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 €18 with a variable cost of €15 per unit. Fixed costs are €7 500 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €1 500 after tax?
p = €18v = €15F = €7 500T = 20%after-tax profit = €1 500
Q = units
2.Break-even analysisHard
A product sells for €22 per unit, with a variable cost of €20 per unit and fixed costs of €4 000 per year. Budgeted sales are 2 800 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €4 000p = €22v = €20budget = 2 800
MS = %
3.Financial accountingMedium
Under IAS 16, which cost should be included in the cost of a new machine?
- AStaff training costs after it starts operating
- BInstallation costs needed to get it working
- CGeneral office overheads for the year
- DRepairs carried out two years later
4.Financial accountingHard
Two firms have the same operating profit, but one is financed mostly by debt. When operating profit falls by 20%, the highly geared firm's net profit:
- AFalls by exactly 20% as well
- BFalls by a smaller percentage
- CFalls by a larger percentage
- DRises because interest is fixed
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
1 500/(1 − 0.2) = €1 875
Units needed
Q = (7 500 + 1 875)/3 = 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) = 4 000/2 = 2 000
Margin of safety
MS = (2 800 − 2 000)/2 800·100 = 28.57%
Answer
MS = 28.57%
3.Financial accounting
Answer: B · Installation costs needed to get it working
Why this is the answer
Purchase price plus directly attributable costs, such as delivery and installation, are capitalised. Training, later repairs and general overheads are expensed.
Answer
B · Installation costs needed to get it working
4.Financial accounting
Answer: C · Falls by a larger percentage
Why this is the answer
Fixed interest stays the same, so any change in operating profit causes a bigger percentage change in profit for shareholders. This is financial risk.
Answer
C · Falls by a larger percentage
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