Please continue with the East Coast Yacht case. This week we will discuss the c

Please continue with the East Coast Yacht case. This week we will discuss the closing case at the end of Chapter 5.
Please read the case and answer questions #1, #2, #3 & #4.

Please review example 5.1 in your book to help with question #2 &# 3.
NB: Please add calculations with your analysis.
Interest Rates and Bond Valuation CHP. 5.
Generally, when you make an investment, you expect that you will get back more money in the future than you invested today. But in January 2019, that wasn’t the case for many bond investors. The yields on 2-year and 5-year German government bonds were about negative .63 percent and negative .39 percent, respectively. The yields on 2-year and 5-year Japanese government bonds were slightly higher, at negative .15 percent and negative .16 percent, respectively. That month, over $11 trillion of government debt worldwide carried a negative yield. In fact, during 2016, the amount of debt worldwide with a negative yield reached a record $13.4 trillion! And negative yields were not restricted to government bonds, as at one point the yield on bonds issued by chocolate maker Nestlé and Deutsche Bank AG both traded with negative yields.
This chapter takes what we have learned about the time value of money and shows how it can be used to value one of the most common of all financial assets, a bond. It then discusses bond features, bond types, and the operation of the bond market. What we will see is that bond prices depend critically on interest rates, so we will go on to discuss some very fundamental issues regarding interest rates. Clearly, interest rates are important to everybody because they underlie what businesses of all types—small and large—must pay to borrow money.
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Our goal in this chapter is to introduce you to bonds. We begin by showing how the techniques we developed in Chapter 4 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 out the chapter with an examination of interest rates and their behavior.
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
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. page 130As 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, or 12 percent, the bond has a 12 percent coupon rate.
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.
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.
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. (Most, but not all, straight coupon bonds in the United States pay interest semiannually. Practice differs around the world.) 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 5.1. What would this bond sell for?
Cash Flows for Xanth Co. Bond
As shown, the Xanth bond has an annual coupon of $80 and a face, or par, value of $1,000 paid at maturity in 10 years.
As illustrated in Figure 5.1, 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:
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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:
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 that a year has gone by. The Xanth bond now has 9 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 9 years at 10 percent is:
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:
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 only pays 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.
A good bond site to visit is, which has loads of useful information.
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.
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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 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.
Online bond calculators are available at; interest rate information is available at and
This case is 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:
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 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 as we calculated.
Based 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:
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.
Learn more about bonds at
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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 that 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 7-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 = 1.082 −1 = .1664, or 16.64%
The effective yield, therefore, is 16.64 percent.
Interest 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:
All other things being equal, the longer the time to maturity, the greater the interest rate risk.
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 5.2. 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. We assume coupons are paid semiannually. 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 1-year bond’s price is relatively insensitive to interest rate changes.
Interest Rate Risk and Time to Maturity
Intuitively, we can see that the reason that shorter-term bonds have less interest rate sensitivity is that 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 page 134the 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.
The 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 while the 30-year bond has somewhat greater interest rate risk because it has a longer maturity, 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 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 have led to the issuance of bonds with much longer terms. In the 1990s, Walt Disney issued “Sleeping Beauty” bonds with a 100-year maturity. Similarly, BellSouth, 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. Before these issues, it appears the last time 100-year bonds were issued was in May 1954, by the Chicago page 135and Eastern Railroad. And low interest rates in recent years have led to more 100-year bonds. Of course, there are even longer term bonds. In 2015, issuance of perpetual bonds hit a record. For example, French energy company Total issued $5.7 billion in perpetual bonds and Volkswagen issued $2.6 billion in perpetual debt.
We can illustrate the effect of interest rate risk using the 100-year BellSouth issue. The following table provides some basic information on this issue, along with its prices on December 31, 1995; July 31, 1996; and February 1, 2018.
Several things emerge from this table. First, interest rates apparently rose between December 31, 1995, and July 31, 1996 (why?). After that, however, they fell (why?). The bond’s price first lost 20 percent and then gained 45.5 percent. These swings illustrate that longer-term bonds have significant interest rate risk.
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 with annual coupons. A broker quotes a price of $955.14. What is the yield on this bond?
We’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:
where r is the unknown discount rate, or yield to maturity. We have one equation here and one unknown, but we cannot solve 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:
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.
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A bond’s yield to maturity should not be confused with its current yield, which is 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 = .0838, or 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 only considers 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 market rates are available at
Our discussion of bond valuation is summarized in Table 5.1. A nearby Spreadsheet Techniques box shows how to find prices and yields the easy way.
