Question

Anna Wright is considering opening a Kwik Oil Change Center. She estimates the following monthly costs: rent $6,000; depreciation on equipment $7,000; and wages $16,400. Additionally, each oil change will include five quarts of oil at $1.80 per quart and one oil filter that will cost $3.00. She must also pay The Kwik Corporation a franchise fee of $1.40 per oil change. In addition, she has collected the following data from the company regarding utility costs. The total utility cost is based on the number of monthly oil changes.

Month	Number of Oil Changes	Utility Cost
April	4,000	$6,000
May	6,000	$7,300
June	9,000	$9,600
July	12,000	$12,600
August	19,000	$15,000

What is the variable cost per oil change?

Answer 1

Answer- The variable cost per oil change is =$14.00.

Explanation- High-Low Method:-

Variable Cost per Unit

Variable cost per unit (b) is calculated using the following formula:

Variable cost per unit = (Y2-Y1)/(X2-X1)

Where,
y2 is the total cost at highest level of activity;
y1 is the total cost at lowest level of activity;
x2 are the number of units/miles/ labor ,machine hours etc. at highest level of activity; and
x1 are the number of units/miles/ labor, machine hours etc. at lowest level of activity

The variable cost per unit is equal to the slope of the cost volume line (i.e. change in total cost ÷ change in number of machine hours).

Total Fixed Cost

Total fixed cost (a) is calculated by subtracting total variable cost from total cost, thus:

Total Fixed Cost = (y2 – b)*x2 = (y1 – b*x1)

We have,
at highest activity: x2 = 19000 oil changes; y2 = $15000
at lowest activity: x1 =   4000 oil changes; y1 = $6000

Utility Cost per oil change = ($15000-$6000) /(19000 oil changes−4000 oil changes)  

= $9000/15000 oil changes

= $0.60 per oil change

Total variable cost per oil change= Oil+ Filter+ Franchise fee+ Utility costs (variable)

  = ($1.80 per quart*5 quart)+$3.00+$1.40+$0.60

= $14