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```									EXAM - INTRO TO DERIVATIVES
NAME:                                                                      Professor Droussiotis

QUESTION #1
Luxury Cotton (“Luxury”), an independent distributor of cotton, is planning to sell 2.0 million lbs of cotton in December 2011 at the spot price on
delivery day. In order to hedge against a possible decline in cotton prices, Luxury wants to enter into a Futures contract and lock in the price.

a. Looking at the WSJ Future’s Contract sheet (Exhibit A), how many contracts should Luxury enter into so that half of it’s exposure it’s hedged for
its December delivery – show calculation?

b. After entering into the December contracts for half it’s delivery exposure, suppose that the only three possible prices for cotton in December is to
stay at the same level, increase by 10 cents and decrease by 15 cents, show the profit and loss from the futures contracts as well as the total
proceeds for Luxury.

Cotton prices in December, per lb
Units            -          \$0.00         +

Revenue from Coffee Sales
Profit on Futures
Total Proceeds

QUESTION #2

Morgan Stanley Investment Bank has two companies as customers who are in the process of raising funds and each has different views on the
interest rate movements in the future. Company A thinks that interest rates would stay low and Company B feels that rates wil l rise.

Company A offered either a Fixed Rate of 7.0% or Float LIBOR + 75 bps
Company B offered either a Fixed Rate of 8.25% or Float LIBOR + 150 bps

Given the different views, the broker recommends that Company A and Company B get into Swap Agreement with a 6.50% Swap price as follows:

a. Show the net interest pay for both parties

Company A                   Company B
View on interest Rates
LIBOR                                              LIBOR                         LIBOR
Float
Fixed
Swap price

Contract Chosen

Pays to Lender
LIBOR
Pay to other Company
Net Pay

Benefits
QUESTION #3
A U.S company with its primary revenues in U.S. dolars has a ₤100 million, 3-year 4.0% British Pound Sterling-denominated bond with a ₤100
par value. The firm wishes to guarantee the Pound Sterling value of the payments. Suppose the effective annual pound sterling-denominated
interest rate (as mentioned above is 4.0%), the dollar-denominated rate is 6.0% and the spot exchange rate is 1.60/₤, calculate the hedged and
unhedged positions, as well as the PV of each position given the forward exchange rates which initially are projected lower against the Dollar.

Unhedged          Forward    Unhedged         PV of
Time               Pounds CF        Exchange   Dollar Cash     UnHedged
(Years)                (₤)             Rate       Flow (\$)       Position
1                                    1.57
2                                    1.58
3                                    1.61
Present Value =

Hedged           PV of
Time                                           Dollar Cash      Hedged
(Years)                                          Flow (\$)        Position
1
2
3
Present Value =

QUESTION #4
Using the various costs in the table below calculate the payoff and profits for investment, assuming that the stock on the maturity date is \$100
.

Strike Price       Cost
(X)            (C)        Payoff          Profit
Call Option                            95            4.00
Put Option                             95            3.00
Call Option                            100           2.50
Put Option                             100           2.50
Call Option                            105           3.00
Put Option                             105           3.50

QUESTION #5
Use the Black-Scholes formula to find the value of a call option on the following stock:

INPUT                                                         OUTPUT
Standard Deviation (σ) =       30%             d1 =
Expiration (in years) (T) =     0.75            d2 =
Risk-Free Rate (Annual) (i) =       6%          N(d1) =
Stock Price (S ) =      70          N(d2) =
Exercise Price (X) =       75
Dividend Yield (annual) (δ) =        0          B/S =
QUESTION #6

Find the value of put option on the stock in the previous problem with the same information above - using the Put-Call Parity method

Reconsider the determination of hedge ratio in the two-stage model, where we showed that two-third share of stock would hedge one option. What
QUESTION #7

You are attempting to value a call option with an exercise price of \$100 and one year to expiration. The underlying stock pay s no dividends, its
current price is \$100, and you believe it has a 50% chance of increasing to \$120 and 50% change of decreasing to \$80. The ris k-free rate of
interest is 5%. Calculate the call option's value using the two-state stock price model.

QUESTION #8

Consider an offshore oil property with an estimated oil reserve of 50 million barrels of oil, where the present value of the development cost is
\$12 per barrel and the development lag is two years. The firm has the rights to exploit this reserve for the next 20 years, and the marginal
value per barrel of oil is \$12 per barrel currently (price per barrel - marginal cost per barrel). Once developed, the net production revenue each
year will be 5% of the value of the reserves. The riskless rate is 8%, and the varinace in ln(oil prices) is 0.03
Given thsi information, calculate the value of the oil reserve using option pricing method.

INPUTS:

INPUT                      OUTPUT
Standard Deviation (σ) =                           d1 =
Expiration (in years) (T) =                         d2 =
Risk-Free Rate (Annual) (i) =                       N(d1) =
Stock Price (S ) =                      N(d2) =
Exercise Price (X) =
Dividend Yield (annual) (δ) =                     Value

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