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

Under the least-squares regression method, the cost function formula is:
y = a + bx
where:
y = total cost;
a = total fixed costs;
b = variable cost per level of activity;
x = level of activity

Whereas, the normal formula for variable cost (i.e b) is:

και η Στy – (Στ) (Σ9) ηΣ2 – (Στ2)


And the normal formula for Fixed cost (i.e a) is:

α-Σ4 - 0Σ.

Therefore, the computation is as under:

Month	Rental Returns (i.e units = x)	Car Wash Costs (i.e total cosy = y)	xy	x2
January	2,400	11,100	26640000	5760000
February	2,500	13,200	33000000	6250000
March	2,700	11,900	32130000	7290000
April	3,000	14,400	43200000	9000000
May	3,600	16,300	58680000	12960000
June	5,100	23,500	119850000	26010000
July	5,500	22,300	122650000	30250000
August	5,500	22,400	123200000	30250000
September	4,700	22,900	107630000	22090000
October	4,000	21,400	85600000	16000000
November	2,200	10,800	23760000	4840000
December	2,800	14,600	40880000	7840000
n = 12	44000	204800	817220000	178540000

Therefore, computation of variable cost i.e b =

και η Στy – (Στ) (Σ9) ηΣ2 – (Στ2)

b= 12(817220000) - (44000) (2048000) 12(178540000) – 440002

b = 9806640000 - 9011200000 2142480000 – 1936000000

b= 795440000 206480000

b = 3,85

Similarly, computation of Fixed cost i.e a =

α-Σ4 - 0Σ.

204800 - 3.85 (44000) a = 12

204800 – 169504.84 a =

35295.16 a = 12

a = 2941