TABLE 5.1 Summary of Bond Valuation
I. Finding the Value of a Bond
Bond value = C × [1 − 1/(1 + r)t] / r + F / (1 + r)t
II. Finding the Yield on a Bond
Given a bond value, coupon, time to maturity, and face value, it is possible to find the implicit discount rate, or yield to maturity, by trial and error only. To do this, try different discount rates until the calculated bond value equals the given value (or let a spreadsheet or a financial calculator do it for you). Remember that increasing the rate decreases the bond value.
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 = .0555, or 5.55 percent. To calculate the yield to maturity, refer back to Example 5.1. Now, in this case, the bond pays $30 every six months and it 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 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.
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.
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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 that we have not discussed. However, setting up a simple spreadsheet to calculate prices or yields is straightforward, as our next two spreadsheets show:
In our spreadsheets, notice that we had to enter two dates, a settlement date and a maturity date. The settlement date is 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 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.
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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.
Information for bond investors can be found at
From a financial point of view, the main differences between debt and equity are the following:
Debt is not an ownership interest in the firm. Creditors generally do not have voting power.
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.
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.
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, there are a number of features that 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 one 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 bond refers 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 CVS Health Corporation. If some of these terms are unfamiliar, have no fear. We will discuss them all presently.
Information on individual bonds can be found at
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Features of a CVS Health Corporation Bond
Amount of issue
$8 billion
The company issued $8 billion worth of bonds.
Date of issue
The bonds were sold on 03/09/2018.
The bonds mature on 03/25/2048.
Face value
The denomination of the bonds is $2,000.
Annual coupon
Each bondholder will receive $101 per bond per year (5.05% of face value).
Offer price
The offer price will be 99.430% of the $2,000 face value, or $1,988.60, per bond.
Coupon payment dates
3/25, 9/25
Coupons of $101/2 = $50.50 will be paid on these dates.
The bonds are not secured by specific assets.
Sinking fund
The bonds have no sinking fund.
Call provision
At any time
The bonds do not have a deferred call.
Call price
Treasury rate plus .30%
The bonds have a “make whole” call price.
S&P BBB, Moody’s Baa2
The bonds have a medium-quality credit rating.
Many of these features will be detailed in the bond indenture, so we discuss this first.
The 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.
The bond indenture is a legal document. It can run several hundred pages and generally makes for very tedious reading. It is an important document, however, because it generally includes the following provisions:
The basic terms of the bonds.
The total amount of bonds issued.
A desсrіption of property used as security.
The repayment arrangements.
The call provisions.
Details of the protective covenants.
We discuss these features next.
TERMS OF A BOND Corporate bonds usually have a par, or face, value (that is, a denomination) of $1,000, although par values of $2,000 like the CVS bond have become relatively common. Essentially, any par value is possible. 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. Par value is also called principal value and it is stated on the bond certificate. So, if a corporation wanted to borrow $1 million, 1,000 bonds with a par value of $1,000 would do the trick, as would 500 bonds with a $2,000 par value.
Corporate bonds are usually in registered form. For example, the indenture might read as follows:
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.
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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.
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.
SECURITYDebt 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, for example, 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 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 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.
The Securities Industry and Financial Markets Association (SIFMA) site is
SENIORITYIn 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.
REPAYMENTBonds 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.
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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.
There are many different kinds of sinking fund arrangements, and the details would be spelled out in the indenture. For example:
Some sinking funds start about 10 years after the initial issuance.
Some sinking funds establish equal payments over the life of the bond.
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 PROVISIONA 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.
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 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.
In recent years, a new type of call provision, a “make-whole” call, has become very 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 CVS issue, we see that the discount rate is “Treasury rate plus .30%.” 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 an additional .30 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 CVS issue does not have a deferred call feature. Why might investors not be too concerned about the absence of this feature?
PROTECTIVE COVENANTSA 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.
A negative covenant is a “thou shalt not” type of covenant. It limits or prohibits actions that the company might take. Here are some typical examples:
The firm must limit the amount of dividends it pays according to some formula.
The firm cannot pledge any assets to other lenders.
The firm cannot merge with another firm.
The firm cannot sell or lease any major assets without approval by the lender.
The firm cannot issue additional long-term debt.
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A positive covenant is a “thou shalt” type of covenant. It specifies an action that the company agrees to take or a condition the company must abide by. Here are some examples:
Want detailed information on the amount and terms of the debt issued by a particular firm? Check out its latest financial statements by searching SEC filings at
The company must maintain its working capital at or above some specified minimum level.
The company must periodically furnish audited financial statements to the lender.
The firm must maintain any collateral or security in good condition.
