GB519 Unit 2 Cost Behavior Analysis Example

Twenty-Four Months of Lab Overhead: A Unit 2 Cost Behavior Analysis With a Saturday-Shift Step

[Student Name]

Purdue University Global

GB519: Measurement and Decision Making

Unit 2 Cost Behavior Analysis

[Instructor Name]

[Date]

The lab and every figure are composite and illustrative; the methods and sources cited are real.

The Question

Fernhill Orthotic Lab fabricates custom foot orthoses, ankle-foot orthoses and spinal braces for clinics. Its overhead covers the supervisor, mill maintenance, oven power, cleaning, software licenses and supplies. The operations manager wants to know what overhead will be next November and December, when demand peaks as patients who have met their insurance deductibles hurry to be fitted before the year ends. The answer depends on how overhead behaves as volume changes, so the analysis begins with the data rather than a formula.

Exhibit 1: The Data and the Plot

Monthly devices fabricated ranged from 1,395 in January of the first year to 2,298 in December of the second. Overhead ranged from $32,770 to $46,480. Plotted with overhead on the vertical axis and devices on the horizontal, twenty of the twenty-four points lie along a rising line. Four points sit well above it: November and December of both years, at 2,135, 2,242, 2,248 and 2,298 devices, with overhead between $45,230 and $46,480.

Those four months share an operating fact. In each, the lab ran a Saturday shift, which brought a shift supervisor, extra cleaning cycles and an added mill maintenance visit. The Saturday shift is a step in fixed cost, not a higher variable rate. Garrison et al. (2021) describe this pattern as a step-fixed cost: flat across a range of activity, then jumping to a new level when capacity is added.

Exhibit 2: Regression on the Single-Shift Months

A least-squares regression on the twenty single-shift months gives:

Fixed component (intercept): about $23,040 a month.

Variable rate (slope): about $6.89 per device.

R-squared: 0.85.

Read aloud, the intercept is the overhead the lab carries in a single-shift month before it makes any device, and the slope is the overhead each added device brings, mostly oven power, cleaning supplies and mill tooling wear. An R-squared of 0.85 means device volume explains about 85 percent of the month-to-month variation in overhead within the single-shift range. The rest reflects timing, such as a maintenance invoice landing in one month rather than another.

Nobody should take the intercept for what a shuttered lab would spend. Montgomery et al. (2021) caution that a regression describes behavior only within the range of the data. No month had fewer than 1,395 devices, so $23,040 is an extrapolation used to describe the line, not a forecast for zero output.

Fitting all twenty-four months gives a higher R-squared, 0.93, and a badly wrong answer: a variable rate of $16.42 per device and a fixed cost near $8,100.

Exhibit 3: Regression Beside High-Low

The high-low method uses only the highest and lowest activity months. The high month, December of the second year, had 2,298 devices and $46,480 of overhead. The low month, January of the first year, had 1,395 devices and $33,250. The method gives a variable rate of $14.65 per device and fixed cost of about $12,810.

The two methods disagree because the high month is a Saturday-shift month. High-low reads the step as if it were variable cost, more than doubling the slope. Anderson et al. (2020) note that a line drawn through two points is only as reliable as those points, and here one of them belongs to a different cost structure. High-low is quick, but it should not be used when an endpoint sits on the other side of a step.

The Step, Priced

Against the single-shift line, the four Saturday-shift months ran $7,480, $7,200, $7,040 and $7,610 above what their volume alone predicts. The average, about $7,330 a month, is the price of the step. The highest single-shift month produced 1,862 devices, so single-shift capacity is near 1,950 a month.

The Forecast

Next November and December the lab expects about 2,350 devices a month. The single-shift line predicts $23,040 plus $6.89 times 2,350, or about $39,230. Because that volume is above single-shift capacity, the Saturday shift adds about $7,330, for forecast overhead of roughly $46,560 a month. A budget built from the all-months line would also land near $46,700 at that volume, but for the wrong reason, and would be badly wrong at any other volume.

When the Saturday Shift Pays

Across Fernhill's product mix, a device brings about $104 of contribution. At that figure, the $7,330 step is covered once the shift produces about 70 devices that would otherwise be lost or delayed. Next December's expected 400 devices above capacity would bring about $41,800 of contribution against the $7,330 step, so the shift is clearly worth running. In a month when the backlog is under 70 devices, the better choice is to quote clinics a slightly longer turnaround.

Limits of the Analysis

Twenty months is a modest sample, and the variable rate could drift if power prices or tooling costs change. The analysis also treats every device as one unit, though a spinal brace uses far more oven and mill time than a foot orthosis. If the mix shifts toward braces, overhead per device will rise even at constant volume, and a regression on machine hours would be worth testing. Garrison et al. (2021) note that the best activity base is the one that most closely drives the cost, and device count is a reasonable but imperfect proxy here.

References

Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2020). Statistics for business and economics (14th ed.). Cengage.

Garrison, R. H., Noreen, E. W., & Brewer, P. C. (2021). Managerial accounting (17th ed.). McGraw Hill.

Montgomery, D. C., Peck, E. A., & Vining, G. G. (2021). Introduction to linear regression analysis (6th ed.). Wiley.