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The term structure of risk-free interest rate in flat in both Japan and the United States
The term structure of risk-free interest rate in flat in both Japan and the United States. The Japanese rate is 1.5% per annum and the U.S rate is 2.5% per annum (both with continuous compounding). A U.S firm has entered into a currency swap in which it receives 3% per annum in yen and pays a 4% annum in dollars once a year. The principals in the two currencies are $10 million and 1,200 million yen. The swap will last for another two years, and the current exchange rate is 108 yen = $1 (So=1/108)
a) value of the dollar bond (in millions of dollars ) is?
b) value of the Japanese bond (in million of Yen) is?
c) value of the swap (in millions of dollars ) is, therefore?
Expert Solution
Annual coupon of the dollar bond = Face value x interest rate = $ 10 million x 4% = 0.4 million
Discount factor for year t = e-rUS x t= e-2.5% x t
| Year, t | Cash flows type | Cash flows ($ milion) | PV factor = e-2.5% x t | PV of cash flows ($ million) = Cash flows x PV factor |
| 1 | Interest | 0.40 | 0.9753 | 0.39 |
| 2 | Interest + Principal | 10.40 | 0.9512 | 9.89 |
| Total value of the bond | 10.28 |
hence, value of the dollar bond (in millions of dollars ) is $ 10.28 million
Part (b)
Annual coupon of the Japanese bond = Face value x interest rate = $ 1,200 million x 3% = 36 million
Discount factor for year t = e-rJapan x t= e-1.5% x t
| Year, t | Cash flows type | Cash flows (Yen million) | PV factor = e-1.5% x t | PV of cash flows (Yen million) = Cash flows x PV factor |
| 1 | Interest | 36 | 0.9851 | 35.46 |
| 2 | Interest + Principal | 1,236 | 0.9704 | 1,199.47 |
| Total value of the bond | 1,234.93 |
Hence, the value of the Japanese bond (in million of Yen) is Yen 1,234.93 million
Part (c)
Spot rate, S0 = $ 1 per 108 yen
Hence, value of the swap (in millions of dollars ) is, therefore = Value of the Japanse bond x S0 - Value of the dollar bond = 1,234.93 x 1/108 - 10.28 = $ 1.15 million
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