Question

Kim Epson operates a full-service car wash, which operates from 8 A.M. to 8 P.M. seven days a week. The car wash has two stations: an automatic washing and drying station that can handle 30 cars per hour and an interior cleaning station that can handle 190 cars per day. Based on a recent year-end review of operations, Kim estimates that future demand for the interior cleaning station for the seven days of the week, expressed in the average number of cars per day, would be as follows: Di Tues. Thurs. Day Cars Mon. 160 Wed. 150 Fri. 280 Sat. 260 Sun. 280 180 140 By installing additional equipment (at a cost of $70,000) Kim can increase the capacity of the interior cleaning to 300 cars per day. Each car wash generates a pretax contribution of $5.00. Should Kim install the additional equipment if she expects a pretax payback period of three years or less? Kim should install the additional equipment because the payback period is 0.18 years. (Enter your response rounded to two decimal places.)

Answer 1

Answer Kim should install the additional equipment because the payback period is 0.18 years

Explanation: total operational hours is 12 hours

automatic washing station capacity= 30 cars/hour= 30*12 cars/ day= 360 cars per day

Interior cleaning station capacity= 190 cars per day

Average demand of day= sum of demands of a week/7 =(160+180+150+140+280+260+280)/7 = 207.14 per day

The capacity if interior cleaning will be 300 per day after buying additional equipment, so Kim will be able to serve 300 cars per day. But average demand will be restricted to 207.14 cars per day.

As each car profits $5, the profit through a day is 207.14*5= $1035.7

Let x be no. of days required to break even $70,000 machine

X*1035.7= 70,000

X= 67.58 days

67.58 days is 0.18 years