# Case Analysis 1. Compute the yield to maturity of Land'o'Toys' bonds before the purchase announcement and use

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## Question:

Case Analysis

1. Compute the yield to maturity of Land'o'Toys' bonds before the purchase announcement and use it to determine the likely current bond rating. (Compare YTM to the table on p. 269).

2.How do the bond investors feel about the announced purchase of Land'o'Toys and why? How would you vote?

Final PDF to printer PART FOUR 7 Valuing Bonds viewpoints Business Application S T O U T , You are the chief financial officer (CFO) for Beach Sand J Resorts. The firm needs $150 million of new capital to renovate a hotel property. As you discuss the firm's plans I with a credit rating agency, you learn that if 15-year bonds L are used to raise this capital, the bonds will be rated BB L and will have to offer a 7 percent return. How many bonds I will you have to issue to raise the necessary capital? What A semiannual interest payments will Beach Sand have to make? (See solution on p. 259) N 9 5 6 T S Personal Application You would like to invest in bonds. Your broker suggests two different bonds. The first, issued by Trust Media, will mature in 2018. Its price is quoted at 96.21 and it pays a 5.7 percent coupon. The second bond suggested, issued by Abalon, Inc., also matures in 2018. This bond's price is 101.94 and pays a 5.375 percent coupon. To help you decide between the bonds, you want to know how much money it will cost to buy 10 bonds, what interest payments you will receive, and what return the bonds offer if purchased today. Also, you want to understand the differences between what the two bonds imply about their risk. (See solution on p. 259) How do you even purchase a bond in the first place? 232 cor6168X_ch07_232-271.indd 232 21/10/13 3:56 PM Final PDF to printer Learning Goals LG7-1 Describe bond characteristics. LG7-2 Identify various bond issuers and their motivation for issuing debt. LG7-3 Read and interpret bond quotes. LG7-4 Compute bond prices using present value concepts. LG7-5 Explain the relationship between bond prices and interest rates. LG7-6 Compute bond yields. LG7-7 Find bond ratings and assess credit risk's effects on bond yields. S T LG7-8 Assess bond market performance. O U to a capitalist economy? Those unfamiliar with the ow important are bonds and the bond market financial markets may have the impressionTthat the stock market dominates capital markets in the United States and in other countries. Stock ,market performance appears constantly on 24-hour TV H news channels and on the evening news. By contrast, we seldom hear any mention of the bond market. While bonds may not generate the same excitement that stocks do, they are an even more important capital source for companies, governments, and other organizations. The bond market is actually larger than the J stock market. At the end of 2012, the U.S. bond market represented roughly $38 trillion in outstanding debt I obligations. At the same time, the market value of all common stock issues was worth less than half of the value of the bond market, at roughly $15.8 trillion. L Bonds also trade in great volume and frequency.L During 2012, the total average daily trading in all types of U.S. bonds reached over $840 billion. Investors are often attracted to the stock market because it offers I the potential for high investor returnsbut great risks come with that high potential return. While some A other bonds also offer high potential rewards and, bonds offer safer and more stable returns than stocks, consequently, higher risk. N In this chapter, we will explore bond characteristics and their price dynamics. You will see that bond pricing uses many time value of money principles that we've used in the preceding chapters. 9 5 7.1 Bond Market Overview 6 Bond Characteristics T Bonds are debt obligation securities that corporations, S the federal government or its agencies, or states and local governments issue to fund various projects or operations. All of these organizations periodically need to raise capital for various reasons, which was formally discussed in Chapter 6. Bonds are also known as fixed-income securities because bondholders (investors) know both how much they will receive in interest payments and when their principal will be returned. From the bond issuer's point of view, the bond is a loan that requires regular interest payments and an eventual repayment of the borrowed principal. Investorsoften pension funds, banks, and mutual fundsbuy bonds to earn investment returns. Most bonds follow a relatively standard structure. A legal contract called the indenture agreement outlines the precise terms between the issuer and the bondholders. Any bond's main characteristics include: bond Publicly traded form of debt. fixed-income securities Any securities that make fixed payments. principal Face amount, or par value, of debt. indenture agreement Legal contract describing the bond characteristics and the bondholder and issuer rights. 