Interest Rates and Bond Valuation
The Revolution Within
July 24, 2019DQ. This question must be answered in a 150 word count.
August 8, 2019| Interest Rates and Bond Valuation | 7 |
WHEN STATES, CITIES, OR OTHER local government entities need to raise money, they can turn to the municipal bond market. With almost $4 trillion in municipal bonds outstanding, it seems that they reach out to this market quite often! There are more than one million municipal bond issues outstanding and more than 44,000 issuers. Normally considered a relatively quiet financial market, the municipal bond market became much more exciting because of the potential for municipal bond defaults. The number of defaults depends on who you ask. From 1970 to 2011, Moody’s reported that only 71 municipal bonds had defaulted. However, an analysis by the Federal Reserve Bank of New York counted 2,521 defaults. The reason for the difference was that Moody’s only included municipal bonds that were rated, while the New York Fed included all municipal bond defaults. A major cause for concern for municipal bond investors was the bankruptcy filing by Detroit, which is the largest municipal bankruptcy in U.S. history. In December 2013, Detroit was ruled eligible for Chapter 9 bankruptcy on its $18.5 billion in debt.
Of course, no municipal bond default to date has exceeded the infamous “Whoops” bonds. Issued by the Washington Public Power Supply System (WPPSS) to fund the construction of five nuclear power plants, WPPSS defaulted on $2.25 billion worth of bonds in 1983, the largest municipal bond default in U.S. history. In the end, investors received only 10 to 40 percent of their original investment.
For updates on the latest happenings in finance, visit www.fundamentalsofcorporatefinance.blogspot.com.
Learning Objectives
After studying this chapter, you should understand:
| LO1 | Important bond features and types of bonds. |
| LO2 | Bond values and yields and why they fluctuate. |
| LO3 | Bond ratings and what they mean. |
| LO4 | The impact of inflation on interest rates. |
| LO5 | The term structure of interest rates and the determinants of bond yields. |
Our goal in this chapter is to introduce you to bonds. We begin by showing how the techniques we developed in Chapters 5 and 6 can be applied to bond valuation. From there, we go on to discuss bond features and how bonds are bought and sold. One important thing we learn is that bond values depend, in large part, on interest rates. We therefore close the chapter with an examination of interest rates and their behavior.
Page 1967.1 Bonds and Bond Valuation
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When a corporation or government wishes to borrow money from the public on a long-term basis, it usually does so by issuing or selling debt securities that are generically called bonds. In this section, we describe the various features of corporate bonds and some of the terminology associated with bonds. We then discuss the cash flows associated with a bond and how bonds can be valued using our discounted cash flow procedure.
BOND FEATURES AND PRICES
As we mentioned in our previous chapter, a bond is normally an interest-only loan, meaning that the borrower will pay the interest every period, but none of the principal will be repaid until the end of the loan. For example, suppose the Beck Corporation wants to borrow $1,000 for 30 years. The interest rate on similar debt issued by similar corporations is 12 percent. Beck will thus pay .12 × $1,000 = $120 in interest every year for 30 years. At the end of 30 years, Beck will repay the $1,000. As this example suggests, a bond is a fairly simple financing arrangement. There is, however, a rich jargon associated with bonds, so we will use this example to define some of the more important terms.
In our example, the $120 regular interest payments that Beck promises to make are called the bond’s coupons. Because the coupon is constant and paid every year, the type of bond we are describing is sometimes called a level coupon bond. The amount that will be repaid at the end of the loan is called the bond’s face value, or par value. As in our example, this par value is usually $1,000 for corporate bonds, and a bond that sells for its par value is called a par value bond. Government bonds frequently have much larger face, or par, values. Finally, the annual coupon divided by the face value is called the coupon rate on the bond; in this case, because $120/1,000 = 12%, the bond has a 12 percent coupon rate.
coupon The stated interest payment made on a bond.
face value The principal amount of a bond that is repaid at the end of the term. Also called par value.
coupon rate The annual coupon divided by the face value of a bond.
The number of years until the face value is paid is called the bond’s time to maturity. A corporate bond will frequently have a maturity of 30 years when it is originally issued, but this varies. Once the bond has been issued, the number of years to maturity declines as time goes by.
maturity The specified date on which the principal amount of a bond is paid.
BOND VALUES AND YIELDS
As time passes, interest rates change in the marketplace. The cash flows from a bond, however, stay the same. As a result, the value of the bond will fluctuate. When interest rates rise, the present value of the bond’s remaining cash flows declines, and the bond is worth less. When interest rates fall, the bond is worth more.
To determine the value of a bond at a particular point in time, we need to know the number of periods remaining until maturity, the face value, the coupon, and the market interest rate for bonds with similar features. This interest rate required in the market on a bond is called the bond’s yield to maturity (YTM). This rate is sometimes called the bond’s yield for short. Given all this information, we can calculate the present value of the cash flows as an estimate of the bond’s current market value.
yield to maturity (YTM) The rate required in the market on a bond.
For example, suppose the Xanth (pronounced “zanth”) Co. were to issue a bond with 10 years to maturity. The Xanth bond has an annual coupon of $80. Similar bonds have a yield to maturity of 8 percent. Based on our preceding discussion, the Xanth bond will pay $80 per year for the next 10 years in coupon interest. In 10 years, Xanth will pay $1,000 to the owner of the bond. The cash flows from the bond are shown in Figure 7.1. What would this bond sell for?
As illustrated in Figure 7.1, the Xanth bond’s cash flows have an annuity component (the coupons) and a lump sum (the face value paid at maturity). We thus estimate the market value of the bond by calculating the present value of these two components separately and adding the results together. First, at the going rate of 8 percent, the present value of the $1,000 paid in 10 years is:
Page 197FIGURE 7.1 Cash Flows for Xanth Co. Bond
Present value = $1,000/1.0810 = $1,000/2.1589 = $463.19
Second, the bond offers $80 per year for 10 years; the present value of this annuity stream is:
We can now add the values for the two parts together to get the bond’s value:
Total bond value = $463.19 + 536.81 = $1,000
This bond sells for exactly its face value. This is not a coincidence. The going interest rate in the market is 8 percent. Considered as an interest-only loan, what interest rate does this bond have? With an $80 coupon, this bond pays exactly 8 percent interest only when it sells for $1,000.
To illustrate what happens as interest rates change, suppose a year has gone by. The Xanth bond now has nine years to maturity. If the interest rate in the market has risen to 10 percent, what will the bond be worth? To find out, we repeat the present value calculations with 9 years instead of 10, and a 10 percent yield instead of an 8 percent yield. First, the present value of the $1,000 paid in nine years at 10 percent is:
Present value = $1,000/1.109 = $1,000/2.3579 = $424.10
Second, the bond now offers $80 per year for nine years; the present value of this annuity stream at 10 percent is:
We can now add the values for the two parts together to get the bond’s value:
Total bond value = $424.10 + 460.72 = $884.82
Page 198A good bond site to visit is bonds.yahoo.com, which has loads of useful information.
Therefore, the bond should sell for about $885. In the vernacular, we say that this bond, with its 8 percent coupon, is priced to yield 10 percent at $885.
The Xanth Co. bond now sells for less than its $1,000 face value. Why? The market interest rate is 10 percent. Considered as an interest-only loan of $1,000, this bond pays only 8 percent, its coupon rate. Because this bond pays less than the going rate, investors are willing to lend only something less than the $1,000 promised repayment. Because the bond sells for less than face value, it is said to be a discount bond.
The only way to get the interest rate up to 10 percent is to lower the price to less than $1,000 so that the purchaser, in effect, has a built-in gain. For the Xanth bond, the price of $885 is $115 less than the face value, so an investor who purchased and kept the bond would get $80 per year and would have a $115 gain at maturity as well. This gain compensates the lender for the below-market coupon rate.
Another way to see why the bond is discounted by $115 is to note that the $80 coupon is $20 below the coupon on a newly issued par value bond, based on current market conditions. The bond would be worth $1,000 only if it had a coupon of $100 per year. In a sense, an investor who buys and keeps the bond gives up $20 per year for nine years. At 10 percent, this annuity stream is worth:
This is just the amount of the discount.
What would the Xanth bond sell for if interest rates had dropped by 2 percent instead of rising by 2 percent? As you might guess, the bond would sell for more than $1,000. Such a bond is said to sell at a premium and is called a premium bond.
This case is just the opposite of that of a discount bond. The Xanth bond now has a coupon rate of 8 percent when the market rate is only 6 percent. Investors are willing to pay a premium to get this extra coupon amount. In this case, the relevant discount rate is 6 percent, and there are nine years remaining. The present value of the $1,000 face amount is:
Online bond calculators are available at personal.fidelity.com; interest rate information is available at money.cnn.com/data/bonds and www.bankrate.com.
Present value = $1,000/1.069 = $1,000/1.6895 = $591.89
The present value of the coupon stream is:
We can now add the values for the two parts together to get the bond’s value:
Total bond value = $591.89 + 544.14 = $1,136.03
Total bond value is therefore about $136 in excess of par value. Once again, we can verify this amount by noting that the coupon is now $20 too high, based on current market conditions. The present value of $20 per year for nine years at 6 percent is:
This is just as we calculated.
Page 199Based on our examples, we can now write the general expression for the value of a bond. If a bond has (1) a face value of F paid at maturity, (2) a coupon of C paid per period, (3) t periods to maturity, and (4) a yield of r per period, its value is:
EXAMPLE 7.1 Semiannual Coupons
In practice, bonds issued in the United States usually make coupon payments twice a year. So, if an ordinary bond has a coupon rate of 14 percent, then the owner will get a total of $140 per year, but this $140 will come in two payments of $70 each. Suppose we are examining such a bond. The yield to maturity is quoted at 16 percent.
Bond yields are quoted like APRs; the quoted rate is equal to the actual rate per period multiplied by the number of periods. In this case, with a 16 percent quoted yield and semiannual payments, the true yield is 8 percent per six months. The bond matures in seven years. What is the bond’s price? What is the effective annual yield on this bond?
Based on our discussion, we know the bond will sell at a discount because it has a coupon rate of 7 percent every six months when the market requires 8 percent every six months. So, if our answer exceeds $1,000, we know we have made a mistake.
To get the exact price, we first calculate the present value of the bond’s face value of $1,000 paid in seven years. This seven-year period has 14 periods of six months each. At 8 percent per period, the value is:
Present value = $1,000/1.0814 = $1,000/2.9372 = $340.46
The coupons can be viewed as a 14-period annuity of $70 per period. At an 8 percent discount rate, the present value of such an annuity is:
The total present value gives us what the bond should sell for:
Total present value = $340.46 + 577.10 = $917.56
To calculate the effective yield on this bond, note that 8 percent every six months is equivalent to:
Effective annual rate = (1 + .08)2 − 1 = 16.64%
The effective yield, therefore, is 16.64 percent.
As we have illustrated in this section, bond prices and interest rates always move in opposite directions. When interest rates rise, a bond’s value, like any other present value, will decline. Similarly, when interest rates fall, bond values rise. Even if we are considering a bond that is riskless in the sense that the borrower is certain to make all the payments, there is still risk in owning a bond. We discuss this next.
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Page 200INTEREST RATE RISK
The risk that arises for bond owners from fluctuating interest rates is called interest rate risk. How much interest rate risk a bond has depends on how sensitive its price is to interest rate changes. This sensitivity directly depends on two things: the time to maturity and the coupon rate. As we will see momentarily, you should keep the following in mind when looking at a bond:
1. All other things being equal, the longer the time to maturity, the greater the interest rate risk.
2. All other things being equal, the lower the coupon rate, the greater the interest rate risk.
We illustrate the first of these two points in Figure 7.2. As shown, we compute and plot prices under different interest rate scenarios for 10 percent coupon bonds with maturities of 1 year and 30 years. Notice how the slope of the line connecting the prices is much steeper for the 30-year maturity than it is for the 1-year maturity. This steepness tells us that a relatively small change in interest rates will lead to a substantial change in the bond’s value. In comparison, the one-year bond’s price is relatively insensitive to interest rate changes.
Intuitively, we can see that longer-term bonds have greater interest rate sensitivity because a large portion of a bond’s value comes from the $1,000 face amount. The present value of this amount isn’t greatly affected by a small change in interest rates if the amount is to be received in one year. Even a small change in the interest rate, however, once it is compounded for 30 years, can have a significant effect on the present value. As a result, the present value of the face amount will be much more volatile with a longer-term bond.
