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.