Solvency Ratios pre

First Principles Thinking: Impact of Leverage Recapitalization

B is correct. We must trace the changes through the accounting equation.

1. Initial State:
$$ \text{Assets} = 5,000 $$
$$ \text{Equity} = 2,000 $$
$$ \text{Liabilities (Initial Debt)} = \text{Assets} - \text{Equity} = 5,000 - 2,000 = 3,000 $$

2. Transaction Effect:
Issuing Bonds: Increases Cash (+1,000) and Increases Debt (+1,000).
Repurchasing Stock: Decreases Cash (-1,000) and Decreases Equity (-1,000).
Net effect on Assets: +1,000 - 1,000 = 0 (Assets remain 5,000).
Net effect on Debt: 3,000 (Initial) + 1,000 (New) = 4,000.
Net effect on Equity: 2,000 (Initial) - 1,000 (Repurchase) = 1,000.

3. Calculate New Ratio:
$$ \text{Debt-to-Assets} = \frac{\text{Total Debt}}{\text{Total Assets}} = \frac{4,000}{5,000} = 0.80 \text{ or } 80\% $$

A is incorrect because it reflects the ratio before the transaction (USD3,000 / USD5,000 = 0.60).

C is incorrect because it represents the Debt-to-Equity ratio (USD4,000 / USD1,000 = 4.0).

First Principles Thinking: Coverage Ratios and Capitalized Interest

A is correct. The Interest Coverage ratio is calculated as EBIT divided by Interest Payments. Crucially, the text notes that to provide a true picture of solvency, the entire amount of interest (both the expensed portion and the capitalized portion) should be used in the denominator.

1. Calculate EBIT:
$$ \text{EBIT} = \text{Net Income} + \text{Tax Expense} + \text{Interest Expense} $$
$$ \text{EBIT} = 450 + 190 + 80 = \text{USD } 720 \text{ million} $$
(Note: Capitalized interest is not added back to calculate EBIT because it was never subtracted from earnings to begin with; it was capitalized onto the balance sheet).

2. Calculate Interest Payments (Gross Interest):
$$ \text{Gross Interest} = \text{Interest Expense} + \text{Capitalized Interest} $$
$$ \text{Gross Interest} = 80 + 20 = \text{USD } 100 \text{ million} $$

3. Calculate Ratio:
$$ \text{Interest Coverage} = \frac{720}{100} = 7.2\text{x} $$

B is incorrect because it excludes capitalized interest from the denominator (USD720 / USD80 = 9.0x) or makes an adjustment to the numerator.

C is incorrect because it ignores capitalized interest in the denominator (USD720 / USD80 = 9.0x).

First Principles Thinking: Defining Capital Structure

B is correct. The Debt-to-Capital ratio is calculated as Total Debt divided by (Total Debt + Total Shareholders' Equity).

First, we must determine Total Debt. According to the text, Total Debt typically includes interest-bearing short-term and long-term debt. It excludes operating liabilities like accounts payable and non-debt liabilities like deferred taxes.

• Short-term interest-bearing debt: USD 150
• Current portion of long-term debt: USD 50 (This is part of interest-bearing debt)
• Long-term bonds payable: $ 950 (Carrying value is used, not face value)

$$ \text{Total Debt} = 150 + 50 + 950 = \text{USD } 1,150 \text{ million} $$

Next, we calculate Total Capital:

$$ \text{Total Capital} = \text{Total Debt} + \text{Total Equity} $$

$$ \text{Total Capital} = 1,150 + 1,850 = \text{USD } 3,000 \text{ million} $$

Finally, the ratio:

$$ \text{Debt-to-Capital} = \frac{1,150}{3,000} = 38.33\% $$

A is incorrect because it likely excludes the current portion of long-term debt (USD1,100 / (USD1,100 + USD1,850) = 37.3%) or uses face value of bonds in a specific way that doesn't align.

C is incorrect because it includes Accounts Payable or Deferred Taxes in the debt figure.

First Principles Thinking: Fixed Charge Coverage

C is correct. The Fixed Charge Coverage ratio measures the number of times a company's earnings (before interest, taxes, and lease payments) can cover its interest and lease payments.