FIGURE 7.2 Interest Rate Risk and Time to Maturity
Page 201The other thing to know about interest rate risk is that, like most things in finance and economics, it increases at a decreasing rate. In other words, if we compared a 10-year bond to a 1-year bond, we would see that the 10-year bond has much greater interest rate risk. However, if you were to compare a 20-year bond to a 30-year bond, you would find that the 30-year bond has somewhat greater interest rate risk because it has a longer maturity, but the difference in the risk would be fairly small.
The reason that bonds with lower coupons have greater interest rate risk is essentially the same. As we discussed earlier, the value of a bond depends on the present value of its coupons and the present value of the face amount. If two bonds with different coupon rates have the same maturity, then the value of the one with the lower coupon is proportionately more dependent on the face amount to be received at maturity. As a result, all other things being equal, its value will fluctuate more as interest rates change. Put another way, the bond with the higher coupon has a larger cash flow early in its life, so its value is less sensitive to changes in the discount rate.
Bonds are rarely issued with maturities longer than 30 years. However, low interest rates in recent years have led to the issuance of much longer-term issues. In the 1990s, Walt Disney issued “Sleeping Beauty” bonds with a 100-year maturity. Similarly, BellSouth (now known as AT&T), Coca-Cola, and Dutch banking giant ABN AMRO all issued bonds with 100-year maturities. These companies evidently wanted to lock in the historical low interest rates for a long time. The current record holder for corporations looks to be Republic National Bank, which sold bonds with 1,000 years to maturity. Although somewhat rare, 100-year bond issues still occur. For example, in January 2014, French-utility company Électricité de France sold $700 million in 100-year bonds in the U.S. at a yield of 6.2 percent. The most recent 100-year issue before that was the November 2011 bond issued by U.S. railroad operator Norfolk Southern Corp.
We can illustrate the effect of interest rate risk using the 100-year BellSouth issue. The following table provides some basic information about this issue, along with its prices on December 31, 1995, May 6, 2008, and February 27, 2014:
Several things emerge from this table. First, interest rates apparently fell slightly between December 31, 1995, and May 6, 2008 (why?). After that, however, they rose (why?). The bond’s price first gained .8 percent and then lost 4 percent.
FINDING THE YIELD TO MATURITY: MORE TRIAL AND ERROR
Frequently, we will know a bond’s price, coupon rate, and maturity date, but not its yield to maturity. For example, suppose we are interested in a six-year, 8 percent coupon bond. A broker quotes a price of $955.14. What is the yield on this bond?
Page 202We’ve seen that the price of a bond can be written as the sum of its annuity and lump sum components. Knowing that there is an $80 coupon for six years and a $1,000 face value, we can say that the price is:
$955.14 = $80 × [1 − 1/(1 + r)6]/r + 1,000/(1 + r)6
where r is the unknown discount rate, or yield to maturity. We have one equation here and one unknown, but we cannot solve it for r explicitly. The only way to find the answer is to use trial and error.
This problem is essentially identical to the one we examined in the last chapter when we tried to find the unknown interest rate on an annuity. However, finding the rate (or yield) on a bond is even more complicated because of the $1,000 face amount.
We can speed up the trial-and-error process by using what we know about bond prices and yields. In this case, the bond has an $80 coupon and is selling at a discount. We thus know that the yield is greater than 8 percent. If we compute the price at 10 percent:
Current market rates are available at www.bankrate.com.
At 10 percent, the value we calculate is lower than the actual price, so 10 percent is too high. The true yield must be somewhere between 8 and 10 percent. At this point, it’s “plug and chug” to find the answer. You would probably want to try 9 percent next. If you did, you would see that this is in fact the bond’s yield to maturity.
A bond’s yield to maturity should not be confused with its current yield, which is simply a bond’s annual coupon divided by its price. In the example we just worked, the bond’s annual coupon was $80, and its price was $955.14. Given these numbers, we see that the current yield is $80/955.14 = 8.38 percent, which is less than the yield to maturity of 9 percent. The reason the current yield is too low is that it considers only the coupon portion of your return; it doesn’t consider the built-in gain from the price discount. For a premium bond, the reverse is true, meaning that current yield would be higher because it ignores the built-in loss.
current yield A bond’s annual coupon divided by its price.
Our discussion of bond valuation is summarized in Table 7.1.
TABLE 7.1 Summary of Bond Valuation
Page 203
EXAMPLE 7.2 Current Events
A bond has a quoted price of $1,080.42. It has a face value of $1,000, a semiannual coupon of $30, and a maturity of five years. What is its current yield? What is its yield to maturity? Which is bigger? Why?
Notice that this bond makes semiannual payments of $30, so the annual payment is $60. The current yield is thus $60/1,080.42 = 5.55 percent. To calculate the yield to maturity, refer back to Example 7.1. In this case, the bond pays $30 every six months and has 10 six-month periods until maturity. So, we need to find r as follows:
$1,080.42 = $30 × [1 − 1/(1 + r)10]/r + 1,000/(1 + r)10
After some trial and error, we find that r is equal to about 2.1 percent. But, the tricky part is that this 2.1 percent is the yield per six months. We have to double it to get the yield to maturity, so the yield to maturity is 4.2 percent, which is less than the current yield. The reason is that the current yield ignores the built-in loss of the premium between now and maturity.
EXAMPLE 7.3 Bond Yields
You’re looking at two bonds identical in every way except for their coupons and, of course, their prices. Both have 12 years to maturity. The first bond has a 10 percent annual coupon rate and sells for $935.08. The second has a 12 percent annual coupon rate. What do you think it would sell for?
Because the two bonds are similar, they will be priced to yield about the same rate. We first need to calculate the yield on the 10 percent coupon bond. Proceeding as before, we know that the yield must be greater than 10 percent because the bond is selling at a discount. The bond has a fairly long maturity of 12 years. We’ve seen that long-term bond prices are relatively sensitive to interest rate changes, so the yield is probably close to 10 percent. A little trial and error reveals that the yield is actually 11 percent:
With an 11 percent yield, the second bond will sell at a premium because of its $120 coupon. Its value is:
CALCULATOR HINTS
How to Calculate Bond Prices and Yields Using a Financial Calculator
Many financial calculators have fairly sophisticated built-in bond valuation routines. However, these vary quite a lot in implementation, and not all financial calculators have them. As a result, we will illustrate a simple way to handle bond problems that will work on just about any financial calculator.
Page 204To begin, of course, we first remember to clear out the calculator! Next, for Example 7.3, we have two bonds to consider, both with 12 years to maturity. The first one sells for $935.08 and has a 10 percent annual coupon rate. To find its yield, we can do the following:
Notice that here we have entered both a future value of $1,000, representing the bond’s face value, and a payment of 10 percent of $1,000, or $100, per year, representing the bond’s annual coupon. Also, notice that we have a negative sign on the bond’s price, which we have entered as the present value.
For the second bond, we now know that the relevant yield is 11 percent. It has a 12 percent annual coupon and 12 years to maturity, so what’s the price? To answer, we just enter the relevant values and solve for the present value of the bond’s cash flows:
There is an important detail that comes up here. Suppose we have a bond with a price of $902.29, 10 years to maturity, and a coupon rate of 6 percent. As we mentioned earlier, most bonds actually make semiannual payments. Assuming that this is the case for the bond here, what’s the bond’s yield? To answer, we need to enter the relevant numbers like this:
Notice that we entered $30 as the payment because the bond actually makes payments of $30 every six months. Similarly, we entered 20 for N because there are actually 20 six-month periods. When we solve for the yield, we get 3.7 percent. The tricky thing to remember is that this is the yield per six months, so we have to double it to get the right answer: 2 × 3.7 = 7.4 percent, which would be the bond’s reported yield.
SPREADSHEET STRATEGIES
How to Calculate Bond Prices and Yields Using a Spreadsheet
Most spreadsheets have fairly elaborate routines available for calculating bond values and yields; many of these routines involve details we have not discussed. However, setting up a simple spreadsheet to calculate prices or yields is straightforward, as our next two spreadsheets show:
Page 205
In our spreadsheets, notice that we had to enter two dates: a settlement date and a maturity date. The settlement date is just the date you actually pay for the bond, and the maturity date is the day the bond actually matures. In most of our problems, we don’t explicitly have these dates, so we have to make them up. For example, because our bond has 22 years to maturity, we just picked 1/1/2000 (January 1, 2000) as the settlement date and 1/1/2022 (January 1, 2022) as the maturity date. Any two dates would do as long as they are exactly 22 years apart, but these are particularly easy to work with. Finally, notice that we had to enter the coupon rate and yield to maturity in annual terms and then explicitly provide the number of coupon payments per year.
Concept Questions
7.1a What are the cash flows associated with a bond?
7.1b What is the general expression for the value of a bond?
7.1c Is it true that the only risk associated with owning a bond is that the issuer will not make all the payments? Explain.
Page 2067.2 More about Bond Features
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In this section, we continue our discussion of corporate debt by describing in some detail the basic terms and features that make up a typical long-term corporate bond. We discuss additional issues associated with long-term debt in subsequent sections.
Securities issued by corporations may be classified roughly as equity securities and debt securities. At the crudest level, a debt represents something that must be repaid; it is the result of borrowing money. When corporations borrow, they generally promise to make regularly scheduled interest payments and to repay the original amount borrowed (that is, the principal). The person or firm making the loan is called the creditor or lender. The corporation borrowing the money is called the debtor or borrower.
From a financial point of view, the main differences between debt and equity are the following:
Information for bond investors can be found at www.investinginbonds.com.
1. Debt is not an ownership interest in the firm. Creditors generally do not have voting power.
2. The corporation’s payment of interest on debt is considered a cost of doing business and is fully tax deductible. Dividends paid to stockholders are not tax deductible.
3. Unpaid debt is a liability of the firm. If it is not paid, the creditors can legally claim the assets of the firm. This action can result in liquidation or reorganization, two of the possible consequences of bankruptcy. Thus, one of the costs of issuing debt is the possibility of financial failure. This possibility does not arise when equity is issued.
IS IT DEBT OR EQUITY?
Sometimes it is not clear if a particular security is debt or equity. For example, suppose a corporation issues a perpetual bond with interest payable solely from corporate income if and only if earned. Whether this is really a debt is hard to say and is primarily a legal and semantic issue. Courts and taxing authorities would have the final say.
Corporations are adept at creating exotic, hybrid securities that have many features of equity but are treated as debt. Obviously, the distinction between debt and equity is important for tax purposes. So, one reason that corporations try to create a debt security that is really equity is to obtain the tax benefits of debt and the bankruptcy benefits of equity.
As a general rule, equity represents an ownership interest, and it is a residual claim. This means that equity holders are paid after debt holders. As a result of this, the risks and benefits associated with owning debt and equity are different. To give just one example, note that the maximum reward for owning a debt security is ultimately fixed by the amount of the loan, whereas there is no upper limit to the potential reward from owning an equity interest.
LONG-TERM DEBT: THE BASICS
Ultimately, all long-term debt securities are promises made by the issuing firm to pay principal when due and to make timely interest payments on the unpaid balance. Beyond this, a number of features distinguish these securities from one another. We discuss some of these features next.
The maturity of a long-term debt instrument is the length of time the debt remains outstanding with some unpaid balance. Debt securities can be short-term (with maturities of Page 207one year or less) or long-term (with maturities of more than one year).1 Short-term debt is sometimes referred to as unfunded debt.2
Debt securities are typically called notes, debentures, or bonds. Strictly speaking, a bond is a secured debt. However, in common usage, the word bondrefers to all kinds of secured and unsecured debt. We will therefore continue to use the term generically to refer to long-term debt. Also, usually the only difference between a note and a bond is the original maturity. Issues with an original maturity of 10 years or less are often called notes. Longer-term issues are called bonds.
The two major forms of long-term debt are public-issue and privately placed. We concentrate on public-issue bonds. Most of what we say about them holds true for private-issue, long-term debt as well. The main difference between public-issue and privately placed debt is that the latter is directly placed with a lender and not offered to the public. Because this is a private transaction, the specific terms are up to the parties involved.
There are many other dimensions to long-term debt, including such things as security, call features, sinking funds, ratings, and protective covenants. The following table illustrates these features for a bond issued by technology giant Cisco Systems. If some of these terms are unfamiliar, have no fear. We will discuss them all presently.
Information about individual bonds can be found at http://finra-markets.morningstar.com.
Many of these features will be detailed in the bond indenture, so we discuss this first.
