Question

Prospero Corporation’s total overhead costs at various levels of activity are presented below:

	Month	Machine-Hours	Total Overhead Costs
	August	8,000	$119,400
	September	12,000	$142,800
	October	16,000	$166,200
	November	4,000	$93,120

Assume that the total overhead costs above consist of utilities, supervisory salaries, and maintenance. The breakdown of these costs at the 4,000 machine-hour level of activity is:

	Utilities (variable)	$11,520
	Supervisory salaries (fixed)	15,600
	Maintenance (mixed)	66,000
	Total overhead costs	$93,120

Prospero Corporation’s management wants to break down the maintenance cost into its basic variable and fixed cost elements.

Required:

(1). Estimate how much of the $166,200 of overhead cost in October was maintenance cost. (Hint: to do this, it may be helpful to first determine how much of the $166,200 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.

(3). Express the company’s total overhead costs in the linear equation form Y = a + bX.

(4). What total overhead costs would you expect to be incurred at an operating activity level of 15,000 machine-hours?

Answer 1

Answer to Requirement 1:

If 4,000 machine hours are used:

Utilities per machine hour = Utilities / Number of machine hours
Utilities per machine hour = $11,520 / 4,000
Utilities per machine hour = $2.88

If 16,000 machine hours are used:

Utilities = Utilities per machine hour * Number of machine hours
Utilities = $2.88 * 16,000
Utilities = $46,080

Total overhead costs = Utilities + Supervisory salaries + Maintenance
$166,200 = $46,080 + $15,600 + Maintenance
Maintenance = $104,520

Answer to Requirement 2:

Variable maintenance per machine hour = (Maintenance for October - Maintenance for November) / (Machine hours for October - Machine hours for November)
Variable maintenance per machine hour = ($104,520 - $66,000) / (16,000 - 4,000)
Variable maintenance per machine hour = $3.21

Fixed maintenance = Maintenance for October - Variable maintenance per machine hour * Machine hours for October
Fixed maintenance = $104,520 - $3.21 * 16,000
Fixed maintenance = $53,160

Cost formula for maintenance = Fixed maintenance + Variable maintenance per machine hour * Number of machine hours
Cost formula for maintenance = $53,160 + $3.21 * Number of Machine hours

Answer to Requirement 3:

Variable overhead cost per machine hour = Utilities + Maintenance
Variable overhead cost per machine hour = $2.88 + $3.21
Variable overhead cost per machine hour = $6.09

Fixed overhead = Supervisory salary + Maintenance
Fixed overhead = $15,600 + $53,160
Fixed overhead = $68,760

Total overhead cost = Fixed overhead + Variable overhead cost per machine hour * Number of machine hours
Total overhead cost = $68,760 + $6.09 * Number of machine hours

Answer to Requirement 4:

Total overhead cost = $68,760 + $6.09 * Number of machine hours
Total overhead cost = $68,760 + $6.09 * 15,000
Total overhead cost = $160,110