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 €45 per unit with a variable cost of €25 per unit. Fixed costs are €40 000 per month. How many units Q must be sold per month to make a profit of €12 000?
F = €40 000p = €45v = €25profit = €12 000
Q = units
2.Break-even analysisHard
A company sells 2 000 units at €40 each, with a variable cost of €30 per unit and fixed costs of €10 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 10%?
Q = 2 000p = €40v = €30F = €10 000%ΔQ = +10%
%ΔΠ = %
3.Financial accountingMedium
When preparing a bank reconciliation, which item explains why the bank statement balance is higher than the cash book balance?
- ACash deposited but not yet credited on the bank statement
- BA direct debit not yet entered in the cash book
- CBank charges not yet entered in the cash book
- DCheques issued but not yet presented to the bank
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 = 2600 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 = 45 − 25 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (40 000 + 12 000)/20 = 2 600
Answer
Q = 2 600 units
2.Break-even analysis
Answer: %ΔΠ = 20 %
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 = 2 000·10 = €20 000
Π = 20 000 − 10 000 = €10 000
DOL
DOL = 20 000/10 000 = 2
Change in profit
%ΔΠ = 2·(+10%) = +20%
Answer
%ΔΠ = +20%
Check: new profit = 2 200·10 − 10 000 = €12 000.00.
3.Financial accounting
Answer: D · Cheques issued but not yet presented to the bank
Why this is the answer
Unpresented cheques have reduced the cash book but not the bank balance. Outstanding deposits, bank charges and unrecorded direct debits work the other way.
Answer
D · Cheques issued but not yet presented to the bank
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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