Darren Mack owns the \"Gas n\' Go\" convenience store and gas station. After hea
ID: 355229 • Letter: D
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 $85,000 to install, but will increase customer traffic in the store by 10,000 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 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. Projected Convenience Store Sales Per Customer $6 $6.50 $8 S11 S12 Projected Profit Margin 15% 25% 25% 30% 35% Year 4 a. What is the NPV of the next five years of cash flows if Darren had five new pumps installed? NPV-S| -(Enter your response rounded to two decimal places.)Explanation / Answer
If 5 new pumps are installed . total investment at year ZERO = $85,000 x 5 = $425,000
Total increase in customers by installing 5 new pumps = 10000/ pump x 5 pumps = 50,000 customers
Accordingly ,
Projected profit per year = Sales/ customer x 50,000 customers x Projected profit margin ( %)
Thus projected profit every year as per above formula as follows :
Year
Projected profit ( $)
1
45,000
2
65,000
3
100,000
4
165,000
5
210,000
Discount rate = 8 percent
Therefore, Discounting factor for year n = ( 1 + 8/100)^n = 1.08^n
Hence, Net present value , $
= - 425,000 + 45,000/1.08 + 65.000/(1.08)^2 + 100,000 / ( 1.08)^3 + 165,000 / ( 1.08)^4 + 210,000/ ( 1.08)^5
= - 425,000 + 41666.66 + 55727.02 + 79383.22 + 121279.92 + 142922.47
= - 425,000 + 440979.29
= $15979.29
NPV = $15979.29
Year
Projected profit ( $)
1
45,000
2
65,000
3
100,000
4
165,000
5
210,000
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