Question

a) ABC Ltd is interested to sell an existing fixed-for-floating interest rate swap to one of its corporate clients. Under the existing swap, ABC Ltd pays 10% pa and receive 3-month LIBOR on a $10 million principal. Cash flows are exchanged every quarter. The swap has a remaining life of 16 months. Data shows that the 3-month LIBOR rate 1 month ago was 11.8% pa; 2 months’ ago it was 12% pa; 3 months’ ago it was 12.2% pa and 4 months’ ago it was 12.3% pa. The relevant discount rate is 12% per annum for all maturities. All rates are compounded quarterly. What is the value of the swap?

b) Will ABC Ltd be receiving or paying the value of the swap in (a)? Elaborate.

Answer 1

The ABC Ltd is paying at 10%pa on $10 million principal.

i.e. $10 m*10%= $1 m per year and $ 8,333 per month

and have received

Interest calculation on LIBOR

4 months ago	12.3%	10,250
3 months ago	12.2%	10,167
2 months ago	12.0%	10,000
1 month ago	11.8%	9,833
Total amount		40,250

for the Last 4 months

It pays $33,333 and received $ 40,250

a) Total benefit at present from past cash flow = $6,916.67

b) ABC Ltd will be receiving the value of swap in (a) because it is paying at 10% pa and received more on LIBOR

Suppose it receives 11.5% pa on LIBOR for rest of 16 months(as no rates are mention so assume at 11.5% from the past trend)

the PV of cash flow will be as follows

month	interest amt	PV of CF
1	9583	9488
2	9583	9394
3	9583	9301
4	9583	9209
5	9583	9118
6	9583	9027
7	9583	8938
8	9583	8849
9	9583	8762
10	9583	8675
11	9583	8589
12	9583	8504
13	9583	8420
14	9583	8336
15	9583	8254
16	9583	8172
		1,41,036

and will pay in future at compounded rate of 10% pa for 16 months

i.e. total = 1000000(1+0.0083)¹⁶ =   1141395

Interest paid = 141395

PV of interest Paid = 120585

Net amount received in SWAP = 141036-120585 = $20,451

P