Calculation Explanation

Step 1: Calculate the default point (strike price)

• Short-term liabilities = $12 billion
• Long-term liabilities = $6 billion
• Default point = Short-term debt + 0.5 × Long-term debt
• Default point = 12 + 0.5 × 6 = 12 + 3 = $15 billion

Step 2: Calculate the distance to default using physical probability formula The Merton model physical probability of default uses:

• Current asset value (V) = $20 billion
• Default point (K) = $15 billion
• Asset volatility (σ) = 35% = 0.35
• Expected return on assets (μ) = 12% = 0.12
• Time horizon (T) = 1 year

Distance to default (d2) = [ln(V/K) + (μ - σ²/2)T] / (σ√T)

Step 3: Compute the values

• ln(V/K) = ln(20/15) = ln(1.3333) = 0.2877
• μ - σ²/2 = 0.12 - (0.35²/2) = 0.12 - (0.1225/2) = 0.12 - 0.06125 = 0.05875
• (μ - σ²/2)T = 0.05875 × 1 = 0.05875
• σ√T = 0.35 × √1 = 0.35

d2 = (0.2877 + 0.05875) / 0.35 = 0.34645 / 0.35 = 0.9899 ≈ 0.99

Step 4: Find the probability of default Probability of default = N(-d2) = N(-0.99) From the provided z-table: P(Z < -0.99) = 0.1611 = 16.11%

Step 5: Verify the answer The calculated probability is 16.11%, which corresponds to option D.

Note: The risk-free rate (1%) is not used in the physical probability calculation, as physical probability uses the expected return on assets rather than the risk-free rate.