Real Options.

Suppose that copper price is currently trading at S0 = $3.50/pound. Futures for delivery of copper in 1 year trade at $3.60/pound. The risk-free rate is 0%. Next year, the price of copper will either rise to $4.20 (60% actual probability) or fall to $3.00 (40% actual probability). Copper may or may not have a storage cost and/or convenience yield.

You have an investment project which has the following cash flows:

You have already spent $3M on R&D toward the project.

To go forward with the project, you will need an additional investment of $1M at t = 0.

At t = 1, you observe the price of copper. After observing the price of copper, if you decide to continue, you must make an additional investment of $1M. Additionally, you will be required to purchase 10M pounds of copper. The investment will then produce an immediate cash flow of $35M at t = 1.

Alternatively, after observing the copper price at t = 1, we can abandon the investment and have no future cash flows.

Suppose that you believe the project is worth investing in, but would like to hedge your risk. Given an example of a derivative security that you could enter into (specify long or short), that you could use to hedge your risk.