Question

Kelvin just purchased £15.2 million goods from a British exporter on credit due 90 days from today.

The spot exchange rate is $1.21/£. The 90-day interest rates in the U.S. and the UK are 1 and 1.5 percent respectively.

The 90-day forward rate on the pound is $1.2090/£.

A 3-month call at strike price of $1.20/£ can be purchased at a premium of $0.016.

A 3-month put option at strike price of $1.20/£ can be purchased at a premium of $0.018 and can be sold at a premium of $.017. Assuming in 90 days the exchange rate will be either $1.20/£ or $1.25/£. Analyze the following scenarios:

a)What is the amount of payables in U.S. dollars assuming the firm hedges with a forward contract?

b)What is the amount of payables in U.S. dollars assuming the firm buys call options to hedge?

c)What is the payoff of a collar involving a long call and short put at the same strike price of $1.20/£

**Just part E - The previous portion is below for
context.**

**e)What is your recommendation as a treasurer of the firm
to the Board of the Directors of Kelvin as to the effectiveness of
any one of the approaches you take in hedging the firm’s exposure
to foreign exchange risk?**

Amount of transaction in question= 15.2 million pounds Days left for the payment to be made in pounds= 90

a) 90 day forward rate on the pound = $1.2090/pound Therefore, the amount of payables in US dollars assuming the firm hedges with a forward contract is 15.2 million pounds* 90 day forward rate= 15.2*1.2090=$18.3768 million

b) if the company buys call options at a premium of $ 0.016 with strike price of $ 1.20 per pound then the company has the right to decide whether it would like to excercise the call option or not on the maturity date. Actual currency price 90 days from now= current spot price *(1+ 90 day interest rate US)/ (1+ 90 day interest rate UK)= 1.21*(1+1%)/(1+1.5%)=$ 1.2040/pound Since post 90 day spot rate on the pound is $1.2040/ pound therefore, it is beneficial for the company to use call option at $ 1.20 per pound, thus the company would need to pay 15.2*1.20= 18.24 million US dollars (excluding option premium)

c) payoff of a collar involving long call and short put can be given by the formula Payoff of a collar= Max(0, actual currency price- strike price)- Max(0, strike price- actual currency price) - call premium (since you have bought the call) + Put premium (since you have written the put) = Max(0,$1.2040/pound- $ 1.20/pound)- Max (0, $1.20/pound-$1.2040/pound)- $0.016+$0.017 Now , understand that buyer's currency is dollars, so he will excercise call option only when he has to pay lesser dollars on euros by exercising call options Since, post 90 days spot rate would be $1.2040/pound , therefore he would be better off by exercising the option Similarly put option will not be excercised since spot prices have gone up instead of decreasing = $0.040/pound- 0-0.016+0.017= 0.04/pound+0.001/option Now for total transaction value of 15.2 million pounds , the payoff would be 0.04*15.2 million + 0.001* no of options...(1) No of options one would buy to cover his position of 15.2 million pounds when strike price is 1.20 dollars per pound and contract size of 1000 dollars= 15.2*`1.20 million dollars/ 1000 dollars = 18240....(2) From (1) & (2), we have Payoff from collar = 0.608 million dollars+0.001*18240 dollars= 0.608 million dollars+0.00001824 million dollars=0.60801824 million dollars or we can say net payables = total payables without collar- payoff from collar=15.2*1.2040 million dollars-0.60801824 million dollars= 17.69 million dollars

Answer #1

Hi,

Incase Mr Kelvin decides to pay today at spot rate -the total payable i.e outflow would be 15.2*1.21= $18.392 million

Choosing the best hedging option (As per the calculations ) :

1)if forward contract is taken up -total outflow is $18.3768 million

2) if call option is opted for -total outflow is $18.24+premium on options

3)if a collar is opted for-total outflow is $17.69 million

Since,the outflow in case of a collar option is the least amongst the 3 hedging strategies,Kelvin should opt for the same

The effectivness of opting a collar would result in a gain of :

future spot rate (as calculated above)=$1.204/pound*15.2=$18.3008 million

collar strategy-$17.69 million

**Effective
Gain=18.3008-17.69=$0.6108million**

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