Math Problem Statement

A firm has net working capital of $350, total liabilities of $3,600, and total assets of $8,000. During the year sales were $10,000, net income, was $650, and paid taxes of $200. What was the Return on Equity during the year?

Solution

To calculate the Return on Equity (ROE), we need to use the formula:

ROE=Net IncomeEquity×100\text{ROE} = \frac{\text{Net Income}}{\text{Equity}} \times 100

First, we need to determine the equity of the firm, which can be calculated as follows:

Equity=Total AssetsTotal Liabilities\text{Equity} = \text{Total Assets} - \text{Total Liabilities}

Step 1: Calculate the firm's equity

Equity=8,0003,600=4,400\text{Equity} = 8,000 - 3,600 = 4,400

Step 2: Calculate Return on Equity (ROE)

ROE=6504,400×100=14.77%\text{ROE} = \frac{650}{4,400} \times 100 = 14.77\%

Therefore, the firm's Return on Equity (ROE) during the year is 14.77%.

Would you like more details on any part of this? Here are 5 related questions:

  1. How is Return on Equity used to assess a firm's financial performance?
  2. What other profitability ratios are related to ROE, and how are they calculated?
  3. What factors can influence a firm's Return on Equity?
  4. How do changes in liabilities and assets affect a company's equity?
  5. How does net income relate to other financial performance indicators?

Tip: A higher ROE typically indicates that the company is more efficient at generating profit from its equity. However, it’s important to also consider other financial ratios for a complete analysis.

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Math Problem Analysis

Mathematical Concepts

Financial Ratios
Return on Equity
Basic Algebra

Formulas

ROE = (Net Income / Equity) × 100
Equity = Total Assets - Total Liabilities

Theorems

Return on Equity Formula

Suitable Grade Level

College/University Level (Finance, Accounting)