Answer: 10.0%

The correct answer is B, 10.0%. The explanation is based on the constant hazard rate model, which is used to calculate the probability of an event occurring within a given time period. In this case, the hazard rate for the company is given as 0.12 per year. The joint probability of survival up to time \( t \) and default over \( (t, t + \Delta t) \) is given by the formula: \[ P[t^* > t \text{ and } t^* < t + \Delta t] = 1 - e^{-\lambda(t + \Delta t)} - (1 - e^{-\lambda t}) = e^{-\lambda \Delta t}(1 - e^{-\lambda t}) \] For the specific scenario where the company survives the first year and defaults in the second year, we apply the formula with \( t = 1 \) and \( \Delta t = 1 \), using the hazard rate \( \lambda = 0.12 \). The calculation becomes: \[ P[t^* > 1 \text{ and } t^* < 1 + 1] = e^{-0.12 \cdot 1}(1 - e^{-0.12 \cdot 1}) \] Plugging in the values, we get: \[ P[t^* > 1 \text{ and } t^* < 2] = e^{-0.12}(1 - e^{-0.12}) \] Calculating this expression yields approximately 10.03%, which is rounded to 10.0% in the provided options. This is the probability that the company will survive the first year and then default before the end of the second year, aligning with option B.

Author: LeetQuiz Editorial Team