WFU Law School
Law & Valuation
4.2.2 Basic Bond Valuation

4.2.3 Behavior of Bond Prices


Financial press information

As the previous examples illustrate, bonds rarely trade at par. Attached is an excerpt from the 07/19/02 Wall Street Journal of bonds traded on the NYSE. Each line is packed with information. Consider the information about these AT&T bonds:

Bond
Cur
Yld
Vol
Close
Net
Chg
AT&T 6-3/4 04
6.9
511
97.50
-.38
AT&T 7-3/4 07
7.9
730
97.75
.13
AT&T 8-1/8 22
9.9
273
82.25
.25
AT&T 8-5/8 31
10.3
219
84.00
-.25

From this information, we learn

  • the first listed AT&T bond has a coupon rate of 6.75% and maturity date in the year 2004
  • its current yield is 6.9%
  • its closing price on 07/18/02 was 97.50 (where 100 is 100% of par)
  • this price is down .38 from the previous day
  • 511,000 bonds were traded on 07/18/02.

This means that if you buy the 6.75% AT&T bond at 97.50% of its face value, the investment will yield interest payments comparable to a 6.9% bond that matures in 2004. Consider the other bonds.


Reasons for bond price fluctuation

Bonds can change in price for essentially two reasons: (1) the issuer's riskiness changes; and (2) economic changes cause interest rates to change - most pronouced for long-term bonds.

Effect of changes in debt rating. What happens if a debt rating agency (such as Moody's) downgrades AT&T debt? The bonds now must offer a higher yield, to compensate for the debt's now perceived higher risk -- the bond's price falls. For example, if the required return (yield) on the second listed bond increased to 8.9%, the price would fall from 97.75 to about $95.08. (The price would rise if AT&T's perceived riskiness fell.)

Effect of changes in interest rates. What happens to the price of AT&T bonds if the Federal Reserve lowers the prime lending rate and markets perceive that long-term interest rates will fall? The bonds now can offer a lower yield, in line with the market's expectation that long-term debt will pay lower interest rates, and the bond's price rises. That is, bond prices rise when interest rates fall. (And bond prices fall, when interest rates rise.) For example, if the yield on long-term bonds fell to 7.8%, the price of the third listed bond would rise to $103.30.


Required return (yield) and bond prices

As we have seen, when a bond's coupon rate differs from its yield, its price will differ from par value. Notice the relationship between a bond's coupon rate and the required return (yield).

Bond trades at discount ... ... when its coupon rate is less than the current yield (its price will be below par).
Bond trades at premium ... ... when its coupon rate is more than the current yield (its price will be above par).

As a bond gets closer to its maturity date, the bond's price approaches par value. That is, the shorter the time until a bond's maturity, the less responsive is the bond's price to interest rate changes. You can confirm this by looking at the attached bond pricing spreadsheet. For this reason, short-term debt has less "interest rate risk" than long-term debt.

See the attached spreadsheet to calculate prices and yields for bonds ppaying semi-annual interest.

Note on junk bonds

During the 1980s, junk bonds rose in prominence (and notoriety) as leveraged buy-outs (LBOs) became popular. Perhaps the most storied of the LBOs of this time was the successful bid of Kohlberg, Kravis, and Roberts (KKR) for RJR Nabisco in late 1988.

Initially, RJR's CEO, F. Ross Johnson, attempted a management buy out (MBO) of the company. This triggered a bidding war eventually resulting in the RJR's board accepting a bid by the buyout firm KKR. Although the KKR bid was not the highest bid, it prevailed largely because the free-spending Johnson was not a part of it. In addition, KKR (the leader in leveraged buyouts) had secured junk-bond financing from the top junk financier, Drexel, Burnham, Lambert (DBL).

Junk bonds are often viewed with disdain by members of the public and even some in the financial community. Their use in LBOs strapped huge debtloads onto acquired companies. Warren Buffett even referred to junk bonds as "bastardized fallen angels." And it didn't help when Michael Milken, DBL's junk bond wizard, was convicted of securities violations conected to his junk bond financings.

Despite all of this, junk bonds remain a source of financing for many companies today, offering a flexible alternative to bank debt. See Stuart C. Gilson and Jerold B. Warner, Junk Bonds, Bank Debt, and Financing Corporate Growth available on SSRN . In addition, investing wisely in junk bonds can be viewed similarly to investing wisely in common stocks as the usual strategy is to maintain a diversified portfolio while looking for undervalued companies. See William A. Klein, High-Yield ("Junk") Bonds as Investments and as Financial Tools, 19 Cardozo L. Rev. 505 (1997).


Note on poison puts

After the leveraged buyout of RJR Nabisco in 1989 (described more fully at 4.3.5), bond issuers began to offer "poison puts" to investors. Meant to protect investors in investment grade debt securities from credit-rating downgrades, the bonds allowed the holder to cash out under specified circumstances -- that is, to "put" the bond to the restructured company.

Besides protecting bondholders, the puts also had the effect of a poison pill. (A poison pill typically operates to dilute a company if an outsider acquires or exercises control, without board approval.) The bond puts were triggered whenever an outsider buys 20% of the issuer's stock, the issuer declares a major cash dividend, or the issuer acquires more than 30% of the stock of another comnpany. Upon one of these triggers, the bond holder has the right to "put" the bonds back to he issuer at face or par value, plus a premium. The issuer is obligated to repurhcase.

The effect of "poison puts" has been to increase the ratings of bonds. Why? Although issuers lost some financing flexiblity, they gained lower interest costs. In addition, poison puts created powerful takeover defenses. Why? An issuer with such obligations was far less attractive than a company whose exisitng bond holders would bear the costs of a credit downgrade.

Examples

An AT&T bond (rated AAA) that pays semi-annual interest has a coupon rate of 6.75% and 2.5 years until maturity

1. What should be its price where par is 100? Assume the following current yields?

Answer 1 (using attached spreadsheet )

Current yield Bond price
4.125% 106.18
7.50% 98.32
12.5% 87.97

2. Assume now different maturities for the bond (current yield of 7.5%), what is the price?

Answer 2 (using attached spreadsheet )

Maturity Bond price
2.5 years

98.32

4.5 years 97.18
19.0 years

92.47

3. Assume now that the bond (maturing in 4.5 years) trades at the following prices, what is the yield?

Answer 3 (using attached spreadsheet )

Bond price Yield
97.18

7.50%

106.53 5.11%
94.10

8.35%

 

4.2.2 Basic Bond Valuation

©2003 Professor Alan R. Palmiter

This page was last updated on: April 2, 2004