233 cor6168X_ch07_232-271.indd 233 21/10/13 3:56 PM Final PDF to printer table 7.1 Typical Bond Features Characteristic Description Common Values Par value The amount of the loan to be repaid. This is often referred to as the principal of the bond. The number of years left until the maturity date. The opportunity for the issuer to repay the principal before the maturity date, usually because interest rates have fallen or issuer's circumstances have changed. When calling a bond, the issuer commonly pays the principal and one year of interest payments. The interest rate used to compute the bond's interest payment each year. Listed as a percentage of par value, the actual payments usually are paid twice per year. The bond's market price reported as a percentage of par value. $1,000 Time to maturity Call Coupon rate Bond price 1 year to 30 years Many bonds are not callable. For those that are, a common feature is that the bond can be called any time after 10 years of issuance. 2 to 10 percent 80 to 120 percent of par value maturity date The date the principal will be repaid (the maturity date). The calendar date on which the bond principal comes due. The par value, or face value, of each bond, which is the principal loan Smust repay. amount that the borrower par value Amount of debt borrowed to be repaid; face value. The coupon (interest) rate. T A description of any property O to be pledged as collateral. Steps that the bondholder Ucan take in the event that the issuer fails to pay the interest or principal. T Table 7.1 describes par value , and other bond characteristics. Most bonds have time to maturity The length of time (in years) until the bond matures and the issuer repays the par value. LG7-1 call An issuer redeeming the bond before the scheduled maturity date. call premium The amount in addition to the par value paid by the issuer when calling a bond. coupon rate The annual amount of interest paid expressed as a percentage of the bond's par value. 234 a par value of $1,000. This is the amount of principal the issuer has promised to repay. Bonds have fixed lives. The bond's life ends when the issuer repays the par value to the buyer onJthe bond's maturity date. Although a bond will mature on a specific calendar Idate, the bond is usually referenced by its time to maturity, that is, 2 years, 5 years, 20 years, and so on. In fact, the market groups L bonds together by their time to maturity and classifies them as short-term bonds, L bonds, regardless of issuer. Long-term bonds medium-term bonds, or long-term carry 20 or 30 years to maturity. I Of course, over time, the 30-year bond becomes a 20-year bond, 10-year bond, and eventually matures. But other time periods to A maturity do exist. For example, in 2011, the railroad company Norfolk Southern N with 100 years to maturity. The bonds have a Corp. issued $400 million of bonds coupon (interest) rate of 6 percent and mature in 2111. When interest rates economywide fall several percentage points (which often 9 takes several years), homeowners everywhere seek to refinance their home mort5 interest payments (and sometimes want to pay gages. They want to make lower down their mortgage principal) 6 every month. Corporations that have outstanding bond debt will also want to refinance those bonds. Sometimes the indenT between a bond issuer and bondholders) allows ture contract (the legal contract S the indenture prohibits refinancing. Bonds that companies to do so; sometimes can be refinanced have a call feature, which means that the issuer can \"call\" the bonds back and repay the principal before the maturity date. To compensate the bondholders for getting the bond called, the issuer pays the principal and a call premium. The most common call premium is one year's worth of interest payments. In some indentures, the call premium declines over time. The bond's coupon rate determines the dollar amount of interest paid to bondholders. The coupon rate appears on the bond and is listed as a percentage of the par value. So a 5 percent coupon rate means that the issuer will pay 5 percent of $1,000, or $50, in interest every year, usually divided into two equal semiannual payments. So a 5 percent coupon bond will pay $25 every six months. Companies set the coupon rate as the prevailing market interest rate at the time of bond issue. The name coupon is a holdover from the past, when bonds were actually part four Valuing of Bonds and Stocks cor6168X_ch07_232-271.indd 234 21/10/13 3:56 PM Final PDF to printer issued with a coupon book. Every six months a MATH COACH bondholder would tear out a coupon and mail it to the issuer, who would then make the interest PERCENT-TO-DECIMAL CONVERSIONS payment. These are sometimes referred to as bearer When discussing interest rates or using them in calculator or bonds (often a feature