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 €35 with a variable cost of €15 per unit. Fixed costs are €20 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €6 000 after tax?
p = €35v = €15F = €20 000T = 25%after-tax profit = €6 000
Q = units
2.Break-even analysisHard
A company sells 8 000 units at €37 each, with a variable cost of €25 per unit and fixed costs of €48 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 8%?
Q = 8 000p = €37v = €25F = €48 000%ΔQ = +8%
%ΔΠ = %
3.Financial accountingMedium
A project has a positive net present value (NPV) at the company's cost of capital. This means:
- AIt has no risk at all
- BIt earns more than the required return and should add value
- CIts reported accounting profit will be positive in every year
- DIt recovers its cost within one year
4.Financial accountingHard
A company "sells" inventory to a bank and must buy it back later at a higher price, keeping the risks and rewards. How should it be accounted for?
- AAs a gain on disposal of inventory
- BAs a contingent asset in the notes
- CAs a secured loan, not a sale
- DAs revenue on the date of transfer
3Solutions
1.Break-even analysis
Answer: Q = 1400 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
6 000/(1 − 0.25) = €8 000
Units needed
Q = (20 000 + 8 000)/20 = 1 400
Answer
Q = 1 400 units
2.Break-even analysis
Answer: %ΔΠ = 16 %
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 = 8 000·12 = €96 000
Π = 96 000 − 48 000 = €48 000
DOL
DOL = 96 000/48 000 = 2
Change in profit
%ΔΠ = 2·(+8%) = +16%
Answer
%ΔΠ = +16%
Check: new profit = 8 640·12 − 48 000 = €55 680.00.
3.Financial accounting
Answer: B · It earns more than the required return and should add value
Why this is the answer
A positive NPV means the present value of inflows exceeds the investment at the required rate, so the project increases shareholder wealth.
Answer
B · It earns more than the required return and should add value
4.Financial accounting
Answer: C · As a secured loan, not a sale
Why this is the answer
Control and risks stay with the company, so the transaction is in substance borrowing secured on inventory. The price difference is an interest cost.
Answer
C · As a secured loan, not a sale
ExamProblems · examproblems.com/courses/management-accounting