BMT has developed a new product. It can go into production for an initial investment of $$4,000,000.$ The equipment will be depreciated using straight$-$line depreciation over $5$ years to a value of zero. The firm believes that net working capital at each date will equal $30$ percent of next year$$s forecast sales. The firm estimates that variable costs are equal to $60\%$ of sales and fixed costs are $$450,000$ per year. Sales forecasts in dollars are below. The project will come to an end after $5$ years, when the product becomes obsolete. The firm$$s tax rate is $30$ percent, and the discount rate is $10$ percent. Calculate the NPV$.$

Year $01234\_\_\_\_\_5$

Sales forecast $($in $$)$: $04,100,0004,500,0005,000,0005,400,0004,800,000$

In problem $3,$ perform sensitivity analysis on the following assumptions and find the revised NPV

$($a$)$ variable costs are equal to $65\%$ of sales

$($b$)$ the discount rate is $12\%$