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 €40 per unit with a variable cost of €30 per unit. Fixed costs are €15 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €15 000p = €40v = €30profit = €6 000
Q = units
2.Break-even analysisHard
A company sells two products. Product A sells for €11 with a variable cost of €8; product B sells for €45 with a variable cost of €30. They sell in a fixed mix of 2 units of A for every 3 of B. Fixed costs are €10 200 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €11, vA = €8pB = €45, vB = €30A : B = 2 : 3F = €10 200
Q = units
3.Financial accountingMedium
Which depreciation method charges the same amount every year?
- AStraight-line
- BSum-of-the-years'-digits
- CUnits of production
- DReducing balance
4.Financial accountingHard
Company P buys 70% of the voting shares of S and gains control. How does P report S in its group accounts?
- AConsolidate 100% of S line by line and show a non-controlling interest
- BShow one equity-method investment line for its 70% share of S
- CAdd only 70% of each of S's assets, liabilities, income and expenses
- DKeep the investment at cost and report only the dividends received from S
3Solutions
1.Break-even analysis
Answer: Q = 2100 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 = 40 − 30 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (15 000 + 6 000)/10 = 2 100
Answer
Q = 2 100 units
2.Break-even analysis
Answer: Q = 1000 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €3, cmB = €15
Weighted contribution margin
(2·3 + 3·15)/5 = €10.20
Break-even units
Q = 10 200/10.2 = 1 000
A: 400, B: 600
Answer
Q = 1 000 units
3.Financial accounting
Answer: A · 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
A · Straight-line
4.Financial accounting
Answer: A · Consolidate 100% of S line by line and show a non-controlling interest
Why this is the answer
A subsidiary is consolidated line by line at 100%. The 30% owned by others is shown as a non-controlling interest within equity.
Answer
A · Consolidate 100% of S line by line and show a non-controlling interest
ExamProblems · examproblems.com/courses/management-accounting