Question

Company CCC3, a low-rated firm, desires a floating-rate, long-term loan. CCC3 presently has access to floating interest rate funds at a margin of 6.5% over LIBOR. Its direct borrowing cost is 14% in the fixed-rate bond market. In contrast, company AAA1, which prefers a fixed-rate loan, has access to fixed-rate funds in the Eurodollar bond market at 12% and floating-rate funds at LIBOR + 3.5%. A financial institution has brought these two firms together and facilitated the swap by taking the counterparty risk and requires a net total compensation package of 0.4% (this does not mean 0.4% from each, it means 0.4% total). (a) What is the size of the mispricing (if any)? (b) Design a swap acceptable to both companies and the financial institution. Split the benefits evenly between the two companies. Diagram the cash flows of the two companies and the financial institution. Clearly indicate the swap rates that the two companies and the institution are using. (c) What is the final borrowing rate for each company?

Answer 1

Given the rates at which Company CCC3 and AAA1 can borrow loan and their preference

Firm	Fixed Rate	Float Rate	Preference
CCC3	14%	L+6.5%	Float
AAA1	12%	L+3.5%	Fixed

Since CCC3 is low-rated firm it is at disadvantage in both the options as compared to AAA1, however by using the principle of Comapartive advantage, both the parties can reduce their borrowing cost by doing an interest rate swap.

We can find total savings in interest cost by comparing these 2 cases

Case 1 - CCC3 Fixed @ 14% and AAA1 Float @ L+3.5% = 14+L+3.5 = L+17.5%

Case 2 - CCC3 Float @ L+6.5% and AAA1 Fixed @ 12% = L+6.5+12 = L+18.5%

Therefore there can be a saving of 1% if interest rate swap is made.

This 1% is reffered to as mispricing as there's a difference in total interest cost in both the cases and such differences can be exploited by way of Interest rate swap. Size of mispricing is 1%.

Since Financial Institution requires a total compensation of 0.4% out of 1% remaining 0.6% can be equally divided between CCC3 and AAA1 at 0.3% each.

Therefore effective interest rate for each will be

CCC3 Existing Float rate (-) Savings i.e L+6.5 - 0.3 = L+6.2%

AAA1 Existing Fixed Rate (-) Savings i.e 12-0.3 = 11.7%

Swap arrangement would look like

Step 1

(i) CCC3 would borrow at Fixed rate of 14% and pay the interest.

(ii) AAA1 would borrow at Float rate of L+3.5% and pay the interest.

Step 2

Financial institution would reimburse CCC3 and AAA1 interest paid as per step 1 respectively

Step 3

CCC3 would pay Financial institution interest computed at L+6.2% i.e Effective interest computed above.

Similarly AAA1 would pay interested computed at 11.7% to the FInancial Institution.

Therefore in this way CCC3 and AAA1 would effectively pay interest at L+6.2% and 11.7% respectively and Financial Institution shall earn net 0.4% as follows

Reimbursement at Step 2: 14% + L+3.5% = L+17.5%

Received in Step 3:   L+6.2%+11.7% = L+17.9%

Net Income 0.4%