Answer-first summary for fast verification
Answer: 8%
## 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
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A portfolio manager at a hedge fund is applying the Merton model to estimate the volatility of a non-dividend-paying firm whose equity shares are held in the fund's portfolio. The manager conducts preliminary analysis on the firm and obtains the following results:
Assuming a constant volatility of firm value, what is the estimate of that volatility?
A
6%
B
8%
C
16%
D
18%
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