This is only a partial list of covenants; a particular indenture may feature many different ones.
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.
Want to know what criteria are commonly used to rate corporate and municipal bonds? Go to,, and
Bond ratings are constructed from information supplied by the corporation and other sources. The rating classes and some information concerning them are shown in the following table.
Note: At times, both Moody’s and S&P use adjustments (called notches) to these ratings. S&P uses plus and minus signs: A+ is the strongest A rating and A− the weakest. Moody’s uses a 1, 2, or 3 designation, with 1 being the highest. Moody’s has no D rating.
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, as of January 2019, page 143Microsoft and Johnson & Johnson were the only U.S.-based nonfinancial companies with a AAA credit rating. AA or Aa ratings indicate very good quality debt and are much more common.
Another good bond market site is
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. For example, 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 February 2016, India-based textile and chemical company Standard Industries sold an issue of 10-year notes rated BBB– by S&P and Ba2 by Moody’s.
A bond’s credit rating can change as the issuer’s financial strength improves or deteriorates. For example, in January 2019, S&P cut the bond rating on PG&E from BBB– to B, lowering the company’s bond rating from investment-grade to junk bond status. S&P cut PG&E’s rating in large part due to potential liabilities from the November 2018 California wildfire. Bonds that drop into junk territory like this are called fallen angels.
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. While that might be a good thing for a college basketball team such as the University of Kentucky Wildcats, in the bond market NCAA means “No Coupon At All,” and it’s not a good thing for investors.
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 2019, the total debt of the U.S. government was about $22 trillion, or approximately $67,000 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 public (in fact, it does so every month). Currently, outstanding Treasury notes and bonds have original maturities ranging from 2 to 30 years.
If you’re nervous about the level of debt piled up by the U.S. government, don’t go to or to! Learn all about government bonds at
Most U.S. Treasury issues are 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 only taxed 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 “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.
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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 January 2019, long-term AAA-rated corporate bonds were yielding about 3.95 percent. At the same time, long-term AAA munis were yielding about 2.85 percent. Suppose an investor was in a 30 percent tax bracket. All else being the same, would this investor prefer a AAA corporate bond or a AAA municipal bond?
To answer, we need to compare the aftertax yields on the two bonds. Ignoring state and local taxes, the muni pays 2.85 percent on both a pretax and an aftertax basis. The corporate issue pays 3.95 percent before taxes, but it pays .0395 × (1 – .30) = .0277, or 2.77 percent, once we account for the 30 percent tax bite. Given this, the muni bond has a slightly better yield.
For information on municipal bonds, including prices, check out
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 tax 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
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 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 the change in the bond’s value for the year.
Notice that under the old rules, zero coupon bonds were more attractive for corporations because the deductions for interest expense were larger in the early years (compare the implicit interest expense with the straight-line expense).
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Under current tax law, EIN could deduct $73.66 (= $582.01 − 508.35) in interest paid the first year, and the owner of the bond would pay taxes on $73.66 of 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, at one time, General Motors had a debenture outstanding for which during the first 20 years of its life, no coupon payments would be made, but after 20 years, it would begin paying coupons at a rate of 7.75 percent per year, payable semiannually.
Floating-Rate Bonds
The conventional bonds we have talked about in this chapter have fixed-dollar obligations because the coupon rate is set as a fixed percentage of the par value. Similarly, the principal is set equal to the par value. Under these circumstances, the coupon payment and principal are completely fixed.
With 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:
The holder has the right to redeem his/her 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.
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 on U.S. inflation-indexed bonds is at
Other Types of Bonds
Many bonds have unusual or exotic features. For example, at one time, Berkshire Hathaway, the company run by the legendary Warren Buffett, issued bonds with a negative coupon. The buyers of these bonds also received the right to purchase shares of stock in Berkshire at a fixed price per share over the subsequent five years. Such a right, which is called a warrant, would be very valuable if the stock price climbed substantially (a later chapter discusses this subject in greater depth).
Bond features are really only limited by the imaginations of the parties involved. Unfortunately, there are far too many variations for us to cover in detail here. We therefore close out this section by mentioning only a few of the more common types. A nearby Finance Matters box has some additional discussion on more exotic bonds.
Income bonds are similar to conventional bonds, except that coupon payments are dependent on company income. Specifically, coupons are paid to bondholders only if the firm’s income is sufficient. This would appear to be an attractive feature, but income bonds are not very common.