of spy or mystery movies), spreadsheet time value of money functions, the value should be because whoever held the coupon book could in percent (%) form, like 2.5%, 7%, and 11%. When using interreceive the payments. Nowadays, issuers register est rates in formulas, the value needs to be in decimal form, like bond owners and automatically wire interest pay0.025, 0.07, and 0.11. ments to the owner's bank or brokerage account. To convert between the two forms of representing an interest Nevertheless, the term coupon persists today. rate, use At original issue, bonds typically sell at par value, Percent (%) Decimal 5 unless interest rates are very volatile. Bondholders 100 recoup the par value on the bond's maturity date. However, at all times in between these two dates, bond price bonds might trade among investors in the secondary bond market. The bond's price as it trades in the secondary market will not likely be the par value. Bonds trade Current price that the bond S thoroughly demonstrate the sells for in the bond market. for higher and lower prices than their par values. We'll reasons for bond pricing in a later section of this chapter. T Bond prices are quoted in terms of percent of par value rather than in dollar terms. Sources of trading informaO tion list a bond that traded at $1,150 as 115, and a bond that traded for $870 as 87. LG7-1 Bond Characteristics U T , EXAMPLE Consider a bond issued 10 years ago with an at-issue time to maturity of 30 years. The bond's coupon rate is 8 percent and it currently trades in the bond market J for 109. Assuming a par value of $1,000, what is the bond's current time to maturity, semiannual interest payment, I and bond price in dollars? 7-1 For interactive versions of this example visit www.mhhe.com/can3e L L Time to maturity 5 30 years 2 10 years 5 20 years I Annual payment 5 0.08 3 $1,000 5 $80, so semiannual payment is $40 A Bond price 5 1.09 3 $1,000 5 $1,090 N SOLUTION: Similar to Problems 7-1, 7-2, 7-3, 7-4, self-test problem 1 9 5 Bond Issuers 6 For many years, bonds were considered stodgy, overly T conservative investments. Not anymore! The fixed-income industry has seen tremendous innovation in the S past couple of decades. The financial industry has created and issued many new LG7-2 types of bonds and fixed-income securities, some with odd-sounding acronyms, like TIGRs, CATS, COUGRs, and PINEs, all of which are securities based on U.S. Treasuries. Even with all the innovation, the traditional three main bond issuers remain: U.S. Treasury bonds, corporate bonds, and municipal bonds. Figure 7.1 shows the amount of money that these bond issuers have raised each year. TREASURY BONDS Treasury bonds carry the \"full-faith-and-credit\" backing of the U.S. government and investors have long considered them among the safest fixed-income investments in the world. The federal government sells Treasury securities through public auctions to finance the federal deficit. When the deficit is large, more bonds come to auction. In addition, the Federal Reserve System (the Fed) uses Treasury securities to implement monetary policy. Technically, chapter 7 cor6168X_ch07_232-271.indd 235 LG7-2 Valuing Bonds 235 21/10/13 3:56 PM Final PDF to printer figure 7.1 Amount of Capital Raised Yearly from Bonds Issued by Local and Federal Government and Corporations Municipal Treasury Corporate 2000 1500 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1996 1995 1994 1993 1992 1991 1990 0 S T O U T , 1999 500 1998 1000 1997 Data Source: Securities Industry and Financial Markets Association Annual Bond Issuance ($ Billions) Local or municipal governments, the U.S. Treasury, and corporations have issued many new types of bonds and fixedincome securities over the past two decades. 2500 Treasury securities issued with 1 to 10 years until maturity are Treasury notes. Securities issued with 10 to 30 J years until maturity are Treasury bonds. Figure 7.1 shows that the number of new Treasuries being offered actually declined in the I deficit declined. However, this reversed in 2002 late 1990s as the federal budget and then dramatically accelerated L in 2009 after the global financial crisis. L CORPORATE BONDS Corporations raise capital to finance investments in I research and development, and general busiinventory, plant and equipment, ness expansion. As managers A decide how to raise capital, corporations can issue debt, equity (stocks), or a mixture of both. The driving force behind a corporation's financing strategy is theN desire to minimize its total capital costs. Through much of the 1990s, corporations tended to issue equity (stocks) to raise capital. Beginning in 1998 and through 9 2012, corporations switched to raising capital by issuing bonds to take advantage of low interest rates and issued $12.8 trillion in 5 in capital reflected in Figure 7.1. new bonds. You can see this rise 6 Treasury InflationProtected Securities TIPS are U.S. government