ACCTG 221 Chap.2 Cost Behaviour and Support Allocation
Cost Behaviour and Support Allocation
Cost behaviour describes how total and per-unit costs respond within a relevant range. Variable cost is constant per unit while fixed cost is constant in total; mixed cost combines both. High-low estimation uses the highest and lowest activity observations, not the highest and lowest costs. Support-department allocation then moves service costs to operating departments.
Direct, step-down and reciprocal methods differ in how fully they recognise services exchanged among support departments.
What this chapter covers
- 01
Variable, fixed, mixed and step cost patterns
- 02
Relevant range and time horizon
- 03
High-low estimation of a mixed cost
- 04
Direct allocation to operating departments
- 05
Step-down order and partial reciprocal recognition
- 06
Simultaneous equations for reciprocal services
Worked example · free
City Services: reciprocal support costs
- +2Let IT = 90,000 + 0.10HR and HR = 60,000 + 0.20IT.
- +2Substitution gives IT = 90,000 + 6,000 + 0.02IT, so 0.98IT = 96,000 and IT = $97,959.18.
- +2HR = 60,000 + 0.20 × 97,959.18 = $79,591.84.
- +1These complete reciprocal totals are then allocated using operating-department shares that exclude self-service.
Key terms
- Relevant range
- The activity interval over which a cost assumption is expected to hold.
- Mixed cost
- A cost containing both fixed and variable components.
- Allocation base
- The measured factor used to distribute a common cost.
- Step-down method
- A sequential method that partly recognises support services.
- Reciprocal method
- An allocation method recognising mutual support through simultaneous equations.
Cost Behaviour and Support Allocation FAQ
Why can fixed cost per unit change?
Fixed cost is constant in total within the relevant range, so dividing it over more units reduces the amount per unit. That arithmetic change does not mean the total fixed resource cost became variable.
Which observations does high-low use?
Use the periods with the highest and lowest activity levels. Their costs may not be the highest and lowest recorded costs because mixed cost can also be affected by unusual events or measurement noise.
Why does allocation order matter under step-down?
The first support department can allocate to every remaining department, while a department closed later cannot send cost back to one already closed. Different orders therefore recognise different portions of reciprocal service.
Exam move
Sketch the expected cost line before calculating. A fixed-cost line is horizontal in total, a variable-cost line starts at the origin, and a mixed-cost line has a positive intercept. For high-low, circle activity first and take the matching cost observations; calculate the variable rate from changes, then substitute into either observation to find fixed cost.
For allocations, distinguish support and operating departments and check every base denominator. In step-down work, cross out a support department after allocation so it never receives cost again. In reciprocal work, define equations in words before algebra.
Finish by proving that the costs allocated to operating departments equal the original direct support costs, allowing for the circular services already resolved in the equations. Add a small evidence table to mixed-cost practice with period, activity and total cost, then identify the high and low activity rows before touching the costs.
After deriving the variable rate, substitute it into both selected observations; the two fixed-cost estimates should agree apart from rounding. If they do not, inspect the paired observations rather than averaging the discrepancy away. Compare the estimate with a scatter of all periods and flag any outlier or activity range that makes a straight line questionable.
For support allocation, redraw the service relationships before choosing a method. Under the direct method, ignore flows among support departments but keep operating-department denominators complete. Under step-down, write the closure order and recalculate each remaining denominator after a department closes.
Under the reciprocal method, name the unknown total costs, write one equation per support department and solve the system before allocating outward. Use a checksum showing that operating departments receive the original support cost total.
Then explain the trade-off: reciprocal allocation recognises mutual service more fully, while additional modelling effort is justified only if the resulting cost information affects pricing, performance or resource decisions. In revision, alternate a cost-estimation question with an allocation question so the shared denominator discipline becomes automatic without confusing their purposes.
Add a final judgement about information quality. A high-low estimate based on two unusual months should be presented as provisional, while an allocation driven by a weak base should be described as a convention rather than a causal product cost. State what additional observation, driver measure or sensitivity result would make the recommendation more reliable.
Keep estimation uncertainty separate from allocation convention, since each limitation calls for different evidence and a different management response.
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