ACF5955 Chap.2 Cost Behaviour and Estimation
Cost Behaviour and Estimation
Cost behaviour describes how total cost responds to activity, while estimation identifies the fixed and variable components used for prediction. This chapter separates total from per-unit logic, defines the relevant range, compares judgement, engineering and quantitative methods, and works the high-low method from activity extremes.
It also shows why a statistical relationship needs an operational cause before management relies on it.
What this chapter covers
- 01
Variable and fixed cost behaviour
- 02
Mixed-cost equations
- 03
Relevant ranges and capacity steps
- 04
Volume and non-volume drivers
- 05
High-low estimation
- 06
Scatter plots and regression judgement
Worked example · free
Estimate a maintenance cost function
- +2Variable rate is the $4,500 cost difference divided by 900 hours, giving $5 per machine hour.
- +2Fixed cost is $18,100 minus $5 times 2,400, giving $6,100.
- +1The estimated function is Y = $6,100 + $5X.
- +2At 2,000 hours, predicted cost is $16,100, subject to the relevant-range assumption.
Key terms
- Variable cost
- A variable cost changes in total with activity while remaining constant per unit within the relevant range.
- Fixed cost
- A fixed cost remains constant in total within the relevant range while its average per unit changes with volume.
- Mixed cost
- A mixed cost combines a fixed base with an activity-driven variable amount.
- Relevant range
- The relevant range is the activity span over which an assumed cost relationship is expected to hold.
Cost Behaviour and Estimation FAQ
Why is fixed cost per unit misleading for decisions?
Fixed total cost does not normally change with one extra unit inside available capacity. Dividing the pool by units creates an average allocation, so treating that average as incremental cost can overstate the cash effect of a decision.
What is the main weakness of high-low?
Only two observations determine the line, so an unusual event at either activity extreme can distort the estimate. A scatter plot and operational review should test the endpoints before the equation is used.
When is regression preferable to high-low?
Regression uses all observations and can quantify fit, making it useful with sufficient reliable data. It still requires causal judgement and adjustment when technology, contracts or capacity conditions will change in the forecast period.
Exam move
Draw total and per-unit behaviour side by side, because many errors come from switching bases. Recompute high-low with units shown, verify fixed cost at both endpoints and write the final equation before predicting. For method-comparison questions, explain the evidence used, the operating conditions required and the remaining risk rather than claiming one technique is always more accurate.
Build a four-panel sketch for variable, fixed, mixed and step cost, using the same activity axis. Under each total-cost graph, write what happens per unit as volume rises. This prevents the common mistake of treating a falling fixed cost per unit as evidence that the total cost is variable. For mixed costs, annotate the intercept, slope and relevant range in words as well as symbols.
Create a high-low worksheet with columns for activity, total cost and any unusual event. Circle the highest and lowest activity observations before looking at cost. Compute the rate with units, recover fixed cost from both points and substitute a third activity level only after the endpoint check closes. If the two fixed-cost answers disagree, stop and diagnose the arithmetic rather than averaging them.
Then draw the observations as a scatter plot and ask whether the selected endpoints represent the pattern. Practise explaining why an outlier may reflect a data error, a capacity step or a real operational event; each possibility calls for different treatment.
Compare managerial judgement, engineering study, high-low and regression by making an evidence table: what information the method uses, what stable relationship it assumes, how quickly it can be applied, and which bias remains. For a new automated process, physical input-output evidence may be stronger than a short historical series. For a mature process, historical estimates may expose relationships that intuition misses.
Add future-oriented adjustments explicitly for wage changes, supplier contracts, technology or planned capacity. Keep allocation separate from behaviour by rewriting allocated unit costs as underlying resource commitments. Ask whether another unit actually changes cash use or merely receives a share of an existing pool.
Finish every estimate with a boundary statement naming the valid activity range, causal driver and operational change most likely to make the equation fail. For timed practice, solve once numerically, then change one endpoint or insert a step cost and explain why the earlier prediction is no longer reliable. Keep an error log that separates selection, unit, arithmetic and interpretation mistakes.
Rework the same dataset after correcting only the identified error, then explain whether the resulting equation remains operationally plausible. Over several drills, this log reveals whether lost marks come from choosing endpoints, switching total and per-unit bases, or trusting an estimate beyond its evidence.
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