bonds where the par value changes with inflation. LG7-2 MUNICIPAL BONDS State and local governments borrow money to build, T repair, or improve streets, highways, hospitals, schools, sewer systems, and so on. S municipal bonds are repaid in two ways. ProjThe interest and principal on these ects that benefit the entire community, such as courthouses, schools, and municipal office buildings, are typically funded by general obligation bonds and repaid using tax revenues. Projects that benefit only certain groups of people, such as toll roads and airports, are typically funded by revenue bonds and repaid from user fees. Interest payments paid to municipal bondholders are not taxed at the federal level, or by the state for which the bond is issued. Other Bonds and Bond-Based Securities Treasury Inflation-Protected Securities (TIPS) have proved one of the most successful recent innovations in the bond market. The U.S. Treasury began issuing this new type of Treasury bond, which is indexed to inflation, in 1997. 236 part four Valuing of Bonds and Stocks cor6168X_ch07_232-271.indd 236 21/10/13 3:56 PM Final PDF to printer TIPS have fixed coupon rates like traditional Treasuries. The new aspect is that the federal government adjusts the par value of the TIPS bond for inflation. Specifically, it increases at the rate of inflation (measured by the consumer price index, CPI). As the bond's par value changes over time, interest payments also change. At maturity, investors receive an inflation-adjusted principal amount. If inflation has been high, investors will expect that the adjusted principal amount will be substantially higher than the original $1,000. Consider a 10-year TIPS issued on January 15, 2009, that pays a 2 1/8 percent coupon. The reference CPI for these bonds is 214.69971. Four years later (on January 15, 2013) the reference CPI was 230.22100. So the par value of the TIPS in early 2013 was $1,072.29 (5 $1,000 3 230.22100 4 214.69971). Therefore, the 2 1/8 percent coupon (paid semiannually) would be $11.39 5 (0.02125 3 $1,072.29 4 2). A TIPS' total return comes from both the interest payments and the inflation adjustment to the par value. LG7-2 S T TIPS Payments O coupon. The reference CPI A TIPS bond was issued on July 15, 2006, that pays a 2 percent at issue was 201.95. The reference CPI for the following interest U payments were: T January 2009 214.70 , July 2009 213.52 January 2010 EXAMPLE 7-2 For interactive versions of this example visit www.mhhe.com/can3e 216.25 J of the TIPS on the three Given these numbers, what is the par value and interest payment interest-payment dates? What is the total return from January I 2009 to January 2010? L Compute the TIPS index ratio for each period as current CPI divided byLthe at-issue CPI: The par value for January 2009 is $1,000 3 214.70 4 201.95 5 $1,063.13,I so the interest payment is 0.025 3 $1,063.13 4 2 5 $13.29. The answers for the next two dates are: A July 2009 N Interest payment 5 $13.22 Par value 5 $1,057.29 SOLUTION: January 2010 Par value 5 $1,070.81 Interest payment 5 $13.39 9 2 $1,063.13 5 $7.68. Adding the The capital gain between January 2009 and January 2010 is $1,070.81 two interest payments together results in $26.61 (5 $13.22 1 $13.39). 5 Thus, the total return is 3.23% 5 ($7.68 1 $26.61)/$1,063.13. Similar to Problems 7-7, 7-8, 7-19, 7-20, 7-33, 7-34 6 T S U.S. government agency securities are debt securities issued to provide low-cost financing for desirable private-sector activities such as home ownership, education, and farming. Fannie Mae, Freddie Mac, Student Loan Marketing Association (Sallie Mae), Federal Farm Credit System, Federal Home Loan Banks, and the Small Business Administration, among others, issue these agency bonds to support particular sectors of the economy. Agency securities do not carry the federal government's full-faith-and-credit guarantee, but the government has never let one of its agencies fail. Because investors believe that the federal government will continue in this watchdog role, agency bonds are thought to be very safe and may provide a slightly higher return than Treasury securities do. chapter 7 cor6168X_ch07_232-271.indd 237 agency bonds Bonds issued by U.S. government agencies. Valuing Bonds 237 21/10/13 3:56 PM Final PDF to printer finance at work personal finance BUY TREASURIES DIRECT! Treasury bonds are U.S. government-issued debt securities that investors trade on secondary markets. The government also issues nonmarketable debt, called \"savings bonds,\" directly to investors. The common EE savings bonds, introduced in 1980, do not pay regular interest payments. Instead, interest accrues and adds to the bond's value. After a 1-year holding period, they can be redeemed at almost any bank or credit union. You can now purchase savings bonds and other Treasury securities (bills, notes, bonds, and TIPS) electronically through the U.S. Treasury's website, treasurydirect.gov. You