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) using the Merton model. The DtD is a measure that approximates the number of standard deviations to reach the default threshold. A higher DtD indicates a lower likelihood of default. The formula for DtD, when simplified for a 1-year horizon and assuming a zero-coupon bond as the only liability, 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 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 ranking is Q; R; P, which corresponds to option C. This ranking is based on the Merton model's assessment of each company's financial condition and market value relative to their debt obligations, with higher DtD values reflecting a lower risk of default.

Author: LeetQuiz Editorial Team