Understanding the Problem

The question asks us to find the Net Profit given the Profit Volume Ratio (PVR), the Margin of Safety (MOS) percentage, and the total Sales Volume.

Key Formulas

We will use the following standard formulas from cost accounting:

• Profit Volume Ratio (PVR): $PVR = \frac{Profit}{Sales}$ or $PVR = \frac{Sales - Variable \ Cost}{Sales}$
• Margin of Safety (MOS): $MOS = \frac{Net \ Profit}{PVR}$ (This holds when MOS is expressed in value, and PVR is the profit ratio)
• Alternatively, Margin of Safety in percentage relates to sales: $MOS (\%) = \frac{Actual \ Sales - Break-Even \ Sales}{Actual \ Sales} \times 100$

Calculations for Net Profit

We are given:

• Sales Volume = ₹ 1,00,000
• Profit Volume Ratio (PVR) = 50% or 0.50
• Margin of Safety (MOS) = 40%

First, calculate the Margin of Safety in value:

MOS (in value) = MOS (%) $\times$ Sales Volume

MOS (in value) = $40\% \times ₹ 1,00,000 = 0.40 \times ₹ 1,00,000 = ₹ 40,000$

Now, we can use the relationship between Net Profit, MOS (in value), and PVR:

Net Profit = MOS (in value) $\times$ PVR

Net Profit = $₹ 40,000 \times 0.50$

Net Profit = ₹ 20,000

Verification (Optional)

We can verify this using break-even analysis:

1. Calculate Break-Even Sales: $Break-Even \ Sales = Sales \ Volume - MOS \ (in \ value)$ $Break-Even \ Sales = ₹ 1,00,000 - ₹ 40,000 = ₹ 60,000$
2. Calculate Fixed Costs: At the break-even point, Profit is zero. $Profit = (Break-Even \ Sales \times PVR) - Fixed \ Costs$ $0 = (₹ 60,000 \times 0.50) - Fixed \ Costs$ $Fixed \ Costs = ₹ 30,000$
3. Calculate Net Profit at the given Sales Volume: $Net \ Profit = (Sales \ Volume \times PVR) - Fixed \ Costs$ $Net \ Profit = (₹ 1,00,000 \times 0.50) - ₹ 30,000$ $Net \ Profit = ₹ 50,000 - ₹ 30,000 = ₹ 20,000$

Both methods yield the same result.

Conclusion

The calculated Net Profit is ₹ 20,000.