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Many bonds have unusual or exotic features. One of the most common types is an asset-backed, or securitized, bond. Mortgage-backed securities were big news in 2007. For several years, there had been rapid growth in so-called subprime mortgage loans, which are mortgages made to individuals with less than top-quality credit. However, a combination of cooling (and in some places dropping) housing prices and rising interest rates caused mortgage delinquencies and foreclosures to rise. This increase in problem mortgages caused a significant number of mortgage-backed securities to drop sharply in value and created huge losses for investors. Bondholders of a securitized bond receive interest and principal payments from a specific asset (or pool of assets) rather than a specific company. For example, at one point, rock legend David Bowie sold $55 million in bonds backed by future royalties from his albums and songs (that’s some serious ch-ch-ch-change!). Owners of these “Bowie” bonds received the royalty payments, so if Bowie’s record sales fell, there was a possibility the bonds could have defaulted. Other artists have sold bonds backed by future royalties, including James Brown, Iron Maiden, and the estate of the legendary Marvin Gaye.
Mortgage-backs are the best-known type of asset-backed security. With a mortgage-backed bond, a trustee purchases mortgages from banks and merges them into a pool. Bonds are then issued, and the bondholders receive payments derived from payments on the underlying mortgages. One unusual twist with mortgage bonds is that if interest rates decline, the bonds can actually decrease in value. This can occur because homeowners are likely to refinance at the lower rates, paying off their mortgages in the process. Securitized bonds are usually backed by assets with long-term payments, such as mortgages. However, there are bonds securitized by car loans and credit card payments, among other assets, and a growing market exists for bonds backed by automobile leases.
The reverse convertible is a relatively new type of structured note. This 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. 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.
CAT bonds are issued to cover insurance companies against natural catastrophes. The type of natural catastrophe is outlined in the bond’s indenture. For example, about 30 percent of all CAT bonds protect against a North Atlantic hurricane. The way these issues are structured is that the borrowers can suspend payment temporarily (or even permanently) if they have significant hurricane-related losses. These CAT bonds may seem like pretty risky investments, and they can be, as losses have occurred. Perhaps the quickest loss was a CAT bond issued five weeks before the 2017 Mexican earthquake. The bond was a total loss.
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.
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 issued has been decreasing in recent years.
For a list of CAT bond defaults, go to
A put bond allows the holder to force the issuer to buy the bond back 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 the face value given that 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 the reverse of the call provision.
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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.
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 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, with an average daily volume over $500 billion.
How Bonds Are Bought and Sold
Most trading in bonds takes place over the counter, or OTC. This means that 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 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 was often not possible to observe either. Transactions were privately negotiated between parties, and there was little or no centralized reporting of transactions.
Although the total volume of trading in bonds far exceeds that in stocks, only a very small fraction of the total bond issues that exist actually trade on a given day. This fact, combined with the historical lack of transparency in the bond market, meant that getting up-to-date prices on individual bonds was difficult or impossible, particularly for smaller corporate or municipal issues.
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 page 148through what is known as the Trade Report and Compliance Engine (TRACE). Now, essentially all publicly traded corporate bonds have trades reported by FINRA.
To learn more about TRACE, visit
TRACE bond quotes are available at We went to the site and entered “Deere” for the well-known manufacturer of green tractors. We found a total of eight bond issues outstanding. Below you can see the information we found for all of these bonds.
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. For example, when we checked, the first bond listed had not traded for two weeks.
As shown in Figure 5.3, the Financial Industry Regulatory Authority (FINRA) provides a daily snapshot of the data from TRACE by reporting the most active issues. The information reported is largely self-explanatory. Notice that the price of the first GE Capital bond listed decreased about .406 percent on this day. What do you think happened to the yield to maturity for this bond? Figure 5.3 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.
Sample TRACE Bond Quotations
Source: FINRA reported TRACE prices.
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.
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
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Figure 5.4 shows a portion of the daily Treasury bond listings from the website 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 6.25 is the bond’s coupon rate.
Sample Wall Street Journal U.S. Treasury Bond Prices
Source:, January 3, 2019.
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 “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 “spread”), and it represents the dealer’s profit.
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 135.7656. With a $1,000 face value, this quote represents $1,357.656. The asked price, or the price at which the dealer is willing to sell the bond, is 135.8281, or $1,358.281.
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 rose by 1.1641 percent, or $11.641, 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 (2.589 percent) is less than its coupon rate (6.25 percent).
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The last bond listed, the 11/15/2048, 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).
Current and historical Treasury yield information is available at
If you examine the yields on the various issues in Figure 5.4, you will clearly see that they vary by maturity. Why this occurs and what it might mean are some 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).
Selected International Government 10-Year Bond Yields
Yield (%)
United States
Source:, January 3, 2019.