can set up an account in minutes and buy savings bonds with cash from your bank account. You can also redeem your bonds and transfer the proceeds back to your bank account. Bonds can be purchased 24 hours a day, 7 days a week at no cost. When bondholders redeem savings bonds, they receive the original value paid plus the accrued interest. Paper bonds ! want to know more? mortgage-backed securities Debt securities whose interest and par value payments originate from real estate mortgage payments. asset-backed securities Debt securities whose payments originate from other loans, such as credit card debt, auto loans, and home equity loans. convertible bond A debt security that can be converted to shares of stock or another type of security. 238 sell at half of the face value; if investors hold them for the full 30 years, they receive the par value. Investors buy electronic bonds at face value and earn interest in addition to the par value. Unlike other bonds, savers need not report income from these interest payments to the IRS until they actually redeem the bonds. So savings bonds count as tax-deferred investments. About one in six Americans owns savings bonds. Savings bonds are used for a variety of purposes, such as personal savings instruments or gifts from grandparents to grandchildren. After the September 11, 2001, terrorist attacks, many Americans wanted to show support for the government. In December 2001, banks selling government EE savings bonds began printing \"Patriot bond\" on them. So EE savings bonds are now often called Patriot Bonds. S T O U Key Words to Search T for Updates: TreasuryDirect (go to www.treasurydirect.gov) , U.S. government agenciesJinvented one popular type of debt security: mortgage-backed securities I (MBSs). Fannie Mae and Freddie Mac offer subsidies or mortgage guarantees for people who wouldn't otherwise qualify L for mortgages, especially first-time homeowners. Fannie Mae started out as a government-owned enterpriseLin 1938 and became a publicly held corporation in 1968. Freddie Mac was chartered I as a publicly held corporation at its inception in 1970. Since 2008, both have been in government conservatorship and run by A the Federal Housing Finance Agency. To increase the amount of money available N market, Fannie Mae and Freddie Mac purchase (liquidity) for the home mortgage home mortgages from banks, credit unions, and other lenders. They combine the mortgages into diversified portfolios of such loans and then issue mortgage9 backed securities, which represent a share in the mortgage debt, to investors. As 5 the underlying portfolio of mortgage loans, homeowners pay off or refinance MBS investors receive interest6and principal payments. After selling mortgages to Fannie Mae or Freddie Mac, mortgage lenders have \"new\" cash to provide T more mortgage loans. This process worked well for decades until the late 2000s, S given to people who couldn't afford them. As when subprime mortgages were you know, defaults on these loans were the underpinnings of the financial crisis. We could apply the same concept to any type of loan; indeed, the financial markets have already invented many such pooled-debt securities. Typical examples include credit card debt, auto loans, home equity loans, and equipment leases. Like mortgage-backed securities, investors receive interest and principal from asset-backed securities as borrowers pay off their consumer loans. The asset-backed securities market is one of the fastest-growing areas in the financial services sector. On the bond's maturity date, the bondholder receives the par value, which is typically $1,000. However, some corporate bonds give the bondholder a choice between the par value and a specified number of shares of stock. This type of bond is referred to as a convertible bond because it can be converted to part four Valuing of Bonds and Stocks cor6168X_ch07_232-271.indd 238 21/10/13 3:56 PM Final PDF to printer finance at work markets MORTGAGE-BACKED SECURITIES AND FINANCIAL CRISIS In the old days, a bank with $100,000 to lend would fund a mortgage and charge a fee for originating the loan. The bank would then collect interest on the loan over time. In the past few decades, the process changed to where that bank could sell that mortgage to investment banks and get the $100,000 back. The bank could then originate another mortgage and collect another fee. Bank revenue transitioned from interest earnings to fee earnings. This worked pretty well for several decades because the bank made more profits and more money was funneled into the community for home buyers. It is the securitization of debt that makes this possible. Financial institutions like Fannie Mae and investment banks bought up these mortgages, pooled them, and issued bonds against them (called mortgage-backed securities, or MBSs) to sell to investors. In effect, buyers of the MBSs are the actual lenders of the mortgage and banks simply