Using the Merton model formula provided to calculate distance to default under the physical measure: Given parameters:

• Current market value of assets ($V$) = USD 380 million
• Face value of zero-coupon bond ($K$) = USD 300 million
• Expected return on assets ($\delta$) = 20% = 0.20
• Asset volatility ($\sigma$) = 30% = 0.30
• Time to maturity ($\tau$) = 5 years

The term inside the probability function is: $z = \frac{\ln\left(\frac{K}{V}\right) - \delta \tau + 0.5 \sigma^2 \tau}{\sigma \sqrt{\tau}}$

Numerator: $\ln(300 / 380) - 0.20 \times 5 + 0.5 \times (0.30)^2 \times 5$ $= -0.236389 - 1.0 + 0.5 \times 0.09 \times 5$ $= -1.236389 + 0.225 = -1.011389$

Denominator: $0.30 \times \sqrt{5} = 0.30 \times 2.236068 = 0.67082$

$z = -1.011389 / 0.67082 \approx -1.5077$

To find the default probability, we evaluate $N(-1.51)$ using a standard normal distribution table: $N(-1.51) \approx 0.0655$, which is approximately 6.6%.