© 2000 John Petroff

A- Bond prices and yields

We start with bonds because determining their value is an immediate extension of the general formula. The coupon states precisely how much is received each year and the indenture specifies the exact dates when coupon and principal will be paid. There is still room for astute trading strategies which will be outlined in Section D of next chapter. For most bonds, calculation of bond value is a straightforward application of time value of money, as already illustrated in examples in Section C of the previous chapter. Bond value BV, i.e. present value of the sum of expected future benefits (i.e. coupon and principal), can be restated formally as

BV = C (1+i)^-1 + … + C (1+i)^-n + P (1+i)^-n

 

where C = coupon

P = principal

i = discount rate

n = years to maturity

Since for most bonds all the stated elements are known, all that remains to be done, is selecting a discount rate i. As shown below, this selection is also rather clear cut for many large corporate bonds.

1)- Corporate bonds

For many major corporate bonds, finding the correct discount rate to use requires simply to look up the rating given by different services and finding a recent list of bond yields published by these rating services. As noted in Chapter 1 Section D-1c, the two major bond rating services in the U.S. are Moody's and Standard & Poor, and there are other services which grade smaller issues. For very small companies, Dun & Bradstreet sells information on virtually all businesses for a fee. How rating services arrive at their ratings is outlined in Section D-4 of next chapter with an example of the method used by Standard & Poor. The rating methods used by Moody's and S&P differ slightly, and individual companies are not always rated by the two services exactly in the same manner.

The meaning of Moody's corporate bond ratings are listed in Table T-3.1 below.

Table T-3.2 presents the equivalency between S& P and Moody' rating, as well as an indication how these ratings correspond to generic ratings.

In Moody's classification bonds rated Aaa to Baa, and in Standard & Poor's classification bonds rated AAA to BBB, are said to be investment grade. This confers on a bond a mark of quality which allows certain institutional investors (such as pension funds and trusts) to invest in them. Because this requirement has originally been instituted by the SEC, and recently proposed changes in the rating process would put even more importance on ratings, the services have objected to an excessive reliance on their ratings and have emphasized that it should be up to investors to make their own interpretation.

Table T-3.3 below shows an example of corporate bond yields presented for different ratings for the months indicated. This chart is published by S&P monthly.

Table T-3.4 shows that yields in different industries are not the same for identical grade bonds.

Differences in yields are naturally the consequence of differences in profitability, sales growth and other conditions particular to each industry (see Chapter 14 Section A-3). Even for a given company, the rating may differ according to particular forms of protection offered in various separate bond issues (see Chapter 12 Section D). Because it takes a few weeks for the latest publication of Moody's (or Standard & Poor) bond yields to be available, it is usually necessary to find the most recent yields of comparable securities from newspapers. For example, one may find in a box called "Active Bond Issues," appearing daily in the New York Times, yields to maturity on newly issued bonds, with rating and industry group also shown for each of these listings.

The following is an example of an early 1995 pricing of a bond issued by Public Service Electric and Gas of New Jersey with a coupon at an annual rate of 6 1/8, maturing in 2002. The rating of PSE&G bonds is A- by Standard & Poor, and a A- bond issue had a yield to maturity of 6.72% at that time. Some simplifying assumption are necessary: coupon payments are twice a year, the maturity date is exactly 7 years from now, and there is no accrued coupon. There are 14 periods and the discount rate is half of 6.72% (see time value of money in Chapter 2 Section C-2). Each semiannual coupon is worth $306.25, that is, face value of $10,000 (i.e. all bonds are priced on the basis of a nominal price of $10,000) multiplied by half of the coupon rate of 6.125% (i.e. 3.0625%). BV = 306.25 (1 - 1/(1 + 0.0672/2)14)/(0.0672/2) + 10000/(1 + 0.0672/2)14 BV = 306.25 x 11.02381 + 10000 x 0.6296 = $9,672.42  This PSE&G bond was quoted in the New York Times at 97 5/8 (i.e. 97.625% of its nominal value, since quotations are made on a 100 basis), and is therefore selling at a price of $9,762.50 (that is, 97.625 x $10,000). The higher actual selling price compared to the estimated price can be attributed to either accrued coupon which was assumed away, or a drop in market rates. In fact, the New York Times reported that yields slid by 0.5% on that day in 1995, and may have caused PSE&G quotations to jump by $50 from the previous day.

Note that the principal is also commonly discounted in the same intraanual manner (i.e. over 14 periods and not over 7 in the example above) as the coupon, even though there is no promise to pay out the principal on those dates. One possible explanation for this is to maintain consistency between coupon and principal calculation.

Most financial publications (such as N.Y .Times, Wall Street Journal and Financial Times) which report bond quotes, also show total yield. This total yield (as defined in Chapter 2 Section F-2) is also known as the yield to maturity or total rate of return: it combines the current yield (i.e. coupon divided by latest quote) with return from appreciation or depreciation of principal if held to maturity. If that yield to maturity is used as discount rate, one would obtain exactly the quoted price because yield to maturity is calculated on the basis of the quoted price in the first place. This means that all the information contained in a quoted price is also contained in the yield to maturity. Thus, it is not necessary to calculate the dollar value of a bond in order to compare it to quoted price. One can just as well compare reported yield to maturity to yields to maturity of comparable bonds that have same rating, same coupon rate and same maturity. How to deal with situation where coupon rates and maturity are different is touched upon in Section 2F-3b of preceding chapter and in Secion 4D-1 of next chapter.

See review questions Q-3A.1 through Q-3A1.12

See research assignments R-3.1, R-3.2 and R-3.3.

2)- Bonds with special rights

As for all securities, it is necessary to read all the clauses of a bond indenture. There may indeed be some additional benefits that the issuer has promised in order to make the bond more attractive, such as put or call provision, conversion right, or other protection. For conversion rights, the addition to value depends on common share value discussed later in Section D of this chapter. If a warrant is attached to a bond, the value of the warrant is separate from the bond and is determined in a similar fashion to that of options, see Section E of this chapter. When a purchase of a bond with an attached warrant is considered, the value is obviously the sum of the two combined.

There are no long term corporate bonds in Russia in 2000. Consequently, there is no need for any rating system of corporate issues. Because of the size and prestige of some large Russian companies (such as GasProm for instance), it seems likely that as soon as inflation rates come down to some manageable level, these companies will find it convenient and cheap to raise needed funds by issuing bonds. These bonds will have to be rated by some competent independent analytical organization to give the public confidence. There are a few government notes with maturities beyond one year. These are priced with the same method as for US issues. However, contrary to US municipal issues that are rated, Russian issues are not.

See review question Q-3A2.1

See research assignment R-3.4.

3)- Municipal bonds

All government jurisdictions do not have the same taxing power and revenue generating ability. Municipalities issue GO bonds (or general obligation bonds) and revenue bonds. Revenue bonds finance various major projects such as roads, schools or hospitals, and are repaid from revenues generated by these facilities. A careful evaluation of the real capacity of these facilities to generate the predicted revenues, is conducted by specialized services which then offer a rating as a result. Rating of municipals is available in S&P Blue Book, also present on-line at http://www.bluelist.com/

Most municipal bonds (as well as some corporate bonds issued by municipalities on corporate behalf) are tax-exempt, but not all. This means that the interest earned by the bondholder needs not be included in bondholder's taxable income. Yields on tax-exempt municipal bonds are significantly lower than corporate bonds because of the potential tax saving. This implies that individuals in low tax brackets will find tax-exempt municipal bonds less attractive than non tax-exempt bonds.

See review questions Q-3A3.1 and Q-3A3.2

See research assignment R-3.5.

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