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 $495$ and volatility $100.$ Assume gold price risk is

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

The firm pays taxes at a rate of $50\%$ over all cash flows exceeding $200.$ Interest expenses

are tax deductible. Suppose that the firm hedges its gold price risk by selling a forward

contract on gold, and chooses its debt level optimally to maximize firm value. If the firm

files for bankruptcy, bankruptcy costs are $50.$ The value of the firm is the expected

discounted value of its cash flow less the expected discounted value of taxes and

bankruptcy costs.

Find the value of the hedged firm with optimal debt level.