earned fees for servicing the loans. Note that this lending model gives banks and mortgage brokers the incentive to initiate as many mortgage loans as they can resell to maximize fee income. Then in 2000 to early 2004, the Federal Reserve kept adjusting interest rates on federal funds downward and kept them low. This both made home ownership more affordable, sparking a housing bubble, and drove investors to look for bonds that paid higher yields. Consequently, many loans were granted to individuals with poor creditworthiness (subprime borrowers). These S T O U T , subprime borrowers were charged higher interest rates. When these subprime mortgages were packed into the pool of mortgages, the MBSs offered higher yields. Thus, there was a high demand from investors for these MBSs, which fostered more poor credit quality loan originations. Then from July 2004 to July 2006, the Federal Reserve started increasing interest rates. This placed some downward pressure on housing prices because it made homes less affordable. At the same time, most subprime mortgages originating from 2005 and 2006 were written on adjustable rates, and those interest rates adjusted upward too, making the payments too high for many borrowers. The subprime borrowers soon began to fall behind on their monthly payments leading to foreclosures and additional downward pressure on housing prices. The devaluation of housing prices eroded the home equity of homeowners and led to further foreclosures and further price decreases. The MBSs also devalued quickly. Who owned MBSs? It turns out that the owners of these securities were financial firms, such as investment banks, commercial banks, insurance companies, mutual funds and pension funds all over the world. Their weakened financial strength led to bank failures, bailouts and a global credit crisis. J Source: Yuliya Demyanyk, and Otto Van Hemert, \"Understanding the I Subprime Mortgage Crisis,\" Review of Financial Studies, 2009. L Key Words to Search for Updates: subprime, MBS, financial crisis want to know more? L ! I company stock. The number of shares of stock forAwhich the bond can be conN verted is specified when the bond is originally issued. Thus, the bondholder will want to receive the shares when the stock price has risen since bond issuance, and they will want the $1,000 when the stock has declined in value. 9 5 Reading Bond Quotes 6 To those familiar with bond terminology, bond quotes provide all of the informaT The volume of Treasury tion needed to make informed investment decisions. S and notes average more securities traded each day is substantial. Treasury bonds LG7-3 than a half billion dollars in trading daily. Investors exhibit much less enthusiasm for corporate or municipal bonds, perhaps because the markets for each particular bond or bonds with the same maturity, coupon rate, and credit ratings are much thinner and, therefore, less liquid. Most bond quote tables report only a small fraction of the outstanding bonds on any given day. Bond quotes can be found in The Wall Street Journal and online at places like Yahoo! Finance (yahoo. finance.com) and BondsOnline (www.bonds-online.com). Table 7.2 shows three bond quote examples. A typical listing for Treasury bonds appears first. Here, this Treasury bond pays bondholders a coupon of 2.375 percent. On a $1,000 par value bond, this interest income would be $23.75 annually, paid as $11.875 every six months per bond. The bond will mature in February of 2015since this is fairly soon, the chapter 7 cor6168X_ch07_232-271.indd 239 Valuing Bonds 239 21/10/13 3:56 PM Final PDF to printer table 7.2 Bond Quote Examples Treasury Securities COUPON RATE 2.375 Corporate Bond COMPANY Anheuser-Busch InBev Municipal Bond ISSUE NYC Muni Wtr Fin Auth premium bond A bond selling for greater than its par value. discount bond A bond selling for lower than its par value. MO/YR BID ASKED CHG ASK YLD Feb 15 104.2188 104.2266 20.0313 0.294 COUPON MATURITY LAST PRICE YIELD 2.50 July 2022 91.470 2.56 COUPON MATURITY PRICE BID YLD 4.500 06-15-37 97.570 4.66 bond is considered a short-term bond. Both the bid and the ask quotes for the bond appear, expressed as percentages of the bond's par value of $1,000. The S investors can sell the bond. A bid of 104.2188 bid price is the price at which means that an investor couldT sell for $1,042.188. Investors can buy this bond at the ask price of 104.2266, or $1,042.266. Since the price is higher than the par O value of the bond, the bond is selling at a premium to par because its coupon U Thus, investors call this kind of security a rate is higher than current rates. premium bond. T Notice that the ask price is ,higher than the bid price. The difference is known as the bid-ask spread. Investors buy at the higher price and sell at the lower price. The bid-ask spread is thus the cost of actively trading bonds. Investors buy and sell with a bond dealer. J Since the bond dealer takes the