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 €23 with a variable cost of €8 per unit. Fixed costs are €37 500 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €7 500 after tax?
p = €23v = €8F = €37 500T = 20%after-tax profit = €7 500
Q = units
2.Break-even analysisHard
A product sells for €42 per unit, with a variable cost of €30 per unit and fixed costs of €9 600 per year. Budgeted sales are 1 120 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €9 600p = €42v = €30budget = 1 120
MS = %
3.Financial accountingMedium
Current assets are €300,000, including inventory of €100,000. Current liabilities are €200,000. What is the quick (acid-test) ratio?
- A1.5
- B0.5
- C2.0
- D1.0
4.Financial accountingHard
A company borrows at 5% interest to invest in assets that earn 12%. What is the likely effect on return on equity?
- AROE stays the same, because debt is not equity
- BROE rises, but financial risk also increases
- CROE rises and financial risk falls
- DROE falls, because interest is an expense
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
7 500/(1 − 0.2) = €9 375
Units needed
Q = (37 500 + 9 375)/15 = 3 125
Answer
Q = 3 125 units
2.Break-even analysis
Answer: MS = 28.57 %
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) = 9 600/12 = 800
Margin of safety
MS = (1 120 − 800)/1 120·100 = 28.57%
Answer
MS = 28.57%
3.Financial accounting
Answer: D · 1.0
Why this is the answer
Quick ratio = (current assets − inventory) ÷ current liabilities = €200,000 ÷ €200,000 = 1.0. Inventory is excluded because it may be slow to turn into cash.
Answer
D · 1.0
4.Financial accounting
Answer: B · ROE rises, but financial risk also increases
Why this is the answer
Positive financial leverage: assets earn more than the debt costs, so profit per euro of equity rises. If returns drop below 5%, leverage works against shareholders.
Answer
B · ROE rises, but financial risk also increases
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