Treasury Quotes
Locate the Treasury issue in Figure 5.4 that matures on May 15, 2021. What is its coupon rate? What is its bid price? What was the previous day’s asked price?
The bond listed as 5/15/2021 is the one we seek. Its coupon rate is 2.625 percent of face value. The bid price is 100.5625, or 100.5625 percent of face value. The ask price is 100.5781, which is up by .2578 from the previous day. This means that the ask price on the previous day was equal to 100.5781 – .2578 = 100.3203.
A Note on 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.
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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 (i.e., its clean price) would be $1,080 –20 = $1,060.6
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 discuss 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.
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 5 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:
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.
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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:
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 had 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 money 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 the 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:
Fisher’s thinking is that investors are not foolish. They know that inflation reduces purchasing power, and, therefore, they will demand an increase in the nominal rate before lending money. Fisher’s hypothesis, typically called the Fisher effect, can be stated as:
A rise in the rate of inflation causes the nominal rate to rise just enough so that the real rate of interest is unaffected. In other words, the real rate is invariant to the rate of inflation.
The Fisher Effect
If investors require a 2 percent real rate of return, and the inflation rate is 8 percent, what must be the approximate nominal rate? The exact nominal rate?
First of all, the nominal rate is approximately equal to the sum of the real rate and the inflation rate: 2 percent + 8 percent = 10 percent. From the Fisher effect, we have:
Therefore, the nominal rate will actually be closer to 10.16 percent. In this example, you can also see how negative nominal interests can come about, e.g., in the unusual situation when inflation rates are expected to be sufficiently negative.
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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.
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 is a reflection of 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 5.5 gives us a long-range perspective on this by showing about two centuries of short- and long-term U.S. Treasury 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.
U.S. Interest Rates: 1800–2018
Source: Siegel, Jeremy J. Stocks for the Long Run, 4th ed. McGraw-Hill, 2008, updated by the authors.
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.
When long-term rates are higher than short-term rates, we say that the term structure is upward sloping, and 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 page 154common 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.
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 very strongly influences the shape of the term structure. Investors thinking about loaning 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.
If investors believe that 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 be a reflection of 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 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
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 5.6 shows how these can interact to produce an upward-sloping term structure (in the top part of Figure 5.6) or a downward-sloping term structure (in the bottom part).
The Term Structure of Interest Rates
In the top part of Figure 5.6, 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 5.6, 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 5.6 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.
Bond Yields and the Yield Curve: Putting It All Together
Going back to Figure 5.4, 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 5.4, the Wall Street Journal website provides a plot of Treasury yields page 155relative to maturity. This plot is called the Treasury yield curve (or just the yield curve). Figure 5.7 shows the yield curve as of April 2019. Note, the yield curve available on the website will display both the current and previous year’s yield curves.
The Treasury Yield Curve: April 2, 2019
Source:, April 2, 2019.
Online yield curve information is available at
As you probably now suspect, the shape of the yield curve is a reflection of 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.
To see the current Treasury yield curve rates, check out the Data and Charts Center at
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.
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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.
Next, 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.
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 on a regular basis. 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.
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.
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This chapter has explored bonds, bond yields, and interest rates. We saw that:
Determining bond prices and yields is an application of basic discounted cash flow principles.
Bond values move in the direction opposite that of interest rates, leading to potential gains or losses for bond investors.
Bonds have a variety of features spelled out in a document called the indenture.
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.
A wide variety of bonds exist, many of which contain exotic or unusual features.
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.
Bond yields and interest rates reflect the effects of six different factors: the real interest rate and five premiums that investors demand as compensation for inflation, interest rate risk, default risk, taxability, and lack of liquidity.
Treasury Bonds Is it true that a U.S. Treasury security is risk free?
Interest Rate Risk Which has greater interest rate risk, a 30-year Treasury bond or a 30-year BB corporate bond?
Treasury Pricing 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?
Yield to Maturity 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.
Call Provisions A company is contemplating a long-term bond issue. It is debating whether or not 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?
Coupon Rate 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.
Real and Nominal Returns Are there any circumstances under which an investor might be more concerned about the nominal return on an investment than the real return?
Bond Ratings 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 in the first place; doing so is strictly voluntary. Why do you think they do it?
Bond Ratings Often, junk bonds are not rated. Why?
Term Structure What is the difference between the term structure of interest rates and the yield curve?
Crossover Bonds Looking back at the crossover bonds we discussed in the chapter, why do you think split ratings such as these occur?
