Understanding Desired Sales Calculation for Target Profit

The question asks us to determine the total sales revenue required for the company to achieve a specific profit target of Rs. 1,20,000. This calculation involves using concepts from cost-volume-profit (CVP) analysis, specifically focusing on fixed costs, variable costs, and contribution margin.

Analyzing the Provided Cost and Sales Data

Let's break down the information given in the table:

Calculating Key Cost Accounting Components

Before we can calculate the desired sales, we need to determine the total variable cost per unit, the contribution margin per unit, and the total fixed costs.

• Total Variable Cost per Unit: This is the sum of all variable costs associated with producing and selling one unit.

  \(\text{Total Variable Cost per unit} = \text{Variable manufacturing cost per unit} + \text{Variable selling cost per unit}\)

  \(\text{Total Variable Cost per unit} = \text{Rs. } 11 + \text{Rs. } 3 = \text{Rs. } 14\)

• Contribution Margin per Unit: This is the revenue per unit remaining after deducting the variable costs per unit. It represents the amount each unit sale contributes towards covering fixed costs and generating profit.

  \(\text{Contribution Margin per unit} = \text{Sale price per unit} - \text{Total Variable Cost per unit}\)

  \(\text{Contribution Margin per unit} = \text{Rs. } 20 - \text{Rs. } 14 = \text{Rs. } 6\)

• Total Fixed Costs: This is the sum of all fixed costs incurred by the company over a year. These costs do not change with the level of production or sales within a relevant range.

  \(\text{Total Fixed Costs} = \text{Fixed factory overheads} + \text{Fixed selling costs}\)

  \(\text{Total Fixed Costs} = \text{Rs. } 5,40,000 + \text{Rs. } 2,52,000 = \text{Rs. } 7,92,000\)

Formula for Desired Sales to Achieve Target Profit

The formula to calculate the number of units that must be sold to achieve a specific target profit is:

\(\text{Desired Sales (Units)} = \frac{\text{Fixed Costs} + \text{Target Profit}}{\text{Contribution Margin per unit}}\)

To find the desired sales in rupees, we multiply the desired sales in units by the sale price per unit:

\(\text{Desired Sales (Rupees)} = \text{Desired Sales (Units)} \times \text{Sale price per unit}\)

Calculating Desired Sales (Rupees)

Using the formula and the values we've calculated:

1. First, calculate the total amount needed to cover fixed costs and achieve the target profit:

   \(\text{Amount Needed} = \text{Fixed Costs} + \text{Target Profit}\)

   \(\text{Amount Needed} = \text{Rs. } 7,92,000 + \text{Rs. } 1,20,000 = \text{Rs. } 9,12,000\)

2. Next, calculate the desired sales in units using the contribution margin per unit:

   \(\text{Desired Sales (Units)} = \frac{\text{Rs. } 9,12,000}{\text{Rs. } 6 \text{ per unit}}\)

   \(\text{Desired Sales (Units)} = 1,52,000 \text{ units}\)

3. Finally, calculate the desired sales in rupees by multiplying the desired units by the sale price per unit:

   \(\text{Desired Sales (Rupees)} = 1,52,000 \text{ units} \times \text{Rs. } 20 \text{ per unit}\)

   \(\text{Desired Sales (Rupees)} = \text{Rs. } 30,40,000\)

Alternatively, we can use the contribution margin ratio. The contribution margin ratio is:

\(\text{Contribution Margin Ratio} = \frac{\text{Contribution Margin per unit}}{\text{Sale price per unit}} = \frac{\text{Rs. } 6}{\text{Rs. } 20} = 0.30 \text{ or } 30\%\)

The formula for desired sales in rupees using the contribution margin ratio is:

\(\text{Desired Sales (Rupees)} = \frac{\text{Fixed Costs} + \text{Target Profit}}{\text{Contribution Margin Ratio}}\)

\(\text{Desired Sales (Rupees)} = \frac{\text{Rs. } 7,92,000 + \text{Rs. } 1,20,000}{0.30}\)

\(\text{Desired Sales (Rupees)} = \frac{\text{Rs. } 9,12,000}{0.30}\)

\(\text{Desired Sales (Rupees)} = \text{Rs. } 30,40,000\)

Both methods yield the same result.

Conclusion on Desired Sales Value

To earn a profit of Rs. 1,20,000, the company needs to achieve sales revenue of Rs. 30,40,000.

Revision Table: Key Calculations

Additional Information: Cost-Volume-Profit (CVP) Analysis

Cost-Volume-Profit (CVP) analysis is a fundamental tool in managerial accounting. It helps managers understand the relationships between costs, volume (sales quantity), and profit. Key concepts in CVP analysis include:

• Break-Even Point: The level of sales (in units or rupees) at which total revenues equal total costs, resulting in zero profit. It's the point where the company just covers all its costs.
• Contribution Margin: The amount of revenue remaining after deducting variable costs. It represents the amount available to cover fixed costs and contribute to profit. It can be expressed per unit or as a total.
• Contribution Margin Ratio: The contribution margin expressed as a percentage of sales revenue. It indicates the proportion of each sales rupee that is available to cover fixed costs and profit.
• Target Profit Analysis: An extension of break-even analysis used to determine the sales level required to achieve a specific profit goal. This is what was calculated in the problem above.
• Margin of Safety: The excess of actual or planned sales over the break-even sales. It indicates how much sales can drop before the company incurs a loss.

CVP analysis relies on several assumptions, such as linearity of costs and revenues, constant sales mix (if multiple products), and constant efficiency. Despite these assumptions, it provides valuable insights for pricing decisions, cost control, and profit planning.