Under the Merton model, the real-world probability of default (PD) is computed using the expected return on firm assets ($\mu$) and is given by $N(-d_2)$, where:

$d_2 = \frac{\ln(V/K) + (\mu - 0.5\sigma^2)T}{\sigma\sqrt{T}}$

Given values:

• $V = 110$
• $K = 130$
• $T = 3$
• $\mu = 0.20$
• $\sigma = 0.30$

Step-by-step calculation:

1. $\ln(V/K) = \ln(110/130) = -0.16705`$2. $(\mu - 0.5\sigma^2)T = (0.20 - 0.5 \times 0.30^2) \times 3 = (0.20 - 0.045) \times 3 = 0.155 \times 3 = 0.465$3`. Numerator =$-0.16705 + 0.465 = 0.29795$4. Denominator = $0.30 \times \sqrt{3} = 0.519615$5. $d_2 = 0.29795 / 0.519615 = 0.5734$

The probability of default is $N(-d_2) = N(-0.5734)$. By looking up $-0.57$ in the standard normal table, the value is approximately 0.2832.