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 €28 with a variable cost of €18 per unit. Fixed costs are €8 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €3 000 after tax?
p = €28v = €18F = €8 000T = 25%after-tax profit = €3 000
Q = units
2.Break-even analysisHard
A product sells for €24 per unit, with a variable cost of €12 per unit and fixed costs of €60 000 per year. Budgeted sales are 8 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €60 000p = €24v = €12budget = 8 000
MS = %
3.Financial accountingMedium
Why can a profitable company run out of cash?
- AProfit always equals cash
- BProfitable companies never pay taxes
- CCash is not recorded in accounting
- DProfit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
4.Financial accountingHard
Operating profit is €200,000 and capital employed (equity plus non-current liabilities) is €1,000,000. What is ROCE?
- A5%
- B20%
- C50%
- D2%
3Solutions
1.Break-even analysis
Answer: Q = 1200 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).
Pre-tax profit needed
3 000/(1 − 0.25) = €4 000
Units needed
Q = (8 000 + 4 000)/10 = 1 200
Answer
Q = 1 200 units
2.Break-even analysis
Answer: MS = 37.5 %
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).
Break-even quantity
Q = F/(p − v) = 60 000/12 = 5 000
Margin of safety
MS = (8 000 − 5 000)/8 000·100 = 37.5%
Answer
MS = 37.5%
3.Financial accounting
Answer: D · Profit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
Why this is the answer
Profit is measured on an accrual basis; growth can tie up cash in inventory and receivables, so cash flow can be negative despite profits.
Answer
D · Profit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
4.Financial accounting
Answer: B · 20%
Why this is the answer
ROCE = €200,000 ÷ €1,000,000 = 20%. It measures returns on all long-term finance, so it can be compared with the cost of borrowing.
Answer
B · 20%
ExamProblems · examproblems.com/courses/management-accounting