Answer: P; R; Q

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 using the Merton model. The DtD 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 the forward time periods are reduced to 1 (t=1) and the drift factors (μ - g^2/2) are assumed to be small and equal to 0, simplifies to: \[ \text{DtD} = \frac{\ln(\frac{V_a}{V_f})}{\sigma_a} \] Where: - \( V_a \) is the market value of assets. - \( V_f \) is the face value of debt. - \( \sigma_a \) 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, indicating it is the least likely to default. Company R has a middle DtD, and Company P has the lowest DtD, making it the most likely to default. Therefore, the correct ranking is Q; R; P, which corresponds to option C.

Author: LeetQuiz Editorial Team