Your company has developed a new type of kitchen blender. The development has cost $$780,000.$ To produce the blender, a new machine is required that will cost $$1,600,000$ to buy and install. This amount is to be linearly depreciated to zero over the life of the project and there is no salvage value. You expect to be able to sell the new blenders over a $5-$year period.

The selling price per unit is expected to be $$80,$ variable costs are $$55$ per unit and fixed costs are $$400,000$ per year. You've collected the following estimates for unit sales and their respective probabilities:

Base case Pessimistic Optimistic

Unit sales per year $($Q$)50,00025,00070,000$

Probability $0\mathrm{.}40\mathrm{.}10\mathrm{.}5$

The required return is $12\%$ and the tax rate is $34\%.$

What is the NPV in the base case?

What is the NPV in the pessimistic case?

What is the NPV in the optimistic case?

What is the expected NPV$?$