Question

For the following problems consider the following three firms:

-XYZ mines copper, with fixed costs of $0.50/lb and variable cost of $0.40/lb.

-Wicro produces wire. It buys copper and manufactures wire. One pound of copper can be used to produce one unit of wire, which sells for the price of copper plus $5. Fixed cost per unit is $3 and noncopper variable cost is $1.50.

-Telco installs telecommunications equipment and uses copper wire from Wicro as an input. For planning purpose, Telco assigns a fixed revenue of $6.20 for each unit of wire it uses.

The 1-year forward price of copper is $1/lb. The 1-year continuously compounded interest rate is 6%. One-year option prices for copper are shown in the table below.

Strike              Call               Put

0.9500          $0.0649         $0.0178

0.9750            0.0500           0.0265

1.0000            0.0376           0.0376

1.0250            0.0274           0.0509

1.0340            0.0243           0.0563

1.0500            0.0194           0.0665

In your answer, at a minimum consider copper prices in 1 year of $0.80, $0.90, $1.00, $1.10, and $1.20.

1) If XYZ does nothing to manage copper price risk, what is its profit 1 year from now, per pound of copper? If on the other hand XYZ sells forward its expected copper production, what is its estimated profit 1 year from now? Construct graphs illustrating both unhedged and hedged profit.

Answer 1

1). Profit if unhedged:

Profit if hedged by selling forward at $1/lb forward price:

Graph: