BUSMGT713 Chap.1 Cost behaviour, contribution and the high-low method
Cost behaviour, contribution and the high-low method
Week 1 of the course is titled cost behaviour, cost management and the elements of costing, and this chapter covers its foundation: telling fixed costs from variable ones and splitting a mixed total into the two parts.
The tool the practice mid-term uses for that split is the high-low method, which takes the months with the highest and lowest activity, reads the change in cost against the change in activity as the variable rate, and treats the remainder as fixed cost. From there the chapter moves to contribution: selling price less variable cost per unit, the contribution margin ratio and the variable cost ratio, which always add to 100%.
A laundry with five months of records carries the method, including a repair month that looks like the obvious high point but is not. Students who can write the cost equation, state its range and turn it into contribution per unit are ready for break-even analysis in Chapter 2.
What this chapter covers
- 01
Fixed, variable and mixed costs and why ledgers record mixed totals
- 02
The high-low method: choosing the periods by activity, not by cost
- 03
Writing and checking a monthly cost equation
- 04
Contribution per unit, the contribution margin ratio and the variable cost ratio
- 05
Operating income from a cost equation at a planned volume
- 06
The relevant range and when a cost line stops being reliable
Worked example · free
Kōwhai Laundry: the repair month against the high-low cost line
- +2Variable cost per load = ($18,160 minus $14,560) divided by (4,700 minus 3,200) = $3,600 divided by 1,500 = $2.40.
- +1Fixed cost = $14,560 minus 3,200 times $2.40 = $6,880 a month, so the line is $6,880 plus $2.40 per load.
- +1May predicted = $6,880 plus 4,100 times $2.40 = $16,720, the same as May's actual cost.
- +2April predicted = $6,880 plus 4,300 times $2.40 = $17,200; actual $18,600 leaves $1,400 above the line, the cost of the repair.
Key terms
- Variable cost
- A cost whose total rises and falls in proportion to activity, such as detergent for each load washed.
- Fixed cost
- A cost that stays constant in total over a period across the normal range of activity, such as monthly rent.
- Mixed cost
- A total that contains a fixed element and a variable element, so it rises with activity but not from zero.
- Relevant range
- The band of activity within which the estimated fixed amount and variable rate can be relied upon.
- Cost equation
- Total cost written as fixed cost plus variable cost per unit multiplied by the number of units.
Cost behaviour, contribution and the high-low method FAQ
Which months does the high-low method use?
It uses the period with the highest level of activity and the period with the lowest level of activity. The cost figures only come in afterwards. A month with an unusually high cost but middling activity, such as a repair month, is ignored, because using it would tilt the line and distort the variable rate.
How do I check a high-low cost equation?
Calculate the fixed cost twice: once from the low month and once from the high month, each time subtracting variable cost per unit times that month's activity. Both answers must match. Then write the full equation, fixed cost plus the variable rate times quantity, because the practice paper asks for the equation rather than two loose numbers.
Why do the contribution margin ratio and variable cost ratio add to 100%?
Each sales dollar is either consumed by variable cost or left over as contribution. The Week 1 marginal costing solution prints the sum as its own row, so stating the check in an answer shows the marker that both ratios were computed from the same price and cost.
Can a cost equation predict any volume?
Only volumes inside the range that produced it. Outside that range, extra shifts, new equipment or bulk discounts can change both the fixed amount and the variable rate, so a prediction far beyond the observed months should be flagged as uncertain.
Is contribution the same as profit?
No. Contribution is what remains after variable costs; profit is what remains after fixed costs as well. A product can have a healthy contribution per unit and still make a loss if sales are too low to cover its fixed costs.
Assessment move
Start each practice problem by sorting the costs into fixed, variable and mixed, with a reason for each. For a mixed total, list the periods in order of activity and circle the two extremes before reading any cost. Compute the variable rate, then the fixed amount from both extremes, and write the equation. Turn it into contribution per unit at the given price and check that the two ratios sum to 100%.
Finally, predict one volume inside the range and one outside, and write a sentence on why the second is less reliable. Repeat with a fresh data set until the routine takes under five minutes.
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