A suggested project requires initial fixed assets of $$227,000,$ has a life of $5$ years, and has no salvage value. Assume depreciation is straight$-$line to zero over the life of the project. Sales are projected at $31,000$ units per year, the price per unit is $$47,$ variable cost per unit is $$23,$ and fixed costs are $$202,900$ per year. The tax rate is $21$ percent and the required return is $12$ percent. Suppose the projections for price, quantity, and cost estimates can vary by $\backslash$pm $5$ percent.

a$.$ Calculate the best$-$case, base$-$case, and worst$-$case NPVs$.$

b$.$ Perform sensitivity analyses on price, quantity and cost variables. Which variable has the highest forecasting risk?