Page 208THE INDENTURE
The indenture is the written agreement between the corporation (the borrower) and its creditors. It is sometimes referred to as the deed of trust. 3 Usually, a trustee (a bank, perhaps) is appointed by the corporation to represent the bondholders. The trust company must (1) make sure the terms of the indenture are obeyed, (2) manage the sinking fund (described in the following pages), and (3) represent the bondholders in default—that is, if the company defaults on its payments to them.
indenture The written agreement between the corporation and the lender detailing the terms of the debt issue.
The bond indenture is a legal document. It can run several hundred pages and generally makes for tedious reading. It is an important document, however, because it generally includes the following provisions:
1. The basic terms of the bonds.
2. The total amount of bonds issued.
3. A description of property used as security.
4. The repayment arrangements.
5. The call provisions.
6. Details of the protective covenants.
We discuss these features next.
Terms of a Bond Corporate bonds usually have a face value (that is, a denomination) of $1,000, although par values of $2,000 like the Cisco bond have become relatively common. Other par values also exist. For example, municipal bonds often have par values of $5,000, and Treasury bonds with par values of $10,000 or $100,000 are often sold. This principal value is stated on the bond certificate. So, if a corporation wanted to borrow $1 million, 1,000 bonds would have to be sold. The par value (that is, initial accounting value) of a bond is almost always the same as the face value, and the terms are used interchangeably in practice.
Corporate bonds are usually in registered form. For example, the indenture might read as follows:
registered form The form of bond issue in which the registrar of the company records ownership of each bond; payment is made directly to the owner of record.
Interest is payable semiannually on July 1 and January 1 of each year to the person in whose name the bond is registered at the close of business on June 15 or December 15, respectively.
This means that the company has a registrar who will record the ownership of each bond and record any changes in ownership. The company will pay the interest and principal by check mailed directly to the address of the owner of record. A corporate bond may be registered and have attached “coupons.” To obtain an interest payment, the owner must separate a coupon from the bond certificate and send it to the company registrar (the paying agent).
Alternatively, the bond could be in bearer form. This means that the certificate is the basic evidence of ownership, and the corporation will “pay the bearer.” Ownership is not otherwise recorded, and, as with a registered bond with attached coupons, the holder of the bond certificate detaches the coupons and sends them to the company to receive payment.
bearer form The form of bond issue in which the bond is issued without record of the owner’s name; payment is made to whomever holds the bond.
There are two drawbacks to bearer bonds. First, they are difficult to recover if they are lost or stolen. Second, because the company does not know who owns its bonds, it cannot notify bondholders of important events. Bearer bonds were once the dominant type, but they are now much less common (in the United States) than registered bonds.
Page 209Security Debt securities are classified according to the collateral and mortgages used to protect the bondholder.
Collateral is a general term that frequently means securities (for example, bonds and stocks) that are pledged as security for payment of debt. For example, collateral trust bonds often involve a pledge of common stock held by the corporation. However, the term collateral is commonly used to refer to any asset pledged on a debt.
Mortgage securities are secured by a mortgage on the real property of the borrower. The property involved is usually real estate—for example, land or buildings. The legal document that describes the mortgage is called a mortgage trust indenture or trust deed.
Sometimes mortgages are on specific property, such as a railroad car. More often, blanket mortgages are used. A blanket mortgage pledges all the real property owned by the company.4
Bonds frequently represent unsecured obligations of the company. A debenture is an unsecured bond, for which no specific pledge of property is made. The term note is generally used for such instruments if the maturity of the unsecured bond is less than 10 or so years when the bond is originally issued. Debenture holders have a claim only on property not otherwise pledged—in other words, the property that remains after mortgages and collateral trusts are taken into account. The Cisco bonds in the table are an example of such an issue.
debenture An unsecured debt, usually with a maturity of 10 years or more.
note An unsecured debt, usually with a maturity under 10 years.
The terminology that we use here and elsewhere in this chapter is standard in the United States. Outside the United States, these same terms can have different meanings. For example, bonds issued by the British government (“gilts”) are called treasury “stock.” Also, in the United Kingdom, a debenture is a secured obligation.
At the current time, public bonds issued in the United States by industrial and financial companies are typically debentures. However, most utility and railroad bonds are secured by a pledge of assets.
Seniority In general terms, seniority indicates preference in position over other lenders, and debts are sometimes labeled as senior or junior to indicate seniority. Some debt is subordinated, as in, for example, a subordinated debenture.
In the event of default, holders of subordinated debt must give preference to other specified creditors. Usually, this means that the subordinated lenders will be paid off only after the specified creditors have been compensated. However, debt cannot be subordinated to equity.
The Securities Industry and Financial Markets Association (SIFMA) website is www.sifma.org.
Repayment Bonds can be repaid at maturity, at which time the bondholder will receive the stated, or face, value of the bond; or they may be repaid in part or in entirety before maturity. Early repayment in some form is more typical and is often handled through a sinking fund.
A sinking fund is an account managed by the bond trustee for the purpose of repaying the bonds. The company makes annual payments to the trustee, who then uses the funds to retire a portion of the debt. The trustee does this by either buying up some of the bonds in the market or calling in a fraction of the outstanding bonds. This second option is discussed in the next section.
sinking fund An account managed by the bond trustee for early bond redemption.
There are many different kinds of sinking fund arrangements, and the details would be spelled out in the indenture. For example:
1. Some sinking funds start about 10 years after the initial issuance.
2. Some sinking funds establish equal payments over the life of the bond.
Page 2103. Some high-quality bond issues establish payments to the sinking fund that are not sufficient to redeem the entire issue. As a consequence, there is the possibility of a large “balloon payment” at maturity.
The Call Provision A call provision allows the company to repurchase or “call” part or all of the bond issue at stated prices over a specific period. Corporate bonds are usually callable.
call provision An agreement giving the corporation the option to repurchase a bond at a specified price prior to maturity.
Generally, the call price is above the bond’s stated value (that is, the par value). The difference between the call price and the stated value is the call premium. The amount of the call premium may become smaller over time. One arrangement is to initially set the call premium equal to the annual coupon payment and then make it decline to zero as the call date moves closer to the time of maturity.
call premium The amount by which the call price exceeds the par value of a bond.
Call provisions are often not operative during the first part of a bond’s life. This makes the call provision less of a worry for bondholders in the bond’s early years. For example, a company might be prohibited from calling its bonds for the first 10 years. This is a deferred call provision. During this period of prohibition, the bond is said to be call protected.
deferred call provision A call provision prohibiting the company from redeeming a bond prior to a certain date.
call-protected bond A bond that, during a certain period, cannot be redeemed by the issuer.
In recent years, a new type of call provision, a “make-whole” call, has become widespread in the corporate bond market. With such a feature, bondholders receive approximately what the bonds are worth if they are called. Because bondholders don’t suffer a loss in the event of a call, they are “made whole.”
To determine the make-whole call price, we calculate the present value of the remaining interest and principal payments at a rate specified in the indenture. For example, looking at our Cisco issue, we see that the discount rate is “Treasury rate plus .15%.” What this means is that we determine the discount rate by first finding a U.S. Treasury issue with the same maturity. We calculate the yield to maturity on the Treasury issue and then add on .15 percent to get the discount rate we use.
Notice that with a make-whole call provision, the call price is higher when interest rates are lower and vice versa (why?). Also notice that, as is common with a make-whole call, the Cisco issue does not have a deferred call feature. Why might investors not be too concerned about the absence of this feature?
Protective Covenants A protective covenant is that part of the indenture or loan agreement that limits certain actions a company might otherwise wish to take during the term of the loan. Protective covenants can be classified into two types: negative covenants and positive (or affirmative) covenants.
protective covenant A part of the indenture limiting certain actions that might be taken during the term of the loan, usually to protect the lender’s interest.
A negative covenant is a “thou shalt not” type of covenant. It limits or prohibits actions the company might take. Here are some typical examples:
1. The firm must limit the amount of dividends it pays according to some formula.
2. The firm cannot pledge any assets to other lenders.
3. The firm cannot merge with another firm.
4. The firm cannot sell or lease any major assets without approval by the lender.
5. The firm cannot issue additional long-term debt.
A positive covenant is a “thou shalt” type of covenant. It specifies an action the company agrees to take or a condition the company must abide by. Here are some examples:
1. The company must maintain its working capital at or above some specified minimum level.
2. The company must periodically furnish audited financial statements to the lender.
3. The firm must maintain any collateral or security in good condition.
Want detailed information about the amount and terms of the debt issued by a particular firm? Check out its latest financial statements by searching SEC filings at www.sec.gov.
Page 211This is only a partial list of covenants; a particular indenture may feature many different ones.
Concept Questions
7.2a What are the distinguishing features of debt compared to equity?
7.2b What is the indenture? What are protective covenants? Give some examples.
7.2c What is a sinking fund?
7.3 Bond Ratings
Firms frequently pay to have their debt rated. The two leading bond-rating firms are Moody’s and Standard & Poor’s (S&P). The debt ratings are an assessment of the creditworthiness of the corporate issuer. The definitions of creditworthiness used by Moody’s and S&P are based on how likely the firm is to default and the protection creditors have in the event of a default.
It is important to recognize that bond ratings are concerned only with the possibility of default. Earlier, we discussed interest rate risk, which we defined as the risk of a change in the value of a bond resulting from a change in interest rates. Bond ratings do not address this issue. As a result, the price of a highly rated bond can still be quite volatile.
Bond ratings are constructed from information supplied by the corporation. The rating classes and some information concerning them are shown in the following table:
Page 212Want to know what criteria are commonly used to rate corporate and municipal bonds? Go to www.standardandpoors.com, www.moodys.com, or www.fitchinv.com.
The highest rating a firm’s debt can have is AAA or Aaa, and such debt is judged to be the best quality and to have the lowest degree of risk. For example, the 100-year BellSouth issue we discussed earlier was rated AAA. This rating is not awarded very often: As of 2014, only four nonfinancial U.S. companies had AAA ratings. AA or Aa ratings indicate very good quality debt and are much more common.
A large part of corporate borrowing takes the form of low-grade, or “junk,” bonds. If these low-grade corporate bonds are rated at all, they are rated below investment grade by the major rating agencies. Investment-grade bonds are bonds rated at least BBB by S&P or Baa by Moody’s.
Rating agencies don’t always agree. To illustrate, some bonds are known as “crossover” or “5B” bonds. The reason is that they are rated triple-B (or Baa) by one rating agency and double-B (or Ba) by another, a “split rating.” For example, in March 2014, real estate investment company Omega Healthcare Investors sold an issue of 10-year notes rated BBB– by S&P and Ba1 by Moody’s.
A bond’s credit rating can change as the issuer’s financial strength improves or deteriorates. For example, in January 2014, Moody’s cut the bond rating on PlayStation 4 manufacturer Sony from Baa3 to Ba1, lowering the company’s bond rating from investment grade to junk bond status. Bonds that drop into junk territory like this are called fallen angels. Although sales of the new PS4 were a positive factor noted by Moody’s, the rating agency felt that the majority of Sony’s core business such as TVs, mobile phones, digital cameras, and personal computers faced difficult times ahead.
Credit ratings are important because defaults really do occur, and when they do, investors can lose heavily. For example, in 2000, AmeriServe Food Distribution, Inc., which supplied restaurants such as Burger King with everything from burgers to giveaway toys, defaulted on $200 million in junk bonds. After the default, the bonds traded at just 18 cents on the dollar, leaving investors with a loss of more than $160 million.
Even worse in AmeriServe’s case, the bonds had been issued only four months earlier, thereby making AmeriServe an NCAA champion. Although that might be a good thing for a college basketball team such as the University of Kentucky Wildcats, in the bond market it means “No Coupon At All,” and it’s not a good thing for investors.
If you’re nervous about the level of debt piled up by the U.S. government, don’t go to www.publicdebt.treas.gov or to www.brillig.com/debt_clock! Learn all about government bonds at www.ny.frb.org.
Concept Questions
7.3a What does a bond rating say about the risk of fluctuations in a bond’s value resulting from interest rate changes?
7.3b What is a junk bond?
7.4 Some Different Types of Bonds
Thus far we have considered only “plain vanilla” corporate bonds. In this section, we briefly look at bonds issued by governments and also at bonds with unusual features.
