Question

Bargain Rental Car offers rental cars in an off-airport location near a major tourist destination in California. Management would like to better understand the variable and fixed portions of it car washing costs. The company operates its own car wash facility in which each rental car that is returned is thoroughly cleaned before being released for rental to another customer. Management believes that the variable portion of its car washing costs relates to the number of rental returns. Accordingly, the following data have been compiled: Month January February March April MAY June July August September October November December Rental Returns Car Wash Costs 2,400 $ 10,800 2,500 $ 13,000 2,700 $ 11,600 3,000 $ 14,000 3,600 $ 16,000 5,000 $ 22,900 5,500 $ 22,000 5,400 $ 21,700 4,700 $ 22,600 3,900 $ 20,500 2,200 $ 10,500 2,700 $ 13,500 Exercise 5A-2 Part 2 2. Using least-squares regression, estimate the variable cost per rental return and the monthly fixed cost incurred to wash cars. (Roun Fixed cost to the nearest whole dollar amount and the Variable cost per unit to 2 decimal places.) Fixed cost per month Variable cost per rental return

Answer 1

Solution:

Month	Rental Returns	Car Wash costs
	x	y	xy	x^2
January	2400	10800	25920000	5760000
February	2500	13000	32500000	6250000
March	2700	11600	31320000	7290000
April	3000	14000	42000000	9000000
May	3600	16000	57600000	12960000
June	5000	22900	114500000	25000000
July	5500	22000	121000000	30250000
August	5400	21700	117180000	29160000
September	4700	22600	106220000	22090000
October	3900	20500	79950000	15210000
November	2200	10500	23100000	4840000
December	2700	13500	36450000	7290000
Total ($\sum$)	43600	199,100	787740000	175100000

Unit variable cost = [ n * $\sum$ xy - ($\sum$x * $\sum$ y) ] / [ n * $\sum$ x^2 - ($\sum$x)^2 ]

= [ 12 x 787740000 - ( 43600 x 199,100) ] / [ 12 x 175100000 - (43600)^2]

= 772120000 / 200240000

= 3.86

Variable cost per rental return = 3.86

Fixed Cost = ( $\sum$ y - unit cost * $\sum$ x) / n

= (199,100 - 3.86 x 43,600) / 12

= 30804 / 12

= 2567

Therefore fixed cost per month = $ 2,567