In the Merton model, the parameters $d_1$ and $d_2$ are related by the formula: $d_1 = d_2 + \sigma \sqrt{T}$

Where:

• $\sigma$ is the volatility of the firm's assets (firm value).
• $T$ is the time to maturity of the debt.

Given:

• $d_1 = 3.217790$
• $d_2 = 3.038905$
• $T = 5$ years

We can rearrange the formula to solve for the volatility ($\sigma$): $\sigma \sqrt{T} = d_1 - d_2$ $\sigma \sqrt{5} = 3.217790 - 3.038905$ $\sigma \sqrt{5} = 0.178885$

Now, solve for $\sigma$: $\sigma = \frac{0.178885}{\sqrt{5}}$ $\sigma = \frac{0.178885}{2.236068} \approx 0.0800$

Thus, the constant volatility of firm value is estimated to be 8%.