Question

Darren Mack owns the​ "Gas n'​ 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'​ Go' 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 ​$125,000 to​ install, but will increase customer traffic in the store by 12,000 customers per year.​ Also, because the​ "Gas n'​ 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 7 percent. The projected convenience store sales per customer and the projected profit margin for the next five years are given in the table below.

                                                                         

Year	Projected Convenience Store Sales Per Customer	Projected Profit Margin
1	​$6	20​%
2	​$7.50	25​%
3	​$9	30​%
4	​$10	35​%
5	​$11	40​%

a. What is the NPV of the next five years of cash flows if Darren had

four new pumps​ installed?

NPV=​$

​(Enter your response rounded to two decimal places.​)

Answer 1

Net present value is calculated as present value of cash inflow less present value of cash outflow
There are four pump installed
No of customers per year	12000*4
No of customers per year	48000
Cash outflow	125000*4
Cash outflow	500000
Calculate net present value of pump installed as shown below:
Year	Sales revenue		Projected profit		Discount factor @ 7%		Present value
0					1	1/(1.07^0)	-$500,000.00
1	$288,000	6*48000	$57,600	288000*20%	0.934579	1/(1.07^1)	$53,831.78
2	$360,000	7.5*48000	$90,000	360000*25%	0.873439	1/(1.07^2)	$78,609.49
3	$432,000	9*48000	$129,600	432000*30%	0.816298	1/(1.07^3)	$105,792.20
4	$480,000	10*48000	$168,000	480000*35%	0.762895	1/(1.07^4)	$128,166.40
5	$528,000	11*48000	$211,200	528000*40%	0.712986	1/(1.07^5)	$150,582.68
Net present value							$16,982.54
Thus, NPV of installing five pumps is $16,982.54