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 measures the number of standard deviations to reach the default threshold, with a higher DtD indicating a lower likelihood of default.

The formula for DtD is simplified to: $\text{DtD} = \frac{\ln(\frac{\text{Va}}{\text{F}})}{\sigma}$ where:

• $\text{Va}$ is the market value of assets,
• $\text{F}$ 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 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 A. P; R; Q, with Company P being the most likely to default, followed by Company R, and then Company Q being the least likely.