Question

Firm A and Firm B enter into a five-year currency swap. Firm A sends B $10,000,000, and in return receives ¥1,200,000,000 from Firm B. Firm A must pay 3% on the yen (to Firm B) while Firm B must pay Firm A 4% on the dollars.

One year later the new swap rates are 2.5% USD and 1.5% JPY. The spot rate is ¥110/$. Ignore bid/ask spreads. What is the value of this swap to Firm A and to Firm B?

Answer 1

Firm A:

Pays $ 10000000 principal to Firm B, receives ¥ 1200000000 principal from Firm B, pays ¥ interest to firm B (for receiving Yens) and receives $ interest from Firm B (for paying $). Principal exchange happens at swap initiation and they are re-exchange at swap termination. This implies that at swap culmination Firm B receives $ principal and pays back the ¥ principal. Further, during the swap tenure Firm A receives $ interest from Firm B (for letting Firm B use the $ 10000000 principal) and pays ¥ interest to Firm B (for borrowing the ¥1200000000 principal from Firm B). The swap value to Firm A at the end of Year 1 should be equal to the difference between the PV of the remaining cash outflows and inflows from Firm A's perspective.

Discount Rate for $ Inflows = 2.5 % and Discount Rate for ¥ Outflows = 1.5 %, Spot Rate = ¥ 110 / $

Annual $ Interest = 0.04 x 10000000 = $ 400000

Annual ¥ Interest = 0.03 x 1200000000 = ¥ 36000000

PV of Cash Inflows = 400000 x (1/0.025) x [1-{1/(1.025)^(4)}] + 10000000 / (1.025)^(4) = $ 10564296.13

PV of Cash Outflows = 36000000 x (1/0.015) x [1-{1/(1.015)^(4)}] + 1200000000 / (1.015)^(4) = ¥ 1269378923.66

Swap Value for Firm A = PV of Cash Inflows - PV of Cash Outflows / Current Spot Rate = 10564296.13 - (1269378923.66/110) = - $ 975512.2669 ~ - $ 975512.27

Firm B: Firm B's cashflows, interest payments and principal repayments will exactly be the opposite of what it is for Firm A, as Firm B is counterparty to Firm A for this swap.

Hence, Swap Value for Firm A (in ¥) = 1269378923.66 - (10564296.13 x 110) = ¥ 107306349.36