Ramaco Inc. is a company that specializes in producing aluminum (or aluminum). The firm produces 10 million kilograms of aluminum in the first year (Q=10m kg), where the variable cost is $0.5 per kilogram (VC = 0.5 per kg), and fixed cost is $10 million (FC = $10m). In the first year, the firm does not have any debt and will not pay any dividends. Without hedging, the cash flow generated by the aluminum production at the end of the first year will depend on the market price of aluminum at the end of the first year and therefore is random. Assume that the market price of aluminum at the end of the first year will either be $2/kg, or $4/kg, with 50% chance for each scenario.

In the second year, the firm will consider investing in a project which enables the firm to establish its own plant to use the aluminum foil for automotive applications. The size of the investment (I) will depend on the total capital it has at the beginning of the second year, which equals to the amount of internal cash flow (w) it generates during the first year.

At the end of the second year, the net value of the project (i.e., NPV) can be expressed as:

F(I) = f(I) I = I I2

Assume that m is a random variable that follows a normal distribution, with E() (i.e., mean of ) = 20, and () (i.e. standard deviation of ) = 2, and the correlation coefficient between and market price at the end of the first year, P, is denoted as corr(,P) = .

Assume that at the beginning of the first year, the firm can use a combination of forward and futures contract of the aluminum to hedge against the market risk of the aluminum prices, and the one-year forward/futures price are $3.0/kg at the beginning of the first year. Ignore taxes or transaction costs of forwards / futures contract, and assume the discount rate is 0.

Ignore the external capital in this question.

Given the range of corr(, P) is between -1 to 1, what is the resulting range for the optimal hedged quantity of aluminum at the beginning of the first year in the forward or futures contract in terms of maximizing the net value of the firm?

Question 13 options:

A)

between 6.3524 millions of kg to 6.5532 millions of kg.

B)

between 6.0124 millions of kg to 6.2538 millions of kg.

C)

between 6.2342 millions of kg to 6.3553 millions of kg.

D)

between 6.5526 millions of kg to 6.6579 millions of kg.

E)

None of the above

Explain step by step