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