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 its 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	Rental Returns		Car Wash Costs
January	2,500		$	11,500
February	2,500		$	13,400
March	2,800		$	12,300
April	3,100		$	15,000
May	3,700		$	16,700
June	5,100		$	24,300
July	5,600		$	22,700
August	5,600		$	23,400
September	4,800		$	23,300
October	4,100		$	22,600
November	2,200		$	11,200
December	3,000		$	16,000

Exercise 5A-2 Part 2 (Algo)

2. Using least-squares regression, estimate the variable cost per rental return and the monthly fixed cost incurred to wash cars. (Round 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

Month	Rental Returns (x)	Car Wash costs (y)	xy	x^2
January	2,500	11,500	28,750,000	6,250,000
February	2,500	13,400	33,500,000	6,250,000
March	2,800	12,300	34,440,000	7,840,000
April	3,100	15,000	46,500,000	9,610,000
May	3,700	16,700	61,790,000	13,690,000
June	5,100	24,300	123,930,000	26,010,000
July	5,600	22,700	127,120,000	31,360,000
August	5,600	23,400	131,040,000	31,360,000
September	4,800	23,300	111,840,000	23,040,000
October	4,100	22,600	92,660,000	16,810,000
November	2,200	11,200	24,640,000	4,840,000
December	3,000	16,000	48,000,000	9,000,000
Total ( )	45,000	212,400	864,210,000	186,060,000

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

=[ 12 x 864,210,000 - ( 45,000 x 212,400 ) ] / [ 12 x 186,060,000 - (45,000)^2]

=10370520000 / 9558000000

=1.09 per rental return

Fixed Cost = [ y - (unit cost * x)] / n

=[ 212,400 - (1.09 * 45,000)] / 12

=163,350 / 12

=13,613 per month