Question

3. Suppose you has $1 million in debt with a floating (flexible) interest rate. You want to buy a 3-year interest rate swap to get a fixed interest rate and protect yourself from interest rate volatility. The notional value of the swap is equal to your debt - $1 million.

a. Suppose the fixed interest rate on the swap (based on the notional value) is 5% (a 2% risk-free rate and a 3% swap spread). What would be the annual fixed-rate payments you would pay on the swap (based on the notional value)?

b. Now suppose the market interest rate on your debt was 7% in the first year, 5% in the second year, and 4% in the third year. How much are the flexible interest rate payments that the seller of this swap would make in each year?

c. A swap involves exchanging one series of payments (or cash flows) for another. Given your answers to ‘a’ and ‘b’, what is the net benefit (or cost) to you of this swap in each year?

Answer 1

Part a

Annual fixed rate payments payable by us will be = 1000000×.05 = 50000$

Part b

Floating payments will be

First year = 1milion ×7% = 70000$

Second year = 1million ×5% = 50000$

Third year = 1million × 4% = 40000$

Part c

Net benifit = receiving leg - payment leg ( need less to say that negative value will be our cost )

Since our receiving leg is floating and payment leg is fixed

Therefore

Benifit

Year 1 70000-50000 =20000$

Year2 50000-50000= 0

Year3 40000-50000 =-10000$ i.e. cost to us in swap

Value of swap for us now will = present value of these benifits at market rates

Value = 20000/1.07 + 0/1.05^2 -10000/1.04^3 = 9801.63$

Since swap value is in our favour it is worth buying