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Using the Du Pont Identity Y3K, Inc., has sales of \(\$ 3,100\), total assets of \(\$ 1,580\), and a debt-equity ratio of 1.20 . If its return on equity is 16 percent, what is its net income?

Short Answer

Expert verified
The net income for Y3K, Inc., is approximately \(\$ 114.87\).

Step by step solution

01

Understand the Du Pont Identity formula

The Du Pont Identity formula is defined as: ROE = ROA x Equity multiplier The return on assets (ROA) is calculated as: ROA = Net income / Total assets The equity multiplier is calculated as: Equity multiplier = Total assets / Total equity Since we are given the debt-equity ratio (Debt / Equity), we can find the total equity as follows: Total Equity = Total assets / (1 + Debt-equity ratio) After finding ROA and the equity multiplier, we will plug them into the Du Pont Identity formula to find the net income.
02

Calculate Total Equity

We are given the total assets and the debt-equity ratio, which we can use to calculate the total equity: Total Equity = Total assets / (1 + Debt-equity ratio) Total Equity = 1,580 / (1 + 1.20) = 1,580 / 2.20 ≈ \$ 718.18
03

Calculate Equity Multiplier

Using the total equity value calculated in step 2, we can now find the equity multiplier: Equity multiplier = Total assets / Total equity Equity multiplier = 1,580 / 718.18 ≈ 2.2
04

Determine the Return on Assets (ROA) using Return on Equity (ROE)

We are given the return on equity (ROE) which is 16%. We can use this and the calculated equity multiplier to determine the return on assets (ROA) ROA = ROE / Equity multiplier ROA = 0.16 / 2.2 ≈ 0.0727
05

Calculate Net Income

Now that we have the return on assets (ROA), we can calculate the net income: Net income = ROA x Total assets Net income = 0.0727 x 1,580 ≈ \$ 114.87 The net income for Y3K, Inc., is approximately \(\$ 114.87\).

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Key Concepts

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

Return on Equity (ROE)
Return on Equity, or ROE, is a crucial financial metric that indicates how efficiently a company is utilizing its equity to generate profit. In simpler terms, it tells us how good a company is at creating profits from shareholders' investments.
\( ROE \) can be calculated using the formula:

\[ \text{ROE} = \frac{\text{Net Income}}{\text{Shareholders' Equity}} \]

This ratio is expressed as a percentage, offering insight into the profitability related to shareholders' equity. A higher ROE generally signals better financial efficiency and profitability. For instance, if a firm has an ROE of 16%, as in Y3K, Inc.'s case, it means that for every dollar of shareholders' equity, the firm produced 16 cents in profit.
  • A higher ROE could indicate successful management and a strong business model.
  • However, it is important to compare ROE with industry standards, as it can vary greatly across different sectors.
Return on Assets (ROA)
Return on Assets (ROA) measures how effectively a company turns its assets into profits. It indicates management efficiency in utilizing resources.
ROA is calculated using the formula:

\[ \text{ROA} = \frac{\text{Net Income}}{\text{Total Assets}} \]

The ratio is presented as a percentage and provides a snapshot of how profitable a company's assets are. For Y3K, Inc., the calculated ROA of approximately 7.27% shows that for every dollar of assets, the company generates roughly 7 cents of profit.
  • A higher ROA indicates better asset efficiency.
  • Like ROE, it's important to compare ROA against industry benchmarks.

By using ROA, stakeholders can assess whether the company is using its assets wisely and efficiently.
Equity Multiplier
The Equity Multiplier is a financial leverage ratio indicating how much of a company’s assets are financed by its shareholders' equity. Essentially, it shows the proportion of a company's assets that are funded by taxing equity to achieve greater returns through borrowing.
The formula for the Equity Multiplier is:

\[ \text{Equity Multiplier} = \frac{\text{Total Assets}}{\text{Total Equity}} \]

In Y3K, Inc.'s scenario, the equity multiplier was calculated to be approximately 2.2. This means that the company's total assets are 2.2 times its equity, indicating a moderate level of leverage.
  • A higher equity multiplier means more assets are financed by debt.
  • This can be beneficial or risky, depending on the firm’s ability to manage debt effectively.

Companies often aim for a balance to maximize growth while maintaining manageable risk levels.
Debt-Equity Ratio
The Debt-Equity Ratio is a measure of a company’s financial leverage, indicating the relative proportion of shareholders' equity and debt a company is using to finance its assets. This ratio provides insights into the financial health of a company, and its ability to finance its operations through debt or equity.
It is calculated using:

\[ \text{Debt-Equity Ratio} = \frac{\text{Total Debt}}{\text{Total Equity}} \]

For Y3K, Inc., the debt-equity ratio is 1.20, meaning that for every dollar of equity, the company has $1.20 in debt.
  • A higher debt-equity ratio often implies greater financial risk.
  • Conversely, a lower ratio might suggest a conservative approach, indicating that the company might be missing out on growth opportunities due to under-leveraging.

Investors generally look at the debt-equity ratio to gauge the level of risk associated with the company’s financial structure.

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Most popular questions from this chapter

Return on Equity Firm \(A\) and Firm B have debt-total asset ratios of \(\mathbf{4 0}\) percent and \(\mathbf{3 0}\) percent and returns on total assets of 12 percent and 15 percent, respectively. Which firm has a greater return on equity?

External Funds Needed Cheryl Colby, CFO of Charming Florist Ltd., has created the firm's pro forma balance sheet for the next fiscal year. Sales are projected to grow by 10 percent to \(\$ 390\) million. Current assets, fixed assets, and short-term debt are 20 percent, 120 percent, and 15 percent of sales, respectively. Charming Florist pays out 30 percent of its net income in dividends. The company currently has \(\$ 130\) million of long-term debt and \(\$ 48\) million in common stock par value. The profit margin is 12 percent. 1\. Construct the current balance sheet for the firm using the projected sales figure. 2\. Based on Ms. Colby's sales growth forecast, how much does Charming Florist need in external funds for the upcoming fiscal year? 3\. Construct the firm's pro forma balance sheet for the next fiscal year and confirm the external funds needed that you calculated in part (b).

Equity Multiplier and Return on Equity Thomsen Company has a debt-equity ratio of .90. Return on assets is 10.1 percent, and total equity is \(\$ 645,000\). What is the equity multiplier? Return on equity? Net income?

Constraints on Growth Bulla Recording, Inc., wishes to maintain a growth rate of 12 percent per year and a debt-equity ratio of .30. Profit margin is 5.9 percent, and the ratio of total assets to sales is constant at .85 . Is this growth rate possible? To answer, determine what the dividend payout ratio must be. How do you interpret the result? .

Full-Capacity Sales Thorpe Mfg., Inc., is currently operating at only 85 percent of fixed asset capacity. Current sales are \(\$ 630,000\). How much can sales increase before any new fixed assets are needed?

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