To calculate the base-case cash flow and NPV, we need to determine the annual cash flows and discount them to present value using the required return of 11 percent. Here are the calculations:
Annual sales revenue:
90,000 units/year * $37.95/unit = $3,415,500
Annual variable costs:
90,000 units/year * $23.20/unit = $2,088,000
Annual fixed costs: $815,000
Annual cash flow:
Cash flow = Sales revenue - Variable costs - Fixed costs
Cash flow = $3,415,500 - $2,088,000 - $815,000
Cash flow = $512,500 per year
Now, let's calculate the NPV:
NPV = (-Initial Cost) + (Cash Flow Year 1 / (1 + Required Return)^1) + (Cash Flow Year 2 / (1 + Required Return)^2) + ... + (Cash Flow Year 6 / (1 + Required Return)^6)
NPV = (-$1,680,000) + ($512,500 / (1 + 0.11)^1) + ($512,500 / (1 + 0.11)^2) + ... + ($512,500 / (1 + 0.11)^6)
Solving this equation will give us the NPV.
Now, let's move on to the sensitivity analysis questions:
1. Sensitivity of NPV to changes in the sales figure:
To determine the sensitivity of NPV to changes in the sales figure, we need to calculate the change in NPV when there is a 1-unit change in sales. We can calculate this as follows:
Change in NPV per unit change in sales = (New NPV - Base NPV) / (New Sales - Base Sales)
However, since the question asks for the sensitivity of NPV to changes in the sales figure, we need to calculate the sensitivity instead of a specific change. The sensitivity is the derivative of NPV with respect to sales. In this case, since sales are projected at 90,000 units per year, the sensitivity of NPV to changes in the sales figure is the same as the NPV per unit of sales:
Sensitivity of NPV to changes in the sales figure = NPV per unit of sales
We would need the NPV calculation to determine the sensitivity.
2. Change in NPV with a 500-unit decrease in projected sales:
To calculate the change in NPV with a 500-unit decrease in projected sales, we need to calculate the new NPV and compare it to the base NPV. The change in NPV would be:
Change in NPV = New NPV - Base NPV
To determine the new NPV, we need to recalculate the annual cash flows and then calculate the new NPV using the same formula as before.
3. Sensitivity of OCF to changes in the variable cost figure:
To determine the sensitivity of Operating Cash Flow (OCF) to changes in the variable cost figure, we need to calculate the change in OCF when there is a $1 change in variable costs. We can calculate this as follows:
Change in OCF per $1 change in variable costs = (New OCF - Base OCF) / (New Variable costs - Base Variable costs)
However, since the question asks for the sensitivity of OCF to changes in the variable cost figure, we need to calculate the sensitivity instead of a specific change. The sensitivity is the derivative of OCF with respect to variable costs. In this case, the sensitivity of OCF to changes in the variable cost figure is the same as the OCF per $1 change in variable costs:
Sensitivity of OCF to changes