Formula: $$ \frac{\text{EBIT} + \text{Lease Payments}}{\text{Interest Payments} + \text{Lease Payments}} $$

1. Calculate EBIT:
Start with Net Income and add back Tax and Interest.
$$ \text{EBT} = \frac{\text{Net Income}}{1 - \text{Tax Rate}} = \frac{200}{0.75} = 266.67 $$
$$ \text{EBIT} = \text{EBT} + \text{Interest} = 266.67 + 50 = 316.67 $$

2. Calculate Numerator:
$$ \text{Numerator} = \text{EBIT} + \text{Lease Payments} = 316.67 + 40 = 356.67 $$

3. Calculate Denominator:
$$ \text{Denominator} = \text{Interest Expense} + \text{Lease Payments} = 50 + 40 = 90 $$

4. Calculate Ratio:
$$ \text{Ratio} = \frac{356.67}{90} \approx 3.96 $$

A is incorrect because it likely calculates Interest Coverage only (USD316.67 / USD50 = 6.33) or omits lease add-back in numerator.

B is incorrect because it includes Depreciation in the numerator (EBITDA based coverage).

First Principles Thinking: Net Debt Concept

A is correct. Net Debt is defined as Total Interest-Bearing Debt minus Cash, Cash Equivalents, and Marketable Securities.

1. Calculate Total Debt:
$$ \text{Total Debt} = \text{Short-term Debt} + \text{Long-term Debt} = 200 + 800 = 1,000 $$

2. Calculate Liquid Assets:
$$ \text{Liquid Assets} = \text{Cash} + \text{Marketable Securities} = 150 + 50 = 200 $$

3. Calculate Net Debt:
$$ \text{Net Debt} = 1,000 - 200 = 800 $$

4. Calculate Ratio:
$$ \text{Net Debt-to-Equity} = \frac{800}{1,200} = 0.67 $$

B is incorrect because it uses Total Debt (Gross) instead of Net Debt (USD1,000 / USD1,200 = 0.83).

C is incorrect because it might include Accounts Payable in debt (USD1,300 - 200) / 1,200 = 0.92.

First Principles Thinking: Debt-to-EBITDA

A is correct. This ratio estimates how many years it would take to repay total debt based on EBITDA.

1. Calculate EBITDA:
$$ \text{EBITDA} = \text{Net Income} + \text{Interest} + \text{Taxes} + \text{Depreciation} + \text{Amortization} $$
$$ \text{EBITDA} = 500 + 80 + 200 + 150 + 50 = \text{USD } 980 \text{ million} $$

2. Identify Total Debt:
$$ \text{Total Debt} = 2,500 $$ (Note: The ratio usually uses Gross Debt, not Net Debt, unless specified as Net Debt-to-EBITDA. The standard formula in the text is Total Debt / EBITDA).

3. Calculate Ratio:
$$ \text{Ratio} = \frac{2,500}{980} = 2.55 $$

B is incorrect because it might exclude Amortization from EBITDA (USD2,500 / USD930 = 2.68) or use Net Debt (USD2,200 / USD980 = 2.24).

C is incorrect because it uses EBIT (USD2,500 / USD780 = 3.21).

First Principles Thinking: Financial Leverage Calculation

A is correct. The Financial Leverage ratio is typically defined as Average Total Assets divided by Average Total Equity. While point-in-time ratios are used for simple solvency checks, the text specifies that for DuPont analysis (which links solvency to profitability), average values are generally used.

1. Calculate Average Total Assets:
$$ \text{Average Assets} = \frac{10,000 + 12,000}{2} = 11,000 $$

2. Calculate Average Total Equity:
$$ \text{Average Equity} = \frac{4,000 + 4,500}{2} = 4,250 $$

3. Calculate Ratio:
$$ \text{Financial Leverage} = \frac{11,000}{4,250} \approx 2.588 $$

B is incorrect because it uses End of Year values (USD12,000 / USD4,500 = 2.67).

C is incorrect because it uses Beginning of Year values (USD10,000 / USD4,000 = 2.50) or calculates Debt-to-Equity.