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 €30 with a variable cost of €20 per unit. Fixed costs are €25 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €5 000 after tax?
p = €30v = €20F = €25 000T = 20%after-tax profit = €5 000
Q = units
2.Break-even analysisHard
A product sells for €8 per unit, with a variable cost of €4 per unit and fixed costs of €6 000 per year. Budgeted sales are 1 950 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €6 000p = €8v = €4budget = 1 950
MS = %
3.Financial accountingMedium
Net working capital is:
- ARevenue minus operating expenses
- BTotal assets minus total liabilities
- CCurrent assets minus current liabilities
- DNon-current assets minus long-term loans
4.Financial accountingHard
Machine hours are scarce. Product X earns €20 contribution and needs 4 hours; product Y earns €15 and needs 2 hours. Which should be made first?
- AX, because it earns more contribution per unit
- BX, because it uses more machine time
- CY, because it earns €7.50 per hour versus €5 for X
- DEither, because the total contribution is the same
3Solutions
1.Break-even analysis
Answer: Q = 3125 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
5 000/(1 − 0.2) = €6 250
Units needed
Q = (25 000 + 6 250)/10 = 3 125
Answer
Q = 3 125 units
2.Break-even analysis
Answer: MS = 23.08 %
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) = 6 000/4 = 1 500
Margin of safety
MS = (1 950 − 1 500)/1 950·100 = 23.08%
Answer
MS = 23.08%
3.Financial accounting
Answer: C · Current assets minus current liabilities
Why this is the answer
Working capital measures the short-term resources available for daily operations: inventory, receivables and cash minus short-term obligations.
Answer
C · Current assets minus current liabilities
4.Financial accounting
Answer: C · Y, because it earns €7.50 per hour versus €5 for X
Why this is the answer
X earns €20 ÷ 4 = €5 per hour, Y earns €15 ÷ 2 = €7.50 per hour. With a scarce resource, maximise contribution per scarce hour.
Answer
C · Y, because it earns €7.50 per hour versus €5 for X
ExamProblems · examproblems.com/courses/management-accounting