Part 1.1. Suppose a firm is considering the following project, where all of the dollar figures are in thousands of dollars. In year 0, the project requires $11,350 investment in plant and equipment, is depreciated using the straight line depreciation method over seven years, and there is a salvage value of $1,400 in year 7. The project is forecast to generate sales of 2,000 units in year 1, rising by 10% every year afterwards, and dropping to zero in year 8. The inflation rate is forecast to be 2.0%. The cost of capital for the project of same risk is forecast to be 11.0%. The tax rate is forecast to be a constant 35.0%.

Sales price per unit is forecast to be $9.70 in year 1 and then grow with inflation. Variable cost per unit is forecast to be $7.40 in year 1 and then grow with inflation. Cash fixed costs are forecast to be $5,280 in year 1 and then grow with inflation. Suppose that the project will require working capital in the amount of $0.87 in year 0 for every unit of next year's forecasted sales and this amount will grow with inflation going forward. What is the project NPV?

Solution Strategy. Forecast key assumptions, discounting, sales revenue per unit, variable costs per unit, and fixed costs over the seven year horizon. Then, forecast the project income and expense items. Calculate the net cash flows. Discount each cash flow back to the present and sum to get the NPV.

Modeling Issue. The inflation rate is forecast separately and explicitly enters into the calculation of: (1) the discount rate (= cost of capital) and (2) price or cost /unit items. This guarantees that we are consistent in the way we are treating the inflation component of cash flows in the numerator of the NPV calculation and the inflation component of the discount rate in the denominator of the NPV calculation. This avoids a common error in practice that people often treat the cash flows and discount rates as if they were unrelated to each other and thus they are inconsistent in way that they implicitly treat the inflation component of each.

Part 1.2. Consider the same project as above. Assume that the product life-cycle of seven years is viewed as a safe bet, but that the scale of demand for the product is highly uncertain. Analyze the sensitivity of the project NPV to the units sales scale factor and to the cost of capital.

Modeling Issue. Assuming the sales unit go up or down by 5%, 10%, 15% and 20% and the cost of capital ranges from +/-2 percentage points and check the ranges of NPV value.