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 can be made in two ways. Method A has fixed costs of €25 000 per year and a variable cost of €18 per unit. Method B, more automated, has fixed costs of €37 000 per year and a variable cost of €15 per unit. At what yearly volume Q do both methods cost the same?
FA = €25 000vA = €18FB = €37 000vB = €15
Q = units
2.Break-even analysisHard
A company sells 1 000 units per month at €21 each, with a variable cost of €6 per unit and fixed costs of €7 500 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 = 1 000p = €21v = €6 → €9F = €7 500
Q = units
3.Financial accountingMedium
Current assets are €300,000 and current liabilities are €150,000. What is the current ratio?
- A2.0
- B4.5
- C0.5
- D1.5
4.Financial accountingHard
The standard price of material is €5 per kg. The company buys 1,000 kg for €5,400. What is the material price variance?
- A€400 favourable
- B€5,400 adverse
- C€400 adverse
- D€0.40 adverse
3Solutions
1.Break-even analysis
Answer: Q = 4000 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).
Equal total costs
25 000 + 18Q = 37 000 + 15Q
Solve for Q
Q = (37 000 − 25 000)/(18 − 15) = 4 000
Answer
Q = 4 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
2.Break-even analysis
Answer: Q = 1250 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 = 1 000·(21 − 6) − 7 500 = €7 500
New contribution margin per unit
21 − 9 = €12
Units for the same profit
Q = (7 500 + 7 500)/12 = 1 250
Answer
Q = 1 250 units
3.Financial accounting
Answer: A · 2.0
Why this is the answer
€300,000 ÷ €150,000 = 2.0, so current assets cover short-term obligations twice.
Answer
A · 2.0
4.Financial accounting
Answer: C · €400 adverse
Why this is the answer
Standard cost of 1,000 kg = €5,000; actual cost = €5,400. Paying more than standard gives a €400 adverse price variance.
Answer
C · €400 adverse
ExamProblems · examproblems.com/courses/management-accounting