7. A computer manufacturer is conducting a project analysis on a new laptop model, and draws up the following assumptions: The project horizon is 3 years and will require an immediate investment of $40 million. Revenue is earned and expenses are paid at the end of each year. A total of 40,000 units will be sold in the first year. In each subsequent year, the number of units sold is expected to be only 60% of that in the previous year. The computers are sold at $2,400 per unit. Fixed costs amount to $8 million per year. Variable costs are given by $6,000x0.85, where x is the number of units sold. Machinery of total value $35 million is depreciated according to the following schedule: Year 1 2 3 Depreciation ($ million) 20 10 5 The tax rate on profits is 30%. For negative before-tax profits, it is assumed that a tax rebate is applicable. (a) Show that the net cash flow at the end of the first year is $33 million to the nearest $1 million. To ensure sufficient accuracy in subsequent calculations, you should calculate this value to the nearest $1,000. [4 marks] (b) Determine whether the manufacturer should proceed with the project using the net present value (NPV) criterion, at a 15% cost of capital per annum. [5 marks] (c) Carry out a sensitivity analysis on the NPV by changing the following assump- tions, one at a time, to the given values: Unit price: $2,100 (pessimistic); $2,700 (optimistic) Fixed costs: $9.5 million (pessimistic); $6.5 million (optimistic) Based on this analysis, explain which assumption is more critical. [7 marks] [Total: 16 marks]