B is correct. The Merton model can be used for estimating the value of equity (E) as presented in Equation (1) below:

$$E = V \cdot N(d_1) - D \cdot N(d_1 - \sigma \sqrt{T - t}) \quad \text{(1)}$$

where:

V = firm value
D = debt value
σ = volatility of firm value
T − t = time remaining to maturity of debt

And:

$$d_1 = \frac{\ln(V) - \ln(D)}{\sigma \sqrt{T - t}} + 0.5 \cdot \sigma \sqrt{T - t} \quad \text{(2)}$$ $$d_2 = (d_1 - \sigma \sqrt{T - t}) \quad \text{(3)}$$

The reading discusses how firm volatility can be derived using simultaneous Equations (1) and (2) with two unknowns, V and σ. Given the parameter values above (in our simplified case), we only need Equation (3) to estimate firm volatility. Thus, using Equation (3):

$$d_2 = 3.038905 = 3.217790 - \sigma \cdot \sqrt{5}$$ $$\sigma = (3.217790 - 3.038905) / 2.23608 = 0.079999 = 8.0\%$$

A is incorrect. 6% is the incorrect result obtained by equating σ to (d₁/d₂ − 1).
C is incorrect. 16% is the incorrect result obtained if 0.5 is applied to the last term in Equation (3).
D is incorrect. 18% is the firm volatility assuming debt matures in 1 year.