A gold-mining firm's strategy is to manage its exposure to gold price risk and reduce fluctuations in its earnings as much as possible. Their rationale is that having stable and predictable cash-flows allows the company to plan their future financial strategy and provide low risk earnings to its investors.

Being a firm with significant amounts of production, it uses a. number of ways to hedge its exposure to gold price. It is now the end of 1997 and for the year 1998, the firm is expecting to produce and sell 2,300,000 ounces of gold and incur total costs of 600 million. All sales are made at the end of the year and the expenses are paid at the beginning of the year. The before-tax earnings of

the firm are given by the gold sales minus the expenses. The annual risk-free rate is 5% and is constant.
The firm is considering the following financing options for this year's expenses:

A. Loan: Borrow all required amount through a bank loan or issuing one-year debt. Assume that the firm can borrow risk-free for one year.

B. Bullion loan: Borrow 750,000 ounces of gold for one year to sell immediately, at a lease rate of 3.p%.

C. Gold security Receive 85 million from investors by issuing special securities that will pay 10% of the firm's production if the price of gold is below $250 per ounce, 20% if the price is between $250 and 8299.99, 30% if the price is between $300 and $349,99, and 40% if it is $350 per ounce or above,

Further, the firm is considering to hedge its exposure to gold price risk using gold derivatives. Available derivatives are futures, forwards, call options and put options. In the Excel spreadsheet you can find the current prices of futures (Table I) and options (Table 2). Table 1 also shows the evolution of the futures prices of gold in the year 1998.

Answer the following questions, providing all necessary formulas, computations, graphs and expla-nations:

1. Suppose that. the firm goes short December-98 futures for a. total quantity of 1 million ounces of gold. The futures is settled monthly and is financially settled at expiration. Provide a table with the firm's cash-flows from the futures position, for the particular scenario of prices shown in Table 1. Also, compute the associated profit.

2. What should the price of a 1-year forward contract on gold be on December 31, 1997? Support your answer with an appropriate strategy. You should provide a. description of your strategy and a. table with position(s), cash-flows and profit, using the specific scenario of prices shown in Table 1.)

3. Write a short memo to the firm's CEO to help her choose between futures and forwards, explaining their differences, including the advantages and disadvantages of the exchange traded derivatives compared to OTC derivatives.

4. Compute the missing option prices in Table 2. Explain how you computed them-and the rationale behind the formula you have used

Suppose the firm finances itself fully with a loan (option A) and is considering the following hedging strategies:

(a) A collar strategy involving the $275 put and $325 call options, on the entire exposure of the firm.

(h) A (almost) pay later strategy whereby the firm sells $300 put options on the entire exposure of the firm, buys half the firm's exposure of $250 puts and half the firm's exposure of $275 puts.

For each strategy provide an accurate plot of the firm's before tax earnings in one year, with all necessary information as to the slope-s, cut-off point(s), break-even point(s), etc. Also, for each strategy explain the pros and cons., comparing them to the no-hedge alternative.

5. Suppose the firm finances itself with the bullion to (option B) and the rest with an ordinary loan (option A). Also, the firm wants to fully protect itself from the downside with a put option with strike $250. Provide the appropriate position of the put option and an accurate plot of the 1-year before tax earnings, in this case.

6. Suppose the firm finances itself with all three options, i.e. the bullion loan, the gold securities and the rest with an ordinary loan. Plot the exposure of the firm, i.e. the 1-year before-tax earnings, in this case. Further, design an appropriate hedging strategy that hedges the firm's earnings completely and compute the resulting certain 1-year earnings. Verify your answer by computing the earnings of the firm for the specific scenario of prices shown in Table 1.