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 Rental Returns Car Wash Costs January 2,400 $ 11,100 February 2,500 $ 13,200 March 2,700 $ 11,900 April 3,000 $ 14,400 May 3,600 $ 16,300 June 5,100 $ 23,500 July 5,500 $ 22,300 August 5,500 $ 22,400 September 4,700 $ 22,900 October 4,000 $ 21,400 November 2,200 $ 10,800 December 2,800 $ 14,600 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. (Round Fixed cost to the nearest whole dollar amount and the Variable cost per unit to 2 decimal places.)

Answer 1

Answer :

Unit variable cost =		n * total of xy - (Total of x * total of y)
		n * total of x^2 -(Total of x)^2
Where
n = 12, Total of xy = 728840000, Total x * total y = 42600 * 187700
Total of x^2 = 167720000 , (Total of x)^2 = 42600 * 42600
Unit variable cost = ((12*728840000) - (42600 * 87700))/((12*167720000 - 1814760000)
=(8746080000 -7996020000) / (2012640000 - 1814760000)
= 750060000 / 197880000
= 3.79
Variable cost per rental return = $3.79
Fixed cost = (Total of y - unit cost * toal of x)/n
=( 187700 - 3.79*42600)/12
=	26246/12
=	$2187

Workings:

Month	Rental returns	Car wash costs
	x	y	xy	x^2
January	2300	10200	23460000	5290000
February	2500	12700	31750000	6250000
March	2700	11000	29700000	7290000
April	2900	13100	37990000	8410000
May	3600	15400	55440000	12960000
June	4900	21700	106330000	24010000
July	5400	21400	115560000	29160000
August	5300	20200	107060000	28090000
September	4600	22000	101200000	21160000
October	3800	18700	71060000	14440000
November	2100	9900	20790000	4410000
December	2500	11400	28500000	6250000
Total	42600	187700	728840000	167720000