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 €22 per unit with a variable cost of €12 per unit. Fixed costs are €10 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €10 000p = €22v = €12profit = €10 000
Q = units
2.Break-even analysisHard
A company sells 5 000 units per month at €38 each, with a variable cost of €30 per unit and fixed costs of €32 000 per month. The variable cost rises by €3 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 5 000p = €38v = €30 → €33F = €32 000
Q = units
3.Financial accountingMedium
Trade receivables are €50,000 and annual credit sales are €365,000. What are the receivable days?
- A36.5 days
- B50 days
- C73 days
- D7.3 days
4.Financial accountingHard
A parent sold goods to its subsidiary at a profit, and the subsidiary still holds them at year end. What must happen on consolidation?
- AThe profit is shown twice, once for each company
- BNothing, because each company is a separate entity
- CThe unrealised profit in inventory is eliminated
- DThe sale is shown as external revenue of the group
3Solutions
1.Break-even analysis
Answer: Q = 2000 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 = 22 − 12 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (10 000 + 10 000)/10 = 2 000
Answer
Q = 2 000 units
2.Break-even analysis
Answer: Q = 8000 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).
Current profit
Π = 5 000·(38 − 30) − 32 000 = €8 000
New contribution margin per unit
38 − 33 = €5
Units for the same profit
Q = (32 000 + 8 000)/5 = 8 000
Answer
Q = 8 000 units
3.Financial accounting
Answer: B · 50 days
Why this is the answer
€50,000 ÷ €365,000 × 365 = 50 days. This is the average time customers take to pay.
Answer
B · 50 days
4.Financial accounting
Answer: C · The unrealised profit in inventory is eliminated
Why this is the answer
Intra-group sales and purchases are cancelled, and profit on goods still held in the group is removed from inventory and group profit until sold outside.
Answer
C · The unrealised profit in inventory is eliminated
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