Delta plans to buy a new machine. The cost of the machine, payable immediately, is P$800,000$ and the machine has an expected life of five years. Additional investment in working capital of P$90,000$ will be required at the start of the first year of 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 P$16$ per unit and will incur variable costs of P$11$ per unit. Incremental fixed costs arising from the operation of the machine will be P$160,000$ per year.

Delta 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. Capital allowances and 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. $(8)$

$($b$)$ Calculate the internal rate of return of investing in the new machine and advise whether the investment is financially acceptable. $(7)$

$($c$)($i$)$ Explain briefly the meaning of the term $$sensitivity analysis$$ in the context of investment appraisal; $(5)$

$($ii$)$ Calculate the sensitivity of the investment in the new machine to a change in selling price and to a change in discount rate, and comment on your findings.