The P/V Ratio of a firm is 50% and margin of safety is 40%. You are required to work out BEP and net profit if the sales volume is Rs. 5,00,000:

Question

Accepted Answer

The correct option is 4:

This question requires the application of Cost-Volume-Profit (CVP) analysis formulas, specifically relating to the Profit/Volume (P/V) Ratio, Sales, Break-Even Point (BEP), and Margin of Safety (MOS). The margin of safety percentage is the crucial link. The Margin of Safety is defined as the excess of actual or budgeted sales over the break-even sales, and can be expressed as a percentage of total sales.

**Step 1: Calculating the Break-Even Point (BEP)**
The formula for Margin of Safety (MOS) percentage in relation to sales and BEP is:
MOS% = (Actual Sales - BEP) / Actual Sales.
Given MOS is 40%, we can rearrange this to find the BEP sales:
BEP = Actual Sales \* (1 - MOS%)
BEP = Rs. 5,00,000 \* (1 - 0.40)
BEP = Rs. 5,00,000 \* 0.60 = Rs. 3,00,000.

**Step 2: Calculating the Net Profit**
Net Profit (P) is calculated by multiplying the Margin of Safety sales by the P/V Ratio.
First, calculate the Margin of Safety in Rupees (MOS Sales):
MOS Sales = Actual Sales - BEP = Rs. 5,00,000 - Rs. 3,00,000 = Rs. 2,00,000.
Then, calculate the Net Profit:
Net Profit = MOS Sales \* P/V Ratio
Net Profit = Rs. 2,00,000 \* 0.50 = Rs. 1,00,000.
Thus, the correct BEP is Rs. 3,00,000 and the Net Profit is Rs. 1,00,000.

The incorrect option is 1:
Rs. 2,50,000 and Rs. 1,50,000 would imply a BEP of Rs. 2,50,000, which means the Margin of Safety is 50% (Rs. 5,00,000 - Rs. 2,50,000) / Rs. 5,00,000, contradicting the given MOS of 40%. Furthermore, a BEP of Rs. 2,50,000 would mean Fixed Cost (FC) is Rs. 1,25,000 (Rs. 2,50,000 \* 0.50 P/V Ratio). At sales of Rs. 5,00,000, Contribution is Rs. 2,50,000 (Rs. 5,00,000 \* 0.50), leading to a Net Profit of Rs. 1,25,000 (Contribution - FC), not Rs. 1,50,000.

The incorrect option is 2:
Rs. 5,00,000 and Rs. 3,00,000 is incorrect because a BEP of Rs. 5,00,000 means that the firm is operating exactly at its Break-Even Point, resulting in zero profit and a Margin of Safety of 0%. This directly contradicts the given MOS of 40% and would not yield a Net Profit of Rs. 3,00,000. The calculated profit value of Rs. 3,00,000 is also inconsistent with the P/V Ratio and sales volume.

The incorrect option is 3:
Rs. 1,50,000 and Rs. 50,000 is incorrect as a BEP of Rs. 1,50,000 would result in a Margin of Safety of 70% ((Rs. 5,00,000 - Rs. 1,50,000) / Rs. 5,00,000), which is not the given 40%. A 70% MOS would equate to MOS Sales of Rs. 3,50,000, and with a P/V Ratio of 50%, the Net Profit would be Rs. 1,75,000 (Rs. 3,50,000 \* 0.50), not Rs. 50,000. This option significantly undervalues the BEP and the corresponding Net Profit based on the stated parameters.