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
In online advertising, what does CPM mean?
- ACustomers per market
- BClicks per month
- CCost per minute of video viewing
- DCost per thousand impressions
2.Marketing principlesHard
A supermarket sells bread below cost to attract shoppers who then buy other, higher-margin items. This is:
- AValue-based pricing
- BPrice skimming
- CCost-plus pricing
- DLoss leader pricing
3.Economics conceptsMedium
A price ceiling set below the equilibrium price typically causes:
- AA surplus
- BAn increase in supply
- CNo change in the market
- DA shortage
4.Economics conceptsHard
Okun's law describes:
- AThe relationship between tax rates and revenue
- BThe link between money supply and prices
- CA positive relationship between inflation and nominal interest rates over time
- DA negative relationship between output growth and changes in unemployment
5.Financial accountingMedium
Operating profit is €120,000 and interest expense is €30,000. What is interest cover?
- A4 times
- B3 times
- C0.25 times
- D90,000 times
6.Financial accountingHard
Closing inventory this year is overstated by €10,000 by mistake. What is the effect on profit, if not corrected?
- AOnly this year's profit is understated
- BThis year's profit is overstated and next year's understated by €10,000
- CBoth years' profits are overstated
- DProfit is unaffected; only the balance sheet changes
7.Break-even analysisMedium
A product sells for €12 per unit with a variable cost of €4 per unit. Fixed costs are €12 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €12 000p = €12v = €4profit = €6 000
Q = units
8.Break-even analysisHard
A product sells for €33 per unit, with a variable cost of €30 per unit and fixed costs of €6 000 per year. Budgeted sales are 3 200 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €6 000p = €33v = €30budget = 3 200
MS = %
3Solutions
1.Marketing principles
Answer: D · Cost per thousand impressions
Why this is the answer
CPM is the price for 1,000 ad impressions. It suits awareness goals; cost per click (CPC) and cost per acquisition (CPA) tie spending to actions.
Answer
D · Cost per thousand impressions
2.Marketing principles
Answer: D · Loss leader pricing
Why this is the answer
A loss leader brings traffic into the store. It works when customers buy enough profitable items during the same visit.
Answer
D · Loss leader pricing
3.Economics concepts
Answer: D · A shortage
Why this is the answer
A binding maximum price raises quantity demanded and lowers quantity supplied, creating excess demand, as with rent control.
Answer
D · A shortage
4.Economics concepts
Answer: D · A negative relationship between output growth and changes in unemployment
Why this is the answer
Okun observed that unemployment falls when real GDP grows faster than its trend rate and rises when growth is below trend.
Answer
D · A negative relationship between output growth and changes in unemployment
5.Financial accounting
Answer: A · 4 times
Why this is the answer
€120,000 ÷ €30,000 = 4. The company earns its interest four times over; low cover signals a risk of not meeting interest payments.
Answer
A · 4 times
6.Financial accounting
Answer: B · This year's profit is overstated and next year's understated by €10,000
Why this is the answer
Higher closing inventory reduces cost of sales, raising this year's profit. Next year opening inventory is too high, increasing cost of sales and lowering profit by the same amount.
Answer
B · This year's profit is overstated and next year's understated by €10,000
7.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).
Contribution margin per unit
p − v = 12 − 4 = €8
Units for the target profit
Q = (F + profit)/(p − v) = (12 000 + 6 000)/8 = 2 250
Answer
Q = 2 250 units
8.Break-even analysis
Answer: MS = 37.5 %
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) = 6 000/3 = 2 000
Margin of safety
MS = (3 200 − 2 000)/3 200·100 = 37.5%
Answer
MS = 37.5%
ExamProblems · examproblems.com/courses/business-fundamentals