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Break-even units and output for desired profit

Short answer

Fixed cost Rs 40,000. Variable cost per unit = (85,000−40,000)/15,000 = Rs 3, price = 105,000/15,000 = Rs 7. Break-even quantity = 40,000/(7−3) = 10,000 units. For desired profit Rs 50,000, output = (40,000+50,000)/4 = 22,500 units.

A company produces an electronics timing switch that is used in consumer and commercial products made by several other manufacturing firms. The fixed cost and total cost are Rs. 40,000 and Rs. 85,000 respectively. The total sales are Rs. 1,05,000 and sales volume is 15,000 for this situation. i) Find the breakeven points in terms of number of units. ii) What should be the output if the profit desired is Rs. 50,000?

Data

  • Fixed cost FC = Rs 40,000; total cost TC = Rs 85,000 at 15,000 units
  • Sales = Rs 105,000 at 15,000 units

Unit values

  • Total variable cost = 85,000 − 40,000 = Rs 45,000, so v = 45,000 / 15,000 = Rs 3 per unit
  • Selling price p = 105,000 / 15,000 = Rs 7 per unit
  • Contribution per unit = p − v = 7 − 3 = Rs 4

(i) Break-even point

Q* = FC / (p − v) = 40,000 / 4 = 10,000 units (Break-even sales = 10,000 × 7 = Rs 70,000.)

(ii) Output for a desired profit of Rs 50,000

Revenue − cost = profit: 7Q − (40,000 + 3Q) = 50,000 Q = (40,000 + 50,000) / 4 = 22,500 units

Check: 22,500 × 7 = 157,500; cost = 40,000 + 67,500 = 107,500; profit = 50,000.

Answer: BEP = 10,000 units; output for Rs 50,000 profit = 22,500 units. (The desired output exceeds the 15,000 units now sold, so sales must grow by 7,500 units.)

✓ Answer checked by Claude Opus 5.5 (high effort)

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