206 Mathematics for Finance
disappointing:sales 5 , 000 , 000
cost of sales − 3 , 000 , 000
earnings before interest and tax 2 , 000 , 000
interest − 53 , 522
earnings before tax 1 , 946 , 478
tax − 389 , 296
net income 1 , 557 , 182
loan repaid − 334 , 510
dividend − 1 , 250 , 000
result − 27 , 328The optimal (in the sense of minimising the loss) strike price is 1. 5734
dollars to a pound, resulting in a loss of£ 24 ,283. If the exchange rate
drops to 1.5 dollars to a pound, the options will not be exercised and the
sum obtained from sales will reach£ 5 , 333 ,333, with a positive final result
of£ 239 ,339. This strategy leads to a better result than the hedge involving
a forward contract only if the rate of exchange drops below 1.42 dollars to
a pound.4.Partial Hedge with Options.To reduce the cost of options the company
can hedge partially by buying call options to cover only a fraction of the
dollar amount from sales. Suppose that the company buys 2, 500 ,000 units
of the same call option as above, paying a half of the previous premium. A
half of the revenue is then exposed to risk. To find VaR at 95% confidence
level we assume that this sum is exchanged at 1.9887 dollars to a pound, as
in the case of an unhedged position, the other half being exchanged at the
exercise price:sales 4 , 511 , 364
cost of sales − 3 , 000 , 000
earnings before interest and tax 1 , 511 , 364
interest − 26 , 761
earnings before tax 1 , 484 , 603
tax − 296 , 921
net income 1 , 187 , 682
loan repaid − 167 , 255
dividend − 1 , 250 , 000
result − 229 , 573If the exchange rate drops to 1.5 dollars to a pound, the company will have
a surplus of£ 428 ,003.