BEP volume and effect of price rise

Assumption

As printed, the selling price (Rs 8,000) is lower than the variable cost (Rs 50,000), so every unit sold loses money and no break-even exists. The price is taken as a misprint for Rs 80,000 per unit (the alternative reading, v = Rs 5,000, is given at the end).

Break-even volume

Contribution per unit = p − v = 80,000 − 50,000 = Rs 30,000 Q* = FC / (p − v) = 60,000,000 / 30,000 = 2,000 units (Break-even sales = 2,000 × 80,000 = Rs 160 million.)

Effect of a 20% price rise

New price p' = 80,000 × 1.20 = Rs 96,000 New contribution = 96,000 − 50,000 = Rs 46,000 New break-even Q' = 60,000,000 / 46,000 = 1,304.3, about 1,305 units

Effect on profit at any volume Q: profit increases by (96,000 − 80,000) × Q = Rs 16,000 per unit sold. At the old break-even volume of 2,000 units, profit changes from nil to 2,000 × 46,000 − 60,000,000 = Rs 32 million profit.

Break-even falls by 695.7 units (34.8%), so the project becomes less risky and more profitable.

Answer: BEP = 2,000 units; after a 20% price rise BEP = about 1,305 units and profit rises by Rs 16,000 per unit sold (Rs 32 million at 2,000 units).

If instead v = Rs 5,000 and p = Rs 8,000: BEP = 60,000,000 / 3,000 = 20,000 units; new p = 9,600 gives BEP = 60,000,000 / 4,600 = 13,043 units.