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 €12 with a variable cost of €4 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 €1 500 after tax?
p = €12v = €4F = €8 000T = 25%after-tax profit = €1 500
Q = units
2.Break-even analysisHard
A product sells for €12 per unit, with a variable cost of €6 per unit and fixed costs of €9 000 per year. Budgeted sales are 2 700 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €9 000p = €12v = €6budget = 2 700
MS = %
3.Financial accountingMedium
Return on equity (ROE) is calculated as:
- ANet profit / shareholders' equity
- BTotal assets / equity
- CCurrent assets / current liabilities
- DNet profit / total revenue
4.Financial accountingHard
A company switches to a depreciation method that gives higher charges. Ignoring tax, what happens to cash flow?
- ACash flow rises by the extra depreciation
- BCash flow is unchanged, although profit falls
- CCash flow falls by the amount of the extra depreciation
- DCash flow and profit both rise
3Solutions
1.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).
Pre-tax profit needed
1 500/(1 − 0.25) = €2 000
Units needed
Q = (8 000 + 2 000)/8 = 1 250
Answer
Q = 1 250 units
2.Break-even analysis
Answer: MS = 44.44 %
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) = 9 000/6 = 1 500
Margin of safety
MS = (2 700 − 1 500)/2 700·100 = 44.44%
Answer
MS = 44.44%
3.Financial accounting
Answer: A · Net profit / shareholders' equity
Why this is the answer
ROE shows how much profit the company generates for each euro of equity invested by shareholders.
Answer
A · Net profit / shareholders' equity
4.Financial accounting
Answer: B · Cash flow is unchanged, although profit falls
Why this is the answer
Depreciation allocates a cost already paid. Changing the method changes reported profit, but no extra cash leaves the business (tax effects aside).
Answer
B · Cash flow is unchanged, although profit falls
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