Finance case questions

Question 6 (Futures):
Packers Inc. is a U.S. based manufacturer of cheese. The company considers expan¬ding its current operations by building a plant in the U.K. The CFO has presented the board with the following cash flow projections:
Required initial outlay in U.S. dollars to be paid immediately is $600,000. The projected cash flows in British pounds due in exactly six months are GBP 500,000.
The CFO informs the board that the U.S. risk-free rate is 5.5% (APR) while the U.K risk free rate is 7.2% (APR). The current spot exchange rate is 1.62 $/GBP (that is, 1.62 dollars buy 1 British pound). The futures price of the pound, for delivery in six months, is 1.61 $/GBP. The CFO assumes that the project is riskless and that given her calculations the firm ought to invest in the new plant.
Assume that interest is compounded semi-annually. Ignore the fact that futures are marked to market and assume that all cash flows connected with the futures contract occur at the maturity of the contract.
a) Should the company undertake this project given the above assumptions?
Answer: Yes
Your reasoning:
Cost of project = $600,000

Revenue from project = £500,000*1.61 = $805,000

Present value of Revenue = $783,455

Profit from project = $783,455 - $600,000 = $183,455

Recommendation = Yes

b) Assume that the CFO can use foreign currency futures contracts on the British Pound. Specifically, she can buy or sell 62,500 pounds per contract for delivery in six months from today. Should she purchase or sell such contracts if she wants to receive U.S. dollars in exactly six months? Specify in your answer the number of contracts.
Answer: _8 contracts
Your reasoning:
The CFO should sell GBP futures contract to receive USD in six months time.

£500,000 worth of contracts at £62,500 each each contract = $ 100,625

500,000 / 62500 = 8 contracts total = $805,000

c) Demonstrate that the hedge in b) works by showing that a fall of the pound to $1.55 or an increase in the pound to $1.65 do not affect the total dollar value of the cash inflow of GBP 500,000.
Your reasoning:
Cost of £ on delivery date = 1.55 $/£ 62,500*8*1.55 = $ 775,000
Cumulative futures gain per £ = 0.6 $/£ 62,500*8*0.06 = $ 30,000
Net cost of £ 1.61 $/£ $ 805,000

Cost of £ on delivery date = 1.65 $/£ 62,500*8*1.65 = $ 825,000
Cumulative futures loss per £ = 0.4 $/£ 62,500*8*0.04 $ (20,000)
Net cost of £ 1.61 $/£ $ 805,000

d)  If six-month futures contracts are not available, can the CFO assure the board that she will be able to lock in the rate for exchanging the 500,000 pounds into dollars six months from today? If so, outline what are the transactions that she needs to undertake in order to guarantee this rate.
Your reasoning:

Question2 (Options):
In February you observe that XYZ's stock price is $103. The March call option with exercise price $100 will expire in exactly one month and is trading at $5. The March put option with exercise price of $100 is trading at $1.50. Assume that the interest rate is 6% p.a. (continuously compounded) and that XYZ will not pay dividends over the next month.
a) Calculate the payoffs for an investor who has bought one call option by completing the table below. Draw the payoff diagram. Do not include the initial option premium in your payoffs.
Stock Price 80 100 120 140
Payoff 0 0 20 80
Your reasoning:
Strike Price $100

Stock Price 80 100 120 140
Payoff 0 0 20 40

The investor will only excersise the call option above the strike price

Payoff

0 $100 Stock Price ST

b) Calculate the payoffs for an investor who has bought one XYZ share and one put option by completing the table below. Draw the payoff diagram. Do not include the initial option premium in your payoffs.
Stock Price 80 100 120 140
Payoff -3 -3 17 37
Your reasoning:
The investor will buy one XYZ share at $103 and one put option

At stock price $80 the investor will Sell the share = $80 - $103 = $-23
Excercises the put option = $100 - $80 = $20

At stock price $100 the investor will Sell the share = $100 - $103 = $-3
Not excercise the put option

At stock price $120 the investor will Sell the share = $120 - $103 = $17
Not excercise the put option

At stock price $140 the investor will Sell the share = $140 - $103 = $37
Not excercise the put option

Stock Price 80 100 120 140
Payoff -3 -3 17 37

Payoff

$100

$100 Stock Price ST

c)  A friend of yours wants to purchase a futures contract on XYZ. Unfortunately, no such contract is available and he asks for your help. You can only buy (or sell) the above call and put options as well as buy (or sell) bonds. Can you replicate the cash flows of the futures contract with these options and bond? How much would your friend have to pay today in order to set up this replication? What is the implied futures price?
Your reasoning:

Question 1 (Futures):
Packers Inc. is a U.S. based manufacturer of cheese. The company considers expan¬ding its current operations by building a plant in the U.K. The CFO has presented the board with the following cash flow projections:
Required initial outlay in U.S. dollars to be paid immediately is $600,000. The projected cash flows in British pounds due in exactly six months are GBP 500,000.
The CFO informs the board that the U.S. risk-free rate is 5.5% (APR) while the U.K risk free rate is 7.2% (APR). The current spot exchange rate is 1.62 $/GBP (that is, 1.62 dollars buy 1 British pound). The futures price of the pound, for delivery in six months, is 1.61 $/GBP. The CFO assumes that the project is riskless and that given her calculations the firm ought to invest in the new plant.
Assume that interest is compounded semi-annually. Ignore the fact that futures are marked to market and assume that all cash flows connected with the futures contract occur at the maturity of the contract.
a) Should the company undertake this project given the above assumptions?
Answer: Yes/No (delete one)
Your reasoning:

b) Assume that the CFO can use foreign currency futures contracts on the British Pound. Specifically, she can buy or sell 62,500 pounds per contract for delivery in six months from today. Should she purchase or sell such contracts if she wants to receive U.S. dollars in exactly six months? Specify in your answer the number of contracts.
Answer: _______
Your reasoning:

c) Demonstrate that the hedge in b) works by showing that a fall of the pound to $1.55 or an increase in the pound to $1.65 do not affect the total dollar value of the cash inflow of GBP 500,000.
Your reasoning:

d)  If six-month futures contracts are not available, can the CFO assure the board that she will be able to lock in the rate for exchanging the 500,000 pounds into dollars six months from today? If so, outline what are the transactions that she needs to undertake in order to guarantee this rate.
Your reasoning:

Question 2 (Options):
In February you observe that XYZ's stock price is $103. The March call option with exercise price $100 will expire in exactly one month and is trading at $5. The March put option with exercise price of $100 is trading at $1.50. Assume that the interest rate is 6% p.a. (continuously compounded) and that XYZ will not pay dividends over the next month.
a) Calculate the payoffs for an investor who has bought one call option by completing the table below. Draw the payoff diagram. Do not include the initial option premium in your payoffs.
Stock Price 80 100 120 140
Payoff
Your reasoning:

b) Calculate the payoffs for an investor who has bought one XYZ share and one put option by completing the table below. Draw the payoff diagram. Do not include the initial option premium in your payoffs.
Stock Price 80 100 120 140
Payoff
Your reasoning:

c)  A friend of yours wants to purchase a futures contract on XYZ. Unfortunately, no such contract is available and he asks for your help. You can only buy (or sell) the above call and put options as well as buy (or sell) bonds. Can you replicate the cash flows of the futures contract with these options and bond? How much would your friend have to pay today in order to set up this replication? What is the implied futures price?
Your reasoning: