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 €23 per unit with a variable cost of €18 per unit. Fixed costs are €12 500 per month. How many units Q must be sold per month to make a profit of €12 000?
F = €12 500p = €23v = €18profit = €12 000
Q = units
2.Break-even analysisHard
A company sells 8 000 units at €33 each, with a variable cost of €18 per unit and fixed costs of €75 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 5%?
Q = 8 000p = €33v = €18F = €75 000%ΔQ = +5%
%ΔΠ = %
3.Financial accountingMedium
Profit for ordinary shareholders is €500,000 and there are 1,000,000 ordinary shares. What are basic earnings per share?
- A€2.00
- B€0.50
- C€0.05
- D€5.00
4.Financial accountingHard
Inventory days are 60, receivable days 45 and payable days 30. What is the cash conversion (operating) cycle?
- A105 days
- B15 days
- C75 days
- D135 days
3Solutions
1.Break-even analysis
Answer: Q = 4900 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 = 23 − 18 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (12 500 + 12 000)/5 = 4 900
Answer
Q = 4 900 units
2.Break-even analysis
Answer: %ΔΠ = 13.33 %
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 = 8 000·15 = €120 000
Π = 120 000 − 75 000 = €45 000
DOL
DOL = 120 000/45 000 = 2.667
Change in profit
%ΔΠ = 2.667·(+5%) = +13.33%
Answer
%ΔΠ = +13.33%
Check: new profit = 8 400·15 − 75 000 = €51 000.00.
3.Financial accounting
Answer: B · €0.50
Why this is the answer
Basic EPS = €500,000 ÷ 1,000,000 = €0.50 per share. Dividing the share price by EPS gives the P/E ratio.
Answer
B · €0.50
4.Financial accounting
Answer: C · 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
C · 75 days
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