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 explore customers' motives and feelings in detail
- BTo survey thousands of people cheaply
- CTo avoid any interviewer influence
- DTo produce statistically representative percentages for the market
2.Marketing principlesHard
Research shows young consumers see a long-established brand as old-fashioned, although product quality is good. What is the most suitable strategy?
- ARepositioning the brand through new communication and image
- BCutting the price to the lowest in the market
- CChanging the distribution to exclusive dealers only
- DWithdrawing the product immediately
3.Economics conceptsMedium
In a simple closed economy without taxes, the MPC is 0.8. The Keynesian spending multiplier is:
- A8
- B0.8
- C1.25
- D5
4.Economics conceptsHard
Which is a key difference between the CPI and the GDP deflator?
- AThe CPI covers investment goods; the GDP deflator does not
- BThe GDP deflator includes imported goods; the CPI does not
- CThey always give exactly the same inflation rate
- DThe CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
5.Financial accountingMedium
Budgeted sales are 1,500 units and the break-even point is 1,000 units. What is the margin of safety?
- A2,500 units
- B500 units
- C1,500 units
- D1,000 units
6.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
- BRises because interest is fixed
- CFalls by a smaller percentage
- DFalls by a larger percentage
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €25 000 per year and a variable cost of €12 per unit. Method B, more automated, has fixed costs of €37 500 per year and a variable cost of €7 per unit. At what yearly volume Q do both methods cost the same?
FA = €25 000vA = €12FB = €37 500vB = €7
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €8 with a variable cost of €5; product B sells for €18 with a variable cost of €10. They sell in a fixed mix of 5 units of A for every 2 of B. Fixed costs are €15 500 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €8, vA = €5pB = €18, vB = €10A : B = 5 : 2F = €15 500
Q = units
3Solutions
1.Marketing principles
Answer: A · 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
A · To explore customers' motives and feelings in detail
2.Marketing principles
Answer: A · Repositioning the brand through new communication and image
Why this is the answer
Repositioning changes how the target segment sees the brand, for example with updated design, new messages and channels the younger audience uses.
Answer
A · Repositioning the brand through new communication and image
3.Economics concepts
Answer: D · 5
Why this is the answer
1 / (1 − 0.8) = 1 / 0.2 = 5, so an extra €1 of spending can raise income by up to €5.
Answer
D · 5
4.Economics concepts
Answer: D · The CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
Why this is the answer
The CPI uses a fixed basket of consumer goods, including imports, while the deflator covers all domestically produced output with changing weights.
Answer
D · The CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
5.Financial accounting
Answer: B · 500 units
Why this is the answer
Margin of safety = budgeted sales − break-even sales = 500 units, or one third of budgeted sales.
Answer
B · 500 units
6.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
7.Break-even analysis
Answer: Q = 2500 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).
Equal total costs
25 000 + 12Q = 37 500 + 7Q
Solve for Q
Q = (37 500 − 25 000)/(12 − 7) = 2 500
Answer
Q = 2 500 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: Q = 3500 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €3, cmB = €8
Weighted contribution margin
(5·3 + 2·8)/7 = €4.43
Break-even units
Q = 15 500/4.429 = 3 500
A: 2 500, B: 1 000
Answer
Q = 3 500 units
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