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 €8 per unit. Fixed costs are €20 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €4 000 after tax?
p = €12v = €8F = €20 000T = 20%after-tax profit = €4 000
Q = units
2.Break-even analysisHard
A company sells 2 250 units at €47 each, with a variable cost of €45 per unit and fixed costs of €3 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 12%?
Q = 2 250p = €47v = €45F = €3 000%ΔQ = +12%
%ΔΠ = %
3.Financial accountingMedium
A provision is recognised when a company has:
- AA profit to distribute
- BA present obligation from a past event, a probable outflow and a reliable estimate
- CCash set aside in a separate account
- DA possible future loss with no obligation
4.Financial accountingHard
Company P buys 70% of the voting shares of S and gains control. How does P report S in its group accounts?
- AConsolidate 100% of S line by line and show a non-controlling interest
- BShow one equity-method investment line for its 70% share of S
- CKeep the investment at cost and report only the dividends received from S
- DAdd only 70% of each of S's assets, liabilities, income and expenses
3Solutions
1.Break-even analysis
Answer: Q = 6250 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
4 000/(1 − 0.2) = €5 000
Units needed
Q = (20 000 + 5 000)/4 = 6 250
Answer
Q = 6 250 units
2.Break-even analysis
Answer: %ΔΠ = 36 %
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 = 2 250·2 = €4 500
Π = 4 500 − 3 000 = €1 500
DOL
DOL = 4 500/1 500 = 3
Change in profit
%ΔΠ = 3·(+12%) = +36%
Answer
%ΔΠ = +36%
Check: new profit = 2 520·2 − 3 000 = €2 040.00.
3.Financial accounting
Answer: B · A present obligation from a past event, a probable outflow and a reliable estimate
Why this is the answer
Provisions are liabilities of uncertain timing or amount. Possible obligations that do not meet the criteria are disclosed as contingent liabilities.
Answer
B · A present obligation from a past event, a probable outflow and a reliable estimate
4.Financial accounting
Answer: A · Consolidate 100% of S line by line and show a non-controlling interest
Why this is the answer
A subsidiary is consolidated line by line at 100%. The 30% owned by others is shown as a non-controlling interest within equity.
Answer
A · Consolidate 100% of S line by line and show a non-controlling interest
ExamProblems · examproblems.com/courses/management-accounting