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Duo Co needs to increase production capacity to meet increasing demand for an existing product, 'Quago', which is used in food processing. A new machine with a useful life of four years and a maximum output of 600,000kg of Quago per year, could be bought for $800,000, payable immediately. The scrap value of the machine after four years would be $30,000. Forecast demand and production of Quago over the next four years is:as follows: YearDemand(kg)11.4million21.5million31.6million41.7million Existing production capacity for Quago is limited to one million kilograms per year and the new machine would only be used for demand additional to this. The current selling price of Quago is $8.00 per kilogram and the variable cost of materials is $5.00 per kilogram. Other variable costs of production are $1.90 per kilogram. Fixed costs of production associated with the new machine would be $240,000 in the first year of production, increasing by $20,000 per year in each subsequent year of operation. Duo Co pays tax one year in arrears at an annual rate of 30% and can claim capital allowances (tax-allowable depreciation) on a 25% reducing balance basis. A balancing allowance is claimed in the final year of operation. Duo Co uses its after-tax weighted average cost of capital when appraising investment projects. It has a cost of equity of 11% and a before-tax cost of debt of 8.6%. The long-term finance of the company, on a market-value basis, consists of 80% equity and 20% debt. Required: (a) Calculate the net present value of buying the new machine and advise on the acceptability of the proposed purchase (work to the nearest $1,000 ). (13 marks) (b) Calculate the internal rate of return of buying the new machine and advise on the acceptability of the proposed purchase (work to the nearest $1,000 ). (4 marks) (c) Explain the difference between risk and uncertainty in the context of investment appraisal, and describe how sensitivity analysis and probability analysis can be used to incorporate risk into the investment appraisal process. (8 marks)