Consider a company with equity value equal to $$80,$ and face value of debt of $$50.$ The annual log$-$return on risk$-$free debt is $3\%.$ If the debt of the company expires in $0\mathrm{.}5$ years, how does the probability of default of the company changes as a function of the volatility of the equity?

In excel please.

a$.$ Create a plot where the distance to default is on the y$-$axes and the volatility of the equity $($from $0\mathrm{.}1$ to $1\mathrm{.}5,$ in increments of $0\mathrm{.}1)$ is on the x$-$axes. That is$,$ what is the relationship between equity $($i$.$e$.$ stock$)$ volatility and the distance to default of the firm?

b$.$ Create a plot where the probability of default is on the y$-$axes and the volatility of the equity $($from $0\mathrm{.}1$ to $1\mathrm{.}5,$ in increments of $0\mathrm{.}1)$ is on the x$-$axes. That is$,$ what is the relationship between equity $($i$.$e$.$ stock$)$ volatility and the probability of default of the firm?

c$.$ Comment the results.