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 €17 per unit with a variable cost of €12 per unit. Fixed costs are €7 500 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €7 500p = €17v = €12profit = €6 000
Q = units
2.Break-even analysisHard
A company sells 630 units at €14 each, with a variable cost of €8 per unit and fixed costs of €3 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 12%?
Q = 630p = €14v = €8F = €3 000%ΔQ = +12%
%ΔΠ = %
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
- CRises because interest is fixed
- DFalls by a larger percentage
3Solutions
1.Break-even analysis
Answer: Q = 2700 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).
Contribution margin per unit
p − v = 17 − 12 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (7 500 + 6 000)/5 = 2 700
Answer
Q = 2 700 units
2.Break-even analysis
Answer: %ΔΠ = 58.15 %
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Contribution margin and profit
CM = 630·6 = €3 780
Π = 3 780 − 3 000 = €780
DOL
DOL = 3 780/780 = 4.846
Change in profit
%ΔΠ = 4.846·(+12%) = +58.15%
Answer
%ΔΠ = +58.15%
Check: new profit = 706·6 − 3 000 = €1 233.60.
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: D · 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
D · Falls by a larger percentage
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