Assignment - NPV and real option valuation
Proposed project: Alchemy Mines is considering an investment in the rights to a silver mine.
Initial investment - The owner of the mine will sell the rights to Alchemy Mines at a cost of $1,000,000 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 silver: 750,000 ounces
Current market price of silver: $16.03 per ounce
Expected price of silver in one year: $16.50 per ounce
Expected fixed costs of mining and refining: $1,500,000
Expected variable costs of mining and refining: $12.50 per ounce
Cost to restore the land and remediate environmental damage: $500,000
No taxes are paid on profits from the project
If the firm decides to mine the silver, it must escrow all funds necessary to pay the costs of mining, refining and restoration upon commencement of mining.
The firm will only mine the silver if it is able to pre-sell the entire recoverable production and receive payment upon commencement of mining.
As a result, for net present valuation purposes, all cash flows for the project occur either at time 0 (the initial payment for the rights) or in 1 year (all other expected cash inflows and outflows for the project).
Additional Information:
The firm estimates additional economic variables as follows:
Risk free interest rate equals 2.5%
Expected market return: 12.2%
Beta for silver mining and smelting: 1.175
Standard deviation of annual returns on silver prices: 23.25%
1. Use net present value analysis to determine whether the firm should accept the proposed Alchemy Mines project.
a. Determine the amount and time of all expected cash flows for the proposed project.
b. Determine the appropriate discount rate (using CAPM).
c. Calculate NPV.
d. Indicate whether Alchemy Mines should accept the project and explain.
2. Use option pricing analysis to determine whether Alchemy Mines should accept the proposed silver mine project.
a. Determine whether the project cash flows have the characteristics of a put option or a call option.
b. 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.)
c. 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.
d. Compare the option value of the mine to the cost to acquire it to determine whether to accept the project.
e. Indicate whether Alchemy Mines should accept the project and explain.
Attachment:- Assignment Files.rar