A company is analyzing a proposed $3$ year project using standard sensitivity analysis. The company expects to sell $15,000$ units, $5$ percent. The expected variable cost per unit is $$8$ and the expected fixed costs are $$40,000.$The fixed and variable cost estimate are considered accurate within a $7$ percent range. The sales price is estimated at $$15$ a unit, $6$ percent. The project requires an initial investment of $$120,000$ for equipment that will be depreciated using straight line method to zero over the project's life. The equipment can be sold for $$30,000$ at the end of the project. The project requires $$12,000$ in net working capital for the three years but will be fully recovered when the project closes. The discount rate is $16\mathrm{.}4$ percent and tax rate is $20$ percent. What is the net present value for the optimistic scenario?