Question

KK, an aspiring entrepreneur wanted to set up a pen drive manufacturing unit. Since technology was changing very fast, he wanted to carefully gauge the demand and the likely profits before investing. Market survey indicated that he would be able to sell 1 lac units before customers shifted to different gadgets. KK realized that he had to incur two kinds of costs: fixed costs (the costs which do not change, irrespective of the number of units of pen drives produced) and variable costs (= variable cost per unit multiplied by the number of units). KK expected the fixed cost to be Rs. 40 lac and the variable cost to be Rs. 100 per unit. He expected each pen drive to be sold at Rs. 200.

What would be the break-even point (defined as no profit, no loss situation) for KK's factory, in terms of sales?

• A. Rs. 80 lac
• B. Rs. 100 lac
• C. Rs. 120 lac
• D. Rs. 140 lac

Hint:

Find the number of units where revenue equals total cost (fixed plus variable cost), then convert that quantity into a sales value by multiplying by the selling price.

Answer 1

The Correct Option is A

A quicker way to reach break-even sales is through the contribution margin, the amount each unit adds towards covering the fixed cost after paying for its own variable cost.

1. Find the contribution per unit: selling price minus variable cost per unit = $200 - 100 = 100$ rupees. This is how much of the fixed cost gets covered by selling one extra pen drive.
2. Find the break-even quantity: divide the fixed cost by the contribution per unit: $\dfrac{40,00,000}{100} = 40,000$ units. Below this quantity KK makes a loss, above it he makes a profit.
3. Convert to a sales value using the contribution margin ratio instead of multiplying directly: the contribution margin ratio is $\dfrac{100}{200} = 0.5$, meaning half of every rupee of sales goes towards covering fixed cost and profit. So break-even sales = $\dfrac{\text{Fixed cost}}{\text{Contribution margin ratio}} = \dfrac{40,00,000}{0.5} = 80,00,000$.

Both routes land on the same figure: break-even sales of Rs. 80 lac, so option A is correct.

Let's summarize:

• Contribution per unit (price minus variable cost) tells you how many units are needed to cover fixed cost.
• Dividing fixed cost by the contribution margin ratio gives break-even sales directly, without first finding the quantity.

So the break-even point in terms of sales is Rs. 80 lac.