Answer: CAD 49.764 million

## Explanation Using the Merton model, we calculate the market value of debt as follows: ### Step 1: Calculate the value of equity (E) The Merton model formula for equity value is: \[ E = V \times N(d_1) - D \times e^{-rT} \times N(d_2) \] Where: - V = CAD 85 million (market value of assets) - N(d₁) = 0.9495 - N(d₂) = 0.8983 - D = CAD 55 million (face value of debt) - r = 5% (annual risk-free rate) - T = 2 years - e⁻ʳᵀ = e⁻⁰·⁰⁵ײ = 0.9048 \[ E = (85,000,000) \times (0.9495) - (55,000,000) \times (0.9048) \times (0.8983) \] \[ E = 80,707,500 - 44,703,001 \] \[ E = CAD 36,004,499 \] ### Step 2: Calculate the market value of debt \[ \text{Market value of debt} = V - E \] \[ \text{Market value of debt} = 85,000,000 - 36,004,499 = CAD 48,995,501 \] This rounds to approximately CAD 48.996 million, which corresponds to **Option B**. ### Why other options are incorrect: - **Option A (CAD 49.764 million)**: This is the face value of debt discounted over 2 years (55,000,000 × 0.9048 = 49,764,000) - **Option C (CAD 53.699 million)**: This results from not applying the discount factor (e⁻ʳᵀ) in the equity formula - **Option D (CAD 54.056 million)**: This results from not applying N(d₂) in the equity formula

Author: LeetQuiz .