opposite side of the transaction, the dealer buys at the low price and sells at the higher price. I The bid-ask spread is part of the dealer's compensation for taking on risk. An investor who bought this bondLand held it to maturity would experience a $42.27 (5 $1,042.27 2 $1,000) capital loss L (24.06 percent [5 2$42.27/$1,042.27]). The bond lost 0.0313 percent of its value during the day's tradinga change of 2$0.31 for a I $1,000 par value bond. Last, the bond is offering investors who purchase it at the A a 0.294 percent annual return. ask price and hold it to maturity Corporate bond quotes provide N similar information. The table shows the quote for a Anheuser-Busch bond that offers bondholders a coupon of 2.50 percent, or $12.50 semiannually (5 $1,000 3 0.025 4 2). The bond would be considered a 9 to maturity), since it matures in the year 2022. mid-term bond (usually 5 years Corporate bonds are also quoted 5 in percentage of par value. The price quote of 97.470 indicates that the last trade occurred at a price of $974.70 per bond. Since 6 the bond is selling for a price lower than its $1,000 par value, it's called a discount bond. An investor who boughtTthis bond would reap a $25.30 (5 $1,000 2 $974.70) capital gain if the bond were held S to maturity. The Anheuser-Busch bond represents an annual return of 2.56 percent for the investor who purchases the bond at $974.70. Companies set a bond's coupon rate when they originally issue the bond. A number of factors determine that coupon rate: The amount of uncertainty about whether the company will be able to make all the payments. The term of the loan. The level of interest rates in the overall economy at the time. Bonds from different companies carry different coupon rates because some, or all, of these determining factors differ. Even a single company that has raised capital through bond issues many times may carry very different coupon rates 240 part four Valuing of Bonds and Stocks cor6168X_ch07_232-271.indd 240 21/10/13 3:56 PM Final PDF to printer on its various issues, because the bond issues would be offered in different years when the overall economic condition and interest rates differ. Table 7.2 also shows a quote for a municipal bond issued by the New York City Municipal Water Finance Authority. This city government agency has raised capital by issuing municipal bonds to build reservoir facilities to provide water to New York City. The bond pays a 4.500 percent coupon, and since it matures in 2037, it's considered a long-term bond. According to Table 7.2, the bond is trading at a price just below par value97.57 percent. Most municipal bonds, unlike other bonds, feature a $5,000 face value rather than the typical par value of $1,000. So, the 97.57 percent price quote represents a dollar amount of $4,878.50 (5 0.9757 3 $5,000). The low rate of return relative to Treasury bonds with similar maturities also has an explanation. Municipal bondholders do not have to pay federal income taxes on the interest payments that they receive from those securities. We explore this (sometimes) substantial advantage further in a later section of this chapter. S T LG7-3 O U Bond Quotes T You note the following bond quotes and wish to determine each bond's price, term, and , interest payments. COUPON J IBID 137.5938 L L MATURITY I Oct 15, 2011 A N MATURITY 5.00 July 1, 2025 Treasury Securities MATURITY RATE MO/YR 9.00 Nov 18 Corporate Bond COMPANY COUPON Kohls Corp 7.375 Municipal Bond ISSUE Florida St Aquis & Bridge Constr EXAMPLE 7-3 For interactive versions of this example visit www.mhhe.com/can3e ASKED CHG ASK YLD 137.6250 20.1563 4.80 LAST PRICE LAST YIELD 110.01 4.991 PRICE YLD TO MAT 106.78 4.458 9 SOLUTION: 5 The Treasury bond matures in November of 2018 and pays 9 percent 6 interest. Investors receive cash interest payment of $45 (5 0.09 3 $1,000 4 2) semiannually. Since the bond T matures in less than ten years but more than one year, we would consider it a mid-term bond. Since no \"n\" appears next to the maturity date, we can S also tell that the security was issued as a bond that would mature in 30 years. Investors could sell this bond for $1,375.94 (5 137.594 3 $1,000) and buy it for $1,376.25 (5 1.37625 3 $1,000). The price fell on this particular day by $1.56 (5 20.0015625 3 $1,000). The dealer earned $0.31 (3 $1,376.25 2 $1,375.94) on each trade of these premium bonds. The Kohls corporate bond pays a semiannual interest payment of $36.88 (5 0.07375 3 $1,000 4 2) and its price is $1,100.10 (5 1.1001 3 $1,000). This premium bond's 7.375 percent rate is likely well above market rates, which is why an investor would be willing to pay a premium for it. The state of Florida issued the muni bond to fund bridge construction. With a $5,000 par value, the interest payments are $125 (5 0.05 3 $5,000 4 2) every six months. The bonds are priced at $5,339.00 (5 1.0678 3 $5,000). Similar to Problems 7-9, 7-10, self-test problem 1 chapter 7 cor6168X_ch07_232-271.indd 241 Valuing Bonds 241 21/10/13 3:56 PM Final PDF to printer TIME OUT 7-1 Describe the different reasons that the U.S. government, local governments, and corporations would issue bonds. 