A company is analyzing a proposed $3-$year project using standard sensitivity analysis. The company expects to sell $15,000$ units, plus or minus $5$ percent. The expected variable cost per unit is $$8$ and the expected fixed costs are $$40,000.$ The fixed and variable cost estimates are considered accurate within a plus or minus $7$ percent range. The sales price is estimated at $$15$ a unit, plus or minus $6$ percent. The project requires an initial investment of $$120,000$ for equipment that will be depreciated using the 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 $12\mathrm{.}8$ percent and tax rate is $20$ percent. What is the net present value for the optimistic scenario? Choose from the following options, only one is correct:

a$.$ $$92,058\mathrm{.}28$

b$.$ $$94,075\mathrm{.}71$

c$.$ $$96,093\mathrm{.}14$

d$.$ $$98,110\mathrm{.}57$

e$.$ $$100,128\mathrm{.}00$