The value of a company's equity is $$20$ million and the volatility of its equity is $60\%.$ The

debt that will have to be repaid in three years is $$25$ million. The risk$-$free interest rate is

$4\%$ per annum. Describe how Merton's model can be used to estimate the value of the

company and the volatility in the value. Check which one of the following is an approximate

solution to this problem.

A$)V_0=25\mathrm{.}0$ and ${}_V=0\mathrm{.}22$;

B$)V_0=33\mathrm{.}0$ and ${}_V=0\mathrm{.}45$;

C$)V_0=41\mathrm{.}0$ and ${}_V=0\mathrm{.}32.$

Estimate the probability of default of the company in three years.