Calculating Selling Price Using P/V Ratio

This problem requires us to calculate the selling price of a product given its variable cost and the desired Profit/Volume (P/V) Ratio. The P/V Ratio is a key profitability metric used in cost accounting and break-even analysis. It shows the relationship between contribution margin and sales value.

Understanding the P/V Ratio

The P/V Ratio, also known as the Contribution Margin Ratio, indicates the percentage of each sales rupee that is available to cover fixed costs and contribute to profit. It is calculated using the following formula:

\text{P/V Ratio} = \frac{\text{Sales} - \text{Variable Cost}}{\text{Sales}} = \frac{\text{Contribution Margin}}{\text{Sales}}

Where:

• Sales: The total revenue from selling the product.
• Variable Cost: Costs that change directly with the level of production or sales (e.g., direct materials, direct labour).
• Contribution Margin: The revenue remaining after deducting variable costs. It contributes towards covering fixed costs and generating profit.

Applying the Formula to Find Selling Price

We are given the following information for the new product:

• Variable Cost (VC) = Rs. 300
• Desired P/V Ratio = 25% or 0.25

We need to find the Selling Price (SP).

Using the P/V Ratio formula:

\text{P/V Ratio} = \frac{\text{SP} - \text{VC}}{\text{SP}}

Substitute the given values into the formula:

0.25 = \frac{\text{SP} - 300}{\text{SP}}

Now, we need to solve this equation for SP. Multiply both sides by SP:

0.25 \times \text{SP} = \text{SP} - 300

Rearrange the terms to isolate SP. Move the 0.25 * SP term to the right side or the -300 term to the left side:

300 = \text{SP} - 0.25 \times \text{SP}

Factor out SP from the right side:

300 = \text{SP} \times (1 - 0.25)

300 = \text{SP} \times 0.75

To find SP, divide both sides by 0.75:

\text{SP} = \frac{300}{0.75}

Converting 0.75 to a fraction (3/4):

\text{SP} = \frac{300}{3/4} = 300 \times \frac{4}{3}

\text{SP} = 100 \times 4

\text{SP} = 400

So, the selling price of the product should be Rs. 400 to maintain a P/V Ratio of 25% when the variable cost is Rs. 300.

Verification

Let's verify the answer:

Selling Price (SP) = Rs. 400

Variable Cost (VC) = Rs. 300

Contribution Margin (CM) = SP - VC = Rs. 400 - Rs. 300 = Rs. 100

P/V Ratio = CM / SP = Rs. 100 / Rs. 400 = 1/4 = 0.25 or 25%

The calculated P/V Ratio matches the desired ratio, confirming that the selling price of Rs. 400 is correct.

Revision Table: Key Formulas

Additional Information: Importance of P/V Ratio in Cost Accounting

The P/V Ratio is a crucial tool in cost accounting and management decision-making. It helps management in several ways:

• Profitability Analysis: It directly indicates the profitability of each unit of sales after covering variable costs. A higher P/V Ratio generally means greater profitability, assuming fixed costs are covered.
• Break-Even Analysis: The P/V Ratio is essential for calculating the break-even point, which is the sales level where total revenue equals total costs (fixed + variable). Break-Even Point (in Sales Value) = Fixed Costs / P/V Ratio.
• Decision Making: It assists in decisions related to pricing, product mix, sales strategies, and evaluating the impact of changes in sales price, variable cost, or sales volume on profit.
• Performance Evaluation: Companies can compare the P/V Ratios of different products or divisions to assess their relative performance and contribution to overall profitability.

Understanding and utilizing the P/V Ratio is fundamental for effective cost management and financial planning within a business.