ACCT20001 Chap.8 Cost Volume Profit Analysis and Cost Estimation
Cost Volume Profit Analysis and Cost Estimation
The subject's own roadmap states the two questions this week answers: how many units must be sold to break even or to reach a target profit, and what costs would be if output changed by a given percentage. Both need the fixed and variable split established earlier in the semester, which is why cost behaviour was taught first and why an error there travels straight into every answer here.
Contribution margin is the only genuinely new idea. Each unit sold brings in its price and consumes its variable cost, and what is left contributes first to covering fixed cost and then to profit, so break-even becomes a division of the fixed block by that contribution.
Expressed as a proportion of each sales dollar, the same idea gives break-even revenue directly, which is the form to use when a question supplies percentages rather than unit figures. A target profit behaves exactly like an extra block of fixed cost. Every result rests on assumptions that are simply the relevant range in another form, so a break-even figure is a statement about a band of activity rather than a point.
The second half of the chapter supplies the split the first half assumes: cost estimation, and the high-low method that separates a mixed cost using the observations at the highest and lowest activity levels.
What this chapter covers
- 01
The two questions the subject states this week answers
- 02
Contribution margin per unit, and why break-even becomes a division
- 03
The contribution margin ratio, and answering in dollars instead of units
- 04
Target profit as an additional block of fixed cost
- 05
Reading a break-even chart, and where the two lines start
- 06
Margin of safety and operating leverage from the same two lines
- 07
Why the assumptions turn the answer into a range
- 08
Mixed costs, and why a ledger never hands you a clean split
- 09
The high-low method, step by step, and its self-check
- 10
What the method throws away, and when that matters
Separate a mixed cost with the high-low method and prove the split
- 1Identify the observations at the highest and lowest activity, not the highest and lowest cost: 1,900 hours and 900 hours.
- 2Divide the change in cost by the change in activity: $15,000 over 1,000 hours, which is $15 a machine hour.
- 1Substitute back into the high point: $47,300 less 1,900 hours at $15, which leaves $18,800 of fixed cost.
- 1Check against the low point: $32,300 less 900 hours at $15 also leaves $18,800, so the split is arithmetically consistent.
Key terms
- Contribution margin
- Selling price less variable cost per unit, being the amount each sale contributes to fixed cost and then to profit.
- Contribution margin ratio
- Contribution margin expressed as a proportion of the selling price, so that break-even can be found directly in sales dollars.
- Break-even point
- The volume or revenue at which total contribution exactly equals total fixed cost, so profit is nil.
- Margin of safety
- The amount by which current or planned sales exceed the break-even level, expressed in units, in dollars or as a percentage.
- Operating leverage
- The ratio of contribution margin to profit, indicating how sharply profit responds to a given change in sales.
- High-low method
- A cost estimation technique that fits a line through the observations at the highest and lowest activity levels to split a mixed cost.
- Target profit volume
- The sales volume at which contribution covers fixed cost plus a stated profit, found by adding the profit to the fixed block.
- Cost estimation
- The family of techniques that recovers a fixed component and a variable rate from past observations of total cost at different activity levels.
Cost Volume Profit Analysis and Cost Estimation FAQ
Why can I not just divide fixed cost by the selling price?
Because each sale also consumes variable cost, so only part of the price is available to cover the fixed block. Dividing by the price assumes every dollar of revenue is contribution, which would only be true if the product cost nothing to make. The division that answers the question uses contribution margin, and this substitution is one of the most common distractors in multiple-choice items on this topic.
Does a lower price always increase volume enough to help?
Rarely, and the arithmetic is worth doing before the argument. A price cut reduces contribution on every unit, so the break-even volume rises immediately and by a larger proportion than the price fell. Falling fixed cost per unit is often offered as the reason it will work, but that is only the arithmetic of spreading a constant total, not a new source of profit, and it cannot offset a smaller contribution from each sale.
Is the high-low method good enough to rely on?
It is quick and it is transparent, and those are real virtues under exam conditions. Its weakness is that it uses two observations and ignores the rest, so a single unusual month at either extreme sets the whole estimate and every forecast built on it. Regression uses all the observations and is the standard answer to that objection.
The examinable habit is to plot the points first and say so if the two extremes sit away from the pattern the others describe.
Exam move
Practise this chapter in both directions. Given price, variable cost and fixed cost, find break-even, target volume and margin of safety; then given break-even and a price, work backwards to the contribution margin. Answer every break-even question twice, once in units and once in dollars, and check that pricing the unit answer reproduces the dollar answer, because that agreement is a free proof of your own arithmetic.
For cost estimation, always show the second substitution: returning the same fixed component from the other observation takes one line and catches nearly every slip. Finally, get into the habit of naming one assumption in your closing sentence, since an answer that states the analysis holds within the relevant range is worth more than one that reports a figure to the nearest unit as though it were certain.
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