Today is t = 0 = March 1, 2001. Firm XYZ sold a piece of equipment to a highly rated corporation, and it is then due to receive payments in 10 equal installments of $3 million each over the next 5 years. The firm would like to use these $3 million semi-annual cash flows to hedge against the coupon payments the firm must make to service a $100 million floating rate bond that it issued in the past and expiring in 5 years. Suppose that the floating rate on the corporate bond is tied to the LIBOR and coupon rate is flat LIBOR. The current level of LIBOR is 5.6%. If the LIBOR were to increase substantially, the cash flows from the installments may not be sufficient to service the debt. Hence, the firm decides to enter into a swap contract with an investment bank, in which the firm pays the fixed semi-annual swap rate c, over a notional of $100 million, and the bank pays the 6-month LIBOR to the firm. The investment bank quotes a 5-year swap rate of 5.8%.

a) Assume the LIBOR turns out to be as follows over the life of the contract. Calculate all the cash flows and fill out the table.

Time	Libor	CF from Bank to Firm	CF from Firm to Bank	Net Cash Flow to Firm
(million $)	(million $)	(million $)
0.0	5.6%
0.5	5.8%
1.0	6.0%
1.5	6.2%
2.0	6.4%
2.5	6.6%
3.0	6.8%
3.5	7.0%
4.0	7.2%
4.5	7.4%
5.0	7.6%

b) Two years have passed. You would like to calculate the value of the swap to the firm at this point (right after the cash flows are exchanged at year two). What is the value of the floating rate leg at this point? What is the value of the fixed leg? What is the value of the swap? Assume you observe the following set of discount factors at that time:

Time (old)	Time (new)	Z (new)
0.0
0.5
1.0
1.5
2.0	0.0
2.5	0.5	0.95
3.0	1.0	0.93
3.5	1.5	0.91
4.0	2.0	0.89
4.5	2.5	0.87
5.0	3.0	0.85