Exercise Session #7 Suggested Solutions

Transcription

1 JEM034 Corporate Finance Winter Semester 207/208 Instructor: Olga Bychkova Date: 2//207 Exercise Session #7 Suggested Solutions Problem Describe each of the following situations in the language of options: a Drilling rights to undeveloped heavy crude oil in Northern Alberta. Development and production of the oil is a negative NPV endeavor. The break even oil price is C$70 per barrel, versus a spot price of C$60. However, the decision to develop can be put off for up to five years. Development costs are expected to increase by 5% per year. b A restaurant is producing net cash flows, after all out of pocket expenses, of $700,000 per year. There is no upward or downward trend in the cash flows, but they fluctuate as a random walk, with an annual standard deviation of 5%. The real estate occupied by the restaurant is owned, not leased, and could be sold for $5 million. Ignore taxes. c A variation on part b: Assume the restaurant faces known fixed costs of $300,000 per year, incurred as long as the restaurant is operating. Thus, Net cash flow = revenue less variable costs fixed costs, $700, 000 =, 000, , 000. The annual standard deviation of the forecast error of revenue less variable costs is 0.5%. The interest rate is 0%. Ignore taxes. d A paper mill can be shut down in periods of low demand and restarted if demand improves sufficiently. The costs of closing and reopening the mill are fixed. e A real estate developer uses a parcel of urban land as a parking lot, although construction of either a hotel or an apartment building on the land would be a positive NPV investment. f Air France negotiates a purchase option for 0 Boeing 787s. Air France must confirm the order by 209. Otherwise Boeing will be free to sell the aircraft to other airlines. a A five year American call option on oil. The initial exercise price is C$70 a barrel, but the exercise price rises by 5% per year. b An American put option to abandon the restaurant at an exercise price of $5 million. The restaurant s current value is $700,000 /r. The annual standard deviation of the changes in the value of the restaurant as a going concern is 5%. c A put option, as in b, except that the exercise price should be interpreted as $5 million in real estate value plus the present value of the future fixed costs avoided by closing down the restaurant. Thus, the exercise price is: $5, 000, $300, = $8, 000, 000.

2 The underlying asset is now P V revenue variable cost, with annual standard deviation of 0.5%. d A complex option that allows the company to abandon temporarily an American put and if the put is exercised to subsequently restart an American call. e An in the money American option to choose between two assets; that is, the developer can defer exercise and then determine whether it is more profitable to build a hotel or an apartment building. By waiting, however, the developer loses the cash flows from immediate development. f A call option that allows Air France to fix the delivery date and price. Problem If you buy a nine month T bill future, you undertake to buy a three month bill in nine months time. Suppose that Treasury bills and notes currently offer the following yields: What is the value of a nine month bill future? If we purchase a 9 month Treasury bill futures contract today, we are agreeing to spend a certain amount of money nine months from now for a 3 month Treasury bill. So, the valuation of this futures contract involves three steps:. Find the expected yield of a 3 month Treasury bill 9 months from now y f. 2. Find the corresponding price of the 3 month Treasury bill 9 months from now P f. Note: P f is the answer to this problem, so step 3 is not a required step for this solution. 3. Find the corresponding spot price today. The yield of a 3 month Treasury bill nine months from today is found as follows where r denotes a spot rate and the subscripts refer to the time to maturity, in months: + r 9 3 /4 + y f /4 = + r 2, /4 + y f /4 = Solving, we find that: y f = 0.06 or.06% annualized rate. It follows that the price per dollar of a 3 month Treasury bill nine months from now will be: $ P f =.06 = $ /4 The corresponding spot price today is: P = $ /4 = $

