Darren Mack owns the$$ "Gas n$\text{'}$ Go$"$ convenience store and gas station. After hearing a marketing$$ lecture, he realizes that it might be possible to draw more customers to his$$ high$-$margin convenience store by selling his gasoline at a lower price.$$ However, the$$ "Gas n$\text{'}$ Go$\text{'}$ is unable to qualify for volume discounts on its gasoline$$ purchases, and therefore cannot sell gasoline for profit if the price is lowered.

Each new pump will cost $$$$155$ comma $000$ to$$ install, but will increase customer traffic in the store by $14$ comma $000$ customers per year.$$ Also, because the$$ "Gas n$\text{'}$ Go$"$ would be selling its gasoline at no$$ profit, Darren plans on increasing the profit margin on convenience store items incrementally over the next five years. Assume a discount rate of $8$ percent. The projected convenience store sales per customer and the projected profit margin for the next five years are given in the table below.

$$ LOADING...

Year

Projected Convenience Store Sales Per Customer

Projected Profit

Margin

$1$

$$$$6$

$20\%$

$2$

$$$$7\mathrm{.}50$

$25\%$

$3$

$$$$9$

$30\%$

$4$

$$$$11$

$35\%$

$5$

$$$$13$

$40\%$

Part $2$

a$.$ What is the NPV of the next five years of cash flows if Darren had four new pumps$$ installed?

NPVequals$$$

$$

enter your response here. $($Enter your response rounded to two decimal places.$)$