Prince Company\'s total overhead costs at various levels of activity are present

Question

Prince Company's total overhead costs at various levels of activity are presented below Total Machine Overhead Month Hours Cost September 119,700 $535,452 October November 161.400 $667,224 December 166,600 $683,656 96,200 $461,192 Assume that the overhead cost above consists of utilities, supervisory salaries, depreciation, and maintenance. The breakdown of these costs at the 96,200-machine-hour level of activity in October is as follows $168,350 Utilities (variable) Supervisory salaries and depreciation (fixed) Maintenance (mixed) 126,000 166,842 Total overhead cost $461,192 The company wants to break down the maintenance cost into its variable and fixed cost elements. Required 1. Estimate how much of the $683,656 of overhead cost in December was maintenance cost. (Hint: To do this, first determine how much of the $683,656 consisted of utilities and supervisory salaries. Think about the behaviour of variable and fixed costs within the relevant range.) (Do not round intermediate calculations.) Level of Activity 96,200 MH 166,600 MH Maintenance cost Using the high-low method, estimate a cost formula for maintenance. (Round variable cost to 2 decimal places and fixed cost to the nearest dollar amount.) 2.

Explanation / Answer

Solution:

1. Maintenance cost at the 96,200 machine-hour level of activity can be isolated:
Maintenance cost = $461,192 – 168,350 - 126,000 = 166,842 (96,200 MH)
Maintenance cost = $683,656 – 291,550 - 126,000 = $266,106 (166,600 MH)

(168,350/96,200MHs = $1.75 per MH)
(166,660 x 1.75 = $291,550)

2.

Using the high–low method, estimate a cost formula for maintenance.
High activity level - Low activity level = Maintenance Cost
$266,106 – 166,842 = 99,624

High activity level - Low activity level = Machine Hours (change)
166,600 – 96,200 = 70,400
Variable cost per unit of activity :
Change in cost / Change in activity = 99,624 / 70,400 = 1.41 per MH
Total fixed cost:
166,842 – 135,642 = 31,200
(96,200 x $1.41 = 113,424)
So, the cost formula is
Y = $31,200 + $1.41X

3. Express the company’s total overhead cost in the form Y = a + bX.
Maintenance cost + Utilities cost = Variable Rate per Machine-Hour
1.41 + 1.75 = 3.16
Maintenance cost + Supervisory salaries cost
31,200 + 166,842 = 198,042
The cost formula would be Y = $198,042 + $3.16X

4. Fixed costs + Variable costs ($3.16MH x 106,200 = 335,592) = Total overhead costs
198,042 + 335,592 = 533,634

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