GOVERNMENT BONDS
The biggest borrower in the world—by a wide margin—is everybody’s favorite family member, Uncle Sam. In early 2014, the total debt of the U.S. government was $17.5 trillion, or about $55,000 per citizen (and growing!). When the government wishes to borrow money for more than one year, it sells what are known as Treasury notes and bonds to the Page 213public (in fact, it does so every month). Currently, outstanding Treasury notes and bonds have original maturities ranging from 2 to 30 years.
Most U.S. Treasury issues are just ordinary coupon bonds. There are two important things to keep in mind, however. First, U.S. Treasury issues, unlike essentially all other bonds, have no default risk because (we hope) the Treasury can always come up with the money to make the payments. Second, Treasury issues are exempt from state income taxes (though not federal income taxes). In other words, the coupons you receive on a Treasury note or bond are taxed only at the federal level.
State and local governments also borrow money by selling notes and bonds. Such issues are called municipal notes and bonds, or just “munis.” Unlike Treasury issues, munis have varying degrees of default risk, and, in fact, they are rated much like corporate issues. Also, they are almost always callable. The most intriguing thing about munis is that their coupons are exempt from federal income taxes (though not necessarily state income taxes), which makes them very attractive to high-income, high–tax bracket investors.
For information on municipal bonds including prices, check out emma.msrb.org.
Because of the enormous tax break they receive, the yields on municipal bonds are much lower than the yields on taxable bonds. For example, in March 2014, long-term Aa-rated corporate bonds were yielding about 4.38 percent. At the same time, long-term Aa munis were yielding about 4.09 percent. Suppose an investor was in a 30 percent tax bracket. All else being the same, would this investor prefer a Aa corporate bond or a Aa municipal bond?
To answer, we need to compare the aftertax yields on the two bonds. Ignoring state and local taxes, the muni pays 4.09 percent on both a pretax and an aftertax basis. The corporate issue pays 4.38 percent before taxes, but it pays only .0438 × (1 − .30) = .0301, or 3.01 percent, once we account for the 30 percent tax bite. Given this, the muni has a better yield.
Another good bond market site is money.cnn.com.
EXAMPLE 7.4 Taxable versus Municipal Bonds
Suppose taxable bonds are currently yielding 8 percent, while at the same time, munis of comparable risk and maturity are yielding 6 percent. Which is more attractive to an investor in a 40 percent bracket? What is the break-even tax rate? How do you interpret this rate?
For an investor in a 40 percent tax bracket, a taxable bond yields 8 × (1 − .40) = 4.8 percent after taxes, so the muni is much more attractive. The break-even tax rate is the tax rate at which an investor would be indifferent between a taxable and a nontaxable issue. If we let t* stand for the break-even tax rate, then we can solve for it as follows:
Thus, an investor in a 25 percent tax bracket would make 6 percent after taxes from either bond.
ZERO COUPON BONDS
A bond that pays no coupons at all must be offered at a price that is much lower than its stated value. Such bonds are called zero coupon bonds, or just zeroes.5
zero coupon bond A bond that makes no coupon payments and is thus initially priced at a deep discount.
Page 214TABLE 7.2 Interest Expense for EIN’s Zeroes
Suppose the Eight-Inch Nails (EIN) Company issues a $1,000 face value, five-year zero coupon bond. The initial price is set at $508.35. Even though no interest payments are made on the bond, zero coupon bond calculations use semiannual periods to be consistent with coupon bond calculations. Using semiannual periods, it is straightforward to verify that, at this price, the bond yields about 14 percent to maturity. The total interest paid over the life of the bond is $1,000 − 508.35 = $491.65.
For tax purposes, the issuer of a zero coupon bond deducts interest every year even though no interest is actually paid. Similarly, the owner must pay taxes on interest accrued every year, even though no interest is actually received.
The way in which the yearly interest on a zero coupon bond is calculated is governed by tax law. Before 1982, corporations could calculate the interest deduction on a straight-line basis. For EIN, the annual interest deduction would have been $491.65/5 = $98.33 per year.
Under current tax law, the implicit interest is determined by amortizing the loan. We do this by first calculating the bond’s value at the beginning of each year. For example, after one year, the bond will have four years until maturity, so it will be worth $1,000/1.078 = $582.01; the value in two years will be $1,000/1.076 = $666.34; and so on. The implicit interest each year is simply the change in the bond’s value for the year. The values and interest expenses for the EIN bond are listed in Table 7.2.
Notice that under the old rules, zero coupon bonds were more attractive because the deductions for interest expense were larger in the early years (compare the implicit interest expense with the straight-line expense).
Under current tax law, EIN could deduct $73.66 in interest paid the first year and the owner of the bond would pay taxes on $73.66 in taxable income (even though no interest was actually received). This second tax feature makes taxable zero coupon bonds less attractive to individuals. However, they are still a very attractive investment for tax-exempt investors with long-term dollar-denominated liabilities, such as pension funds, because the future dollar value is known with relative certainty.
Some bonds are zero coupon bonds for only part of their lives. For example, General Motors has a debenture outstanding that matures on March 15, 2036. For the first 20 years of its life, no coupon payments will be made; but, after 20 years, it will begin paying coupons semiannually at a rate of 7.75 percent per year.
FLOATING-RATE BONDS
The conventional bonds we have talked about in this chapter have fixed-dollar obligations because the coupon rates are set as fixed percentages of the par values. Similarly, the principal amounts are set equal to the par values. Under these circumstances, the coupon payments and principal are completely fixed.
Page 215With floating-rate bonds (floaters), the coupon payments are adjustable. The adjustments are tied to an interest rate index such as the Treasury bill interest rate or the 30-year Treasury bond rate.
The value of a floating-rate bond depends on exactly how the coupon payment adjustments are defined. In most cases, the coupon adjusts with a lag to some base rate. For example, suppose a coupon rate adjustment is made on June 1. The adjustment might be based on the simple average of Treasury bond yields during the previous three months. In addition, the majority of floaters have the following features:
1. The holder has the right to redeem the note at par on the coupon payment date after some specified amount of time. This is called a put provision, and it is discussed in the following section.
2. The coupon rate has a floor and a ceiling, meaning that the coupon is subject to a minimum and a maximum. In this case, the coupon rate is said to be “capped,” and the upper and lower rates are sometimes called the collar.
A particularly interesting type of floating-rate bond is an inflation-linked bond. Such bonds have coupons that are adjusted according to the rate of inflation (the principal amount may be adjusted as well). The U.S. Treasury began issuing such bonds in January of 1997. The issues are sometimes called “TIPS,” or Treasury Inflation-Protected Securities. Other countries, including Canada, Israel, and Britain, have issued similar securities.
Official information about U.S. inflation-indexed bonds is at www.publicdebt.treas.gov.
OTHER TYPES OF BONDS
Many bonds have unusual or exotic features. So-called catastrophe, or cat, bonds provide an interesting example. In August 2013, Northshore Re Limited, a reinsurance company, issued $200 million in cat bonds (reinsurance companies sell insurance to insurance companies). These cat bonds covered hurricanes and earthquakes in the U.S. In the event of one of these triggering events, Northshore Re would receive cash flows to offset its loss.
The largest single cat bond issue to date is a series of six bonds sold by Merna Reinsurance in 2007. The six bond issues were to cover various catastrophes the company faced due to its reinsurance of State Farm. The six bonds totaled about $1.2 billion in par value. During 2013, about $7.6 billion in cat bonds were issued, and there was about $20.6 billion par value in cat bonds outstanding at the end of the year.
At this point, cat bonds probably seem pretty risky. It therefore might be surprising to learn that since cat bonds were first issued in 1997, only four have not been paid in full. For example, because of Hurricane Katrina, cat bondholders lost $190 million. Cat bond-holders also lost $300 million due to the 2011 tsunami in Japan. During 2011, two other cat bond issues, each worth $100 million, were triggered due to an unusually active tornado season.
Another possible bond feature is a warrant. A warrant gives the buyer of a bond the right to purchase shares of stock in the company at a fixed price. Such a right would be very valuable if the stock price climbed substantially (a later chapter discusses this subject in greater depth). Because of the value of this feature, bonds with warrants are often issued at a very low coupon rate.
As these examples illustrate, bond features are really limited only by the imaginations of the parties involved. Unfortunately, there are far too many variations for us to cover in detail here. We therefore close this discussion by mentioning a few of the more common types.
Income bonds are similar to conventional bonds, except that coupon payments depend on company income. Specifically, coupons are paid to bondholders only if the firm’s Page 216income is sufficient. This would appear to be an attractive feature, but income bonds are not very common.
A convertible bond can be swapped for a fixed number of shares of stock anytime before maturity at the holder’s option. Convertibles are relatively common, but the number has been decreasing in recent years.
A put bond allows the holder to force the issuer to buy back the bond at a stated price. For example, International Paper Co. has bonds outstanding that allow the holder to force International Paper to buy the bonds back at 100 percent of face value if certain “risk” events happen. One such event is a change in credit rating from investment grade to lower than investment grade by Moody’s or S&P. The put feature is therefore just the reverse of the call provision.
The reverse convertible is a relatively new type of structured note. One type generally offers a high coupon rate, but the redemption at maturity can be paid in cash at par value or paid in shares of stock. For example, one recent General Motors (GM) reverse convertible had a coupon rate of 16 percent, which is a very high coupon rate in today’s interest rate environment. However, at maturity, if GM’s stock declined sufficiently, bondholders would receive a fixed number of GM shares that were worth less than par value. So, while the income portion of the bond return would be high, the potential loss in par value could easily erode the extra return.
Perhaps the most unusual bond (and certainly the most ghoulish) is the “death bond.” Companies such as Stone Street Financial purchase life insurance policies from individuals who are expected to die within the next 10 years. They then sell bonds that are paid off from the life insurance proceeds received when the policyholders pass away. The return on the bonds to investors depends on how long the policyholders live. A major risk is that if medical treatment advances quickly, it will raise the life expectancy of the policyholders, thereby decreasing the return to the bondholder.
Structured notes are bonds that are based on stocks, bonds, commodities, or currencies. One particular type of structured note has a return based on a stock market index. At expiration, if the stock index has declined, the bond returns the principal. However, if the stock index has increased, the bond will return a portion of the stock index return, say 80 percent. Another type of structured note will return twice the stock index return, but with the potential for loss of principal.
A given bond may have many unusual features. Two of the most recent exotic bonds are CoCo bonds, which have a coupon payment, and NoNo bonds, which are zero coupon bonds. CoCo and NoNo bonds are contingent convertible, putable, callable, subordinated bonds. The contingent convertible clause is similar to the normal conversion feature, except the contingent feature must be met. For example, a contingent feature may require that the company stock trade at 110 percent of the conversion price for 20 out of the most recent 30 days. Valuing a bond of this sort can be quite complex, and the yield to maturity calculation is often meaningless.
SUKUK
Worldwide demand for assets that comply with shariah, or Islamic law and cultural tradition, has grown dramatically. Assets, including deposits at Islamic financial institutions, totaled about $1.8 trillion in 2013, up from $1.3 trillion in 2011. One of the major differences between Western financial practices and shariah is that Islamic law does not permit charging or paying riba, or interest. Given our current discussion about bonds, this means that anyone following shariah cannot buy or issue conventional bonds.
To accommodate the restriction on interest payments, Islamic bonds, or sukuk, have been created. There are many possible structures to sukuk, such as partial ownership in a debt (Sukuk Murabaha) or an asset (Sukuk Al Ijara). In case of a Sukuk Al Ijara, there is a binding promise to repurchase a certain asset by the issuer at maturity. Before the sukuk matures, rent is paid on the asset. While we have noted that traditional bonds can be relatively illiquid, most sukuk are bought and held to maturity. As a result, secondary markets in sukuk are extremely illiquid.
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IN THEIR OWN WORDS …
Edward I. Altman on Junk Bonds and Leveraged Loans
One of the most important developments in corporate finance over the last 30 years has been the reemergence of publicly owned and traded low-rated corporate debt. Originally offered to the public in the early 1900s to help finance some of our emerging growth industries, these high-yield, high-risk bonds virtually disappeared after the rash of bond defaults during the Depression. Recently, however, the junk bond market has been catapulted from being an insignificant element in the corporate fixed-income market to being one of the fastest-growing and most controversial types of financing mechanisms. Technically, high-yield bonds are bonds issued by companies whose rating given by one or more of the major rating agencies, i.e., Fitch, Moody’s or Standard & Poor’s, is below investment grade, e.g., below BBB– by S&P.