Municipal Bonds Why is it that municipal bonds are not taxed at the federal level but are taxable across state lines? Why is it that U.S. Treasury bonds are not taxable at the state level? (You may need to dust off the history books for this one.)
Bond Market What are the implications for bond investors of the lack of transparency in the bond market?
Treasury Market Take a look back at Figure 5.4. Notice the wide range of coupon rates. Why are they so different?page 158
Rating AgenciesA controversy erupted regarding bond-rating agencies when some agencies began to provide unsolicited bond ratings. Why do you think this is controversial?
Bonds as Equity 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”?
Bond Prices versus Yields
What is the relationship between the price of a bond and its YTM?
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?
What is the relationship between the current yield and YTM for premium bonds? For discount bonds? For bonds selling at par value?
Interest Rate Risk All else being the same, which has more interest rate risk, a long-term bond or a short-term bond? What about a low coupon bond compared to a high coupon bond? What about a long-term, high coupon bond compared to a short-term, low coupon bond?
(Questions 1–15)
Valuing Bonds What is the dollar price of a zero coupon bond with 21 years to maturity, semiannual compounding, and a par value of $1,000, if the YTM is:
4 percent
10 percent
14 percent
Valuing Bonds Microhard has issued a bond with the following characteristics:
Par: $1,000
Time to maturity: 18 years
Coupon rate: 7 percent
Semiannual payments
Calculate the price of this bond if the YTM is:
7 percent
9 percent
5 percent
Bond YieldsQin Corp. issued 15-year bonds two years ago at a coupon rate of 5.1 percent. The bonds make semiannual payments. If these bonds currently sell for 96 percent of par value, what is the YTM?
Coupon Rates Lei Corporation has bonds on the market with 12.5 years to maturity, a YTM of 7.2 percent, a par value of $1,000, and a current price of $1,030. The bonds make semiannual payments. What must the coupon rate be on these bonds?
Valuing BondsEven though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company has a bond outstanding with a par value of €1,000, 16 years to maturity, and a coupon rate of 3.8 percent paid annually. If the yield to maturity is 3.1 percent, what is the current price of the bond?
Bond Yields A Japanese company has a bond outstanding that sells for 95.4 percent of its ¥100,000 par value. The bond has a coupon rate of 4.9 percent paid annually and matures in 18 years. What is the yield to maturity of this bond?page 159
Calculating Real Rates of Return If Treasury bills are currently paying 5.1 percent and the inflation rate is 2.9 percent, what is the approximate real rate of interest? The exact real rate?
Inflation and Nominal Returns Suppose the real rate is 2.3 percent and the inflation rate is 3.5 percent. What rate would you expect to see on a Treasury bill?
Nominal and Real Returns An investment offers a total return of 13.5 percent over the coming year. Powell Arms thinks the total real return on this investment will be only 8.6 percent. What does Powell believe the inflation rate will be over the next year?
Nominal versus Real Returns Say you own an asset that had a total return last year of 10.9 percent. If the inflation rate last year was 3.8 percent, what was your real return?
Zero Coupon Bonds You find a zero coupon bond with a par value of $10,000 and 13 years to maturity. If the yield to maturity on this bond is 4.9 percent, what is the dollar price of the bond? Assume semiannual compounding periods.
Valuing BondsLayton Corp. has a $2,000 par value bond outstanding with a coupon rate of 4.6 percent paid semiannually and 13 years to maturity. The yield to maturity of the bond is 3.8 percent. What is the dollar price of the bond?
Valuing Bonds Union Local School District has bonds outstanding with a coupon rate of 3.9 percent paid semiannually and 16 years to maturity. The yield to maturity on these bonds is 4.2 percent and the bonds have a par value of $5,000. What is the price of the bonds?
Using Treasury Quotes Locate the Treasury bond in Figure 5.4 that matures in May 2028. What is its coupon rate? What is its bid price? What was the previous day’s asked price? Assume a par value of $1,000.
Using Treasury Quotes Locate the Treasury bond in Figure 5.4 that matures in February 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 $1,000 par value.
(Questions 16–25)
Bond Price Movements Miller Corporation has a premium bond making semiannual payments. The bond has a coupon rate of 7.4 percent, a YTM of 5.4 percent, and 13 years to maturity. The Modigliani Company has a discount bond making semiannual payments. This bond has a coupon rate of 5.4 percent, a YTM of 7.4 percent, and also 13 years to maturity. If interest rates remain unchanged, what do you expect the price of these bonds to be 1 year from now assuming both bonds have a par value of $1,000? In 3 years? In 8 years? In 12 years? In 13 years? What’s going on here? Illustrate your answers by graphing bond prices versus time to maturity.
