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
Business Fundamentals: cram pack
Formula sheets, the key method steps for every topic and 8 practice problems, with full solutions at the back.
1Formulas and methods
2Practice problems
1.Marketing principlesMedium
Why might a researcher choose in-depth interviews rather than a large questionnaire?
- ATo avoid any interviewer influence
- BTo survey thousands of people cheaply
- CTo produce statistically representative percentages for the market
- DTo explore customers' motives and feelings in detail
2.Marketing principlesHard
A company sells printers cheaply but charges high prices for ink cartridges. This is:
- ACaptive product pricing
- BBundle pricing
- CPenetration pricing for both products
- DPsychological pricing
3.Economics conceptsMedium
Crowding out refers to:
- AImports replacing domestic production
- BOvercrowded public services
- CToo many firms entering a market
- DHigher government borrowing raising interest rates and reducing private investment
4.Economics conceptsHard
In Spence's job market signalling model, education can be valuable to employers even if it does not raise productivity because:
- AEmployers are required by law to hire graduates
- BIt is less costly for high-ability workers to acquire, so it reveals their type
- CIt reduces the wages employers must pay
- DIt guarantees that every graduate is highly productive
5.Financial accountingMedium
Trade receivables are €50,000 and annual credit sales are €365,000. What are the receivable days?
- A73 days
- B7.3 days
- C50 days
- D36.5 days
6.Financial accountingHard
A company borrows at 5% interest to invest in assets that earn 12%. What is the likely effect on return on equity?
- AROE falls, because interest is an expense
- BROE rises, but financial risk also increases
- CROE stays the same, because debt is not equity
- DROE rises and financial risk falls
7.Break-even analysisMedium
A product sells for €16 with a variable cost of €6 per unit. Fixed costs are €15 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €3 000 after tax?
p = €16v = €6F = €15 000T = 25%after-tax profit = €3 000
Q = units
8.Break-even analysisHard
A company sells 10 000 units at €55 each, with a variable cost of €45 per unit and fixed costs of €50 000. By what percentage %ΔΠ does operating profit change if sales volume falls by 15%?
Q = 10 000p = €55v = €45F = €50 000%ΔQ = −15%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: D · To explore customers' motives and feelings in detail
Why this is the answer
In-depth interviews give rich, qualitative insight into why people behave as they do. Questionnaires suit measuring how many people think or do something.
Answer
D · To explore customers' motives and feelings in detail
2.Marketing principles
Answer: A · Captive product pricing
Why this is the answer
Captive product pricing sets a low price for the main product and earns margins on necessary consumables.
Answer
A · Captive product pricing
3.Economics concepts
Answer: D · Higher government borrowing raising interest rates and reducing private investment
Why this is the answer
When government borrowing raises interest rates, some private investment is no longer profitable, reducing the net effect of fiscal expansion.
Answer
D · Higher government borrowing raising interest rates and reducing private investment
4.Economics concepts
Answer: B · It is less costly for high-ability workers to acquire, so it reveals their type
Why this is the answer
If acquiring education costs less for able workers, only they find it worth getting, so it separates types and solves the hidden information problem.
Answer
B · It is less costly for high-ability workers to acquire, so it reveals their type
5.Financial accounting
Answer: C · 50 days
Why this is the answer
€50,000 ÷ €365,000 × 365 = 50 days. This is the average time customers take to pay.
Answer
C · 50 days
6.Financial accounting
Answer: B · ROE rises, but financial risk also increases
Why this is the answer
Positive financial leverage: assets earn more than the debt costs, so profit per euro of equity rises. If returns drop below 5%, leverage works against shareholders.
Answer
B · ROE rises, but financial risk also increases
7.Break-even analysis
Answer: Q = 1900 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 − 0.25) = €4 000
Units needed
Q = (15 000 + 4 000)/10 = 1 900
Answer
Q = 1 900 units
8.Break-even analysis
Answer: %ΔΠ = −30 %
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 = 10 000·10 = €100 000
Π = 100 000 − 50 000 = €50 000
DOL
DOL = 100 000/50 000 = 2
Change in profit
%ΔΠ = 2·(−15%) = −30%
Answer
%ΔΠ = −30%
Check: new profit = 8 500·10 − 50 000 = €35 000.00.
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