Answer: 10.0%

The correct answer to the question is B, which is 10.0%. The explanation for this answer is based on the constant hazard rate model. The hazard rate, denoted as \( h(t) \), is a measure of the likelihood of a default event occurring at time \( t \), given that the company has survived up to that time. In this case, the hazard rate is given as 0.12 per year. The probability that the company will survive the first year is calculated by the survival function \( S(t) = e^{-H(t)} \), where \( H(t) \) is the cumulative hazard function. For the first year, the cumulative hazard is \( H(1) = 0.12 \times 1 = 0.12 \), so the survival probability is \( S(1) = e^{-0.12} \). The probability that the company will default in the second year, given that it has survived the first year, is calculated by the hazard rate at time \( t \) multiplied by the survival probability up to time \( t \). For the second year, the cumulative hazard from the beginning of the second year to the end of the second year is \( H(1+1) - H(1) = 0.12 \times 1 = 0.12 \). The probability of default in the second year is then \( h(1+1) \times S(1) = 0.12 \times e^{-0.12} \). The joint probability of surviving the first year and defaulting in the second year is the product of the survival probability for the first year and the default probability for the second year, which is \( e^{-0.12} \times (0.12 \times e^{-0.12}) \). Simplifying this expression gives \( e^{-0.12} \times (1 - e^{-0.12}) \), which equals approximately 10.03%. However, since the answer options are discrete percentages, the closest correct answer is 10.0%, which corresponds to option B.

Author: LeetQuiz Editorial Team