Marginal Costing and Break Even Analysis Questions and Answers

Answer: B

CVP (cost-volume-profit) analysis is the evaluation tool for managerial decisions. It studies how cost and profit respond to changes in volume, which helps in decisions about pricing, product mix, the break-even point and the level of activity needed for a target profit. Job costing, contract costing and process costing are methods of ascertaining cost for different types of production, not tools for evaluating decisions.

Answer: C

The break-even sales are Rs. 83,333. The contribution is sales less variable cost, 1,00,000 - 40,000 = 60,000, so the P/V ratio is 60 per cent. \[\text{BEP} = \frac{\text{Fixed cost}}{\text{P/V}}\] \[= \frac{50{,}000}{0.60} \approx 83{,}333\] Check: at this sales value the contribution is 60 per cent of it, about 50,000, which exactly covers the fixed cost. Rs. 50,000 is the fixed cost itself, and Rs. 1,00,000 is the actual sales, so neither is the break-even point.

Answer: B

The statement that is not an assumption is total variable cost does not change.

Break-even analysis assumes that costs can be split into fixed and variable parts, that total fixed cost stays constant over the relevant range, that variable cost per unit stays constant, so that total variable cost rises in direct proportion to output, that the selling price and general price level stay unchanged, and that the product mix is constant.

If total variable cost did not change, it would behave as a fixed cost and there would be no break-even point to find. The other three options are standard assumptions.

Answer: D

At the operating break-even point EBIT is zero.

The operating break-even point is the level of sales at which revenue just covers all operating costs, fixed and variable, so earnings before interest and tax are nil. In terms of contribution, total contribution equals fixed operating cost.

Sales revenue covering only the fixed cost would ignore variable cost. Equality of fixed and variable cost has nothing to do with break-even. The phrase 'revenue variable cost' in option B is not a defined measure.

Answer: C

Required sales are found by dividing Desired profit plus fixed cost by the contribution margin ratio.

Each rupee of sales leaves a contribution equal to the contribution margin (P/V) ratio. To earn a target profit, total contribution must cover the fixed costs and then provide the profit:

\[ \begin{aligned} &\text{Required sales} \\ &= \frac{\text{Fixed cost} + \text{Desired profit}}{\text{P/V ratio}} \end{aligned} \]

Dividing fixed cost alone gives the break-even sales, where profit is zero. Dividing desired profit alone ignores the fixed costs that must be recovered first, and variable cost is already taken out in computing the contribution margin ratio.

Answer: A

The new total profit is ₹ 87,500.

Variable cost per unit stays at 18 + 9 + 8 = ₹ 35. The new price is 75 percent of ₹ 50, and the new volume is 130 percent of 1,50,000 units:

\[ \begin{aligned} \text{Price} &= 50 \times 0.75 = 37.50 \\ \text{Units} &= 150000 \times 1.30 = 195000 \\ \text{Contribution/unit} &= 37.50 - 35 = 2.50 \end{aligned} \]

\[ \begin{aligned} \text{Contribution} &= 195000 \times 2.50 = 487500 \\ \text{Profit} &= 487500 - 400000 = 87500 \end{aligned} \]

The fixed overhead of ₹ 4,00,000 does not change with volume. The other figures do not follow from the data: the price cut squeezes the unit contribution from ₹ 15 to ₹ 2.50, and the extra 30 percent volume only partly makes up for it, so profit falls from ₹ 18,50,000 to ₹ 87,500.

Answer: D

The required sales are about Rs. 70,31,689.

Required sales = (fixed costs + desired profit) / P/V ratio. Contribution per unit is 37.50 - 17.50 = Rs. 20, so:

\[ \begin{aligned} \text{P/V ratio} &= \frac{20}{37.50} = 53.33\% \\ \text{Required contribution} &= 35{,}00{,}000 + 2{,}50{,}000 \\ &= 37{,}50{,}000 \\ \text{Sales} &= \frac{37{,}50{,}000}{0.5333} \approx 70{,}31{,}689 \end{aligned} \]

The option figure comes from rounding the P/V ratio to 53.33%. With the exact ratio of 8/15 the answer is 187,500 units × Rs. 37.50 = Rs. 70,31,250, which is still nearest option D. Depreciation is part of the Rs. 35,00,000 of fixed cost and needs no separate treatment here; it matters only for a cash break-even point.

Rs. 75,00,000 is what results from taking the P/V ratio as 50%, and Rs. 70,00,000 and Rs. 73,50,000 do not cover the required contribution at the actual ratio.

Answer: C

Margin of safety improves with a decrease of variable cost per unit.

Margin of safety is actual sales minus break-even sales, and break-even sales are fixed cost divided by the P/V ratio. Cutting variable cost per unit raises contribution per unit and the P/V ratio, so the break-even point falls and the gap between actual and break-even sales widens.

The other three work the wrong way. Higher variable cost or a lower selling price shrinks contribution and raises the break-even point, and a fall in sales volume brings actual sales closer to break-even.

Answer: A

Sales at 100% capacity are ₹ 25,00,000.

With a variable cost ratio of 70%, the P/V ratio is the complement, 30%. Break-even sales are fixed cost divided by the P/V ratio:

\[ \begin{aligned} \text{BEP} &= \frac{6{,}00{,}000}{0.30} = 20{,}00{,}000 \\ \text{100\% sales} &= \frac{20{,}00{,}000}{0.80} = 25{,}00{,}000 \end{aligned} \]

Since break-even occurs at 80% of capacity, full capacity sales are ₹ 25,00,000. The option of ₹ 20,00,000 is the break-even sales figure itself, and ₹ 30,00,000 and ₹ 40,00,000 do not follow from the data.

Answer: A

The new break-even sales are Rs. 10,80,000.

\[ \begin{aligned} \text{New price} &= 40 - 10\% = \text{Rs. } 36 \\ \text{Contribution} &= 36 - 30 = \text{Rs. } 6 \\ \text{BEP (units)} &= \frac{1,80,000}{6} = 30,000 \end{aligned} \]

\[ \text{BEP (Rs.)} = 30,000 \times 36 = \text{Rs. } 10,80,000 \]

At the original price the contribution was Rs. 10 and break-even sales Rs. 7,20,000 (18,000 units at Rs. 40). The 10% price cut reduces contribution per unit by 40%, which is why break-even sales rise so sharply.