The term junk emanates from the dominant type of low-rated bond issues outstanding prior to 1977 when the “market” consisted almost exclusively of original-issue investment-grade bonds that fell from their lofty status to a higher-default risk, speculative-grade level. These so called fallen angels amounted to about $8.5 billion in 1977. At the end of 2008, fallen angels comprised about 25 percent of the $1 trillion publicly owned junk bond market. The high-yield bond market in Europe began to grow only recently and reached about €175 billion in 2008.
Beginning in 1977, issuers began to go directly to the public to raise debt capital for growth purposes. Early issuers of junk bonds were energy-related firms, cable TV companies, airlines, and assorted other industrial companies. The emerging growth company rationale coupled with relatively high returns to early investors helped legitimize this sector.
By far the most important and controversial aspect of junk bond financing was its role in the corporate restructuring movement from 1985 to 1989. High-leverage transactions and acquisitions, such as leveraged buyouts (LBOs), which occur when a firm is taken private, and leveraged recapitalizations (debt-for-equity swaps), transformed the face of corporate America, leading to a heated debate as to the economic and social consequences of firms’ being transformed with debt–equity ratios of at least 6:1. Similar, but less emotional, comments accompanied a second LBO movement in 2004–2007.
These transactions involved increasingly large companies, and the multibillion dollar takeover became fairly common, finally capped by the huge $251 billion RJR Nabisco LBO in 1989. LBOs were typically financed with about 60 percent senior bank and insurance company debt, about 25–30 percent subordinated public debt (junk bonds), and 10–15 percent equity. The junk bond segment is sometimes referred to as “mezzanine” financing because it lies between the “balcony” senior debt and the “basement” equity. In the most recent LBO binge, however, more than 30 percent of the financing was equity but the transactions were, on average, much larger than in the late 1980s, with only RJR Nabisco from the earlier vintage still in the “top-10 LBOs.”
These restructurings resulted in huge fees to advisors and underwriters and huge premiums to the old shareholders who were bought out, and they continued as long as the market was willing to buy these new debt offerings at what appeared to be a favorable risk–return trade-off. The bottom fell out of the market in the last six months of 1989 due to a number of factors including a marked increase in defaults, government regulation against S&Ls holding junk bonds, and at least one highly publicized bankruptcy of a highly leveraged financial restructuring—Federated Department Stores.
In the early 1990s, the financial market was questioning the very survival of the junk bond market. The answer as to its survival was a resounding “yes,” as the amount of new issues soared to record annual levels of $40 billion in 1992, almost $80 billion in 1993, and in 1997 reached an impressive $119 billion. Coupled with plummeting default rates (under 2.0 percent each year in the 1993–97 period) and attractive returns in these years, the risk–return characteristics were extremely favorable.
The junk bond market in the late 1990s was a quieter one compared to that of the 1980s, but, in terms of growth and returns, it was healthier than ever before. While the low default rates in 1992–98 helped to fuel new investment funds and new issues, the market experienced its ups and downs in subsequent years. Indeed, default rates started to rise in 1999 and accelerated in 2000–2002. The latter year saw defaults reach record levels as the economy slipped into a recession and investors suffered from the excesses of lending in the late 1990s.
Since the mid-1990s, a “sister” high-yield debt market has developed in the private leveraged loan market. This low-quality market grew enormously in the United States and Europe in the 2005–2007 period and was at least 30 percent larger than the high-yield bond market in 2008. One of the main reasons for the recent growth and popularity of leveraged loans issued by non-investment grade companies was that the issuing bank could easily sell these loans into structured finance vehicles called collateralized loan obligations (CLOs). Usually these private, leveraged loan debt securities have registered lower default rates than high-yield bonds, but there were indications that this usual pattern was going to change due to its greater expansion and liberal terms in the years prior to 2008.
The market for leveraged financing rebounded quickly in 2003 and continued to prosper until the credit crisis of 2007–2008. With the “flight-to-quality” caused by the sub-prime mortgage market meltdown in the second half of 2007 and 2008, returns to investors in high-yield bonds and leveraged loans fell considerably, new issues dried up, Page 218and default rates increased from the unusually low-risk years that coincided with the leveraged excesses. Despite these highly volatile events and problems with liquidity, we were convinced that high-yield bonds, and their private debt companion, leveraged loans, would continue in the future to be a major source of corporate debt financing and a legitimate asset class for investors.
Indeed, the high yield bond market, as well as all risky bonds and common stocks, staged a remarkable recovery after the first quarter of 2009, and for the entire year 2009 the returns to high yield bond and leveraged loan investors was the highest in the almost 40 years of the modern era of leveraged finance markets. This amazing turnaround, despite near-record defaults in 2009, was remarkable in the speed and extent of the recovery, with returns of about 60% for high-yield bond investors. Impressive positive returns and record new issuance of highly leveraged financed projects and refinancing continued through 2013 for returns and through 2014 for new issuance. And, the market was incredibly accepting of relative higher yielding bonds and loans in the low interest rate environment. But, we are now (late 2014) concerned about another bubble building as the current benign credit cycle, with low default rates and highly risky new issuance, continues for the five years since the last market downturn. Perhaps the next few years will be quite volatile with rising default rates and lower recoveries and returns. But, as always, the leveraged finance market will continue to exist and possibly expand in the U.S. and especially in Europe.
Edward I. Altman is Max L. Heine Professor of Finance and Director of Credit and Debt Markets Research at the NYU Salomon Center at the Stern School of Business. He is widely recognized as one of the world’s leading experts on bankruptcy and credit analysis as well as the high-yield and distressed debt markets.
Concept Questions
7.4a Why might an income bond be attractive to a corporation with volatile cash flows? Can you think of a reason why income bonds are not more popular?
7.4b What do you think would be the effect of a put feature on a bond’s coupon? How about a convertibility feature? Why?
7.5 Bond Markets
Excel Master It!
Excel Master coverage online
Bonds are bought and sold in enormous quantities every day. You may be surprised to learn that the trading volume in bonds on a typical day is many, many times larger than the trading volume in stocks (by trading volume we simply mean the amount of money that changes hands). Here is a finance trivia question: What is the largest securities market in the world? Most people would guess the New York Stock Exchange. In fact, the largest securities market in the world in terms of trading volume is the U.S. Treasury market.
WORK THE WEB
Bond quotes have become more available with the rise of the Internet. One site where you can find current bond prices is finra-markets.morningstar.com. We went to the website and searched for bonds issued by Coca-Cola. Here is a look at part of what we found for one of the bonds:
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The bond has a coupon rate of 3.20 percent and matures on November 1, 2023. The last sale on this bond was at a price of 97.80 percent of par, which gives a yield to maturity of about 3.471 percent. Not only does the site provide the most recent price and yield information, but it also provides more important information about the bond, such as the credit rating, coupon date, call date, and call price. We’ll leave it up to you to have a look at the page and the rest of the information available there.
Questions
1. Go to this website and find the bond shown above. What is the credit rating on this bond? What was the size of the bond issue? What were the yield to maturity and price when the bond was issued?
2. If you search for Chevron bonds (CVX), you will find bonds for several companies listed. Why do you think Chevron has bonds issued with different corporate names?
Page 220HOW BONDS ARE BOUGHT AND SOLD
As we mentioned all the way back in Chapter 1, most trading in bonds takes place over the counter, or OTC. Recall that this means there is no particular place where buying and selling occur. Instead, dealers around the country (and around the world) stand ready to buy and sell. The various dealers are connected electronically.
One reason the bond markets are so big is that the number of bond issues far exceeds the number of stock issues. There are two reasons for this. First, a corporation would typically have only one common stock issue outstanding (there are exceptions to this that we discuss in our next chapter). However, a single large corporation could easily have a dozen or more note and bond issues outstanding. Beyond this, federal, state, and local borrowing is simply enormous. For example, even a small city would usually have a wide variety of notes and bonds outstanding, representing money borrowed to pay for things like roads, sewers, and schools. When you think about how many small cities there are in the United States, you begin to get the picture!
Because the bond market is almost entirely OTC, it has historically had little or no transparency. A financial market is transparent if it is possible to easily observe its prices and trading volume. On the New York Stock Exchange, for example, it is possible to see the price and quantity for every single transaction. In contrast, in the bond market, it is often not possible to observe either. Transactions are privately negotiated between parties, and there is little or no centralized reporting of transactions.
Although the total volume of trading in bonds far exceeds that in stocks, only a small fraction of the total bond issues that exist actually trade on a given day. This fact, combined with the lack of transparency in the bond market, means that getting up-to-date prices on individual bonds can be difficult or impossible, particularly for smaller corporate or municipal issues. Instead, a variety of sources of estimated prices exist and are commonly used.
BOND PRICE REPORTING
In 2002, transparency in the corporate bond market began to improve dramatically. Under new regulations, corporate bond dealers are now required to report trade information through what is known as the Trade Reporting and Compliance Engine (TRACE). Our nearby Work the Web box shows you how to get bond quotes.
To learn more about TRACE, visit www.finra.org.
TRACE bond quotes are available at www.finra-markets.morningstar.com. As shown in Figure 7.3, the Financial Industry Regulatory Authority (FINRA) provides a daily snapshot from TRACE by reporting the most active issues. The information shown is largely self-explanatory. Notice that the price of the Apple bond dropped about .406 percentage points on this day. What do you think happened to the yield to maturity for this bond? Figure 7.3 focuses on the most active bonds with investment grade ratings, but the most active high-yield and convertible bonds are also available on the website.
If you go to the website and click on a particular bond, you will get a lot of information about the bond, including the credit rating, the call schedule, original issue information, and trade information.
As we mentioned before, the U.S. Treasury market is the largest securities market in the world. As with bond markets in general, it is an OTC market, so there is limited transparency. However, unlike the situation with bond markets in general, trading in Treasury issues, particularly recently issued ones, is very heavy. Each day, representative prices for outstanding Treasury issues are reported.
Figure 7.4 shows a portion of the daily Treasury note and bond listings from the web-site wsj.com. Examine the entry that begins “5/15/2030.” Reading from left to right, the “5/15/2030” tells us that the bond’s maturity is May 15, 2030. The next column is the coupon rate, which is 6.250 percent for this bond. Treasury bonds all make semiannual payments and have a face value of $1,000, so this bond will pay $31.25 per six months until it matures.
The Federal Reserve Bank of St. Louis maintains dozens of online files containing macroeconomic data as well as rates on U.S. Treasury issues. Go to research.stlouisfed.org/fred2/
Page 221FIGURE 7.3 Sample TRACE Bond Quotations
The next two pieces of information are the bid and asked prices. In general, in any OTC or dealer market, the bid price represents what a dealer is willing to pay for a security, and the asked price (or just “ask” price) is what a dealer is willing to take for it. The difference between the two prices is called the bid–ask spread (or just “spread”), and it represents the dealer’s profit.
bid price The price a dealer is willing to pay for a security.
asked price The price a dealer is willing to take for a security.
bid–ask spread The difference between the bid price and the asked price.
Treasury prices are quoted as a percentage of face value. The bid price, or what a dealer is willing to pay, on the 5/15/2030 bond is 136.8359. With a $1,000 face value, this quote represents $1,368.359. The asked price, or the price at which the dealer is willing to sell the bond, is 136.9141, or $1,369.141.
The next number quoted is the change in the asked price from the previous day, measured as a percentage of face value, so this issue’s asked price fell by .7813 percent, or $7.813, in value from the previous day. Finally, the last number reported is the yield to maturity, based on the asked price. Notice that this is a premium bond because it sells for more than its face value. Not surprisingly, its yield to maturity (3.289 percent) is less than its coupon rate (6.25 percent).
The very last ordinary bond listed, the 2/15/2044, is often called the “bellwether” bond. This bond’s yield is the one that is usually reported in the evening news. So, for example, when you hear that long-term interest rates rose, what is really being said is that the yield on this bond went up (and its price went down).
If you examine the yields on the various issues in Figure 7.4, you will clearly see that they vary by maturity. Why this occurs and what it might mean is one of the things we discuss in our next section. Government (referred to as “sovereign”) bond yields also vary by country of origin. Below we show the 10-year bond yields of several countries. The yields vary according to default risks and foreign exchange risks (to be discussed later in the text).
Current and historical Treasury yield information is available at www.publicdebt.treas.gov.
Page 222FIGURE 7.4 Sample Wall Street Journal U.S. Treasury Note and Bond Prices
SOURCE: Table recreated with data from wsj.com March 7, 2014.
SOURCE: Data pulled from www.bloomberg.com, March 7, 2014.
