Proposed project: Alchemy Mines is considering an investment in the rights to a gold mine.

Initial investment

The owner of the mine will sell the rights to Alchemy Mines at a cost of $2,500,000 payable immediately. Purchase of the rights entitles Alchemy Mines to all mining rights provided mining commences within one year and continues without interruption until the entire deposit is recovered and the land restored in compliance with regulatory requirements. If mining does not commence in one year, the title to the mine reverts to the seller.

Expected operating variables The firm has made the following assumptions regarding operating cash flows for the mine:

Recoverable gold: 25,000 ounces

Current market price of gold: $1635.90 per ounce

Expected price of gold in one year: $1665.30 per ounce

Expected fixed costs of mining and refining: $5,000,000

Expected variable costs of mining and refining: $1355.00 per ounce

Cost to restore the land and remediate environmental damage: $250,000

No taxes are paid on profits from the project

If the firm mines the gold, all cash in- and out-flows from mining and selling the gold and for remediation will occur in one year.

Additional Information:

The firm estimates additional economic variables as follows:

Risk free interest rate equals 1.25%

Expected market return: 11.50%

Beta for gold mining and smelting: 0.35

Standard deviation of annual returns on gold prices: 0.1650

2. Use option pricing analysis to determine whether Alchemy Mines should accept the proposed gold mine project.

a. Find the implicit strike price, that is, the expected spot gold price at which the firm will elect to mine and process the ore rather than just walk away from the project. (Remember that for an option, the option premium is a sunk cost and does not affect the decision to exercise.)

b. Calculate the option value of the mine using the Black-Scholes options pricing model.

Note: You can calculate the option value for a single ounce of gold using per ounce price and costs, then multiply that by the total amount of gold to get the total option value of the mine. Alternatively, you can calculate the option value using the total price of gold and the total costs.

c. Compare the option value of the mine to the cost to acquire rights to the mine to determine whether to accept the project.

d. Indicate whether Alchemy Mines should accept the project and explain.

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