Explanation

In the Merton model for credit risk, the value of risky debt can be calculated using the put-call parity relationship:

Value of Risky Debt = Value of Risk-Free Debt - Value of Put Option

Where:

• Value of Risk-Free Debt = Face Value × e^(-rT)
• Value of Put Option = $6.95 million (given)

Step 1: Calculate the value of risk-free debt

Face Value = $80 million Risk-free rate (r) = 4% = 0.04 Time to maturity (T) = 5 years

Value of Risk-Free Debt = $80 million × e^(-0.04 × 5) = $80 million × e^(-0.20) = $80 million × 0.8187 = $65.50 million

Step 2: Calculate the value of risky debt

Value of Risky Debt = $65.50 million - $6.95 million = $58.55 million

However, this calculation gives us $58.55 million, which corresponds to option C. But let me verify this approach.

Actually, in the Merton model: Value of Debt = Value of Risk-Free Debt - Put Option Value

So: Value of Debt = $65.50 million - $6.95 million = $58.55 million

But wait, let me reconsider. The put option value represents the credit risk premium. The correct relationship is:

Value of Debt = Present Value of Face Value - Put Option Value

So: Value of Debt = $65.50 million - $6.95 million = $58.55 million

This matches option C ($58.55 million). However, let me double-check the calculation:

Present Value of Face Value = $80 × e^(-0.04×5) = $80 × 0.8187 = $65.496 million ≈ $65.50 million

Value of Debt = $65.50 million - $6.95 million = $58.55 million

Therefore, the correct answer is C ($58.55 million)

The put option value of $6.95 million represents the cost of credit insurance, which is subtracted from the risk-free value of the debt to get the market value of the risky debt.