The Armer Company is accumulating data to be used in preparing its annual profit

Question

The Armer Company is accumulating data to be used in preparing its annual profit plan for the coming year. The cost behavior pattern of the maintenance costs must be determined. The accounting staff has suggested that linear regression be employed to derive an equation in the form of y = a + bx for maintenance costs. Data regarding the maintenance hours and costs for last year and the results of the regression analysis are as follows:

     

     

   
What is the fixed cost per month using the high-low method to estimate the cost equation?

Hours of Activity Maintenance Costs   January 490              $ 4,200                February 340              3,200                March 390              3,700                April 280              2,760                May 480              4,390                June 290              2,850                July 300              3,000                August 500              4,640                September 470              4,170                October 480              4,080                November 330              3,500                December 330              3,000                Sum 4,680              43,490                Average 390              3,624             

Explanation / Answer

High-Low Method Formulas

Variable Cost per Unit

Variable cost per unit (b) is calculated using the following formula:

Variable Cost per Unit =

y2 y1

x2 x1

Where,
y2 is the total cost at highest level of activity;
y1 is the total cost at lowest level of activity;
x2 are the number of units/labor hours etc. at highest level of activity; and
x1 are the number of units/labor hours etc. at lowest level of activity

The variable cost per unit is equal to the slope of the cost volume line (i.e. change in total cost ÷ change in number of units produced).

Total Fixed Cost

Total fixed cost (a) is calculated by subtracting total variable cost from total cost, thus:

Total Fixed Cost = y2 bx2 = y1 bx1

We have,
at highest activity: x2 = 500; y2 = $4,640
at lowest activity: x1 = 280; y1 = $2760

Variable Cost per Unit = ($4,640 $2760) ÷ (500 280) = $8.55 per unit
Total Fixed Cost = $4,640 ($8.55 × 500) = $2,760 ($8.55 × 280) = $366
Cost Volume Formula: y = $ 366 + 8.55x

Fixed cost per month using the high-low method to estimate the cost equation = $366

Variable Cost per Unit =

y2 y1

x2 x1

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