Answer: The company's PD is 5.20%, and a limitation of the Merton model is that it is costly, especially for smaller firms, to continuously calibrate PD on historical series of actual defaults.

The correct answer is C. Using the Merton model, the probability of default (PD) is calculated using the formula: \[ PD = N\left(\frac{\ln(\frac{F}{V}) + \mu(T - t)}{\sigma\sqrt{T - t}}\right) \] where: - \( V \) is the value of the company's assets (CAD 400 million) - \( F \) is the face value of the company's debt (CAD 300 million) - \( \mu \) is the expected rate of return of the value of the company's assets (15% or 0.15) - \( \sigma \) is the instantaneous volatility of the value of the company's assets (25% or 0.25) - \( T - t \) is the remaining time to maturity for the company's debt (1 year) Plugging in the values: \[ PD = N\left(\frac{\ln(\frac{300}{400}) + 0.15 \times 1}{0.25 \times \sqrt{1}}\right) \] \[ PD = N(-1.626) \] \[ PD = 5.20\% \] (Using Excel: PD = NORMSDIST(-1.626) = 0.051975) The Merton model has several limitations. It is applicable to liquid, publicly traded names only, and there is a continuous need for calibration of the PD on historical series of actual defaults as an analytical requirement, a maintenance requirement, which is costly for smaller organizations. The Merton model also relies on the continually changing movements in market prices, volatility, and interest rates. Option A is incorrect because the calculation error led to a PD of 3.03%, and the Merton model can indeed be applied to debt holdings maturing in more than 1 year. Option B is incorrect because the PD is not 4.04%, and the limitation mentioned is not accurate. Option D is incorrect because the PD is not 12.49%, and while the Merton model does rely on changing market conditions, the limitation mentioned is not a direct limitation of the model itself.

Author: LeetQuiz Editorial Team