Interest Rate Risk Laurel, Inc., and Hardy Corp. both have 7.3 percent coupon bonds outstanding, with semiannual interest payments, and both are currently priced at the par value of $1,000. The Laurel, Inc., bond has 4 years to maturity, whereas the Hardy Corp. bond has 23 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? If interest rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of these bonds be then? Illustrate your answers by graphing bond prices versus YTM. What does this problem tell you about the interest rate risk of longer-term bonds?
Interest Rate Risk The Faulk Corp. has a bond with a coupon rate of 6.4 percent outstanding. The Gonas Company has a bond with a coupon rate of 12.6 percent outstanding. Both bonds have 18 years to maturity, make semiannual payments, and have a YTM of 9.5 percent. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? What if interest rates suddenly fall by 2 percent instead? What does this problem tell you about the interest rate risk of lower coupon bonds?
Bond YieldsStuart Software has 5.7 percent coupon bonds on the market with 11 years to maturity. The bonds make semiannual payments and currently sell for 93 percent of par. What is the current yield on the bonds? The YTM? The effective annual yield?
Bond Yields Baxter Co. wants to issue new 20-year bonds for some much-needed expansion projects. The company currently has 5.6 percent coupon bonds on the market that sell for $1,094.30,page 160 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? Both bonds have a par value of $1,000.
Accrued Interest You purchase a bond with an invoice price of $945. The bond has a coupon rate of 5.6 percent, and there are two months to the next semiannual coupon date. What is the clean price of the bond?
Accrued Interest You purchase a bond with a coupon rate of 7.1 percent and a clean price of $1,030. If the next semiannual coupon payment is due in four months, what is the invoice price?
Finding the Bond Maturity Cavo Corp. has 6.3 percent coupon bonds making annual payments with a YTM of 7.14 percent. The current yield on these bonds is 6.95 percent. How many years do these bonds have left until they mature?
Using Bond Quotes Suppose the following bond quote for IOU Corporation appears in the financial page of today’s newspaper. Assume the bond has a face value of $1,000 and the current date is April 15, 2019. What is the yield to maturity of the bond? What is the current yield?
Finding the Maturity You’ve just found a 10 percent coupon bond on the market that sells for par value. What is the maturity on this bond?
(Questions 26–34)
Components of Bond Returns Bond P is a premium bond with a coupon of 7.8 percent. Bond D has a coupon rate of 4.2 percent and is currently selling at a discount. Both bonds make annual payments, have a YTM of 6 percent, and have eight 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 interrelationship among the various types of yields.
Holding Period Yield You will earn the YTM on a bond if you hold the bond until maturity and 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).
Suppose that today you buy a bond with an annual coupon rate of 5.4 percent for $945. The bond has 21 years to maturity. What rate of return do you expect to earn on your investment?
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?
Valuing Bonds The Grimm 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 6 years, then pays $800 every six months over the subsequent 8 years, and finally pays $1,000 every six months over the last 6 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 5.3 percent compounded semiannually, what is the current price of Bond M? Of Bond N?
Valuing the Call Feature At one point, some Treasury bonds were callable. Consider the prices on the following three Treasury issues as of February 24, 2019:
The bond in the middle is callable in February 2020. What is the implied value of the call feature? (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 161
Treasury Bonds 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?
Real Cash Flows An engineer earned $26,300 per year when he began his career. Thirty years later, his annual salary was $105,350. The inflation index over this same period grew from 455.18 to 1,046.27. What was his real annual salary increase? What is his current salary in real terms?
Real Cash Flows 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 $5. Based on actuarial tables, “Joltin’ Joe” could expect to live for 30 years after the actress died. Assume that the EAR is 5.9 percent. Also, assume that the price of the flowers will increase at 3.1 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.
Real Cash Flows You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $600 per month in a stock account in real dollars and $275 per month in a bond account in real dollars. The effective annual return of the stock account is expected to be 12 percent, and the bond account will have an annual return of 7 percent. When you retire, you will combine your money into an account with an effective annual return of 8 percent. 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?
Real Cash Flows Paul Adams owns a health club in downtown Los Angeles. He charges his customers an annual fee of $900 and has an existing customer base of 575. Paul plans to raise the annual fee by 6 percent every year and expects the club membership to grow at a constant rate of 3 percent for the next five years. The overall expenses of running the health club are $95,000 a year and are expected to grow at the inflation rate of 2 percent annually. After five years, Paul plans to buy a luxury boat for $450,000, close the health club, and travel the world in his boat for the rest of his life. What is the annual amount that Paul can spend while on his world tour if he will have no money left in the bank when he dies? Assume Paul has a remaining life of 25 years and earns 9 percent on his savings.
