The correct answer is D.

Distance-to-default is the expected difference between the asset value of the firm relative to the default barrier, after correcting and normalizing for the volatility of assets. It approximates the number of standard deviations to reach the default threshold; thus, the higher the DtD, the least likely to default.

$$\text{DtD} = \frac{\ln V_\alpha - \ln F + (\mu - \frac{\sigma^2_\alpha}{2})}{\sigma_\alpha \sqrt{t}}$$

DtD can be simplified by reducing the forward time periods to 1 (t=1) and minimizing the drift factors $(\mu - \frac{\sigma}{2})$ that tend to be small (assumed to equal 0) over one period to yield:

$$\text{DtD} \cong \frac{\ln V_\alpha - \ln F}{\sigma_\alpha}$$

Applying this formula, we calculate the Distance-to-Default for each company:

• DtD for Company P = $\frac{\ln(\frac{100}{70})}{0.10} = 3.56$
• DtD for Company Q = $\frac{\ln(\frac{180}{120})}{0.08} = 5.07$
• DtD for Company R = $\frac{\ln(\frac{200}{100})}{0.06} = 11.55$
• DtD for Company S = $\frac{\ln(\frac{250}{170})}{0.12} = 3.21$

Ranking the counterparties from least likely to default (highest DtD) to most likely to default (lowest DtD): R (11.55), Q (5.07), P (3.56), S (3.21).