# Question

Suppose that firms face a 40% income tax rate on positive profits and that net losses receive no credit. (Thus, if profits are positive, after-tax income is (1âˆ’ 0.4)Ã— profit, while if there is a loss, after-tax income is the amount lost.) Firms A and B have the same cash flow distribution as in the previous problem. Suppose the appropriate effective annual discount rate for both firms is 10%.

a. What is the expected pre-tax profit for A and B?

b. What is the expected after-tax profit for A and B?

c. What would Firms A and B pay today to receive next year's expected cash flow for sure, instead of the variable cash flows described above? For the following problems use the BSCall option pricing function with a stock price of $420 (the forward price), volatility of 5.5%, continuously compounded interest rate of 4.879%, dividend yield of 4.879%, and time to expiration of 1 year. The problems require you to vary the strike prices.

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

â€¢Wirco 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.

â€¢Telco installs telecommunications equipment and uses copper wire fromWirco as an input. For planning purposes, 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.17

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

a. What is the expected pre-tax profit for A and B?

b. What is the expected after-tax profit for A and B?

c. What would Firms A and B pay today to receive next year's expected cash flow for sure, instead of the variable cash flows described above? For the following problems use the BSCall option pricing function with a stock price of $420 (the forward price), volatility of 5.5%, continuously compounded interest rate of 4.879%, dividend yield of 4.879%, and time to expiration of 1 year. The problems require you to vary the strike prices.

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

â€¢Wirco 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.

â€¢Telco installs telecommunications equipment and uses copper wire fromWirco as an input. For planning purposes, 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.17

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

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