Page 223A NOTE ABOUT BOND PRICE QUOTES
If you buy a bond between coupon payment dates, the price you pay is usually more than the price you are quoted. The reason is that standard convention in the bond market is to quote prices net of “accrued interest,” meaning that accrued interest is deducted to arrive at the quoted price. This quoted price is called the clean price. The price you actually pay, however, includes the accrued interest. This price is the dirty price, also known as the “full” or “invoice” price.
An example is the easiest way to understand these issues. Suppose you buy a bond with a 12 percent annual coupon, payable semiannually. You actually pay $1,080 for this bond, so $1,080 is the dirty, or invoice, price. Further, on the day you buy it, the next coupon is due in four months, so you are between coupon dates. Notice that the next coupon will be $60.
clean price The price of a bond net of accrued interest; this is the price that is typically quoted.
dirty price The price of a bond including accrued interest, also known as the full or invoice price. This is the price the buyer actually pays.
The accrued interest on a bond is calculated by taking the fraction of the coupon period that has passed, in this case two months out of six, and multiplying this fraction by the next coupon, $60. So, the accrued interest in this example is 2/6 × $60 = $20. The bond’s quoted price (that is, its clean price) would be $1,080 − $20 = $1,060.6
Concept Questions
7.5a Why do we say bond markets may have little or no transparency?
7.5b In general, what are bid and ask prices?
7.5c What is the difference between a bond’s clean price and dirty price?
7.6 Inflation and Interest Rates
So far, we haven’t considered the role of inflation in our various discussions of interest rates, yields, and returns. Because this is an important consideration, we consider the impact of inflation next.
REAL VERSUS NOMINAL RATES
In examining interest rates, or any other financial market rates such as discount rates, bond yields, rates of return, and required returns, it is often necessary to distinguish between real rates and nominal rates. Nominal rates are called “nominal” because they have not been adjusted for inflation. Real rates are rates that have been adjusted for inflation.
real rates Interest rates or rates of return that have been adjusted for inflation.
nominal rates Interest rates or rates of return that have not been adjusted for inflation.
To see the effect of inflation, suppose prices are currently rising by 5 percent per year. In other words, the rate of inflation is 5 percent. An investment is available that will be worth $115.50 in one year. It costs $100 today. Notice that with a present value of $100 and a future value in one year of $115.50, this investment has a 15.5 percent rate of return. In calculating this 15.5 percent return, we did not consider the effect of inflation, however, so this is the nominal return.
What is the impact of inflation here? To answer, suppose pizzas cost $5 apiece at the beginning of the year. With $100, we can buy 20 pizzas. Because the inflation rate is Page 2245 percent, pizzas will cost 5 percent more, or $5.25, at the end of the year. If we take the investment, how many pizzas can we buy at the end of the year? Measured in pizzas, what is the rate of return on this investment?
Our $115.50 from the investment will buy us $115.50/5.25 = 22 pizzas. This is up from 20 pizzas, so our pizza rate of return is 10 percent. What this illustrates is that even though the nominal return on our investment is 15.5 percent, our buying power goes up by only 10 percent because of inflation. Put another way, we are really only 10 percent richer. In this case, we say that the real return is 10 percent.
Alternatively, we can say that with 5 percent inflation, each of the $115.50 nominal dollars we get is worth 5 percent less in real terms, so the real dollar value of our investment in a year is:
$115.50/1.05 = $110
What we have done is to deflate the $115.50 by 5 percent. Because we give up $100 in current buying power to get the equivalent of $110, our real return is again 10 percent. Because we have removed the effect of future inflation here, this $110 is said to be measured in current dollars.
The difference between nominal and real rates is important and bears repeating:
The nominal rate on an investment is the percentage change in the number of dollars you have.
The real rate on an investment is the percentage change in how much you can buy with your dollars—in other words, the percentage change in your buying power.
THE FISHER EFFECT
Our discussion of real and nominal returns illustrates a relationship often called the Fisher effect (after the great economist Irving Fisher). Because investors are ultimately concerned with what they can buy with their money, they require compensation for inflation. Let R stand for the nominal rate and r stand for the real rate. The Fisher effect tells us that the relationship between nominal rates, real rates, and inflation can be written as:
Fisher effect The relationship between nominal returns, real returns, and inflation.
where h is the inflation rate.
In the preceding example, the nominal rate was 15.50 percent and the inflation rate was 5 percent. What was the real rate? We can determine it by plugging in these numbers:
This real rate is the same as we found before. If we take another look at the Fisher effect, we can rearrange things a little as follows:
What this tells us is that the nominal rate has three components. First, there is the real rate on the investment, r. Next, there is the compensation for the decrease in the value of the Page 225money originally invested because of inflation, h. The third component represents compensation for the fact that the dollars earned on the investment are also worth less because of inflation.
This third component is usually small, so it is often dropped. The nominal rate is then approximately equal to the real rate plus the inflation rate:
EXAMPLE 7.5 The Fisher Effect
If investors require a 10 percent real rate of return, and the inflation rate is 8 percent, what must be the approximate nominal rate? The exact nominal rate?
The nominal rate is approximately equal to the sum of the real rate and the inflation rate: 10% + 8% = 18%. From the Fisher effect, we have:
Therefore, the nominal rate will actually be closer to 19 percent.
It is important to note that financial rates, such as interest rates, discount rates, and rates of return, are almost always quoted in nominal terms. To remind you of this, we will henceforth use the symbol R instead of r in most of our discussions about such rates.
INFLATION AND PRESENT VALUES
One question that often comes up is the effect of inflation on present value calculations. The basic principle is simple: Either discount nominal cash flows at a nominal rate or discount real cash flows at a real rate. As long as you are consistent, you will get the same answer.
To illustrate, suppose you want to withdraw money each year for the next three years, and you want each withdrawal to have $25,000 worth of purchasing power as measured in current dollars. If the inflation rate is 4 percent per year, then the withdrawals will simply have to increase by 4 percent each year to compensate. The withdrawals each year will thus be:
What is the present value of these cash flows if the appropriate nominal discount rate is 10 percent? This is a standard calculation, and the answer is:
PV = $26,000/1.10 + $27,040/1.102 + $28,121.60/1.103 = $67,111.65
Notice that we discounted the nominal cash flows at a nominal rate.
To calculate the present value using real cash flows, we need the real discount rate.
Using the Fisher equation, the real discount rate is:
Page 226By design, the real cash flows are an annuity of $25,000 per year. So, the present value in real terms is:
PV = $25,000[1 − (1/1.05773)]/.0577 = $67,111.65
Thus, we get exactly the same answer (after allowing for a small rounding error in the real rate). Of course, you could also use the growing annuity equation we discussed in the previous chapter. The withdrawals are increasing at 4 percent per year; so using the growing annuity formula, the present value is:
This is exactly the same present value we calculated before.
Concept Questions
7.6a What is the difference between a nominal and a real return? Which is more important to a typical investor?
7.6b What is the Fisher effect?
7.7 Determinants of Bond Yields
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We are now in a position to discuss the determinants of a bond’s yield. As we will see, the yield on any particular bond reflects a variety of factors, some common to all bonds and some specific to the issue under consideration.
THE TERM STRUCTURE OF INTEREST RATES
At any point in time, short-term and long-term interest rates will generally be different. Sometimes short-term rates are higher, sometimes lower. Figure 7.5 gives us a long-range perspective on this by showing over two centuries of short- and long-term interest rates. As shown, through time, the difference between short- and long-term rates has ranged from essentially zero to up to several percentage points, both positive and negative.
The relationship between short- and long-term interest rates is known as the term structure of interest rates. To be a little more precise, the term structure of interest rates tells us what nominal interest rates are on default-free, pure discount bonds of all maturities. These rates are, in essence, “pure” interest rates because they involve no risk of default and a single, lump sum future payment. In other words, the term structure tells us the pure time value of money for different lengths of time.
term structure of interest rates The relationship between nominal interest rates on default-free, pure discount securities and time to maturity; that is, the pure time value of money.
When long-term rates are higher than short-term rates, we say that the term structure is upward sloping; when short-term rates are higher, we say it is downward sloping. The term structure can also be “humped.” When this occurs, it is usually because rates increase at first, but then begin to decline as we look at longer- and longer-term rates. The most common shape of the term structure, particularly in modern times, is upward sloping; but the degree of steepness has varied quite a bit.
What determines the shape of the term structure? There are three basic components. The first two are the ones we discussed in our previous section: the real rate of interest and the rate of inflation. The real rate of interest is the compensation investors demand for forgoing the use of their money. You can think of it as the pure time value of money after adjusting for the effects of inflation.
Page 227FIGURE 7.5 U.S. Interest Rates: 1800–2013
SOURCE: Jeremy J. Siegel, Stocks for the Long Run, 4th edition, © McGraw-Hill, 2008, updated by the authors.
The real rate of interest is the basic component underlying every interest rate, regardless of the time to maturity. When the real rate is high, all interest rates will tend to be higher, and vice versa. Thus, the real rate doesn’t really determine the shape of the term structure; instead, it mostly influences the overall level of interest rates.
In contrast, the prospect of future inflation strongly influences the shape of the term structure. Investors thinking about lending money for various lengths of time recognize that future inflation erodes the value of the dollars that will be returned. As a result, investors demand compensation for this loss in the form of higher nominal rates. This extra compensation is called the inflation premium.
inflation premium The portion of a nominal interest rate that represents compensation for expected future inflation.
If investors believe the rate of inflation will be higher in the future, then long-term nominal interest rates will tend to be higher than short-term rates. Thus, an upward-sloping term structure may reflect anticipated increases in inflation. Similarly, a downward-sloping term structure probably reflects the belief that inflation will be falling in the future.
The third, and last, component of the term structure has to do with interest rate risk. As we discussed earlier in the chapter, longer-term bonds have much greater risk of loss resulting from changes in interest rates than do shorter-term bonds. Investors recognize this risk, and they demand extra compensation in the form of higher rates for bearing it. This extra compensation is called the interest rate risk premium. The longer is the term to maturity, the greater is the interest rate risk, so the interest rate risk premium increases with maturity. However, as we discussed earlier, interest rate risk increases at a decreasing rate, so the interest rate risk premium does as well.7
interest rate risk premium The compensation investors demand for bearing interest rate risk.
Page 228FIGURE 7.6 The Term Structure of Interest Rates
Putting the pieces together, we see that the term structure reflects the combined effect of the real rate of interest, the inflation premium, and the interest rate risk premium. Figure 7.6 shows how these can interact to produce an upward-sloping term structure (in the top part of Figure 7.6) or a downward-sloping term structure (in the bottom part).
In the top part of Figure 7.6, notice how the rate of inflation is expected to rise gradually. At the same time, the interest rate risk premium increases at a decreasing rate, so the combined effect is to produce a pronounced upward-sloping term structure. In the bottom part of Figure 7.6, the rate of inflation is expected to fall in the future, and the expected decline is enough to offset the interest rate risk premium and produce a downward-sloping term structure. Notice that if the rate of inflation was expected to decline by only a small amount, we could still get an upward-sloping term structure because of the interest rate risk premium.
We assumed in drawing Figure 7.6 that the real rate would remain the same. Actually, expected future real rates could be larger or smaller than the current real rate. Also, for simplicity, we used straight lines to show expected future inflation rates as rising or declining, but they do not necessarily have to look like this. They could, for example, rise and then fall, leading to a humped yield curve.
Page 229FIGURE 7.7 The Treasury Yield Curve: March 2014
SOURCE: Data pulled from wsj.com, March 7, 2014.
BOND YIELDS AND THE YIELD CURVE: PUTTING IT ALL TOGETHER
Going back to Figure 7.4, recall that we saw that the yields on Treasury notes and bonds of different maturities are not the same. Each day, in addition to the Treasury prices and yields shown in Figure 7.4, The Wall Street Journal provides a plot of Treasury yields relative to maturity. This plot is called the Treasury yield curve (or just the yield curve). Figure 7.7 shows the yield curve as of March 2014.
Treasury yield curve A plot of the yields on Treasury notes and bonds relative to maturity.
As you probably now suspect, the shape of the yield curve reflects the term structure of interest rates. In fact, the Treasury yield curve and the term structure of interest rates are almost the same thing. The only difference is that the term structure is based on pure discount bonds, whereas the yield curve is based on coupon bond yields. As a result, Treasury yields depend on the three components that underlie the term structure—the real rate, expected future inflation, and the interest rate risk premium.
