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 sells for €55 per unit with a variable cost of €45 per unit. Fixed costs are €50 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €50 000p = €55v = €45profit = €5 000
Q = units
2.Break-even analysisHard
A company sells two products. Product A sells for €23 with a variable cost of €15; product B sells for €30 with a variable cost of €20. They sell in a fixed mix of 4 units of A for every 1 of B. Fixed costs are €16 800 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €23, vA = €15pB = €30, vB = €20A : B = 4 : 1F = €16 800
Q = units
3.Financial accountingMedium
An asset costs €50,000, has a residual value of €5,000 and a useful life of 5 years. What is the annual straight-line depreciation?
- A€9,000
- B€11,000
- C€5,000
- D€10,000
4.Financial accountingHard
Production exceeds sales this period, so inventory rises. How does absorption costing profit compare with marginal costing profit?
- AAbsorption costing shows a loss
- BAbsorption costing profit is higher
- CThey are always equal
- DMarginal costing profit is higher this period
3Solutions
1.Break-even analysis
Answer: Q = 5500 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).
Contribution margin per unit
p − v = 55 − 45 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (50 000 + 5 000)/10 = 5 500
Answer
Q = 5 500 units
2.Break-even analysis
Answer: Q = 2000 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €8, cmB = €10
Weighted contribution margin
(4·8 + 1·10)/5 = €8.40
Break-even units
Q = 16 800/8.4 = 2 000
A: 1 600, B: 400
Answer
Q = 2 000 units
3.Financial accounting
Answer: A · €9,000
Why this is the answer
(Cost − residual value) ÷ useful life = (€50,000 − €5,000) ÷ 5 = €9,000 per year.
Answer
A · €9,000
4.Financial accounting
Answer: B · Absorption costing profit is higher
Why this is the answer
Under absorption costing part of this period's fixed overhead sits in closing inventory instead of being expensed, so reported profit is higher when inventory rises.
Answer
B · Absorption costing profit is higher
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