Question

You are given the following prices for a zero coupon bond that matures for 1 on the maturity date: Maturity DatePrice 1 year0.965 2 years0.920 3 years0.875 4 years0.825 5 years0.770 Josh and Phillip enter into a four year swap with a notional amount of 200,000. The swap has annual settlement periods. Under the swap, Josh will pay Phillip the fixed swap rate at the end of each year while Phillip will pay Josh the variable rate where the variable rate is the one year spot rate at the beginning of each year. Determine the net swap payment at the end of the first year.

Answer 1

The net swap payment at the end of the first year is $2,509.

A fixed swap rate is an agreed-upon interest rate in a swap contract that remains constant throughout the life of the agreement, used to exchange fixed and floating interest payments between parties.

Fixed swap rate = 1 - PVn / ΣPV

Fixed swap rate at year 1:

= 1 - 0.825 / 0.965 + 0.95 + 0.875 + 0.825

= 0.0488

The Variable rate equals One year spot rate at the beginning of the year which is:

= (1/0.965) - 1

= 0.03626943

Josh to pay to Philip this amout:

= 200000* 0.0488

= 97623

Phillip will pay this amount to josh

= 200000*0.03626943

= 7254.

The net pay that Josh will pay is

= $97623 - $7254

= $2,509

Answer 2

The net swap payment at the end of the first year is:

= $7,000.

Step-by-step explanation:

a) Data and Calculations:

Zero coupon bond that matures for 1 on the maturity date

Maturity Date Price

1 year 0.965

2 years 0.920

3 years 0.875

4 years 0.825

5 years 0.770

Net swap payment at the end of the first year = fixed swap rate - variable swap rate * notional principal amount

= (1 - 0.965) * $200,000

= $7,000

b) Swaps are used by entities to hedge against their exposure to interest rate fluctuations. A swap reduces the uncertain future cash flows by allowing entities to take advantage of future market realities by revising their own debt obligations with a counterparty. In our example, Phillip agrees to pay Josh a variable swap rate while Josh pays Phillip a fixed swap rate. At the end of each period, the swap rates are netted off before applying the notional principal amount to arrive at the net swap payment.