Required informatio Problem 6-38 High-Low Method; Fitness Centers (LO 6-1, 6-2,

Question

Required informatio Problem 6-38 High-Low Method; Fitness Centers (LO 6-1, 6-2, 6-5) [The following information applies to the questions displayed below.] 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 Hours of Maintenance Maintenance Costs Month January February March April May une July August September October November December Total Service 530 470 290 480 320 440 340 420 450 390 380 340 4,594 4,190 2,770 4,320 3,060 4,200 3,040 3,530 3,960 3,220 3,260 3,080 4,850 $43,224 Average 404* $3,602* Rounded

Explanation / Answer

Nation’s Capital Fitness Inc

The equation for monthly maintenance cost in Y = a + bX form is,

Y = $566 + $7.60X

Determination of the variable and fixed cost components –

High values –

Hours of maintenance service 530

Corresponding Maintenance cost, $4594

Low values –

Hours of maintenance service, 290

Corresponding maintenance cost, $2,770

Computation of variable cost per hour = ($4,594 - $2,770)/(530 – 290) = $7.60 per hour

Fixed cost = $4,594 x ($7.60 x 530 Hrs) = $4,594 - $4,028

Fixed cost per month = $566

The equation form of Y = a + bX

Where, monthly maintenance cost = Y

Fixed cost per month = a

Variable cost per hour = b

Number of hours = X

Variable component is the variable cost per hour, which is arrived at as follows,

High values –

Hours of maintenance service 530

Corresponding Maintenance cost, $4594

Low values –

Hours of maintenance service, 290

Corresponding maintenance cost, $2,770

Computation of variable cost per hour = ($4,594 - $2,770)/(530 – 290) = $7.60 per hour

Using the equation, Y = a + bX

Y = total maintenance cost

Where, Fixed monthly cost, a = $566

Variable cost per hour, b = $7.60

Hours of activity, X = 680

Substituting the values,

Y = $566 + ($7.60 x 680)

Y = $566 + $5,168 = $5,734

The variable cost per hour would remain constant for any activity level.

Hence, the variable cost per hour for 690 hours of activity = $7.60 per hour

The fixed cost per hour = $566/690 hours

Fixed cost per hour at 690 hours of activity = $0.82

Because it will change as the number of hours changes.

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