cost of capital of $11\%,$ which it uses as a discount rate in investment appraisal. The company pays profit tax one year in arrears at an annual rate of $30\%$ per year. Tax$-$allowable depreciation will be claimed on a straightline basis. Inflation should be ignored.

Required:

a$.$ Calculate the net present value of investing in the new machine and advise whether the investment is financially acceptable.

$(7$ marks$)$

b$.$ Calculate the internal rate of return of investing in the new machine and advise whether the investment is financially acceptable.

$(4$ marks$)$

c$.$ Calculate the discounted pay$-$back period for the new machine and advise whether the investment is financially acceptable. Assume management has set a cut off period of three $(3)$ years. $(4$ marks$)$

d$.$ Explain briefly the meaning of the term 'sensitivity analysis' in the context of investment appraisal.

$(2$ marks$)$

e$.$ Briefly discuss three $(3)$ disadvantages of the pay$-$back period investment appraisal approach.

$(3$ marks$)$