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 €25 with a variable cost of €20 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 €3 000 after tax?
p = €25v = €20F = €7 500T = 20%after-tax profit = €3 000
Q = units
2.Break-even analysisHard
A company sells 1 000 units at €51 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 = 1 000p = €51v = €45F = €3 000%ΔQ = +12%
%ΔΠ = %
3.Financial accountingMedium
Why can a profitable company run out of cash?
- ACash is not recorded in accounting
- BProfit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
- CProfit always equals cash
- DProfitable companies never pay taxes
4.Financial accountingHard
Inventory days are 60, receivable days 45 and payable days 30. What is the cash conversion (operating) cycle?
- A135 days
- B105 days
- C75 days
- D15 days
3Solutions
1.Break-even analysis
Answer: Q = 2250 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
3 000/(1 − 0.2) = €3 750
Units needed
Q = (7 500 + 3 750)/5 = 2 250
Answer
Q = 2 250 units
2.Break-even analysis
Answer: %ΔΠ = 24 %
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 = 1 000·6 = €6 000
Π = 6 000 − 3 000 = €3 000
DOL
DOL = 6 000/3 000 = 2
Change in profit
%ΔΠ = 2·(+12%) = +24%
Answer
%ΔΠ = +24%
Check: new profit = 1 120·6 − 3 000 = €3 720.00.
3.Financial accounting
Answer: B · Profit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
Why this is the answer
Profit is measured on an accrual basis; growth can tie up cash in inventory and receivables, so cash flow can be negative despite profits.
Answer
B · Profit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
4.Financial accounting
Answer: C · 75 days
Why this is the answer
60 + 45 − 30 = 75 days between paying suppliers and collecting cash from customers. A shorter cycle needs less working capital finance.
Answer
C · 75 days
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