Financial Risk Manager Part 2

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Explanation:

\text{PD} = N\left(\frac{\ln(F) - \ln(V) - (\mu - \frac{\sigma^2}{2})(T - t)}{\sigma\sqrt{T - t}}\right)

Where:
F = debt face value.
V = firm asset value.
μ = expected return in the “risky world”.
T = time remaining to maturity.
σ = volatility (standard deviation of asset values).
N = cumulated normal distribution operator.

In this case, we have:

\text{PD} = N\left(\frac{\ln(16710000) - \ln(17701000) - (0.12 - \frac{0.22^2}{2})(1)}{0.22\sqrt{1}}\right)

= N(-0.6973) = 1 - 0.7571 = 0.2429

Explanation:

\text{PD} = N\left(\frac{\ln(F) - \ln(V) - (\mu - \frac{\sigma^2}{2})(T - t)}{\sigma\sqrt{T - t}}\right)

In this case, we have:

\text{PD} = N\left(\frac{\ln(16710000) - \ln(17701000) - (0.12 - \frac{0.22^2}{2})(1)}{0.22\sqrt{1}}\right)

= N(-0.6973) = 1 - 0.7571 = 0.2429

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Q.5438 Use the Merton's model to estimate the probability of default (PD) for a non-dividend-paying company with only long-term using the following information.

Company’s assets `$17`,701,000
Company’s debt `$16`,710,000
Company’s Return on Assets 12%
Volatility of Company’s Assets 22%
Annual interest rate 5%
Time before maturity of debt 1 year

What is the probability of default (PD) for the company?

Company’s assets	`$17`,701,000
Company’s debt	`$16`,710,000
Company’s Return on Assets	12%
Volatility of Company’s Assets	22%
Annual interest rate	5%
Time before maturity of debt	1 year

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Last updated: July 5, 2026 at 07:27

24.29%

82.05%

69.73%

75.71%