Question

Assume firm A wants to borrow float while firm B wants to borrow fixed. Firm A is offered 10% fixed borrowing cost and LIBOR + 0.3% float borrowing cost while firm B is offered 11.2% fixed borrowing cost and LIBOR + 1% float borrowing cost.

(a) Show how the two firms can reduce their borrowing costs equally by entering into an interest rate plain vanilla swap? Use a table to demonstrate your solution

(b) If the agreed-upon notional amount is $100m (no need to know the swap tenor), how much each party annually pays the other in absolute amounts? (assume that the LIBOR = 5%). Show your answer in a table similar to that in (a) solution You need to tabulate the cash flows associated with the loan based on the information above. (hint: assume the year has 360 days and each quarter has 90 days)

Answer 1

Part A - Show how the two firms can reduce their borrowing costs equally by entering into an interest rate plain vanilla swap? Use a table to demonstrate your solution.

Given the rates at which Firm A and B can borrow loan and their preference

Firm	Fixed Rate	Float Rate	Preference
A	10%	L+0.3%	Float
B	11.2%	L+1%	Fixed

It is evident from above Firm A enjoys higher credit rating and can borrow funds at a cheaper rate than Firm B in both the cases.

However by using the principle of Comapartive advantage, both the parties can reduce their borrowing cost by doing an interest rate swap.

First we need to find Total savings they can do through swap. Consider these 2 scenarios

Scenario	Firm A	Firm B	Total outflow of interest
1	Fixed 10%	Float L+1%	10+L+1 = L+11%
2	Float L+0.3%	Fixed 11.2%	L+0.3+11.2 = L+11.5%

As we can see difference between interest outflow between 2 scenarios is

(L+11) - (L+11.5) = 0.5%

Therefore we can split this savings of 0.5% between 2 equally i.e 0.25%

Therefore effective rate for Firm A for Float should be

Existing Float rate (-) Savings i.e (L+0.3%) - 0.25% = L+0.05%

Likewise for Firm B Fixed rate should be

Existing Fixed Rate (-) Savings i.e 11.2% - 0.25% = 10.95%

Swap arrangement would look like

(i) Firm A would borrow at Fixed rate of 10%.

(ii) Firm B would borrow at Float rate of L+1%.

(iii) Both parties would agree a rate for swapping their interest commitments

Lets assume Firm A would pay LIBOR (L) to Firm B

Firm A	Firm B
Borrows at	10%	Borrows at	L+1%
Receives from Firm B	(9.95%)	Receives from Firm A	(L)
Pays to Firm B	L	Pays to Firm A	9.95
Net interest cost	L+0.05%	Net interest Cost	10.95%
Savings	0.25%	Savings	0.25%

Part B

Agreed upon notional amount $100,000,000, LIBOR = 5% Calculated annually

Particulars	Firm A	Firm B
Rate	Amount in $	Rate	Amount in $
Borrows at	10%	10,000,000	L+1% = 6%	6,000,000
Receives from Other	9.95%	(9,950,000)	L = 5%	(5,000,000)
Pays to Other	L = 5%	5,000,000	9.95%	9,950,000
Net interest Cost		5,050,000		10,950,000

Therefore Firm A pays $ 5,000,000 to B

Firm B pays $ 9,950,000 to A