The correct ranking of the counterparties, from most likely to least likely to default, is determined by calculating the Distance to Default (DtD) for each company. The DtD is a measure that approximates the number of standard deviations to reach the default threshold, with a higher DtD indicating a lower likelihood of default.

The formula for DtD, when simplified for a 1-year horizon and assuming small drift factors, is:

$\text{DtD} = \frac{\ln(\frac{V_a}{F})}{\sigma}$

where:

• $V_a$ is the market value of assets,
• $F$ is the face value of debt,
• $\sigma$ is the annual volatility of asset values.

Using the provided data:

• For Company P: $\text{DtD} = \frac{\ln(\frac{100}{60})}{0.10} = 5.11$
• For Company Q: $\text{DtD} = \frac{\ln(\frac{150}{100})}{0.07} = 5.79$
• For Company R: $\text{DtD} = \frac{\ln(\frac{250}{160})}{0.08} = 5.58$

Based on these calculations:

• Company Q has the highest DtD (5.79), indicating it is the least likely to default.
• Company R has a DtD of 5.58, placing it in the middle in terms of default likelihood.
• Company P has the lowest DtD (5.11), making it the most likely to default.

Therefore, the correct answer is B. Q; P; R, with Q being the least likely to default, followed by R, and then P being the most likely to default.