Cost Estimation Methods

Review Problem 5.3

Alta Production, Inc., reported the following production costs for the 12 months January through December. (This is the same company featured in Note 5.15 "Review Problem 5.2".)

Reporting Period (Month) Total Production Costs Level of Activity (Units Produced)
January $460,000 300
February 300,000 220
March 480,000 330
April 550,000 390
May 570,000 410
June 310,000 240
July 440,000 290
August 455,000 320
September 530,000 380
October 250,000 150
November 700,000 450
December 490,000 350


  1. Using this information, perform the four steps of the high-low method to estimate costs and state your results in cost equation form Y = f + vX.
  2. Assume Alta Production, Inc., will produce 400 units next month. Calculate total production costs for the month.
  3. What is the potential weakness in using this approach to estimate costs?

Solution to Review Problem 5.3

  1. The four steps are as follows:

    Step 1. Identify the high and low activity levels from the data set.

    The highest level of activity occurred in November (450 units; $700,000 production costs), and the lowest level of activity occurred in October (150 units; $250,000 production costs).

    Step 2. Calculate the variable cost per unit (v).

 Unit variable cost = Change in cost \div Change in activity

= ($700,00 - $250,000) \div (450 units - 150 units)

= $1,500

Step 3. Calculate the total fixed cost (f).

After completing step 2, the equation to describe the line is partially complete and stated as Y = f + $1,500X. To calculate total fixed costs, simply select either the high or low activity level, and fill in the data to solve for f (total fixed costs), as shown.

Using the high activity level,

  Y = f + \upsilon X

$700,000 = f + ($1,500 x 450 units)

f = ($1,500 x 450 units)

f = $700,000 - $675,000

f = $25,000

Thus total fixed cost is $25,000.

 

Step 4. State the results in equation form Y = f + vX.

We know from step 2 that the variable cost per unit is $1,500, and from step 3 that total fixed costs are $25,000. Thus the equation used to estimate total production costs is

Y = $25,000 + $1,500 X

2. Using the equation from part 1, simply substitute 400 units for X, as follows:

Y = $25,000 + ($1,500 x 400 units)

Y = $25,000 + $600,000

Y = $625,000

Thus total production costs are expected to be $625,000 for next month.

3. This approach only considers the high and low activity levels in establishing an estimate of fixed and variable costs. The high and low data points may not represent the data set as a whole, and using these points can result in distorted estimates. In reviewing the set of data points for January through December, it appears that October and November are relatively extreme points when compared to the other 10 months. Because the cost equation is based solely on these two points, the resulting estimate of production costs for 400 units of production (in part 2) may not be accurate.