The current value of the assets of Sibasa Mangoes Estate is R$180$m$.$ The assets are

financed by a mix of equity and zero$-$coupon debt. The current value of the zero$-$coupon

debt is R$85$m and the final amount to be paid on maturity after six years is R$110$m$,$ with

an effective interest rate of $13\%.$ The volatility in Sibasa Mangoes Estate$$s asset value

is $25\%.$ The following is required:

a$.$ Compute the PD of Sibasa Mangoes Estate based on the Merton model.

b$.$ What is the impact if the volatility suddenly increases to $27\%?(10)$