Question 1
The current price of the stock Freezeco is £200. During each six-month period it will either
rise by 10% or fall by 10%. The interest rate is 6% per six-month period. (Assume puts here
are for one share). Show your calculations; do not just give an answer.
a. Calculate the value of a one-year European put option on Freezeco’s stock with an
exercise price of £200. (2 points)
b. Recalculate the value of the Freezeco put option, assuming that it is an American
option. (2 points)
Question 2
Plot the value of a two-year European put option (once again, for one share) with a strike
price of £20 on Jordi Co. as a function of the stock price. Jordi Co. has a constant dividend
yield per year of 5% and its volatility is 20% per year. The risk-free rate of interest is 4% per
year. Explain why there is a region where the option trades for less than its intrinsic value
(the value on a payoff diagram). Please either use excel or handplot increments of 1 in the
stock price over a range of S=10 to S=30. Also note that we need to evaluate the current
price of the stock excluding dividends prior to expiration (since a European option doesn’t
include the right to the dividends). Include the calculations and data points. (4 points)
Question 3
The price of oil is currently $25 per barrel. Next year it will either increase by 50% to $37.50
or fall by 25% to $18.75. A firm is considering investing in a new oil field, where geological
surveys show there are 4 million barrels of oil underground. If the investment goes ahead, it
must be paid for today, but the oil can be sold either today or next year. The cost of the
investment is $110 million, although the project can be cancelled next year, recouping $85
million if drilling has not already begun.
The discount rate is 5%. Assume that the probability of an increase in the price of oil is 50%.
a) Should the firm go ahead with the investment? What is the value of the option to
cancel the project next year? (2 points)
Suppose there is an election next year, and an opposition party has threatened to impose
windfall taxes on oil companies. This tax would be 20% of oil revenues, but only if oil prices
rise to $37.50. The management of the firm believes that there is a 20% chance of the
ractical Work Questions
opposition party gaining power. The management also believe that by making a political
donation to the incumbent today, they can reduce the probability of an opposition win to
10%, although the size of the donation still needs to be negotiated.
b) Would the firm go ahead with the project without a political donation? What is the
maximum amount the firm would be willing to donate? (2 points)
Question 4
You have recently been named CFO of a large corporation based in Rio de Janeiro, Brazil.
The CEO has asked you to raise R$12,000,000 (Brazilian reals) one year from now to fund a
future investment. The company has to raise the capital either through a U.S. (in US$) or a
Brazilian (in R$) based bank. The annual interest rates on U.S. and Brazilian bills are 1% and
10% respectively. The current exchange rate is R$1.8 per US$ and the futures price for
delivery one year from now is R$1.9 per US$.
a. Assume the interest rates and the current exchange rates given above are correct.
What should the futures price of one R$ be in US$ according to the covered interest
rate parity theorem? (1 point)
b. Given your answer in part (a), you should be able to benefit from an arbitrage
opportunity that would allow you to raise the necessary money at no cost for the
company. Why? (1 point)
c. Describe in a table like the one below the necessary actions (and associated cash
flows in R$) you need to take in order earn R$12,000,000 in one year at no cost. The
possible actions that you can take are lending in either currency, borrowing in either
currency, and buying or selling futures contracts. As above, the current exchange
rate is R$1.8 per US$1 and assume the actual future exchange rate in one year is X. (2
points) – look at table
(Please look at the assignment in pdf format – File named Assignment)
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