Firm IBM is in a currency swap that was initiated several years ago. According to the swap, IBM receives 8% in sterling and pays 10% in dollar annually, plus the exchange of the principles at initiation and maturity. The principal amounts in the two currencies are 15 million dollars and 10 million pounds. Currently, there are two years remaining in the swap. The spot exchange rate is $1.5 per pound. The simple interest rates are 5% for US and 5% for UK per annum.

(a) What is the current value of the swap to IBM?

F(0,1)=S(0)*(1+R_d)/(1+R_f)= 1.5*1.05/1.05 = 1.5

F(0,2)=S(0)*(1+R_d)/(1+R_f)= 1.5*1.1/1.1 = 1.5

At t=0, value to IBM = 10m *S(0) - 15m = 0

At t=1, value to IBM = 0.08*10m *F(0,1)-0.1*15m = 1.2-1.5 = -0.3m

At t=2, value to IBM = (1.2+10)*F(0,2)-(1.5+15) = 16.8-16.5 = 0.3m

The t=0 value of the swap to IBM

= (10m *S(0) - 15m) + (1.2-1.5)/1.05 + (16.8-16.5)/1.1 = -0.013m

(b) If the value of the swap becomes zero to IBM after the coupon exchange one year later and the US and UK interest rates remain at 5%, what must the spot exchange rate be one year later?

(10m *S(0) - 15m) + (Cf*1.2- 1.5)/1.05 + ((1+Cf)*10-16.5)/1.1 = 0,

1.14Cf-1.429+(10+10Cf-16.5)/1.1 = 0,

1.14Cf-1.429-5.91+9.1Cf = 0,

10.24Cf = 7.339, Cf = 0.7167 = 71.67% 1.5*0.7167 = 1.075 -> 1.075 per pound

2. Firm IBM initiates a one-year swap in which IBM swaps a sterling loan with a dollar loan, paying coupon on the sterling and receiving coupon on the dollar loan at maturity. The principal amounts in the two currencies are $15 million and 10 million pounds. The current exchange rate is $1.5 per pound. The one-year simple interest rates are 2% for US and 4% for UK. The initial value of the swap is zero to IBM. If the coupon rate is 10% per year for the dollar loan, what is the coupon rate on the sterling loan?