Emperor$$s Clothes Fashions can invest $$6$ million in a new plant for producing invisible makeup. The plant has an expected life of $5$ years, and expected sales are $7$ million jars of makeup a year. Fixed costs are $$3\mathrm{.}1$ million a year, and variable costs are $$1\mathrm{.}20$ per jar. The product will be priced at $$2\mathrm{.}90$ per jar. The plant will be depreciated straight$-$line over $5$ years to a salvage value of zero. The opportunity cost of capital is $10\%,$ and the tax rate is $40\%.$

$1.$ What is project NPV under these base$-$case assumptions?

$2.$ What is NPV if variable costs turn out to be $$2\mathrm{.}00$ per jar?

$3.$ What is NPV if fixed costs turn out to be $$2\mathrm{.}8$ million per year?

$4.$ At what price per jar would the project's NPV equal zero?