Explanation

Using the Merton model equation for d₂:

$d₂ = d₁ - σ√T$

Where:

• d₁ = 3.217790
• d₂ = 3.038905
• T = 5 years
• σ = volatility of firm value (what we're solving for)

Rearranging the equation: $σ√T = d₁ - d₂$ $σ√5 = 3.217790 - 3.038905$ $σ√5 = 0.178885$ $σ = \frac{0.178885}{√5}$ $σ = \frac{0.178885}{2.236068}$ $σ = 0.079999 ≈ 8.0\%$

Why other options are incorrect:

• A (6%): Incorrect result obtained by equating σ to (d₁/d₂ - 1)
• C (16%): Incorrect result obtained if 0.5 is applied to the last term in the equation
• D (18%): Firm volatility assuming debt matures in 1 year instead of 5 years