5. Your company is purchasing a large amount of machinery from the UK, in the am

Question

5. Your company is purchasing a large amount of machinery from the UK, in the amount of GBP400mn, due in one year’s time. After looking at market pricing and analysing the backdrop for the UK pound, you come up with the following numbers:

Spot exchange rate:                                                                                                                                                                                                                                          1.200 USD per GBP

Expected exchange rate in one year’s time:                          1.250 USD per GBP

One year forward rate:                                                                                                                                                                                                      1.225 USD per GBP

a.            Graph the cost of:

(i) the unhedged purchase in USD terms as a function of the future exchange rate in one year’s time.

(ii) the fully hedged purchase; and

(iii) the purchase with a 40% hedge ratio.

b.           You call your broker for options prices, and find the prices below for an option maturing in one year’s time.

(i) Which option would you use to lock in the USD value of the purchase?

(ii) Graph the cost of the purchase (plus the option hedge) as a function of the future exchange rate in one year’s time.

At-the-money GBP put option:                                                                3% of the USD notional amount

At-the-money GBP call option call:                           4% of the USD notional amount

Explanation / Answer

a.

i. One year future expected cost of machinery in USD terms:

1 GBP = 1.250 USD

400 mn GBP = 400*1.25 mn USD = 500 mn USD

ii. For hedging the position, the buyer will book the purchases at the 1 year forward contract rate. By doing so, the buyer is protected from currency movements and will have to pay at the fixed rate irrespective of the actual exhange rate. Suppose, if actual exchange rate at the end of one year is greater than forward rate, then buyer will benefit from the contract. and vice versa.

Cost of Machinery = 400 mn USD

Forward rate : 1 GBP = 1.225 USD = 490 mn USD (hence considering the future expected rate of 500 mn, the buyer will save 10 mn US$)

iii. At 40% hedge, only 40% of the purchase value will be hedged. Balance will have to be paid at the actual rate after one year which is currently expected to be 1.25 USD.

Cost of machinery = (400*40%*1.225) + (400*60%*1.250) USD

= 196+300 = 496 US$

b. Lets convert the rates in terms of GBP

Spot rate: 1 USD = 1/1.2 GBP = 0.83 GBP

Similarly,

Expected one year later rate = 0.80 GBP

Whereas, the foreward rate at which we can hedge is 0.81 GBP. Therefore there is additional risk of GBP falling which can be benefitted using a put option.

As per the expected future rates, there is a risk of GBP falling further. Hence we need to take a put option at the current spot price. Premium = 3% of 1.2 USD = 0.036

Total Cost at one year future rate = 400*1.25 $ = 500 mn USD

Profit / (loss) from put option = 0.83 - 0.80 - 0.036 = (0.0027) = (1.07) mn GBP

= 1.25*1.07 USD mn = 1.33 USD mn

Total cost = 501.33 USD mn

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