Math Problem Statement

Based on the information provided below for Atlantic Corp. and Southern Corp., assess the financial performance of these companies. The tax rate is 40% and the interest rate is 10%. For simplicity, assume that the companies have no other liabilities other than the debt specified.

Atlantic Corp. Southern Corp. EBIT 582 591 Debt 420 1610 Equity 1030 490 Calculate the ROE for Atlantic Corp. and Southern Corp. Enter your answer as a percentage between 0% and 100% with two decimal numbers and without the percent sign (e.g. if your answer is 32.596%, then you would enter 32.60)

What is the ROE for Atlantic Corp.?

Solution

To calculate the Return on Equity (ROE) for Atlantic Corp., we use the formula:

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

Step 1: Calculate Net Income

Net income is derived from the Earnings Before Interest and Taxes (EBIT), with adjustments for interest and taxes.

Net Income=(EBITInterest)×(1Tax Rate)\text{Net Income} = (\text{EBIT} - \text{Interest}) \times (1 - \text{Tax Rate})

Where:

  • EBIT for Atlantic Corp. = 582
  • Debt for Atlantic Corp. = 420
  • Interest rate = 10%
  • Tax rate = 40%

The interest payment is calculated as:

Interest=Debt×Interest Rate=420×0.10=42\text{Interest} = \text{Debt} \times \text{Interest Rate} = 420 \times 0.10 = 42

Now calculate the Net Income:

Net Income=(58242)×(10.40)=540×0.60=324\text{Net Income} = (582 - 42) \times (1 - 0.40) = 540 \times 0.60 = 324

Step 2: Calculate ROE

Now, calculate ROE using the equity:

ROE=3241030×100=31.46%\text{ROE} = \frac{324}{1030} \times 100 = 31.46\%

The ROE for Atlantic Corp. is 31.46.

Would you like more details, or do you have any questions? Here are 5 related questions to deepen your understanding:

  1. What would happen to ROE if the tax rate increased?
  2. How does increasing debt affect ROE, assuming constant EBIT?
  3. What is the significance of ROE in assessing company performance?
  4. Can high ROE always be considered good for a company's financial health?
  5. How does interest rate variability affect the Net Income and ROE?

Tip: ROE can be influenced significantly by financial leverage, so consider both debt and equity when assessing performance.

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Math Problem Analysis

Mathematical Concepts

Finance
Return on Equity (ROE)
Interest
Net Income
Tax Calculations

Formulas

ROE = (Net Income / Equity) * 100
Net Income = (EBIT - Interest) * (1 - Tax Rate)
Interest = Debt * Interest Rate

Theorems

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Suitable Grade Level

Undergraduate Finance or Business School Level