In a fixed-for-fixed currency swap, 4% on a US dollar principal of $160 million is received and 5% on a British pound principal of 100 million pounds is paid

For determining swap value, we need to calculate future cash flows. Here we are receiving USD and paying GBP. In 2.5 years time we need to pay back USD 160 Million and we will receive GBP 100 million.

A. Future cash flow for USD payment:

Loan amount = $160 million

Interest rate = 4% p.a.

Discount rate = 6%

Cumulative PV factor for 2.5 years = [1/(1+0.06)^1]+[1/(1+0.06)^2]+[(1/(1+0.06)^2)/(1+0.03)]

= 2.697

Interest amount per annum = $160 million*4% = $4 million

Present value of interest amount = Interest for 2.5 years*Cumulative PV factor

= $4 million*2.697 = $10.79 million

Present value of maturity payment = Bond amount*PV factor at 2.5 year = $160 million*[(1/(1+0.06)^2)/(1+0.03)]= $160 million*0.8641 = $138.25 million

Present value of USD Payment = PV of Interest + PV of USD Principal = $10.79 million+$138.25 million = $149.04 million

GBP value = $149.04/1.55 = £96.15 million

B. Future cash flow of GBP receipts =

Loan given = £100 Million

Interest rate = 5%

Interest received p.a. = Bond amount*interest rate

= £100*5% = £5 million

PV of Interest = £5 million*2.697 = £13.485 million

PV of Principal amount at 2.6 year = £100*0.8641 = £86.41 million

PV of GBP receipts = £13.485 million + £86.41 million = £99.86 million

Value of swap = GBP receipts - GBP equivalent of USD payment = £99.86 million - £96.15 million = £3.71 million

Conclusion: After 2.5 years when bond matures, company will gain £3.71 million on fixed to fixed swap