1. 1.Consider a firm whose earnings face a binomial distribution at the end of the period:

• If the retail price of the product is high, the firm will make $120 million EBT (earnings before taxes) with a probability of 0.6;
• If the retail price is low, the firm's EBT will be reduced to $40 million with a probability of 0.4.

1. The tax rate is a convex function of EBT (earnings before taxes):

• Tax rate is 15% (of EBT) when EBT is less than or equal to $50 million;
• Tax rate is 20% when EBT is more than $50 million but less than or equal to $75 million;
• Tax rate is 25% when EBT is more than $75 million but less than or equal to $100 million;
• Tax rate is 30% when EBT is above $100 million.

1. Suppose that the firm decides to partially hedge its risk exposure, and after the hedging, the new distribution of the firm's EBT is $100 million with a probability of 0.6 and $70 million with a probability of 0.4.What are the benefits of hedging in terms of expected tax payments?

A.$1.25 million

B.$1.50 million

C.$1.75 million

D.$2 million

E.$3.4 million

2.ABC Inc. needs to consider the optimal investment and hedging strategies over the next two years.In the first year, the firm will produce 1 million units of its products and the internal cash flow generated will equal to its revenue, because cost of the production is negligible. The market price of the product is P, which is a random variable with E(P)=1, and(P)=2.5. At the beginning of the second year, the firm will invest all the internal cash flows into a project which has a net value function, F(I) =I - 0.2I², where I represents the total investment, andis a random variable with E()=5,()=3, and corr(, P) =.

Assume discount rate is 0, ignore external capital and and ignore any other costs. Assume that the firm can use a combination of forward and futures contracts to hedge against the uncertainties of market price of its product, where the forward price in these contracts = 1 ($/unit).The firm needs to enter the forward and/or futures contract at the beginning of the first year.

If corr(, P) == 0, what is the optimal hedging strategy for the firm at t = 0?

If corr(, P) == 0.2, what is the optimal hedging strategy for the firm at t = 0?

What is the range of corr(, P) that makes partial hedging better than full hedging in terms of maximizing the net value of the firm?

A.Full hedging, i.e., sell 1 million units in the forward / futures contract at t = 0.

B.No hedging.

C.Partial hedging, and specifically, sell 0.4 million units in the forward / futures contract.

D.Partial hedging, and specifically, sell 0.6 million units in the forward / futures contract.

E.None of the above.

3.Based on the information on the previous question, if corr(, P) == 0.2, what is the optimal hedging strategy for the firm at t = 0?

A.Full hedging, i.e., sell 1 million units in the forward / futures contract at t = 0.

B.No hedging.

C.Partial hedging, and specifically, sell 0.4 million units in the forward / futures contract.

D.Partial hedging, and specifically, sell 0.6 million units in the forward / futures contract.

E.None of the above

4.Based on the information on the previous question, what is the range of corr(, P) that makes partial hedging better than full hedging in terms of maximizing the net value of the firm?

A.The correlation coefficient needs to be between 0 and 1.

B.The correlation coefficient needs to be between -1 and 0.

C.The correlation coefficient needs to be higher than -0.333 but smaller than 0.

D.The correlation coefficient needs to be higher than 0 but smaller than 0.333.

E.None of the above