Question

Nova Company’s total overhead cost at various levels of activity are presented below:

Month	Machine- Hours			Total Overhead Cost
April		47,000		$	192,050
May		37,000		$	168,550
June		57,000		$	215,550
July		67,000		$	239,050

Assume that the total overhead cost above consists of utilities, supervisory salaries, and maintenance. The breakdown of these costs at the 37,000 machine-hour level of activity is:

Utilities (variable)	$	48,100
Supervisory salaries (fixed)		66,000
Maintenance (mixed)		54,450
Total overhead cost	$	168,550

Nova Company’s management wants to break down the maintenance cost into its variable and fixed cost elements.

Required:

1. Estimate how much of the $239,050 of overhead cost in July was maintenance cost. (Hint: to do this, it may be helpful to first determine how much of the $239,050 consisted of utilities and supervisory salaries. Think about the behavior of variable and fixed costs.)

2. Using the high-low method, estimate a cost formula for maintenance in the form Y = a + bX.

3. Express the company’s total overhead cost in the form Y = a + bX.

4. What total overhead cost would you expect to be incurred at an activity level of 42,000 machine-hours?

Answer 1

Utilities cost per machine hour = Total utilities cost at 37000 machine hour level of activity / 37000 = 48100 / 37000

1.30

Required 1 :
	July
Total overhead cost	239050
(-) Utilities cost ( 67000 * 1.30 )	87100
(-) Supervisory salaries	66000
Maintenance cost	85950

Required 2 :
	Machine hours	Maintenance cost
High level of activity (July)	67000	85950
(-) Low level of activity (May)	37000	54450
Difference	30000	31500

Variable maintenance cost per machine hour = Difference in maintenance cost / Difference in Machine hours = 31500 / 30000	1.05
Now let us calculate the fixed maintenance cost using the information of high level of activity
Total maintenance cost = ( Machine hours * Variable maintenance cost per machine hours ) + Fixed maintenance cost
85950 = ( 67000 * 1.05 ) + Fixed maintenance cost
85950 = 70350 + Fixed maintenance cost
Fixed maintenance cost = 85950 - 70350	15600

Cost formula for maintenance :
Y = 15600 + 1.05 X

Required 3 :
Cost formula for total overhead :
Y = ( 15600 + 66000 ) + ( 1.05 + 1.30 ) X
Y = 81600 + 2.35X

Required 4 :
Let us calculate the Total overhead cost at an an activity level of 42000 machine hours using the cost formula derived in requirement 3 :
Y = 81600 + 2.35 * ( 42000 )	180300