3. Biogen expects to receive royalty payments totaling £1.25 million next month. It is interested in protecting these receipts against a drop in the value of the pound. It can sell 30-day pound futures at a price of $1.6513 per pound or it can buy pound put options with a strike price of $1.6612 at a premium of 2.0 cents per pound. The spot price of the pound is currently $1.6560, and the pound is expected to trade in the range of $1.6250 to $1.7010. Biogen’s treasurer believes that the most likely price of the pound in 30 days will be $1.6400. a. How many futures contracts will Biogen need to protect its receipts? How many options contracts? b. Diagram Biogen’s profit and loss associated with the put option position and the futures position within its range of expected exchange rates (see Exhibit 8.6). Ignore transaction costs and margins. c. Calculate what Biogen would gain or lose on the option and futures positions within the range of expected future exchange rates and if the pound settled at its most likely value. d. What is Biogen’s break-even future spot price on the option contract? On the futures contract? e. Calculate and diagram the corresponding profit and loss and break-even positions on the futures and options contracts for those who took the other side of these contracts.
(a.)
. How many futures contracts will Biogen need to protect its receipts? How many options contracts
Answer
Biogen will 20 futures contracts to protect its anticipated royalty receipts of £1.25 million and with a futures contract size of £62,500.
The option contract size is half that of the futures contract, or £31,250, Biogen will need 40 put options to hedge its receipts.
(b)
b. Diagram Biogen’s profit and loss associated with the put option position and the futures position within its range of expected exchange rates (see Exhibit 8.6). Ignore transaction costs and margins.
Answer:
At present i could not upload the diagram because system does not support but i write down th calculation
| 1.625 | 1.64 | 1.6513 | 1.6612 | 1.701 | |
| OPTION | |||||
| Inflow | 2076500 | 2076500 | 2076500 | ||
| Outflow | |||||
| Put premium | -25000 | -25000 | -25000 | -25000 | -25000 |
| Exercise cost | -2031250 | -2050000 | -2064125 | ||
| 20250 | 1500 | -12625 | -25000 | -25000 | |
| Future | |||||
| Inflow | 2064125 | 2064125 | 2064125 | 2064125 | 2064125 |
| Outflow | -2031250 | -2050000 | -2064125 | 2071625 | -2126250 |
| Profit | 32875 | 14125 | 0 | 7500 | -62125 |
(c.)
Calculate what Biogen would gain or lose on the option and futures positions within the range of expected future exchange rates and if the pound settled at its most likely value.
Answer
. If Biogen buys the put options, it must pay a put premium
Put premium is calculated as follow
=f 0.02 x 1,250,000
= $25,000.
If the pound settles at its maximum value, Biogen will not exercise and it loses the put premium. But if the pound settles at its minimum of $1.6250, Biogen will exercise at $1.6612 and earn $0.0362/£or a total of
= 0.0362 x 1,250,000
= $45,250.
Now we will calculate net gain of Biogen
net gain will be
=$45,250 – $25,000
= $20,250.
For the futures position, Biogen will lock in a price of $1.6513/£ for total revenue of 2,064,125 calculated as follow
= $1.6513 x 1,250,000
= $2,064,125.
If the pound settles at its minimum value, Biogen will have a gain per pound on the futures contracts of$0.0263/£
Calculation as follow
Gain per pond
=$1.6513 – $1.6250
= $0.0263/£ (remember it is selling pounds at a price of $1.6513 when the spot price is only $1.6250) for a total gain of 0.0263 x 1,250,000 = $32,875. On the other hand, if the pound appreciates to $1.70100, Biogen lose $1.7010 – $1.6513 = $0.0497/£ for a total loss on the futures contract of 0.0497 x 1,250,000 = $62,125.
If the pound settles at its most likely price of $1.6400, Biogen will exercise its put option and earn $1.6612 – $1.6400 = $0.0212/£, or $26,500. Subtracting off the put premium of $25,000 yields a net gain of $1,500. If Biogen hedges with futures contracts, it will sell pounds at $1.6513 when the spot rate is $1.6400. This will yield Biogen a gain of $0.0113/£ for a total gain on the futures contract equal to 0.0113 x 1,250,000 = $14,125.
(d.)
What is Biogen’s break-even future spot price on the option contract? On the futures contract
Answer
On the option contract, the spot rate will have to sink to the exercise price less the put premium forBiogen to break even on the contract, or $1.6612 – $0.02 = $1.6412. In the case of the futures contract, breakeven occurs when the spot rate equals the futures rate, or $1.6513.
(e.)
Calculate and diagram the corresponding profit and loss and break-even positions on the futures and options contracts for those who took the other side of these contracts.
Answer :
The sellers’ profit and loss and break-even positions on the futures and optionscontracts will be the mirror image of Biogen’s position on these contracts.
example,
the sellers of the future sand options contracts will break even at future spot prices of $1.6513/£ and $1.6412/£, respectively. Similarly, ifthe pound falls to its minimum value, the options sellers will lose $20,250 and the futures sellers will lose $32,875. But if the pound hits its maximum value of $1.7010, the options sellers will earn $25,000 and the futures sellerswill earn $62,125.
