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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.

Short Answer

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

Step by step solution

01

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 \(a\):\[(a) = \frac{21\%}{15\%} = 1.4\]
02

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 \((b)\):\[(b) = 8\% \times 1.75 = 14\%\]
03

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 \(c\):\[(c) = \frac{18\%}{0.75} = 24\%\]
04

Solve for (d) - Investment Turnover

Here, the rate of return is 27% and profit margin is 18%, so \(27\% = 18\% \times (d)\). Solve for \(d\):\[(d) = \frac{27\%}{18\%} = 1.5\]
05

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 \((e)\):\[(e) = 12\% \times 2.0 = 24\%\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

Sierra Sporting Goods Co. operates two divisions—the Camping Equipment Division and the Ski Equipment Division. The following income and expense accounts were provided from the trial balance as of June 30, 2006, the end of the current fiscal year, after all adjustments, including those for inventories, were recorded and posted: Sales—Camping Equipment Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \(380,000 Sales—Ski Equipment Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575,000 Cost of Goods Sold—Camping Equipment Division . . . . . . . . . . . . . . . . . . . . . . . . . . 205,000 Cost of Goods Sold—Ski Equipment Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275,000 Sales Expense—Camping Equipment Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60,000 Sales Expense—Ski Equipment Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82,000 Administrative Expense—Camping Equipment Division . . . . . . . . . . . . . . . . . . . . . . . 38,800 Administrative Expense—Ski Equipment Division . . . . . . . . . . . . . . . . . . . . . . . . . . . 51,200 Advertising Expense . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25,800 Transportation Expense . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20,140 Accounts Receivable Collection Expense . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11,620 Warehouse Expense . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60,000 The bases to be used in allocating expenses, together with other essential information, are as follows: a. Advertising expense—incurred at headquarters, charged back to divisions on the basis of usage: Camping Equipment Division, \)11,200; Ski Equipment Division, \(14,600. b. Transportation expense—charged back to divisions at a transfer price of \)3.80 per bill of lading: Camping Equipment Division, 2,400 bills of lading; Ski Equipment Division, 2,900 bills of lading. c. Accounts receivable collection expense—incurred at headquarters, charged back to divisions at a transfer price of $2.80 per invoice: Camping Equipment Division, 1,800 sales invoices; Ski Equipment Division, 2,350 sales invoices. d. Warehouse expense—charged back to divisions on the basis of floor space used in storing division products: Camping Equipment Division, 10,000 square feet; Ski Equipment Division, 5,000 square feet. Prepare a divisional income statement with two column headings: Camping Equipment Division and Ski Equipment Division. Provide supporting schedules for determining service department charges.

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?

Data for the North, East, South, and West Divisions of Columbia Wireless Communication Company are as follows: $$ \begin{array}{lcccccc} & \text { Sales } & \begin{array}{c} \text { Income } \\ \text { from } \\ \text { Operations } \end{array} & \begin{array}{c} \text { Invested } \\ \text { Assets } \end{array} & \begin{array}{c} \text { Rate of } \\ \text { Return on } \\ \text { Investment } \end{array} & \begin{array}{c} \text { Profit } \\ \text { Margin } \end{array} & \begin{array}{c} \text { Investment } \\ \text { Turnover } \end{array} \\ \hline \text { North } & \$ 365,000 & (\mathrm{a}) & \text { (b) } & 20 \% & 16 \% & \text { (c) } \\ \text { East } & \text { (d) } & \$ 60,000 & (\mathrm{e}) & (\mathrm{f}) & 12.5 \% & 0.64 \\ \text { South } & \$ 326,000 & (\mathrm{~g}) & \$ 407,500 & 12 \% & \text { (h) } & \text { (i) } \\ \text { West } & \$ 850,000 & \$ 119,000 & \$ 680,000 & (\mathrm{j}) & \text { (k) } & \text { (I) } \end{array} $$ a. Determine the missing items, identifying each by the letters (a) through (1). b. Determine the residual income for each division, assuming that the minimum acceptable rate of return established by management is \(10 \%\). c. Which division is the most profitable in terms of (1) return on investment and (2) residual income?

The American Express Company is a major financial services company, noted for its American Express \({ }^{\mathbb{B}}\) card. Below are some of the performance measures used by the company in its balanced scorecard. \(\begin{array}{ll}\text { Average cardmember spending } & \text { Number of merchant signings } \\ \text { Cards in force } & \text { Number of card choices } \\ \text { Earnings growth } & \text { Number of new card launche } \\\ \text { Hours of credit consultant training } & \text { Return on equity } \\\ \text { Investment in information technology } & \text { Revenue growth } \\\ \text { Number of Internet features } & \end{array}\) For each measure, identify whether the measure best fits the innovation, customer, internal process, or financial dimension of the balanced scorecard.

In divisional income statements prepared for Black Top Paving Company, the Payroll Department costs are charged back to user divisions on the basis of the number of payroll checks, and the Purchasing Department costs are charged back on the basis of the number of purchase requisitions. The Payroll Department had expenses of \(24,450, and the Purchasing Department had expenses of \)10,400 for the year. The following annual data for Residential, Commercial, and Highway Divisions were obtained from corporate records: \begin{tabular}{lrrr} & Residential & Commercial & Highway \\ \hline Sales & \(\$ 400,000\) & \(\$ 500,000\) & \(\$ 1,000,000\) \\ Number of employees: & & & \\ Weekly payroll (52 weeks per year) & 80 & 40 & 60 \\ Monthly payroll & 14 & 11 & 10 \\ Number of purchase requisitions per year & 1,000 & 850 & 750 \end{tabular} a. Determine the annual amount of payroll and purchasing costs charged back to the Residential, Commercial, and Highway Divisions from payroll and purchasing services. b. Why does the Residential Division have a larger service department charge than the other two divisions, even though its sales are lower?

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