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 630 units at €38 each. The variable cost is €30 per unit and fixed costs are €4 000. Find the degree of operating leverage DOL at this sales level.
Q = 630p = €38v = €30F = €4 000
DOL =
2.Break-even analysisHard
A product sells for €28 per unit, with a variable cost of €20 per unit and fixed costs of €9 600 per year. Budgeted sales are 1 500 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €9 600p = €28v = €20budget = 1 500
MS = %
3.Financial accountingMedium
Trade receivables are €50,000 and annual credit sales are €365,000. What are the receivable days?
- A73 days
- B50 days
- C36.5 days
- D7.3 days
4.Financial accountingHard
A company's debt-to-equity ratio rises sharply. What does this usually indicate?
- AThat shareholders invested more money
- BHigher financial risk because the company relies more on borrowed money
- CBetter liquidity in the short term
- DHigher profitability
3Solutions
1.Break-even analysis
Answer: DOL = 4.846
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 = 630·(38 − 30) = €5 040
Operating profit
Π = 5 040 − 4 000 = €1 040
DOL
DOL = 5 040/1 040 = 4.846
Answer
DOL = 4.846
2.Break-even analysis
Answer: MS = 20 %
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) = 9 600/8 = 1 200
Margin of safety
MS = (1 500 − 1 200)/1 500·100 = 20%
Answer
MS = 20%
3.Financial accounting
Answer: B · 50 days
Why this is the answer
€50,000 ÷ €365,000 × 365 = 50 days. This is the average time customers take to pay.
Answer
B · 50 days
4.Financial accounting
Answer: B · Higher financial risk because the company relies more on borrowed money
Why this is the answer
A higher ratio means more leverage: interest and repayments must be met whatever the results, so financial risk rises, although returns to shareholders may also rise.
Answer
B · Higher financial risk because the company relies more on borrowed money
ExamProblems · examproblems.com/courses/management-accounting