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 €19 per unit with a variable cost of €15 per unit. Fixed costs are €8 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €8 000p = €19v = €15profit = €5 000
Q = units
2.Break-even analysisHard
A company sells 12 500 units per month at €14 each, with a variable cost of €8 per unit and fixed costs of €30 000 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 = 12 500p = €14v = €8 → €11F = €30 000
Q = units
3.Financial accountingMedium
Which depreciation method charges the same amount every year?
- AReducing balance
- BSum-of-the-years'-digits
- CUnits of production
- DStraight-line
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?
- ANothing, because each company is a separate entity
- BThe sale is shown as external revenue of the group
- CThe profit is shown twice, once for each company
- DThe unrealised profit in inventory is eliminated
3Solutions
1.Break-even analysis
Answer: Q = 3250 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 = 19 − 15 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (8 000 + 5 000)/4 = 3 250
Answer
Q = 3 250 units
2.Break-even analysis
Answer: Q = 25000 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 = 12 500·(14 − 8) − 30 000 = €45 000
New contribution margin per unit
14 − 11 = €3
Units for the same profit
Q = (30 000 + 45 000)/3 = 25 000
Answer
Q = 25 000 units
3.Financial accounting
Answer: D · Straight-line
Why this is the answer
Straight-line spreads the depreciable amount evenly. Reducing balance charges more in early years; units of production follows actual use.
Answer
D · Straight-line
4.Financial accounting
Answer: D · 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
D · The unrealised profit in inventory is eliminated
ExamProblems · examproblems.com/courses/management-accounting