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Explanation:
To find the Return on Equity (ROE), we must first calculate the Net Income for each firm: Net Income = (EBIT - Interest Expense) × (1 - Tax Rate)
$2,500,000 × 3.40% = $85,000.
Net Income = ($75,000 - $85,000) × (1 - 0.21) = -$7,900.
ROE = -$7,900 / $3,000,000 = -0.26%.$1,000,000 × 3.40% = $34,000.
Net Income = ($75,000 - $34,000) × (1 - 0.21) = $32,390.
ROE = $32,390 / $4,000,000 = 0.81%.$1,000,000 × 3.40% = $34,000.
Net Income = ($75,000 - $34,000) × (1 - 0.21) = $32,390.
ROE = $32,390 / $2,900,000 = 1.12%.Firm C has the highest current ROE. Firm B and Firm C generated the same Net Income ($32,390), but Firm C requires a lower equity base, resulting in a higher ROE.
Let's also evaluate the hypothetical ROE without credit losses by adding the provision back to EBIT:
$75,000 + $50,000 = $125,000. Net Income = ($125,000 - $85,000) × 0.79 = $31,600. ROE = $31,600 / $3,000,000 = 1.05%.$75,000 + $15,000 = $90,000. Net Income = ($90,000 - $34,000) × 0.79 = $44,240. ROE = $44,240 / $4,000,000 = 1.11%.$75,000 + $1,000 = $76,000. Net Income = ($76,000 - $34,000) × 0.79 = $33,180. ROE = $33,180 / $2,900,000 = 1.14%.Even without credit losses, Firm C would still have the highest ROE. Therefore, only statement A is correct.
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24.2.3. Firm A, Firm B, and Firm C are three companies in the bottled water industry. All companies have a mix of debt and equity in their capital structure. In 2022 all three companies had credit losses that lowered EBIT. Below is a summary of their financial information for the year 2022.
| Firm A | Firm B | Firm C | |
|---|---|---|---|
| Total Assets | $5,500,000 | $5,000,000 | $3,900,000 |
| Total Debt | $2,500,000 | $1,000,000 | $1,000,000 |
| Debt Interest Rate | 3.40% | 3.40% | 3.40% |
| Total Equity | $3,000,000 | $4,000,000 | $2,900,000 |
| Provision for Loan Loss | $50,000 | $15,000 | $1,000 |
| EBIT | $75,000 | $75,000 | $75,000 |
| Tax Rate | 21% | 21% | 21% |
Given the above information, which firm has the higher return on equity (ROE)?
A
Firm C has the highest ROE due to its lower equity position.
B
Firm A had the higher ROE because of its large debt position.
C
Without credit losses, firm A would have had the highest ROE.
D
Without credit losses, firm B would have had the highest ROE.