If the selling price of a product (per unit) is ₹ 20, variable cost (per unit) is ₹ 14, fixed factory overheads (per year) is ₹ 5,40,000 and fixed selling overheads is ₹ 2,52,000, the break-even in terms of sales volume and the number of units to be sold to earn a profit of ₹ 60,000 will be which one of the following?Break-even Volume of Sales Units to be sold for the desired profit (1) ₹ 24,60,000 1,36,000 units (2) ₹ 25,40,000 1,40,000 units (3) ₹ 26,40,000 1,42,000 units (4) ₹ 28,60,000 1,48,000 units
₹ 26,40,000 and 1,42,000 units
Concept: In marginal costing, contribution per unit equals selling price minus variable cost, and the break-even point is where total contribution just covers total fixed cost; sales value break-even uses the P/V ratio, while units for a target profit add the profit to fixed cost.
Contribution per unit \(= 20 - 14 = 6\), and the P/V ratio \(= \frac{6}{20} = 0.3\). Total fixed cost \(= 5{,}40{,}000 + 2{,}52{,}000 = 7{,}92{,}000\) (both factory and selling overheads are fixed).
Break-even sales value \(= \frac{\text{Fixed cost}}{\text{P/V ratio}} = \frac{7{,}92{,}000}{0.3} = 26{,}40{,}000\).
Units to earn a profit of 60,000 \(= \frac{\text{Fixed cost} + \text{Profit}}{\text{Contribution per unit}} = \frac{7{,}92{,}000 + 60{,}000}{6} = \frac{8{,}52{,}000}{6} = 1{,}42{,}000\) units.
Checking the options: only option (3) pairs the correct break-even value of 26,40,000 with 1,42,000 units; the others use a wrong fixed-cost or contribution figure and are ruled out.
Hence the break-even is ` 26,40,000 and 1,42,000 units are needed for the desired profit.
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