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Darren Mack owns the? "Gas n'? Go" convenience store and gas station
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.?)
Expert Solution
| 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 | ||||||||
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