Question

A company has a fixed cost of INR 3,00,000 and a variable cost of INR 150 per unit for manufacturing of a product. The company sells 5,000 units of that product making a profit equivalent to 20% of the total sales revenue.

The break-even quantity for that product is _____ units (rounded off to the nearest integer).

Hint:

First find the selling price per unit using the given profit percentage of revenue, then apply the break-even formula: Fixed Cost divided by (Selling Price minus Variable Cost).

Answer 1

Correct Answer: 2667

Step 1: Understanding the Concept:
This is a break-even analysis problem where the selling price is not given directly.
We first need to find the selling price per unit from the condition that profit equals 20% of the sales revenue, then use the standard break-even formula.

Step 2: Key Formula or Approach:
Profit is defined as:
\[ \text{Profit} = (P - v)Q - FC \]
where P is the selling price per unit, v is the variable cost per unit, Q is the quantity sold, and FC is the fixed cost.
Since profit equals 20% of total revenue \( PQ \), we can write \( \text{Profit} = 0.2PQ \) and solve directly for P.
The break-even quantity is then:
\[ Q_{BEP} = \frac{FC}{P - v} \]

Step 3: Detailed Explanation:
Given: FC = 300000, v = 150, Q = 5000.
Setting the two expressions for profit equal:
\[ (P - 150)(5000) - 300000 = 0.2 \times P \times 5000 \]
\[ 5000P - 750000 - 300000 = 1000P \]
\[ 4000P = 1050000 \]
\[ P = 262.5 \]
Now apply the break-even formula:
\[ Q_{BEP} = \frac{300000}{262.5 - 150} = \frac{300000}{112.5} = 2666.67 \]

Final Answer:
Rounding to the nearest integer, the break-even quantity is 2667 units.
\[ \boxed{Q_{BEP} = 2667 \text{ units}} \]