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 company sells 1 880 units at €16 each. The variable cost is €4 per unit and fixed costs are €18 000. Find the degree of operating leverage DOL at this sales level.
Q = 1 880p = €16v = €4F = €18 000
DOL =
2.Break-even analysisHard
A product sells for €26 per unit, with a variable cost of €6 per unit and fixed costs of €16 000 per year. Budgeted sales are 920 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €16 000p = €26v = €6budget = 920
MS = %
3.Financial accountingMedium
Why can a profitable company run out of cash?
- AProfitable companies never pay taxes
- BCash is not recorded in accounting
- CProfit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
- DProfit always equals cash
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
- BKeep the investment at cost and report only the dividends received from S
- CShow one equity-method investment line for its 70% share of S
- DAdd only 70% of each of S's assets, liabilities, income and expenses
3Solutions
1.Break-even analysis
Answer: DOL = 4.947
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.
Total contribution margin
CM = 1 880·(16 − 4) = €22 560
Operating profit
Π = 22 560 − 18 000 = €4 560
DOL
DOL = 22 560/4 560 = 4.947
Answer
DOL = 4.947
2.Break-even analysis
Answer: MS = 13.04 %
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).
Break-even quantity
Q = F/(p − v) = 16 000/20 = 800
Margin of safety
MS = (920 − 800)/920·100 = 13.04%
Answer
MS = 13.04%
3.Financial accounting
Answer: C · 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
C · Profit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
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
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