The Acme Battery Manufacturing Company has a rapidly growing product line that requires two work centers, X and Y for manufacture. Work Center X has a current capacity of $30,000$ units per year, and Work Center Y is capable of $50,000$ units per year, totaling capacity of $80,000$ units per year on the product line. This year $($year $0),$ sales of the product line are expected to reach $80,000$ units. Growth is projected at an additional $20,000$ units each year through year $3.$ Pre$-$tax profits are expected to be $$10$ per unit throughout the $3-$year planning period. Two alternatives are being considered:

$1)$ Expand both Work Centers X and Y at the end of year $0$ to a capacity of $60,000$ units per year each, at a total cost for both Work Centers of $$500,000$;

$2)$ Expand Work Center X at the end of year $0$ to $50,000$ units per year, matching Work Center Y$,$ at a cost of $$300,000,$ then expanding both Work Centers to $70,000$ units per year each at the end of year $2,$ at an additional cost at that time of $$350,000.$

The Company will not consider projects that don't show a $3$rd year positive net present value using a discount rate of $10\%.$

What is the net present value $($NPV$)$ of the pre$-$tax cash flow for alternative #$1$ compared to the base case of doing nothing for the next three years?

What is the net present value $($NPV$)$ of the pre$-$tax cash flow for alternative #$2$ compared to the base case of doing nothing for the next three years?

What action, if any, should the Acme Company take?

Details Please$-$ how do you calculate NPV$?$