Question

Nation’s Capital Fitness, Inc., operates a chain of fitness centers in the Washington, D.C., area. The firm’s controller is accumulating data to be used in preparing its annual profit plan for the coming year. The cost behavior pattern of the firm’s equipment maintenance costs must be determined. The accounting staff has suggested the use of the high-low method to develop an equation, in the form of  Y = a + bX, for maintenance costs. Data regarding the maintenance hours and costs for last year are as follows:

Month	Hours of Maintenance Service					Maintenance Costs
January			560				$	5,374
February			480					4,190
March			250					2,770
April			500					4,260
May			360					2,990
June			440					4,140
July			350					3,070
August			420					3,550
September			460					3,950
October			360					3,280
November			380					3,260
December			350					3,090
Total			4,910				$	43,924
Average			409	*			$	3,660	*

*Rounded

1. Using the high-low method of cost estimation, estimate the behavior of the maintenance costs incurred by Nation’s Capital Fitness, Inc. Express the cost behavior pattern in equation form.

2.Using your answer to requirement 1, what is the variable component of the maintenance cost?

3. Compute the predicted maintenance cost at 640 hours of activity.

4-a. Compute the variable cost per hour and the fixed cost per hour at 650 hours of activity.

4-b. Why is the fixed cost per hour possibly misleading?

• Because it will not change as the number of hours changes.

• Because it will change as the number of hours changes.

Answer 1

• Working

	Month	Units	Cost
High Level	Jan	560	$                     5,374.00
Low Level	Mar	250	$                     2,770.00
Difference		310	$                     2,604.00
A	Difference in Cost		$                     2,604.00
B	Difference in units		310
C = A/B	Variable cost per unit		$                           8.400
Working		High Level	Low Level
A	Total Cost	$                   5,374.00	$                     2,770.00
B	Total Units	560	250
C	Variable cost per unit	$                           8.40	$                             8.40
D = B x C	Total Variable cost	$                   4,704.00	$                     2,100.00
E = A - D	Total Fixed Cost	$                       670.00	$                         670.00

• Requirement 1

Y = a + bX
Y = $ 670 + ($8.40) X

• Requirement 2
  Variable component of maintenance cost = $ 8.40 per hour
• [3]
  Predicted cost = $ 670 + (640 hours x $ 8.40)
  = 670 + 5376
  = $ 6046
• [4a]
  Variable cost per hour = $ 8.40
  Fixed Cost per hour = $ 670 / 650 hours = $ 1.03
• [4b]
  Because it will change as the number of hours changes.