Example $10\mathrm{.}3$

The current value of the assets of the firm $-$ XYZ Ltd $-$ is $$100m.$ The assets are financed by a mix of equity and zero coupon debt. The current value of zero coupon debt is $$60\mathrm{.}65m$ and the final amount to be paid on maturity after $5$ years is $$100m$ with an effective interest rate of $10\%.$ The volatility in XYZ$\text{'}$s asset value is $20\%.$ Compute $($i$)$ the PD of XYZ Ltd based on the Merton Model and $($ii$)$ the impact if the volatility suddenly increases to $25\%$ due to a sudden change in business dynamics.