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# All in Cost of Fixed Rate Issuance

The All-in-Cost of Fixed Issuance

The borrower

Borrowers (issuers) often use the bond market to access medium and longer dated funding. Some issuers prefer variable rate liabilities, some fixed rate liabilities. All issuers want to be able to borrow the required amount at the lowest possible cost but just how does a fixed coupon bond issuer calculate the cost of funds on a floating rate basis? Let’s see. For simplicity we will assume the bond that is issued by the borrower is as follows:

Principal:         \$100,000,000

Coupon:           5.00% annual

Maturity:          5 years

Issue price:     100% (par value)

This means the issuer obtains \$100m and investors receive a total of \$5,000,000 per annum in interest from the issuer. They are happy that they know their regular interest income but this may not suit the issuer. The issuer may prefer to have the liability on a floating rate basis. For some borrowers like banks this is consistent with their balance sheet structure. They prefer to have assets and liabilities on a variable rate basis in order to minimise interest rate risk. This is where an interest rate swap is used.

The swap

The swap allows the issuer to exchange a fixed interest rate for Libor. In order to keep the following examples simple we will assume the interest basis for bond and swap markets is identical as are the fixed and floating payments on a swap. In real life this is not the case and adjustments to the calculations are required.

Suppose the 5 year swap rate is 3.70%. This means the issuer can receive 3.70% and pay Libor on a swap. This is what the bond and swap cash flows would look like for the issuer:

Can you see the problem? The interest received from the swap is not enough to meet the coupon payments on the bond. This is because the bond coupon is higher than the swap rate. So what can the issuer do?

The issuer can ask the swap counterparty to pay a higher fixed rate. The swap counterparty will only do this if the Libor rate on the floating side of the swap is adjusted in order to sufficiently offset the higher fixed rate. In this case the adjustment is 130 basis points (5.00%-3.70%).

The all-in-cost for this issuer is Libor plus 130 basis points. You should now be able to see that there is a very close relationship between the all-in-cost and the borrowing and swap rates. The higher the borrowing rate is relative to the swap rate the greater the all-in-cost for the issuer.

What if the bond is not issued at par?

Often bonds are issued at a small discount to par. Here is such an example:

Principal:          \$100,000,000

Coupon:            5.00% annual

Maturity:           5 years

Issue price:      99.50%

Proceeds:         \$99,500,000

Swap rate:        3.70% annual

If the issuer enters a swap receiving the fixed rate at 5.00% the offsetting Libor payment will, as before, have a margin of 130 basis points. But on this occasion the issuer receives \$99.5m but repays \$100m at maturity.

Clearly the fixed cost of borrowing is higher than 5.00% because the bond is issued at a discount to par value. The 0.5m difference needs to be factored into the funding cost. This will also impact on the swapped cost. There are several ways of doing this and what follows is the simplest.

The issuer asks the swap counterparty to make a front end payment on the swap of \$0.5m (this is like a loan). The issuer now has \$99.5m + \$0.5m = \$100m.

But to do this the swap counterparty must receive from the issuer a sum of money that has a present value of at least \$0.5m. How can this be factored into the Libor payment? It’s easy, the margin is increased.

To keep this simple one basis point on the floating side of the swap is worth \$10,000 each year. If you discount five annual payments of \$10,000 at the swap rate of 3.70% the net present value is \$44,896.

Take the \$500,000 up-front amount and divide this by \$44,896 and you obtain (approximately) 11 basis points. In other words 11 basis points on \$100m paid annually for the life of the deal has a present value that is equal to the up-front payment of \$500,000. So what’s the all in cost?

The all in cost for \$100m swapped to a floating rate is now Libor + 130 + 11 = Libor + 141 basis points. This is what it looks like:

If the all-in-cost of borrowing of Libor +141 basis points compares favourably to other forms of finance the borrower is likely to proceed.

Naturally enough the swap counterparty (often the same entity as the dealer placing the bond with investors) will try to profit from the swap and also any credit margin that is applicable to the loan.

It is at this point in the negotiation that borrowers need to be careful. Every one basis point the dealer takes over and above “fair value” on this deal is a loss to borrower of nearly \$45,000.

This will be greater for larger and longer dated transactions.