A firm with required rate of return $10\%$ and tax rate $20\%$ evaluates the following $3-$year investment plan: Initial investment is $$30,000$ depreciated linearly to zero, project is expected to sell

$1,000$ additional units for $$30$ each. The variable cost is $$10/$unit and the project has also a fixed

cost of $$5,000/$year$.$

$1.$ Estimate the NPV of the project.

$2.$ Do a sensitivity analysis on price, estimating the NPV for $$25$ and $$35.$

$3.$ Do a sensitivity analysis on initial investment, estimating the NPV if the initial investment is

$$24,000$ or $$36,000$