FIN 3150

Assignment 6 Real option valuation (valuation of a project using option pricing)

Proposed project:

A firm is considering an investment in the rights to Alchemy Mines.

Initial investment

The owner of the mine will sell the rights to the firm at a cost of $1,000,000 payable immediately. Payment of that amount entitles the firm to all rights to mine provided mining commences within one year and continues without interruption until the entire deposit is recovered. 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 silver: 75000 pounds;

Current market price of silver: $16.48 per ounce;

Expected price of silver in one year: $16.405 per ounce;

Expected fixed costs of mining and refining: $700,000;

Expected variable costs of mining and refining: $14.8575 per ounce; and

Cost to recover land and remediated environmental damage: $150,000.

If the firm decides to commence mining, it will at the time mining commences escrow all funds necessary to complete mining, refining and remediation. It will also presell all the silver and receive all revenues, based on the spot price of silver at that time, when mining comments. [That is, for valuation purposes, all cash flows for the project occur either at time 0 or time 1.]

Additional Information:

The firm estimates additional economic variables as follows:

Risk free interest rate equals 1.0%;

Expected market return: 12.2%;

Beta for silver production: 0.36; and

Standard deviation of annual returns on silver prices: 16.64%

1. Use net present value analysis to determine whether the firm should accept the proposed Alchemy Mines project.

Determine the expected cash flows and the appropriate discount rate (using CAPM).

Calculate NPV.

Determine whether the firm should accept the project.

2. Use option pricing analysis to determine whether the firm should accept the proposed Alchemy mines project.

Determine whether project cash flows have the characteristics of a put option or a call option.

Find the implicit strike price (that is, the expected spot silver price in one year at which the firm will elect to commence mining and processing rather than just walk away from the project. Remember that for purposes of calculating the strike price, any amounts already spent are sunk costs.)

Calculate the option value of the mine using the Black-Scholes options pricing model. (You can calculate the option value for a single ounce of silver using per ounce price and costs, then multiply that by the total amount of silver to get the total option value of the mine. Alternatively, you can calculate the option value of the mine using the total price of silver and the total costs.

The option value of the mine is then compared to the cost to acquire it to determine if the project should be accepted.