Calculating the Cost of a Eurobond Issue To compare the cost of issuing bonds in the domestic and Eurobond

Calculating the Cost of a Eurobond Issue To compare the cost of issuing bonds in the domestic and Eurobond

market, the first step is to calculate the all-in-cost of funds of an issue. The all-in-cost of funds considers the interest cost and the costs associ- ated with issuing a bond issue. The all-in-cost of funds of a bond issue is the interest rate that will make the present value of the cash flow that the issuer must make to bondholders equal to the net proceeds received by the issuer. Once the all-cost-of-funds is calculated, adjustments must

be made to consider differences in the frequency at which interest pay- ments are made. For example, consider a U.S. corporation that plans to issue $50 million of 10-year bonds in the United States. Suppose further that its investment banker indicates that 9% coupon bonds can be issued and that the issuance costs will be: (1) $300,000 in underwriter spread and (2) $184,683 in registration and legal fees. Thus, the net proceeds to the issuer would be $49,515,317.

The coupon payments are semiannual payments since this is the practice in the U.S. bond market. The all-in-cost of funds is the interest rate that will make the present value of the semiannual payments equal to the proceeds of $49,515,317. It can be shown that 4.575% is the semiannual all-in-cost of funds. The cost is annualized by doubling the semiannual cost and is called the bond-equivalent yield. In our illustra- tion, the all-in-cost of funds calculated on a bond equivalent basis is 9.150% (2 × 4.575%).

Consider now the same corporation that can issue a 10-year $50 million Eurodollar bond. Its investment banker indicates that a 9.125% coupon is required and that the issuance costs would be: (1) $290,000 in underwriter spread and (2) $43,543 in registration and legal fees.

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Thus, the net proceeds to the issuer would be $49,666,457. The pay- ments are annual, not semiannual as with the U.S. bond issue. It can be shown that an annual interest rate of 9.23% makes the present value of the annual payments equal to the proceeds, $49,666,457.

It would seem that for our two hypothetical bond issues, the all-in- cost of funds is lower for the U.S. bond issue (9.15%) than for the Euro- dollar bond issue (9.23%) by eight basis points. This is an incorrect conclusion because of the convention used in the United States to annu- alize a semiannual rate. An adjustment is required to make a direct com- parison between the all-in-cost on a U.S. bond issue and that on a Eurodollar bond issue. It should be clear that the ability to pay annually rather than semiannually effectively reduces the cost of funding for an issuer. Given the all-in-cost on a Eurodollar bond issue, its all-in-cost (AIC) on a bond-equivalent basis is computed as follows:

2[(1 + AIC on Eurodollar bond) – 1]

Using our hypothetical Eurodollar bond issue that has a 9.23% all- in-cost, the all-in-cost on a bond equivalent basis is:

Notice that the bond-equivalent yield will always be less than the Euro- dollar bond’s yield to maturity. Now comparing the all-in-cost of the two bond issues on a bond equivalent basis, it can be seen that the Euro- bond issue is cheaper by 12 basis points (9.03% versus 9.15%).

Alternatively, to convert the all-in-cost on a bond-equivalent basis of a U.S. bond issue to an annual pay basis so that it can be compared to the all-in-cost of a Eurodollar bond, the following formula can be used:

AIC on a bond-equivalent basis  2 AIC on an annual-pay basis =  1 + ---------------------------------------------------------------------------------  – 1

2  For example, the all-in-cost on a bond equivalent basis for the U.S. bond

issue is 9.15%, so the all-in-cost on an annual pay basis would be: [(1 + 0.0915/2) 2 – 1] = 0.0936 = 9.36% The all-in-cost on an annual basis is always greater than the all-in-cost on

a bond-equivalent basis. Our conclusion once again is that the all-in-cost is higher for the U.S. bond issue relative to the Eurodollar bond issue.

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