Debt-to-Equity Ratio

Meridian Tools has total debt of $80 million and total stockholders' equity of $160 million. What is its debt-to-equity ratio?

1. A.2.0xWrong. This inverts the ratio (equity ÷ debt instead of debt ÷ equity).
2. B.0.33xWrong. This is debt ÷ (debt + equity) — the debt-to-capital ratio, not debt-to-equity.
3. C.0.5xCorrect. $80M ÷ $160M = 0.5x.
4. D.1.5xWrong. This does not correspond to any correct combination of the given figures.

Why: Debt-to-equity = total debt ÷ total equity = $80M ÷ $160M = 0.5x.

A company reports a debt-to-capital ratio of 40% (total capital = total debt + total equity). What is its debt-to-equity ratio?

1. A.0.40xWrong. This simply restates the debt-to-capital ratio as if it were debt-to-equity.
2. B.0.60xWrong. This is the equity-to-capital fraction, not the debt-to-equity ratio.
3. C.1.50xWrong. This does not follow from the correct conversion of the given figure.
4. D.0.67xCorrect. Debt ÷ equity = 0.40 ÷ 0.60 ≈ 0.67x.

Why: If debt ÷ capital = 0.40, then debt = 0.40 of capital and equity = 0.60 of capital, so debt ÷ equity = 0.40 ÷ 0.60 ≈ 0.67x. Debt-to-capital and debt-to-equity are different fractions of the same capital structure and are not numerically interchangeable.

Thornbury Cabinet has 10 million common shares outstanding, $200 million of book equity and no debt. It borrows $80 million and uses the entire proceeds to repurchase 4 million of its own shares at $20 per share. Ignoring taxes and transaction costs, immediately after the recapitalization its debt-to-equity ratio, shares outstanding and book value per share will be, respectively, approximately:

1. A.Rises from 0 to about 0.67; stays at 10 million shares; falls to $12.00.Incorrect. Repurchased shares are retired or held in treasury and are no longer outstanding, so the share count must fall to 6 million.
2. B.Stays at 0; falls to 6 million shares; falls to $12.00.Incorrect. The company now carries $80 million of debt, so the ratio cannot stay at zero.
3. C.Rises from 0 to about 0.67; falls to 6 million shares; stays at $20.Correct. Equity drops to $120 million, so 80 / 120 = 0.67, and $120 million over 6 million shares is still $20 per share.
4. D.Rises from 0 to about 0.40; falls to 6 million shares; rises to $33.33.Incorrect. 0.40 divides the new debt by the OLD equity, and book value per share does not rise because the shares were bought at book value.

Why: The buyback removes $80 million of cash and cancels 4 million shares, so equity falls from $200 million to $120 million and shares fall from 10 million to 6 million. Debt is now $80 million, so the debt-to-equity ratio is $80 / $120 = 0.67. Book value per share is $120 million / 6 million = $20, exactly what it was before ($200 / 10 = $20). Repurchasing shares at a price equal to book value per share leaves book value per share unchanged; only a repurchase above or below book value moves it.