Problem 12 - Accounting

Question

One item is omitted from each of the following computations of the rate of return on investment: $$ \begin{aligned} &\text { Rate of return on investment }=\text { Profit margin } \times \text { Investment turnover }\\\ &\begin{array}{clccc} \hline 21 \% & = & 15 \% & \times & \text { (a) } \\ \text { (b) } & = & 8 \% & \times & 1.75 \\ 18 \% & = & \text { (c) } & \times & 0.75 \\ 27 \% & = & 18 \% & \times & \text { (d) } \\ \text { (e) } & = & 12 \% & \times & 2.0 \end{array} \end{aligned} $$ Determine the missing items, identifying each by the appropriate letter.

Step-by-Step Solution

Answer

(a) = 1.4, (b) = 14%, (c) = 24%, (d) = 1.5, (e) = 24%.

Step 1: Solve for (a) - Investment Turnover

We use the formula for rate of return: \(\text{Rate of Return} = \text{Profit Margin} \times \text{Investment Turnover}\). Here, the rate of return is 21% and profit margin is 15%, so the equation is \(21\% = 15\% \times (a)\). Solve for \(a\):\[(a) = \frac{21\%}{15\%} = 1.4\]

Step 2: Solve for (b) - Rate of Return

In this case, the Profit Margin is 8% and the Investment Turnover is 1.75, so we use the formula \((b) = 8\% \times 1.75\). Calculate \((b)\):\[(b) = 8\% \times 1.75 = 14\%\]

Step 3: Solve for (c) - Profit Margin

Given that the rate of return is 18% and the investment turnover is 0.75, the equation is \(18\% = (c) \times 0.75\). Solve for \(c\):\[(c) = \frac{18\%}{0.75} = 24\%\]

Step 4: Solve for (d) - Investment Turnover

Here, the rate of return is 27% and profit margin is 18%, so \(27\% = 18\% \times (d)\). Solve for \(d\):\[(d) = \frac{27\%}{18\%} = 1.5\]

Step 5: Solve for (e) - Rate of Return

The profit margin is 12% and the investment turnover is 2.0, so we have \((e) = 12\% \times 2.0\). Calculate \((e)\):\[(e) = 12\% \times 2.0 = 24\%\]

Key Concepts

Profit Margin

The profit margin is a crucial indicator of a company's profitability. It helps in understanding how efficiently a company converts its revenue into profit after accounting for all expenses. Profit margins are typically expressed as a percentage
and can be calculated for different levels of operations.

• **Gross Profit Margin** measures the percentage of revenue that exceeds the cost of goods sold (COGS). It shows how efficiently a company uses materials and labor in production.
• **Operating Profit Margin** takes into account all operating expenses, subtracting them from gross profit to see what percentage of revenue turns into operating profit.
• **Net Profit Margin** includes all expenses, including operating expenses, taxes, and interest, to show the actual percentage of revenue that becomes net income.

Calculating the profit margin at any of these levels involves dividing the profit by total revenue and multiplying by 100.For example, if a company's net income is \(20,000 and the total revenue is \)100,000, the net profit margin would be \(\text{Net Profit Margin} = \frac{20,000}{100,000} \times 100 = 20\%\). Understanding profit margins helps evaluate the performance and efficiency in generating profits.

Investment Turnover

Investment turnover measures how efficiently a company utilizes its assets to generate revenue. It is a sign of asset efficiency and is calculated by dividing sales revenue by the total investment in the business.
The formula looks like this: \[ \text{Investment Turnover} = \frac{\text{Sales Revenue}}{\text{Total Investment}} \]Higher investment turnover indicates that a company is effectively turning its investments into sales. This is especially critical for businesses that rely heavily on asset management.
The key to improving investment turnover often involves optimizing the use of assets through various strategies:

• Streamlining processes to increase sales without equally increasing investments.
• Managing inventory effectively to avoid overstocking or shortages.
• Using technology to improve operational efficiency.

By focusing on these areas, companies can enhance their investment turnover ratio, reflecting a better utilization of resources to boost sales and profitability.

Accounting Calculations

In accounting, calculations are essential for evaluating financial health and guiding business decisions. They help interpret financial statements accurately and derive meaningful analytics, such as the rate of return on investment (ROI).
ROI is a common measure used to assess the effectiveness of an investment. It is determined by calculating how much profit or cost-saving is generated versus the initial amount of investment. The formula for ROI is:\[ \text{ROI} = \frac{\text{Net Profit}}{\text{Investment Cost}} \times 100 \]Using the rate of return on investment helps investors and analysts assess:

• How well resources are being used to generate profits.
• The feasibility and financial potential of investments.
• How different investments compare in terms of profitability.

It's crucial to ensure all accounting calculations are accurate and consistent to reflect the true financial position of a business. This leads to better investment decisions and strategic planning, ultimately guiding businesses towards financial stability and growth.