International Finance: Putting Theory Into Practice

7.2. THE FIXED-FOR-FIXED CURRENCY SWAPS 271

Table 7.2:Fixed-for-fixed Currency Swap: Marked-upUSDrate

loan swap Combined

jpy1000 borr’d jpy1000 lent, usd10m borr’d

at 1% at 1% at 3.438 823%

principal att jpy1000m <jpy1000m> usd10m usd10m

interest (p.a.) <jpy10m> jpy10m <usd343,882.30> <usd343,882.30>

principal atT <jpy1000m> jpy1000m <usd10m> <usd10m>

usd10m, with an annual interest payment consisting of theusdrisk-free rate (3
percent) plus a risk spread which is, very literally, the risk spread on ajpyloan
from the house bank: 1% – 0.6% = 0.4% onjpy1000m.^4

The above solution is still somewhat unelegant because the company pays part
of its annual interest payments injpy, an undesirable feature if it basically wants a
usdloan. There are two simple solutions:

• either replace the seven annualjpy4m payments by an equivalent upfront fee,
  which is of course theirpv:
  Equivalent upfront fee = 4m×a(0.6%, 7 years)
  = 4m× 6. 834 ,979 =jpy 27. 339 , 917 m, (7.3)


• or replace it by an equivalentusdannuity:

FindX∗such that St×

pvof annuityusdX∗

︷ ︸︸ ︷

X∗×a(3%, 7 years)

︸ ︷︷ ︸

... translated intojpy

= 4m×a(0.6%, 7 years)

︸ ︷︷ ︸

pvof annuityjpy4m

⇒X∗ =

4 m

St

a(0.6%, 7 years)

a(3%, 7 years)

(7.4)

=

4 m

100

6. 834 , 979

6. 230 , 282

=usd 43 , 882. 30 m

Technically, we ask the swap dealer to pay us 1% (our borrowing rate) on the

yens instead of 0.6% (the swap rate), and in return we increase the dollar in-

terest paid to the swap dealer by the equivalent amount. Table 7.2 summarizes

the modified solution.

The second solution immediately allows us to discover whether the swapped loan
is more attractive than a directusdloan (an alternative we have not yet looked

(^4) Note that, since these two amounts are in different currencies with a stochastic future exchange
rate, there is no way to amalgamate them into one number or one percentage. That is, 3 percent
inusdand 0.4 percent injpyis not 3.4 percent.