Compute Sales When - Fixed Cost Rs.40,000 Profit Rs. 20,000 BEP Rs. 80,000

Q. Compute Sales When - Fixed Cost Rs.40,000 Profit Rs. 20,000 BEP Rs. 80,000

To compute sales in the context of fixed costs, profit, and the break-even point (BEP), it's important to understand the relationship between these elements and how they fit into a business's financial structure. In this problem, we are given that the fixed costs are Rs. 40,000, the target profit is Rs. 20,000, and the break-even point (BEP) in sales is Rs. 80,000. We will go step by step through the process, breaking down the formulas and concepts necessary to compute the required sales.

1. Understanding Fixed Costs, Profit, and BEP

Before proceeding to the calculation, let's first clarify the concepts involved:

·        Fixed Costs: These are costs that do not vary with the level of production or sales, such as rent, salaries, and insurance. In this case, the fixed costs are Rs. 40,000. Fixed costs are incurred regardless of how much the company sells or produces.

·        Profit: The profit is the amount of money a business makes after all expenses have been deducted from revenue. In this scenario, we are aiming for a profit of Rs. 20,000.

·        Break-Even Point (BEP): The BEP is the point at which total sales exactly cover total costs, meaning there is no profit or loss. The BEP is Rs. 80,000 in this case, meaning the business needs to achieve Rs. 80,000 in sales to break even—i.e., to cover both fixed and variable costs, with zero profit or loss.

The goal is to compute the total sales required to achieve a specific profit of Rs. 20,000, given the fixed costs and BEP.

2. Basic Sales Equation

The sales equation is crucial for understanding how sales, fixed costs, and profit interact. The general formula for sales is:

$$\text{Sales} = \text{Fixed Costs} + \text{Variable Costs} + \text{Profit}$$

However, this formula assumes we know the total costs (fixed and variable), and in this case, we don’t have direct information on variable costs, so we need to approach this calculation by working with the concept of contribution margin.

3. Contribution Margin

The contribution margin is the amount from each sale that contributes toward covering fixed costs and generating profit. It is calculated as:

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$$\text{Contribution Margin} = \text{Selling Price per Unit} - \text{Variable Cost per Unit}$$

The contribution margin ratio, which represents the proportion of sales that contributes to covering fixed costs and generating profit, can be calculated as:

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$$\text{Contribution Margin Ratio} = \frac{\text{Contribution Margin per Unit}}{\text{Selling Price per Unit}}$$

4. Break-Even Point and Contribution Margin

The break-even point in sales is the level of sales at which total contribution margin equals fixed costs. Therefore, we can relate the BEP to the contribution margin ratio using the following formula:

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$$\text{BEP in Sales} = \frac{\text{Fixed Costs}}{\text{Contribution Margin Ratio}}$$

Given that the BEP is Rs. 80,000 and the fixed costs are Rs. 40,000, we can rearrange this equation to solve for the contribution margin ratio:

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$$\text{Contribution Margin Ratio} = \frac{\text{Fixed Costs}}{\text{BEP in Sales}} = \frac{40,000}{80,000} = 0.5$$

Thus, the contribution margin ratio is 50%. This means that for every unit of sale, 50% of the revenue contributes toward covering fixed costs and generating profit.

5. Calculating the Sales to Achieve Target Profit

Now that we know the contribution margin ratio is 0.5, we can calculate the sales required to achieve a target profit of Rs. 20,000. The formula to calculate the required sales to achieve a desired profit is:

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$$\text{Required Sales} = \frac{\text{Fixed Costs} + \text{Target Profit}}{\text{Contribution Margin Ratio}}$$

Substituting the given values:

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$$\text{Required Sales} = \frac{40,000 + 20,000}{0.5} = \frac{60,000}{0.5} = 120,000$$

Therefore, to achieve a profit of Rs. 20,000, the business must generate total sales of Rs. 120,000.

6. Verifying the Calculation

To verify this calculation, let’s break down the components:

• Fixed Costs = Rs. 40,000
• Target Profit = Rs. 20,000
• Contribution Margin Ratio = 50%

At sales of Rs. 120,000, the contribution margin would be:

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$$\text{Contribution Margin} = 120,000 \times 0.5 = 60,000$$

This contribution margin of Rs. 60,000 would first cover the fixed costs of Rs. 40,000, leaving a profit of Rs. 20,000, which matches our target.

7. Conclusion

To summarize, the total sales required to achieve a profit of Rs. 20,000, given the fixed costs of Rs. 40,000 and a break-even point of Rs. 80,000, is Rs. 120,000. This calculation is based on the contribution margin ratio, which was derived from the relationship between fixed costs and the BEP. By understanding this relationship, businesses can more effectively plan their sales targets to meet both fixed costs and desired profit levels.

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This approach can be applied to various business scenarios, adjusting for different fixed costs, target profits, and break-even points to help companies set realistic sales targets and assess their financial performance.

 

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