Question

At time t, 3M borrows ¥12.8 billion at an interest rate of 1.2 percent, paid semi-annually, for a period of two years. (It therefore pays 1.2% divided by two semi-annually). It then enters into a two-year yen/dollar swap with Bankers Trust (BT) on a notional principal amount of $100 million (¥12.8 billion at the current spot rate). Every six months, 3M pays BT U.S. dollar LIBOR6 divided by two, while BT makes payments to 3M of 1.3 percent divided by two in yen. At maturity, BT and 3M reverse the notional principals.

a. Assume that LIBOR6 (annualized) and the ¥/$ exchange rate evolve as follows. Calculate the dollar amount that 3M pays to BT and receives from BT each six-month period. Calculate the net dollar amount that 3M pays to BT ("-") or receives from BT ("+") each six-month period.

Time(month)	LIBOR6	YEN/USD (spot(	Receipt	Payment	Net $ Receipt (+)/ payment(-)
t	5.7%	128
t+6	5.4%	132
t+12	5.3%	137
t+18	5.9%	131
t+24	5.8%	123

b. Taking into account the loan and the swap, what are the net payments that 3M will make each period?

c. Write down the equation that will need to be solved to determine the all-in costs of finance of 3M.

Answer 1

Answer (a.) The semiannual receipts, payments, and net receipts (payments) are as follows:

Time	Libor 6	Yen/USD Spot	Receipt	Payment	Net $ receipt (+)/payment (-)
t	5.7%	128
t+6	5.4%	132	(12,800,000,000 x 1.3% / 2 x 1/132) = $ 630,303	($100,000,000 x5.4% / 2) = $ 2,700,000	$ 2,069,697
t+12	5.3%	137	(12,800,000,000 x 1.3% / 2 x 1/137) = $ 607,299	($100,000,000 x5.3% / 2) = $ 2,650,000	$ 2,042,701
t+18	5.9%	131	(12,800,000,000 x 1.3% / 2 x 1/131) = $ 635,114	($100,000,000 x5.9% / 2) = $ 2,950,000	$ 2,314,886
t+24	5.8%	123	(12,800,000,000 x 1.3% / 2 x 1/123) = $ 676,422	($100,000,000 x5.8% / 2) = $ 2,900,000	$ 2,223,578

(b.) The net payments made semiannually by 3M are as follows:

Time	Libor 6	Yen/USD Spot	Receipt	Payment	Net $ receipt (+)/payment (-)
t	5.7%	128			-$100,000,000
t+6	5.4%	132	$ 48,485	($100,000,000 x5.4% / 2) = $ 2,700,000	$ 2,651,515
t+12	5.3%	137	$ 46,715	($100,000,000 x5.3% / 2) = $ 2,650,000	$ 2,603,285
t+18	5.9%	131	$ 48,855	($100,000,000 x5.9% / 2) = $ 2,950,000	$ 2,901,145
t+24	5.8%	123	$ 52,033	($100,000,000 x5.8% / 2) = $ 2,900,000	$102,847,967

NOTE: The net payment is computed as the LIBOR6 payment made to BT minus the dollar value of the 0.05% semiannual difference between the yen interest received and the yen interest paid (shown in the column labeled Receipt.

(c.) By using interest rate parity, we can compute the 6-month forward rate as (time t + 18 as ¥128.58/$)