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
A "push" promotional strategy focuses on:
- APromoting the product to intermediaries such as wholesalers and retailers
- BUsing word-of-mouth exclusively
- CLowering prices online only
- DCreating end-consumer demand through mass advertising so customers ask retailers for it
2.Marketing principlesHard
Geoffrey Moore's "chasm" in technology markets refers to the gap between which adopter groups?
- AEarly majority and late majority
- BEarly adopters and the early majority
- CInnovators and early adopters
- DLate majority and laggards
3.Economics conceptsMedium
Rising consumer confidence would most likely:
- AShift aggregate demand to the right
- BHave no effect on the economy
- CShift aggregate supply to the left
- DShift aggregate demand to the left
4.Economics conceptsHard
In the Prisoner's Dilemma, the Nash equilibrium is:
- ABoth players defect, even though both cooperating would be better
- BBoth players cooperate
- COne player cooperates and the other defects, so only one of them gains
- DThere is no equilibrium
5.Financial accountingMedium
Why can a profitable company run out of cash?
- AProfit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
- BProfitable companies never pay taxes
- CCash is not recorded in accounting
- DProfit always equals cash
6.Financial accountingHard
The going concern assumption means financial statements are prepared assuming the entity:
- AWill continue to operate for the foreseeable future
- BWill make a profit every year
- CHas no debts
- DWill be sold within one year
7.Break-even analysisMedium
A product sells for €22 per unit with a variable cost of €18 per unit. Fixed costs are €6 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €6 000p = €22v = €18profit = €2 000
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €18 with a variable cost of €12; product B sells for €22 with a variable cost of €10. They sell in a fixed mix of 3 units of A for every 1 of B. Fixed costs are €18 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €18, vA = €12pB = €22, vB = €10A : B = 3 : 1F = €18 000
Q = units
3Solutions
1.Marketing principles
Answer: A · Promoting the product to intermediaries such as wholesalers and retailers
Why this is the answer
Push strategies use trade promotions and personal selling to channel partners; pull strategies stimulate end-consumer demand so retailers stock the product.
Answer
A · Promoting the product to intermediaries such as wholesalers and retailers
2.Marketing principles
Answer: B · Early adopters and the early majority
Why this is the answer
Early adopters accept risk for advantage, while the early majority want proven, complete solutions and references. Many products fail to make this transition.
Answer
B · Early adopters and the early majority
3.Economics concepts
Answer: A · Shift aggregate demand to the right
Why this is the answer
Higher confidence raises consumption at every price level, shifting AD right and raising output and, possibly, prices in the short run.
Answer
A · Shift aggregate demand to the right
4.Economics concepts
Answer: A · Both players defect, even though both cooperating would be better
Why this is the answer
Each player's best response is to defect whatever the other does, so mutual defection is the equilibrium, although mutual cooperation would give both a higher payoff.
Answer
A · Both players defect, even though both cooperating would be better
5.Financial accounting
Answer: A · 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
A · Profit includes credit sales and non-cash items, while cash may be tied up in receivables and inventory
6.Financial accounting
Answer: A · Will continue to operate for the foreseeable future
Why this is the answer
Unless management intends or must liquidate, assets and liabilities are measured assuming continued operations; material doubts must be disclosed.
Answer
A · Will continue to operate for the foreseeable future
7.Break-even analysis
Answer: Q = 2000 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 = 22 − 18 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (6 000 + 2 000)/4 = 2 000
Answer
Q = 2 000 units
8.Break-even analysis
Answer: Q = 2400 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 = €6, cmB = €12
Weighted contribution margin
(3·6 + 1·12)/4 = €7.50
Break-even units
Q = 18 000/7.5 = 2 400
A: 1 800, B: 600
Answer
Q = 2 400 units
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