Break-even analysis
- Contribution margin
- CM = p − v
- Break-even quantity
- QBE = FC/(p − v)
- Target profit
- Q = (FC + profit)/(p − v)
- Profit
- π = (p − v)·Q − FC
- Margin of safety
- (Q − QBE)/Q
Management Accounting: cram pack
Formula sheets, the key method steps for every topic and 4 practice problems, with full solutions at the back.
1Formulas and methods
2Practice problems
1.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €30 000 per year and a variable cost of €18 per unit. Method B, more automated, has fixed costs of €37 500 per year and a variable cost of €15 per unit. At what yearly volume Q do both methods cost the same?
FA = €30 000vA = €18FB = €37 500vB = €15
Q = units
2.Break-even analysisHard
A product sells for €31 per unit, with a variable cost of €25 per unit and fixed costs of €12 000 per year. Budgeted sales are 3 200 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €12 000p = €31v = €25budget = 3 200
MS = %
3.Financial accountingMedium
Which costs are relevant when making a business decision?
- AFuture cash flows that differ between the alternatives
- BAll costs in last year's income statement
- CCosts already paid for the project
- DAllocated fixed overheads that do not change with the decision
4.Financial accountingHard
Two firms have the same operating profit, but one is financed mostly by debt. When operating profit falls by 20%, the highly geared firm's net profit:
- ARises because interest is fixed
- BFalls by exactly 20% as well
- CFalls by a smaller percentage
- DFalls by a larger percentage
3Solutions
1.Break-even analysis
Answer: Q = 2500 units
Cost-volume-profit: each unit sold earns a contribution margin, price minus variable cost per unit. Profit = Q·(p − v) − F, where F is the fixed cost. At the break-even point profit is zero, so Q = F/(p − v).
Equal total costs
30 000 + 18Q = 37 500 + 15Q
Solve for Q
Q = (37 500 − 30 000)/(18 − 15) = 2 500
Answer
Q = 2 500 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
2.Break-even analysis
Answer: MS = 37.5 %
Cost-volume-profit: each unit sold earns a contribution margin, price minus variable cost per unit. Profit = Q·(p − v) − F, where F is the fixed cost. At the break-even point profit is zero, so Q = F/(p − v).
Break-even quantity
Q = F/(p − v) = 12 000/6 = 2 000
Margin of safety
MS = (3 200 − 2 000)/3 200·100 = 37.5%
Answer
MS = 37.5%
3.Financial accounting
Answer: A · Future cash flows that differ between the alternatives
Why this is the answer
Relevant costs are future, incremental cash flows. Sunk costs, committed costs and unchanged allocated overheads are ignored.
Answer
A · Future cash flows that differ between the alternatives
4.Financial accounting
Answer: D · Falls by a larger percentage
Why this is the answer
Fixed interest stays the same, so any change in operating profit causes a bigger percentage change in profit for shareholders. This is financial risk.
Answer
D · Falls by a larger percentage
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