Question

JPMorgan Chase and Facebook agree on an interest rate swap on September 25, 2018 on a notional principal of $500 million. JPMorgan Chase will make annual floating payments according to the 1-year LIBOR plus 50 basis points. Facebook in return will make fixed-rate payments on annual basis. The first cash flow exchange will occur on September 25, 2019. The contract will last for a period of 5 years, e.g., there will be a total of 5 payments for each company. On September 25, 2018, the following LIBOR zero rates and continuously compounded risk-free interest rates are as follows: Maturity LIBOR Zero Rate (%) Forward LIBOR (%) Risk-free Rate (%) 1 year 3.00 ? 2.25 2 years 3.25 ? 2.50 3 years 3.75 ? 2.75 4 years 4.00 ? 3.00 5 years 4.25 ? 3.50 a) If there is no cash settlement at the initiation of the contract, what should be the fair fixed rate that Facebook should pay? b) If Facebook prefers a fixed rate of 5% annually, what cash settlement is needed between the parties on September 25, 2018 in order to have a fair contract? c) On September 25, 2020, the LIBOR zero rates and risk-free interest rates become: Maturity LIBOR Zero Rate (%) Forward LIBOR (%) Risk-free Rate (%) 1 year 3.50 ? 2.75 2 years 3.75 ? 3.00 3 years 4.00 ? 3.25 Compute the value of the swap to Facebook (assuming it pays a 5% fixed rate).

Answer 1

	Million$
Principal Amount	500
Interest rate swap	25-Sep-18
	JP Morgan Chase	Facebook
Interest payment	Floating	Fixed
	LIBOR+0.50

a)	Year	LIBOR	Risk free rate	Floating rate(LIBOR+0.5)	Floating interest
	Y1	3	2.25	3.50	17.50
	Y2	3.25	2.5	3.75	18.75
	Y3	3.75	2.75	4.25	21.25
	Y4	4	3	4.50	22.50
	Y5	4.25	3.5	4.75	23.75
				Total interest payment by JP Morgan Chase	103.75
				Fair Fixed interest payment for Facebook	103.75
				Fair Fixed interest rate for Facebook	4.15

b)	Year	LIBOR	Risk free rate	Floating rate(LIBOR+0.5)	Floating interest	Fixed interest @5%	Difference	Present value of difference	Here, Risk free rate is considered discounting rate
	Y1	3	2.25	3.50	17.50	25	7.50	7.33
	Y2	3.25	2.5	3.75	18.75	25	6.25	6.10
	Y3	3.75	2.75	4.25	21.25	25	3.75	3.65
	Y4	4	3	4.50	22.50	25	2.50	2.43
	Y5	4.25	3.5	4.75	23.75	25	1.25	1.21
							Cash settlement at initiation for fair contract	20.72

c)	Year	LIBOR	Risk free rate	Floating rate(LIBOR+0.5)	Floating interest	Fixed interest @5%	Value of swap(JP Morgan)	Value of swap(facebook)
	Y1	3	2.25	3.50	17.50	25	17.11	24.45
	Y2	3.25	2.5	3.75	18.75	25	18.29	24.39
Rate changed from Y3	Y3	3.5	2.75	4.00	20.00	25	19.46	24.33
Y4	3.75	3	4.25	21.25	25	20.63	24.27
Y5	4	3.25	4.50	22.50	25	21.79	24.21
							97.30	121.66