Problem 13 - Accounting

Question

The condensed income statement for the New England Division of Eastern Gas Co. is as follows (assuming no service department charges): $$ \begin{array}{lr} \text { Sales } & \$ 700,000 \\ \text { Cost of goods sold } & 320,000 \\ \text { Gross profit } & \$ 380,000 \\ \text { Administrative expenses } & 222,500 \\ \hline \text { Income from operations } & \$ 157,500 \\ \hline \end{array} $$ The manager of the New England Division is considering ways to increase the rate of return on investment. a. Using the DuPont formula for rate of return on investment, determine the profit margin, investment turnover, and rate of return on investment of the New England Division, assuming that \(1,250,000 of assets have been invested in the New England Division. b. If expenses could be reduced by \)39,375 without decreasing sales, what would be the impact on the profit margin, investment turnover, and rate of return on investment for the New England Division?

Step-by-Step Solution

Answer

a. Profit Margin: 22.5%, Investment Turnover: 0.56, ROI: 12.6%. b. New Profit Margin: 28.125%, New ROI: 15.75%.

Step 1: Understand the DuPont Formula

The DuPont formula breaks down Return on Investment (ROI) into two components: Profit Margin and Asset Turnover. The formula is given by: \( ROI = ext{Profit Margin} \times ext{Investment Turnover} \). Here, Profit Margin is \( \frac{\text{Income from Operations}}{\text{Sales}} \) and Investment Turnover is \( \frac{\text{Sales}}{\text{Assets}} \). ROI can then be calculated as the product of these two.

Step 2: Calculate Profit Margin

Using the given data, the Profit Margin is calculated as: \( \text{Profit Margin} = \frac{\text{Income from Operations}}{\text{Sales}} = \frac{157,500}{700,000} = 0.225 \). So, the Profit Margin is 22.5%.

Step 3: Calculate Investment Turnover

Investment Turnover is determined by \( \text{Investment Turnover} = \frac{\text{Sales}}{\text{Assets}} = \frac{700,000}{1,250,000} = 0.56 \). This indicates that the division turns over its investment 0.56 times in a period.

Step 4: Calculate Rate of Return on Investment

The overall ROI is the product of Profit Margin and Investment Turnover: \( ROI = 0.225 \times 0.56 = 0.126 \). Thus, the rate of return on investment is 12.6%.

Step 5: Revised Profit Margin After Reducing Expenses

If expenses are reduced by $39,375, the new Income from Operations is \( 157,500 + 39,375 = 196,875 \). The new Profit Margin becomes \( \text{Profit Margin} = \frac{196,875}{700,000} = 0.28125 \). Hence, the new Profit Margin is 28.125%.

Step 6: Calculate Revised ROI Based on New Profit Margin

Using the new Profit Margin, the revised ROI is calculated as: \( ROI = 0.28125 \times 0.56 = 0.1575 \). Thus, the new rate of return on investment is 15.75%.

Key Concepts

Profit Margin

Profit margin is a crucial financial metric that shows how much of sales revenue is converted into profit. In simple terms, it represents the portion of sales that exceeds operating expenses. Profit margin is a percentage that indicates the efficiency of a business in managing its costs related to producing or delivering goods and services.
To calculate the profit margin, you use the formula:

• \( \text{Profit Margin} = \frac{\text{Income from Operations}}{\text{Sales}} \)

For the New England Division example, the profit margin is calculated as \( \frac{157,500}{700,000} = 0.225 \), or 22.5%.
Reducing costs can significantly affect the profit margin. In the case where expenses are reduced by \(39,375, the income from operations increases to \)196,875, improving the profit margin to \( \frac{196,875}{700,000} = 0.28125 \), or 28.125%. This increase reflects the efficiency gains in converting sales into profit.

Investment Turnover

Investment turnover measures how efficiently a company uses its assets to generate sales. It provides insight into the management's ability to maximize asset use and enhance business growth.
The formula for investment turnover is straightforward:

• \( \text{Investment Turnover} = \frac{\text{Sales}}{\text{Assets}} \)

In the context of our example, it's calculated as \( \frac{700,000}{1,250,000} = 0.56 \). A turnover of 0.56 means that the division generated 56 cents from every dollar of investment.
Increasing investment turnover typically involves either boosting sales or optimizing asset use. While the turnover itself doesn't change due to cost reductions, improving efficiency or reallocating assets can help increase this figure over the long run.

Rate of Return on Investment

The rate of return on investment (ROI) essentially tells you how much profit is generated from an amount invested in the business. It combines both profit margin and investment turnover into a single metric for analysis and performance evaluation. The DuPont formula helps to simplify this understanding:

• \( ROI = \text{Profit Margin} \times \text{Investment Turnover} \)

Applying this to our case, the original ROI is: \( 0.225 \times 0.56 = 0.126 \), which equates to 12.6%.
Upon reducing expenses and hence increasing the profit margin to 28.125%, the new ROI is: \( 0.28125 \times 0.56 = 0.1575 \), or 15.75%.
ROI reflects the overall efficiency of investment use. Improving the ROI indicates enhanced financial health and more value creation from investments.