Rio Tinto Inc., which is a Canadian company and one of the global leaders in aluminum mining and production, is re-examining its capital structure and whether it has any excess debt capacity. In 2015, Rio Tinto had 12.2 million shares outstanding at $210 per share and debt outstanding of $3 billion (book as well as market value). The debt had a rating of B and an interest rate of 10.12%. In addition, the firm had leases outstanding, with annual lease payments of $150 million (lease payments are perpetual and made at the end of the year). The beta of the stock is 1.26, and the firm faces a tax rate of 35%. The Treasury bond rate is 6.12%. The market risk-premium is 5.5%.

a. What is the firm's current debt/equity ratio?

b. Estimate the current cost of capital of Rio Tinto

c. Your analysis shows that the optimal debt ratio (debt/total firm value) should be 30%. At this level of debt, the rating will be BBB and the interest rate on debt will be 8.12%. Estimate the optimal cost of capital.

d. Rio Tinto is considering acquiring a patent that would allow it to have exclusive rights on aluminum production in South Africa for the next 15 years. The initial investment related to the patent is $500 million and the related increase in cash flow will be $300 million with a standard deviation of 25%. Assume that the risk-free rate is now 4%. What is the maximum price that Rio Tinto would pay for this patent?