3 Problem In September 204 swap dealers were quoting a rate for five year euro interest rate swaps of 4.5% against Euribor the short term interest rate for euro loans. Euribor at that time was 4.%. Suppose that A arranges with a dealer to swap a e0 million five year fixed rate loan for an equivalent floating rate loan in euros. a What is the value of this swap at the time that it is entered into? b Suppose that immediately after A has entered into the swap, the long term interest rate rises by %. Who gains and who loses? c What is now the value of the swap? a The NPV of a swap at initiation is zero, assuming the swap is fairly priced. b If the long term rate rises, the value of a five year note with a coupon rate of 4.5% would decline to e9,573,000: 450, , 000, = 9, 573, 000. With hindsight, it is clear that A would have been better off keeping the fixed rate debt. A loses as a result of the increase in rates, and the dealer gains. c A now has a liability equal to: 0, 000, 000 9, 573, 0000 = 427, 000. The dealer has a corresponding asset. Problem Consider the commodities and financial assets listed in the following table: The risk free interest rate is 6% a year, and the term structure is flat. a Calculate the six month futures price for each case. b Explain how a magnoosium producer would use a futures market to lock in the selling price of a planned shipment of,000 tons of magnoosium six months from now. c Suppose the producer takes the actions recommended in your answer to b, but after one month magnoosium prices have fallen to $2,200. What happens? Will the producer have to undertake additional futures market trades to restore its hedged position? d Does the biotech index futures price provide useful information about the expected future performance of biotech stocks? e Suppose Allen Wrench stock falls suddenly by $0 per share. Investors are confident that the cash dividend will not be reduced. What happens to the futures price? 3

4 f Suppose interest rates suddenly fall to 4%. The term structure remains flat. What happens to the six month futures price on the five year Treasury note? What happens to a trader who shorted 00 notes at the futures price calculated in part a? g An importer must make a payment of one million ruples three months from now. Explain two strategies the importer could use to hedge against unfavorable shifts in the ruple dollar exchange rate. a To calculate the six month futures price, we use the following basic relationships for commodities and for financial futures, respectively: F t = S 0 + r f net convenience yield t, F t = S 0 + r f y t. Thus, the six month futures prices are: Magnoosium: 2, = $2, 828 per ton. Oat Bran: = $0.44 per bushel. Biotech: = $44.4. Allen Wrench: /58 = $ Year T Note: /08.93 = $08.2. Ruple: For the currency futures i.e., the Westonian ruple, the spot currency quote is an indirect quote i.e., ruples per dollar rather than a direct quote i.e., dollars per ruple. If I buy ruples today in the spot market, I pay $ /3. per ruple in the spot market and earn interest of = or 5.83% for six months. If I buy ruples in the futures market, I pay $ /X per ruple where X is the indirect futures quote and I earn 6% interest on my dollars. Thus, the futures price of one ruple should be: = = Therefore, a futures buyer should demand 3.07 ruples for $. b The magnoosium producer would sell,000 tons of six month magnoosium futures. c Because magnoosium prices have fallen, the magnoosium producer will receive payment from the exchange. It is not necessary for the producer to undertake additional futures market trades to restore its hedge position. d No, the futures price depends on the spot price, the risk free rate of interest, and the convenience yield. e The futures price will fall to $48.24 same calculation as above, with a spot price of $48: = $ f First, we recalculate the current spot price of the 5 year Treasury note. The spot price given $08.93 is based on semi annual interest payments of $4 each annual coupon rate is 8% and a flat term structure of 6% per year. Assuming that 6% is the compounded rate, the six month rate is: /2 = or 2.956%. 4

5 Thus, $08.93 = $4 + $ Incorporating similar assumptions with the new term structure specified in the problem, the new spot price of the 5 year Treasury note will be $8.6. Assuming that 4% is the compounded rate, the six month rate is: /2 = or.98%. Therefore, the new spot price of the 5 year Treasury note is: $8.6 = $4 + $ Thus, the futures price of the 5 year T note will be: = $ The dealer who shorted 00 notes at the previous futures price has lost money. g The importer could buy a three month option to exchange dollars for ruples, or the importer could buy a futures contract, agreeing to exchange dollars for ruples in three months time. 5