Question

Required information [The following information applies to the questions displayed below.] 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 Rental Returns 2,400 2,500 2,700 2,900 3,600 April 4,900 May June July August September October November December Car Wash Costs $ 10,500 $ 12,900 $ 11,300 $ 13,500 $ 15,709 $ 22,300 $ 21,700 $ 20,900 $ 22,300 $ 19,600 $ 10,200 $ 12,500 5,500 5,400 4,700 3,800 2,100 2,600 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 returnſ

Answer 1

month	Rental Returns	Car Wah Cost	X2	xy
january	2,400	10,500	5,760,000	25,200,000
february	2,500	12,900	6,250,000	32,250,000
march	2,700	11,300	7,290,000	30,510,000
april	2,900	13,500	8,410,000	39,150,000
may	3,600	15,700	12,960,000	56,520,000
june	4,900	22,300	24,010,000	109,270,000
july	5,500	21,700	30,250,000	119,350,000
august	5,400	20,900	29,160,000	112,860,000
september	4,700	22,300	22,090,000	104,810,000
october	3,800	19,600	14,440,000	74,480,000
november	2,100	10,200	4,410,000	21,420,000
december	2,600	12,500	6,760,000	32,500,000
sum	43,100	193,400	171,790,000	758,320,000

As per least Square Regression Method

y = mx + b

as per costing terms
	y=total cost
	m=variable cost per unit
	b=fixed cost per period

m =	N Σ(xy) − Σx Σy
	N Σ(x2) − (Σx)2

where Σx	43,100
Σy	193,400
Σx2	171,790,000
Σxy	758,320,000

m =

3.74

b = (Σy − m Σx)/N

b = (193400-(3.74*43100))/12

=2683.83

total fixed cost

=2683.83*12

32205.96

note:since y = mx + b stands for every m and b, for costing fixed cost can be calculated either by ignoring N from equation or multiplying with N after calculation

Total variable cost	=43100*3.74	161194
total fixed cost	=2683.83*12	32205.96