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 €20 with a variable cost of €12 per unit. Fixed costs are €6 400 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €1 500 after tax?
p = €20v = €12F = €6 400T = 25%after-tax profit = €1 500
Q = units
2.Break-even analysisHard
A company sells 800 units at €34 each, with a variable cost of €30 per unit and fixed costs of €2 000. By what percentage %ΔΠ does operating profit change if sales volume falls by 12%?
Q = 800p = €34v = €30F = €2 000%ΔQ = −12%
%ΔΠ = %
3.Financial accountingMedium
Fixed costs are €20,000, the selling price is €50 and the variable cost is €30 per unit. What is the break-even point?
- A400 units
- B2,000 units
- C667 units
- D1,000 units
4.Financial accountingHard
Inventory days are 60, receivable days 45 and payable days 30. What is the cash conversion (operating) cycle?
- A105 days
- B75 days
- C135 days
- D15 days
3Solutions
1.Break-even analysis
Answer: Q = 1050 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).
Pre-tax profit needed
1 500/(1 − 0.25) = €2 000
Units needed
Q = (6 400 + 2 000)/8 = 1 050
Answer
Q = 1 050 units
2.Break-even analysis
Answer: %ΔΠ = −32 %
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 = 800·4 = €3 200
Π = 3 200 − 2 000 = €1 200
DOL
DOL = 3 200/1 200 = 2.667
Change in profit
%ΔΠ = 2.667·(−12%) = −32%
Answer
%ΔΠ = −32%
Check: new profit = 704·4 − 2 000 = €816.00.
3.Financial accounting
Answer: D · 1,000 units
Why this is the answer
Contribution per unit = €50 − €30 = €20. Break-even = €20,000 ÷ €20 = 1,000 units.
Answer
D · 1,000 units
4.Financial accounting
Answer: B · 75 days
Why this is the answer
60 + 45 − 30 = 75 days between paying suppliers and collecting cash from customers. A shorter cycle needs less working capital finance.
Answer
B · 75 days
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