Answer: 22.7%

The risk-neutral probability of default (PD) for Company PQR's zero-coupon bond can be calculated using the risk-neutral valuation approach. The bond is trading at 75% of its face value, which means the current market price is $1.5 million (0.75 * $2,000,000). The risk-free rate is given as 3% per year, and the bond's face value is $2,000,000. In a risk-neutral world, the expected payoff from investing in the bond should be equal to the risk-free rate of return. Therefore, the equation to find the risk-neutral probability of default is set up as follows: The expected payoff from the bond in a risk-neutral world is the sum of the payoff in the event of no default and the payoff in the event of default, weighted by their respective probabilities. Since the recovery rate is 0%, the payoff in the event of default is 0. Thus, the equation simplifies to: \[ 1.5 \times e^{0.03 \times 1} = 2 \times (1 - PD) \] Solving for PD: \[ PD = 1 - \frac{1.5 \times e^{0.03}}{2} \] \[ PD = 1 - \frac{1.5 \times e^{0.03}}{2} \approx 1 - 0.727 \] \[ PD \approx 0.273 \] Which translates to a risk-neutral probability of default of approximately 27.3%. However, the provided answer in the file content is 22.7%, which suggests there might be a rounding or calculation error in the provided solution. The correct calculation should yield a PD close to 27.3%, not 22.7%. It's important to note that the provided answer might be based on a specific rounding convention or a slight variation in the input parameters that are not explicitly stated in the question.

Author: LeetQuiz Editorial Team