Bond Quotes You can find current bond prices at You want to find the bond prices and yields for bonds issued by Clorox. You can enter the ticker symbol “CLX” to do a search. What is the shortest maturity bond issued by Clorox that is outstanding? What is the longest maturity bond? What is the credit rating for Clorox’s bonds? Do all of the bonds have the same credit rating? Why do you think this is?
Yield Curves You can find information regarding the most current bond yields at Find the yield curve for U.S. Treasury bonds. What is the general shape of the yield curve? What does this imply about expected future inflation? Now graph the yield curve for AAA, AA, and A rated corporate bonds. Is the corporate yield curve the same shape as the Treasury yield curve? Why or why not?
Default Premiums The Federal Reserve Bank of St. Louis has files listing historical interest rates on its website Find the link for “FRED” data. You will find listings for Moody’s Seasoned Aaa Corporate Bond Yield and Moody’s Seasoned Baa Corporate Bond Yield. A default premium can be calculated as the difference between the Aaa bond yield and the Baa bond yield. Calculate the default premium using these two bond indexes for the most recent 36 months. Is the default premium the same for every month? Why do you think this is?
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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:
Amount of liability:
Current YTM:
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.
Assume 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?
Assume that immediately after the company purchases the bonds, interest rates either rise or fall by 1 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 bonds 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 the weighted average of the duration of the assets in the portfolio. In other words, to find the duration of a portfolio, you take the weight of each asset multiplied by its duration and then sum the results.
What is the duration of the liability for Ice Cubes, Inc.?
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?
Bond A
Bond B
Coupon rate
Coupons per year
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CLOSING CASE CHP. 5 (questions to discuss are rightly under below heading or introduction).
After Dan’s EFN analysis for East Coast Yachts (see the Closing Case in Chapter 3), Larissa has decided to expand the company’s operations. She has asked Dan to enlist an underwriter to help sell $45 million in new 30-year bonds to finance new construction. Dan has entered into discussions with Renata Harper, an underwriter from the firm of Crowe & Mallard, about which bond features East Coast Yachts should consider and also what coupon rate the issue will likely have. Although Dan is aware of bond features, he is uncertain as to the costs and benefits of some of them, so he isn’t clear on how each feature would affect the coupon rate of the bond issue.
1. You are Renata’s assistant, and she has asked you to prepare a memo to Dan 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.
a.The security of the bond, that is, whether or not the bond has collateral.
b.The seniority of the bond.
c.The presence of a sinking fund.
d. A call provision with specified call dates and call prices.
e. A deferred call accompanying the above call provision.
f. A make-whole call provision.
g. Any positive covenants. Also, discuss several possible positive covenants East Coast Yachts might consider.
h. Any negative covenants. Also, discuss several possible negative covenants East Coast Yachts might consider.
i. A conversion feature (note that East Coast Yachts is not a publicly traded company).
j. A floating rate coupon.
Dan is also considering whether to issue coupon-bearing bonds or zero-coupon bonds. The YTM on either bond issue will be 5.5 percent. The coupon bond would have a 5.5 percent coupon rate. The company’s tax rate is 21 percent.
2. How many of the coupon bonds must East Coast Yachts issue to raise the $45 million? How many of the zeroes must it issue?
3. In 30 years, what will be the principal repayment due if East Coast Yachts issues the coupon bonds? What if it issues the zeroes?
4. What are the company’s considerations in issuing a coupon bond compared to a zero-coupon bond?
5. Suppose East Coast Yachts issues the coupon bonds with a make-whole call provision. The make-whole call rate is the Treasury rate plus .40 percent. If East Coast calls the bonds in seven years when the Treasury rate is 4.8 percent, what is the call price of the bond? What if it is 6.2 percent?
6. Are investors really made whole with a make-whole call provision?
7. After considering all the relevant factors, would you recommend a zero-coupon issue or a regular coupon issue? Why? Would you recommend an ordinary call feature or a make-whole call feature? Why?
1 There 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.
2 The 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.
3 The words loan agreement or loan contract are usually used for privately placed debt and term loans.
4 Real property includes land and things “affixed thereto.” It does not include cash or inventories.
5 A bond issued with a very low coupon rate (as opposed to a zero-coupon rate) is an original-issue-discount (OID) bond.
6 The 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 above, we implicitly treated the months as having exactly the same length (i.e., 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.
7 In 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 sometimes called a maturity risk premium. Our terminology is consistent with the modern view of the term structure.

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