Valuing the Swap

PV of Each Leg

A swap value is the difference between the two leg values.

highlighted = computed this step

Present value of the fixed leg

The fixed leg at 5% has present value notional times fixed rate times the sum of discount factors. The sum of discount factors is 27/10, so the fixed-leg present value is $13.50.

PVfixed=N⋅K∑t=1ndt\text{PV}_{\text{fixed}}=N\cdot K\sum_{t=1}^n d_t

Present value of the floating leg

The floating leg has present value notional times one minus the last discount factor. Since the last discount factor is 21/25, the floating-leg present value is $16.00.

PVfloat=N(1−dn)=$16.00\text{PV}_{\text{float}}=N(1-d_n)=\$16.00
Swap leg PVsFixed and floating leg values are recomputed from discount factors.PV of each legLegFormulaPVFixed legN × K × Σd$13.50Floating legN × (1 - d_n)$16.00Value to fixed payerFloating PV - fixed PV$+2.50

Value to the fixed payer

Value to the fixed-rate payer is floating-leg present value minus fixed-leg present value. At the fixed rate 5%, the value is $2.50.

Vpayer=PVfloat−PVfixed=$2.50V_{\text{payer}}=\text{PV}_{\text{float}}-\text{PV}_{\text{fixed}}=\$2.50