Consider a firm that will produce one unit of gold a year from today. The price of gold next

year is normally distributed with mean $427$ and volatility $100.$ Assume gold price risk is

diversifiable, and the riskless rate is $5\%($continuously compounded$).$

Consider a firm with outstanding debt that has promised to repay $300$ next year $($principal

plus interest$).$ If the firm files for bankruptcy, bankruptcy costs are $50.$ Assume that the firm

pays no taxes, so that the value of the firm is the expected discounted value of its cash flow

less the expected discounted value of bankruptcy costs.

Suppose that the firm hedges its gold price risk by selling a forward contract on gold. Find

the value of the hedged levered firm.