Assume that your bank underwrote $5$ loans to various hedge funds based in Cayman Islands each valued at $$1$M$.$ The PDs $(5\%$ each$)$ of each hedge fund are

independent of each other and follow a binomial distribution. Assume that recovery rate is $30\%$ for each loan. What is the $99\mathrm{.}9\%$ Credit Value at Risk $($CVAR$)?$ Please explain each step in your calculation.