Treasury notes and bonds have three important features that we need to remind you of: They are default-free, they are taxable, and they are highly liquid. This is not true of bonds in general, so we need to examine what additional factors come into play when we look at bonds issued by corporations or municipalities.
Online yield curve information is available at www.bloomberg.com/markets.
The first thing to consider is credit risk—that is, the possibility of default. Investors recognize that issuers other than the Treasury may or may not make all the promised payments on a bond, so they demand a higher yield as compensation for this risk. This extra compensation is called the default risk premium. Earlier in the chapter, we saw how bonds were rated based on their credit risk. What you will find if you start looking at bonds of different ratings is that lower-rated bonds have higher yields.
default risk premium The portion of a nominal interest rate or bond yield that represents compensation for the possibility of default.
An important thing to recognize about a bond’s yield is that it is calculated assuming that all the promised payments will be made. As a result, it is really a promised yield, and it may or may not be what you will earn. In particular, if the issuer defaults, your actual yield will be lower— probably much lower. This fact is particularly important when it comes to junk bonds. Thanks to a clever bit of marketing, such bonds are now commonly called high-yield bonds, which has a much nicer ring to it; but now you recognize that these are really high promised yield bonds.
To see how the yield curve has changed over time, check out the “living yield curve” at www.marketwatch.com.
Page 230Next, recall that we discussed earlier how municipal bonds are free from most taxes and, as a result, have much lower yields than taxable bonds. Investors demand the extra yield on a taxable bond as compensation for the unfavorable tax treatment. This extra compensation is the taxability premium.
taxability premium The portion of a nominal interest rate or bond yield that represents compensation for unfavorable tax status.
Finally, bonds have varying degrees of liquidity. As we discussed earlier, there are an enormous number of bond issues, most of which do not trade regularly. As a result, if you wanted to sell quickly, you would probably not get as good a price as you could otherwise. Investors prefer liquid assets to illiquid ones, so they demand a liquidity premium on top of all the other premiums we have discussed. As a result, all else being the same, less liquid bonds will have higher yields than more liquid bonds.
liquidity premium The portion of a nominal interest rate or bond yield that represents compensation for lack of liquidity.
CONCLUSION
If we combine all of the things we have discussed regarding bond yields, we find that bond yields represent the combined effect of no fewer than six things. The first is the real rate of interest. On top of the real rate are five premiums representing compensation for (1) expected future inflation, (2) interest rate risk, (3) default risk, (4) taxability, and (5) lack of liquidity. As a result, determining the appropriate yield on a bond requires careful analysis of each of these effects.
Concept Questions
7.7a What is the term structure of interest rates? What determines its shape?
7.7b What is the Treasury yield curve?
7.7c What six components make up a bond’s yield?
7.8 Summary and Conclusions
This chapter has explored bonds, bond yields, and interest rates:
1. Determining bond prices and yields is an application of basic discounted cash flow principles.
2. Bond values move in the direction opposite that of interest rates, leading to potential gains or losses for bond investors.
3. Bonds have a variety of features spelled out in a document called the indenture.
4. Bonds are rated based on their default risk. Some bonds, such as Treasury bonds, have no risk of default, whereas so-called junk bonds have substantial default risk.
5. A wide variety of bonds exist, many of which contain exotic or unusual features.
6. Almost all bond trading is OTC, with little or no market transparency in many cases. As a result, bond price and volume information can be difficult to find for some types of bonds.
7. Bond yields and interest rates reflect the effect of six different things: the real interest rate and five premiums that investors demand as compensation for inflation, interest rate risk, default risk, taxability, and lack of liquidity.
In closing, we note that bonds are a vital source of financing to governments and corporations of all types. Bond prices and yields are a rich subject, and our one chapter, necessarily, touches on only the most important concepts and ideas. There is a great deal more we could say, but, instead, we will move on to stocks in our next chapter.
Page 231
CONNECT TO FINANCE
Do you use Connect Finance to practice what you learned? If you don’t, you should – we can help you master the topics presented in this material. Log on to connect.mheducation.com to learn more!
Can you answer the following Connect Quiz questions?
| Section 7.1 | An 8 percent, semiannual coupon bond has a face value of $1,000 and a current market value of $1,030. What is the current yield? |
| Section 7.3 | The 10-year bonds issued by KP Enterprises were rated as BBB and Baa last year. This year, the bonds are rated as CC and Ca. What term best applies to these bonds today? |
| Section 7.4 | What type of bonds is most apt to have a “collar”? |
| Section 7.6 | Kate wants to earn a 4 percent real rate of return. To do this, what nominal rate must she earn if the inflation rate is 3.6 percent? |
| Section 7.7 | The term structure of interest rates is based on what type of bonds? |
CHAPTER REVIEW AND SELF-TEST PROBLEMS
7.1 Bond Values A Microgates Industries bond has a 10 percent coupon rate and a $1,000 face value. Interest is paid semiannually, and the bond has 20 years to maturity. If investors require a 12 percent yield, what is the bond’s value? What is the effective annual yield on the bond?
7.2 Bond Yields A Macrohard Corp. bond carries an 8 percent coupon, paid semiannually. The par value is $1,000, and the bond matures in six years. If the bond currently sells for $911.37, what is its yield to maturity? What is the effective annual yield?
ANSWERS TO CHAPTER REVIEW AND SELF-TEST PROBLEMS
7.1 Because the bond has a 10 percent coupon yield and investors require a 12 percent return, we know that the bond must sell at a discount. Notice that, because the bond pays interest semiannually, the coupons amount to $100/2 = $50 every six months. The required yield is 12%/2 = 6% every six months. Finally, the bond matures in 20 years, so there are a total of 40 six-month periods.
The bond’s value is thus equal to the present value of $50 every six months for the next 40 six-month periods plus the present value of the $1,000 face amount:
Notice that we discounted the $1,000 back 40 periods at 6 percent per period, rather than 20 years at 12 percent. The reason is that the effective annual yield on the bond is 1.062 − 1 = 12.36%, not 12 percent. We thus could have used 12.36 percent per year for 20 years when we calculated the present value of the $1,000 face amount, and the answer would have been the same.
Page 2327.2 The present value of the bond’s cash flows is its current price, $911.37. The coupon is $40 every six months for 12 periods. The face value is $1,000. So the bond’s yield is the unknown discount rate in the following:
$911.37 = $40 × [1 − 1/(1 + r)12]/r + 1,000/(1 + r)12
The bond sells at a discount. Because the coupon rate is 8 percent, the yield must be something in excess of that.
If we were to solve this by trial and error, we might try 12 percent (or 6 percent per six months):
This is less than the actual value, so our discount rate is too high. We now know that the yield is somewhere between 8 and 12 percent. With further trial and error (or a little machine assistance), the yield works out to be 10 percent, or 5 percent every six months.
By convention, the bond’s yield to maturity would be quoted as 2 × 5% = 10%. The effective yield is thus 1.052 − 1 = 10.25%.
CONCEPTS REVIEW AND CRITICAL THINKING QUESTIONS
1. Treasury Bonds [LO1] Is it true that a U.S. Treasury security is risk-free?
2. Interest Rate Risk [LO2] Which has greater interest rate risk, a 30-year Treasury bond or a 30-year BB corporate bond?
3. Treasury Pricing [LO1] With regard to bid and ask prices on a Treasury bond, is it possible for the bid price to be higher? Why or why not?
4. Yield to Maturity [LO2] Treasury bid and ask quotes are sometimes given in terms of yields, so there would be a bid yield and an ask yield. Which do you think would be larger? Explain.
5. Call Provisions [LO1] A company is contemplating a long-term bond issue. It is debating whether to include a call provision. What are the benefits to the company from including a call provision? What are the costs? How do these answers change for a put provision?
6. Coupon Rate [LO1] How does a bond issuer decide on the appropriate coupon rate to set on its bonds? Explain the difference between the coupon rate and the required return on a bond.
7. Real and Nominal Returns [LO4] Are there any circumstances under which an investor might be more concerned about the nominal return on an investment than the real return?
8. Bond Ratings [LO3] Companies pay rating agencies such as Moody’s and S&P to rate their bonds, and the costs can be substantial. However, companies are not required to have their bonds rated; doing so is strictly voluntary. Why do you think they do it?
9. Bond Ratings [LO3] Often, junk bonds are not rated. Why?
10. Term Structure [LO5] What is the difference between the term structure of interest rates and the yield curve?
11. Crossover Bonds [LO3] Looking back at the crossover bonds we discussed in the chapter, why do you think split ratings such as these occur?
Page 23312. Municipal Bonds [LO1] Why is it that municipal bonds are not taxed at the federal level, but are taxable across state lines? Why are U.S. Treasury bonds not taxable at the state level? (You may need to dust off the history books for this one.)
13. Bond Market [LO1] What are the implications for bond investors of the lack of transparency in the bond market?
14. Rating Agencies [LO3] A controversy erupted regarding bond-rating agencies when some agencies began to provide unsolicited bond ratings. Why do you think this is controversial?
15. Bonds as Equity [LO1] The 100-year bonds we discussed in the chapter have something in common with junk bonds. Critics charge that, in both cases, the issuers are really selling equity in disguise. What are the issues here? Why would a company want to sell “equity in disguise”?
BASIC
(Questions 1–17)
1. Interpreting Bond Yields [LO1] Is the yield to maturity on a bond the same thing as the required return? Is YTM the same thing as the coupon rate? Suppose today a 10 percent coupon bond sells at par. Two years from now, the required return on the same bond is 8 percent. What is the coupon rate on the bond then? The YTM?
2. Interpreting Bond Yields [LO2] Suppose you buy a 7 percent coupon, 20-year bond today when it’s first issued. If interest rates suddenly rise to 15 percent, what happens to the value of your bond? Why?
3. Valuing Bonds [LO2] Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of €1,000, 23 years to maturity, and a coupon rate of 5.8 percent paid annually. If the yield to maturity is 4.7 percent, what is the current price of the bond?
4 . Bond Yields [LO2] A Japanese company has a bond outstanding that sells for 91.53 percent of its ¥100,000 par value. The bond has a coupon rate of 3.4 percent paid annually and matures in 16 years. What is the yield to maturity of this bond?
5. Coupon Rates [LO2] Essary Enterprises has bonds on the market making annual payments, with eight years to maturity, a par value of $1,000, and selling for $948. At this price, the bonds yield 5.9 percent. What must the coupon rate be on the bonds?
6. Bond Prices [LO2] Sqeekers Co. issued 15-year bonds a year ago at a coupon rate of 4.1 percent. The bonds make semiannual payments and have a par value of $1,000. If the YTM on these bonds is 4.5 percent, what is the current bond price?
7. Bond Yields [LO2] Heginbotham Corp. issued 20-year bonds two years ago at a coupon rate of 5.3 percent. The bonds make semiannual payments. If these bonds currently sell for 105 percent of par value, what is the YTM?
8 . Coupon Rates [LO2] DMA Corporation has bonds on the market with 14.5 years to maturity, a YTM of 5.3 percent, a par value of $1,000, and a current price of $965. The bonds make semiannual payments. What must the coupon rate be on these bonds?
9. Zero Coupon Bonds [LO2] You find a zero coupon bond with a par value of $10,000 and 17 years to maturity. If the yield to maturity on this bond is 4.9 percent, what is the price of the bond? Assume semiannual compounding periods.
10. Valuing Bonds [LO2] Yan Yan Corp. has a $2,000 par value bond outstanding with a coupon rate of 4.9 percent paid semiannually and 13 years to maturity. The yield to maturity of the bond is 3.8 percent. What is the price of the bond?
Page 23411. Valuing Bonds [LO2] Union Local School District has a bond outstanding with a coupon rate of 3.7 percent paid semiannually and 16 years to maturity. The yield to maturity on this bond is 3.9 percent, and the bond has a par value of $5,000. What is the price of the bond?
12 . Calculating Real Rates of Return [LO4] If Treasury bills are currently paying 5.1 percent and the inflation rate is 2.2 percent, what is the approximate real rate of interest? The exact real rate?
13. Inflation and Nominal Returns [LO4] Suppose the real rate is 1.9 percent and the inflation rate is 3.1 percent. What rate would you expect to see on a Treasury bill?
14. Nominal and Real Returns [LO4] An investment offers a total return of 11.5 percent over the coming year. Janice Yellen thinks the total real return on this investment will be only 9 percent. What does Janice believe the inflation rate will be over the next year?
15. Nominal versus Real Returns [LO4] Say you own an asset that had a total return last year of 11.65 percent. If the inflation rate last year was 3.4 percent, what was your real return?
