To earn a target profit of 200 000, that firm must sell
Answer: C
Correct answer: 25 000 units
The target profit is treated as an additional fixed cost to be covered:
\[ Q = \frac{F + \text{target}}{c} = \frac{300\,000 + 200\,000}{20} = 25\,000 \ \text{units} \]The same formula gives the break-even quantity when the target is zero, so this is one relation rather than two.
Please log in or register to report this question.
If that firm's fixed cost rises to 400 000, its break-even quantity becomes
Answer: D
Correct answer: 20 000 units
With the contribution unchanged at 20,
\[ Q_{BE} = \frac{400\,000}{20} = 20\,000 \ \text{units} \]A third more fixed cost has raised the break-even quantity by a third, since the break-even is directly proportional to the fixed cost. The margin of safety at 20,000 units has vanished entirely.
Please log in or register to report this question.
If instead that firm's variable cost rises to 35, its break-even quantity becomes
Answer: A
Correct answer: 20 000 units
The contribution falls to \( 50 - 35 = 15 \), so
\[ Q_{BE} = \frac{300\,000}{15} = 20\,000 \ \text{units} \]A five rupee rise in variable cost has done exactly as much damage as a 100,000 rise in fixed cost did in the previous item - a useful comparison, since the variable cost change looks much the smaller of the two on the face of it.
Please log in or register to report this question.
Alternative A has fixed costs of 100 000 and variable cost 12 a unit; B has 250 000 and 7 a unit. Their indifference point is
Answer: B
Correct answer: 30 000 units
The indifference point is where the two total costs are equal:
\[ 100\,000 + 12Q = 250\,000 + 7Q \]\[ 5Q = 150\,000 \quad \Rightarrow \quad Q = 30\,000 \ \text{units} \]Below 30,000 the lower fixed cost of A wins; above it the lower variable cost of B does. The decision between the two is therefore entirely a judgement about expected volume.
Please log in or register to report this question.
At 40 000 units, which of those two alternatives is cheaper?
Answer: C
Correct answer: B, at 530 000 against A’s 580 000
At 40,000 units,
\[ A: 100\,000 + 12(40\,000) = 580\,000 \]\[ B: 250\,000 + 7(40\,000) = 530\,000 \]so B is cheaper by 50,000. This is above the indifference volume of 30,000, exactly as the previous item predicts, and the saving grows by 5 for every further unit.
Please log in or register to report this question.
A firm sells two products in a 3 to 1 mix with contributions of 20 and 40. Its weighted average contribution per unit is
Answer: D
Correct answer: 25
The mix is three of the first for every one of the second, so the weighted average is
\[ \frac{3(20) + 1(40)}{4} = \frac{100}{4} = 25 \]The simple average of 30 would be right only if the two sold in equal numbers, and it overstates the contribution because the lower-margin product dominates the mix.
Please log in or register to report this question.
With fixed costs of 500 000 and that weighted contribution of 25, the break-even volume is
Answer: A
Correct answer: 20 000 units in the stated mix
Dividing the fixed cost by the weighted contribution,
\[ \frac{500\,000}{25} = 20\,000 \ \text{units} \]that is 15,000 of the first product and 5000 of the second. The qualification matters: the answer holds only at the assumed three-to-one mix, and any shift towards the lower-margin product raises the figure.
Please log in or register to report this question.
A plant with revenue of 800 000, variable costs of 700 000 and fixed costs of 250 000, of which 100 000 are avoidable by closing, should
Answer: B
Correct answer: keep operating, revenue covering variable plus avoidable fixed cost
Only the avoidable costs are relevant to a closure decision. The plant earns a contribution of \( 800\,000 - 700\,000 = 100\,000 \), which exactly meets the 100,000 of fixed cost that closing would save; the other 150,000 continues either way and is irrelevant. Closing would therefore save nothing and would lose whatever the plant contributes in future. The accounting loss of 150,000 is the unavoidable overhead and is not a reason to close.
Please log in or register to report this question.
Match the change with its effect on the break-even quantity.
1. Fixed cost rises 2. Selling price rises 3. Variable cost per unit rises
P. Falls Q. Rises, the cost line shifting up R. Rises, the cost line steepening
Answer: C
Correct answer: 1-Q, 2-P, 3-R
The three changes act differently on the chart. A rise in fixed cost lifts the whole cost line without changing its slope, so the crossing moves right. A rise in selling price steepens the revenue line, so the crossing moves left and the break-even falls. A rise in variable cost per unit steepens the cost line, so the crossing again moves right - the same direction as a fixed cost rise but by a different mechanism.
Please log in or register to report this question.
Match the quantity with its formula.
1. Break-even quantity 2. Break-even sales value 3. Contribution margin ratio
P. Contribution divided by price Q. Fixed cost divided by contribution per unit R. Fixed cost divided by the contribution margin ratio
Answer: D
Correct answer: 1-Q, 2-R, 3-P
The three formulae are related but distinct. The break-even quantity is fixed cost over contribution per unit. The break-even sales value is fixed cost over the contribution margin ratio, which gives the same answer expressed in money. And the ratio itself is contribution over price. Confusing the two divisors is the commonest error, and the units are the check: a quantity comes from dividing by a rupees-per-unit figure, a value from dividing by a pure ratio.
Please log in or register to report this question.
