Warden Co 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 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 $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. Warden Co 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. (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) (i) Explain briefly the meaning of the term ‘sensitivity analysis’ in the context of investment appraisal; (1 mark) (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. (6 marks) (d) Discuss the nature and causes of the problem of capital rationing in the context of investment appraisal, and explain how this problem can be overcome in reaching the optimal investment decision for a company. (7 marks)