16. Using Treasury Quotes [LO2] Locate the Treasury issue in Figure 7.4 maturing in February 2038. What is its coupon rate? What is its bid price? What was the previous day’s asked price? Assume a par value of $10,000.
17. Using Treasury Quotes [LO2] Locate the Treasury bond in Figure 7.4 maturing in August 2039. Is this a premium or a discount bond? What is its current yield? What is its yield to maturity? What is the bid–ask spread in dollars? Assume a par value of $10,000.
INTERMEDIATE
(Questions 18–31)
18. Bond Price Movements [LO2] Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 8.5 percent, has a YTM of 7 percent, and has 13 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 7 percent, has a YTM of 8.5 percent, and also has 13 years to maturity. What is the price of each bond today? If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In three years? In eight years? In 12 years? In 13 years? What’s going on here? Illustrate your answers by graphing bond prices versus time to maturity.
19. Interest Rate Risk [LO2] Both Bond Sam and Bond Dave have 6.5 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 3 years to maturity, whereas Bond Dave has 20 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam? Of Bond Dave? If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Sam be then? Of Bond Dave? Illustrate your answers by graphing bond prices versus YTM. What does this problem tell you about the interest rate risk of longer-term bonds?
20. Interest Rate Risk [LO2] Bond J has a coupon rate of 3 percent. Bond K has a coupon rate of 9 percent. Both bonds have 19 years to maturity, make semiannual payments, and have a YTM of 6 percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? What if rates suddenly fall by 2 percent instead? What does this problem tell you about the interest rate risk of lower-coupon bonds?
21. Bond Yields [LO2] Bourdon Software has 6.4 percent coupon bonds on the market with 18 years to maturity. The bonds make semiannual payments and currently sell for 106.8 percent of par. What is the current yield on the bonds? The YTM? The effective annual yield?
Page 23522. Bond Yields [LO2] Chamberlain Co. wants to issue new 20-year bonds for some much-needed expansion projects. The company currently has 7 percent coupon bonds on the market that sell for $1,083, make semiannual payments, and mature in 20 years. What coupon rate should the company set on its new bonds if it wants them to sell at par?
23. Accrued Interest [LO2] You purchase a bond with an invoice price of $1,035. The bond has a coupon rate of 5.9 percent, and there are four months to the next semiannual coupon date. What is the clean price of the bond?
24. Accrued Interest [LO2] You purchase a bond with a coupon rate of 4.7 percent and a clean price of $951. If the next semiannual coupon payment is due in two months, what is the invoice price?
25. Finding the Bond Maturity [LO2] Shinoda Corp. has 8 percent coupon bonds making annual payments with a YTM of 7.2 percent. The current yield on these bonds is 7.55 percent. How many years do these bonds have left until they mature?
26 . Using Bond Quotes [LO2] Suppose the following bond quotes for IOU Corporation appear in the financial page of today’s newspaper. Assume the bond has a face value of $2,000 and the current date is April 19, 2015. What is the yield to maturity of the bond? What is the current yield?
27. Bond Prices versus Yields [LO2]
a. What is the relationship between the price of a bond and its YTM?
b. Explain why some bonds sell at a premium over par value while other bonds sell at a discount. What do you know about the relationship between the coupon rate and the YTM for premium bonds? What about for discount bonds? For bonds selling at par value?
c. What is the relationship between the current yield and YTM for premium bonds? For discount bonds? For bonds selling at par value?
28 . Interest on Zeroes [LO2] Imagination Dragons Corporation needs to raise funds to finance a plant expansion, and it has decided to issue 25-year zero coupon bonds with a par value of $1,000 each to raise the money. The required return on the bonds will be 5.8 percent. Assume semiannual compounding periods.
a. What will these bonds sell for at issuance?
b. Using the IRS amortization rule, what interest deduction can the company take on these bonds in the first year? In the last year?
c. Repeat part (b) using the straight-line method for the interest deduction.
d. Based on your answers in (b) and (c), which interest deduction method would the company prefer? Why?
29. Zero Coupon Bonds [LO2] Suppose your company needs to raise $47 million and you want to issue 20-year bonds for this purpose. Assume the required return on your bond issue will be 6 percent, and you’re evaluating two issue alternatives: a semiannual coupon bond with a coupon rate of 6 percent and a zero coupon bond. Your company’s tax rate is 35 percent. Both bonds will have a par value of $1,000.
a. How many of the coupon bonds would you need to issue to raise the $47 million? How many of the zeroes would you need to issue?
Page 236b. In 20 years, what will your company’s repayment be if you issue the coupon bonds? What if you issue the zeroes?
c. Based on your answers in (a) and (b), why would you ever want to issue the zeroes? To answer, calculate the firm’s aftertax cash outflows for the first year under the two different scenarios. Assume the IRS amortization rules apply for the zero coupon bonds.
30. Finding the Maturity [LO2] You’ve just found a 10 percent coupon bond on the market that sells for par value. What is the maturity on this bond?
31. Real Cash Flows [LO4] You want to have $2.6 million in real dollars in an account when you retire in 40 years. The nominal return on your investment is 10.8 percent and the inflation rate is 3.7 percent. What real amount must you deposit each year to achieve your goal?
CHALLENGE
(Questions 32–38)
32. Components of Bond Returns [LO2] Bond P is a premium bond with a coupon rate of 10 percent. Bond D has a coupon rate of 4 percent and is currently selling at a discount. Both bonds make annual payments, have a YTM of 7 percent, and have 10 years to maturity. What is the current yield for bond P? For bond D? If interest rates remain unchanged, what is the expected capital gains yield over the next year for bond P? For bond D? Explain your answers and the interrelationships among the various types of yields.
33. Holding Period Yield [LO2] The YTM on a bond is the interest rate you earn on your investment if interest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY).
a. Suppose that today you buy a bond with an annual coupon rate of 7 percent for $1,060. The bond has 17 years to maturity. What rate of return do you expect to earn on your investment? Assume a par value of $1,000.
b. Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. What price will your bond sell for? What is the HPY on your investment? Compare this yield to the YTM when you first bought the bond. Why are they different?
34. Valuing Bonds [LO2] Jallouk Corporation has two different bonds currently outstanding. Bond M has a face value of $20,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $1,100 every six months over the subsequent eight years, and finally pays $1,400 every six months over the last six years. Bond N also has a face value of $20,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. If the required return on both these bonds is 5.6 percent compounded semiannually, what is the current price of bond M? Of bond N?
35. Valuing the Call Feature [LO2] At one point, certain U.S. Treasury bonds were callable. Consider the prices in the following three Treasury issues as of May 15, 2014:
The bond in the middle is callable in February 2015. What is the implied value of the call feature? Assume a par value of $1,000. (Hint: Is there a way to combine the two noncallable issues to create an issue that has the same coupon as the callable bond?)
Page 23736. Treasury Bonds [LO2] The following Treasury bond quote appeared in The Wall Street Journal on May 11, 2004:
Why would anyone buy this Treasury bond with a negative yield to maturity? How is this possible?
37. Real Cash Flows [LO4] When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh flowers on her grave every Sunday as long as he lived. The week after she died in 1962, a bunch of fresh flowers that the former baseball player thought appropriate for the star cost about $7. Based on actuarial tables, “Joltin’ Joe” could expect to live for 30 years after the actress died. Assume that the EAR is 7.3 percent. Also, assume that the price of the flowers will increase at 3.7 percent per year, when expressed as an EAR. Assuming that each year has exactly 52 weeks, what is the present value of this commitment? Joe began purchasing flowers the week after Marilyn died.
38. Real Cash Flows [LO4] You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $800 per month in a stock account in real dollars and $400 per month in a bond account in real dollars. The effective annual return of the stock account is expected to be 11 percent, and the bond account will earn 7 percent. When you retire, you will combine your money into an account with a an effective return of 9 percent. The returns are stated in nominal terms. The inflation rate over this period is expected to be 4 percent. How much can you withdraw each month from your account in real terms assuming a 25-year withdrawal period? What is the nominal dollar amount of your last withdrawal?
EXCEL MASTER IT! PROBLEM
Companies often buy bonds to meet a future liability or cash outlay. Such an investment is called a dedicated portfolio because the proceeds of the portfolio are dedicated to the future liability. In such a case, the portfolio is subject to reinvestment risk. Reinvestment risk occurs because the company will be reinvesting the coupon payments it receives. If the YTM on similar bonds falls, these coupon payments will be reinvested at a lower interest rate, which will result in a portfolio value that is lower than desired at maturity. Of course, if interest rates increase, the portfolio value at maturity will be higher than needed.
Suppose Ice Cubes, Inc., has the following liability due in five years. The company is going to buy five-year bonds today to meet the future obligation. The liability and current YTM are below.
a. At the current YTM, what is the face value of the bonds the company has to purchase today to meet its future obligation? Assume that the bonds in the relevant range will have the same coupon rate as the current YTM and these bonds make semiannual coupon payments.
b. Assume that the interest rates remain constant for the next five years. Thus, when the company reinvests the coupon payments, it will reinvest at the current YTM. What is the value of the portfolio in five years?
Page 238c. Assume that immediately after the company purchases the bonds, interest rates either rise or fall by one percent. What is the value of the portfolio in five years under these circumstances?
One way to eliminate reinvestment risk is called immunization. Rather than buying bonds with the same maturity as the liability, the company instead buys bonds with the same duration as the liability. If you think about the dedicated portfolio, if the interest rate falls, the future value of the reinvested coupon payments decreases. However, as interest rates fall, the price of the bond increases. These effects offset each other in an immunized portfolio.
Another advantage of using duration to immunize a portfolio is that the duration of a portfolio is simply the weighted average of the duration of the assets in the portfolio. In other words, to find the duration of a portfolio, you simply take the weight of each asset multiplied by its duration and then sum the results.
d. What is the duration of the liability for Ice Cubes, Inc.?
e. Suppose the two bonds shown below are the only bonds available to immunize the liability. What face amount of each bond will the company need to purchase to immunize the portfolio?
MINICASE
Financing S&S Air’s Expansion Plans with a Bond Issue
Mark Sexton and Todd Story, the owners of S&S Air, have decided to expand their operations. They instructed their newly hired financial analyst, Chris Guthrie, to enlist an underwriter to help sell $35 million in new 10-year bonds to finance construction. Chris has entered into discussions with Renata Harper, an underwriter from the firm of Raines and Warren, about which bond features S&S Air should consider and what coupon rate the issue will likely have.
Although Chris is aware of the bond features, he is uncertain about the costs and benefits of some features, so he isn’t sure how each feature would affect the coupon rate of the bond issue. You are Renata’s assistant, and she has asked you to prepare a memo to Chris describing the effect of each of the following bond features on the coupon rate of the bond. She would also like you to list any advantages or disadvantages of each feature.
QUESTIONS
1. The security of the bond—that is, whether the bond has collateral.
2. The seniority of the bond.
3. The presence of a sinking fund.
4. A call provision with specified call dates and call prices.
5. A deferred call accompanying the call provision.
6. A make-whole call provision.
7. Any positive covenants. Also, discuss several possible positive covenants S&S Air might consider.
8. Any negative covenants. Also, discuss several possible negative covenants S&S Air might consider.
9. A conversion feature (note that S&S Air is not a publicly traded company).
10. A floating-rate coupon.
__________
1There is no universally agreed-upon distinction between short-term and long-term debt. In addition, people often refer to intermediate-term debt, which has a maturity of more than 1 year and less than 3 to 5, or even 10, years.
2The word funding is part of the jargon of finance. It generally refers to the long term. Thus, a firm planning to “fund” its debt requirements may be replacing short-term debt with long-term debt.
3The words loan agreement or loan contract are usually used for privately placed debt and term loans.
4Real property includes land and things “affixed thereto.” It does not include cash or inventories.
5A bond issued with a very low coupon rate (as opposed to a zero coupon rate) is an original-issue discount (OID) bond.
6The way accrued interest is calculated actually depends on the type of bond being quoted—for example, Treasury or corporate. The difference has to do with exactly how the fractional coupon period is calculated. In our example here, we implicitly treated the months as having exactly the same length (30 days each, 360 days in a year), which is consistent with the way corporate bonds are quoted. In contrast, for Treasury bonds, actual day counts are used.
7In days of old, the interest rate risk premium was called a “liquidity” premium. Today, the term liquidity premium has an altogether different meaning, which we explore in our next section. Also, the interest rate risk premium is some