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 €20 000 per year and a variable cost of €8 per unit. Method B, more automated, has fixed costs of €35 000 per year and a variable cost of €2 per unit. At what yearly volume Q do both methods cost the same?
FA = €20 000vA = €8FB = €35 000vB = €2
Q = units
2.Break-even analysisHard
A company sells 1 200 units at €38 each, with a variable cost of €30 per unit and fixed costs of €6 400. By what percentage %ΔΠ does operating profit change if sales volume rises by 12%?
Q = 1 200p = €38v = €30F = €6 400%ΔQ = +12%
%ΔΠ = %
3.Financial accountingMedium
A machine with a carrying amount of €3,000 is sold for €4,000. What is recorded in the income statement?
- AA gain on disposal of €1,000
- BRevenue of €4,000
- CA loss on disposal of €1,000
- DA gain on disposal of €4,000
4.Financial accountingHard
An asset has a carrying amount of €500,000, fair value less costs of disposal of €380,000 and value in use of €420,000. What impairment loss is recognised?
- A€120,000
- B€200,000
- C€80,000
- D€0
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
20 000 + 8Q = 35 000 + 2Q
Solve for Q
Q = (35 000 − 20 000)/(8 − 2) = 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: %ΔΠ = 36 %
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Contribution margin and profit
CM = 1 200·8 = €9 600
Π = 9 600 − 6 400 = €3 200
DOL
DOL = 9 600/3 200 = 3
Change in profit
%ΔΠ = 3·(+12%) = +36%
Answer
%ΔΠ = +36%
Check: new profit = 1 344·8 − 6 400 = €4 352.00.
3.Financial accounting
Answer: A · A gain on disposal of €1,000
Why this is the answer
Gain or loss on disposal = proceeds − carrying amount = €4,000 − €3,000 = €1,000 gain. It is not part of normal revenue.
Answer
A · A gain on disposal of €1,000
4.Financial accounting
Answer: C · €80,000
Why this is the answer
Recoverable amount = max(€380,000, €420,000) = €420,000. Impairment = €500,000 − €420,000 = €80,000.
Answer
C · €80,000
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