7-2 What is the following bond's price and what dollar amount will the bond pay for its semiannual interest payment? 7.2 LG7-4 zero coupon bond A bond that does not make interest payments but generally sells at a deep discount and then pays the par value at the maturity date. COMPANY COUPON MATURITY PRICE YIELD Home Depot Inc. 5.40 Mar 1, 2018 100.06 5.391 Bond Valuation Present Value of Bond Cash Flows S Any bond's value computation directly applies time value of money concepts. Tpayments that they are scheduled to receive and Bondholders know the interest Oat maturity. The current price of a bond is, therethe repayment of the par value fore, the present value of these U future cash flows discounted at the prevailing market interest rate. The prevailing market interest rate will depend on the bond's term to maturity, credit quality, andTtax status. The simplest type of bond, for time value of money calculations is a zero coupon bond. As you might guess from its name, a zero coupon bond makes no interest payments. Instead, the bond pays only the par value payment at its J bond sells at a substantial discount from its par maturity date. So a zero coupon value. For example, a bond with I a par value of $1,000, maturing in 20 years, and priced to yield 6 percent, might L be purchased for about $306.56. At the end of 20 years, the bond investor will receive $1,000. The difference between $1,000 and $306.56 (which is $693.44)Lrepresents the interest income received over the 20 years based upon the discount rate of 6 percent. The time line for this zero I coupon bond valuation appears as: Period Cash flow 0 A N 5 6% 10 15 20 years 1,000 PV5? 9 CALCULATOR HINTS N 5 40 I53 PMT 5 0 FV 5 1000 CPT PV 5 2306.56 242 We compute the zero's price by finding the present value of the $1,000 cash 5 flow received in 20 years. However, to be consistent with regular coupon-paying bonds, zero coupon bonds are 6 priced using semiannual compounding. So the formula and calculator valuation T would use 40 semiannual periods at a 3 percent interest rate rather than 20 periods at 6 percent. Using the present value equation S of Chapter 4 results in PV 5 FVN $1,000 $1,000 5 5 5 $306.56 N 40 3.262 (1 1 i) 1.03 So the zero coupon bond's price is indeed a steep discount to its par value. This makes sense because investors would only buy a security that pays $1,000 in many years for a price that is much lower to make enough profit to make up for the forgone semiannual interest payments. For comparison's sake, instead of the 20-year zero, consider a 20-year bond with a 7 percent coupon. So this 20-year maturity bond pays $35 in interest payments every six months. We can think of these interest payments as an annuity stream. If the market discount rate is 6 percent annually, the time line appears as part four Valuing of Bonds and Stocks cor6168X_ch07_232-271.indd 242 21/10/13 3:56 PM Final PDF to printer 3% Period Cash flow Semiannual periods 0 1 2 3 4 ... 37 38 39 40 PV5? 35 35 35 35 ... 35 35 35 35 1,000 The time line shows the 40 semiannual payments (with the accompanying semiannual interest rate at 3 percent) of $35 and the par value payment at the bond's maturity. Think through this: When bonds pay semiannual payments, the discount rate must be a semiannual rate. Thus, the 6 percent annual rate becomes a 3 percent semiannual rate. So we then compute the price of this bond by adding the present value of the interest payment annuity cash flow to the present value of the future par value. A combination of the present value equations for the annuity cash flows and the value of the par redemption appear in the bond valuation equation 7-1: LG7-4 Present value of bond 5 Present value of interest payments 1 Present value of par value S 1 T 12 (1 1 i)N O $1,000 T1 (7-1) 5 PMT 3 D )N i (1 1 i U T where PMT is the interest payment, N is the number , of periods until maturity, and i is the market interest rate per period on securities with the same bond characteristics. If this bond paid interest annually, then these variables would take yearly period values. Since this bond pays semiannually, PMT, N, and i are all J denoted in semiannual periods. The price of this coupon bond should be: I 12 Bond price 5 $35 3 D 1 L (1 1 0.03)40 $1,000 T1 L 0.03 (1I 1 0.03)40 A N 5 $809.017 1 $306.557 5 $1,115.57 Of the $1,115.57 bond price, most of the value comes from the semiannual $35 coupon payments ($809.017) and not the value from the future par value pay9 ment ($306.557). Because equation 7-1 is quite complex, we usually5compute bond prices using a financial calculator or computer program. An investor 6 would compute the bond value using a financial calculator by entering N 5 40, I 5 3, PMT 5 35, FV 5 1000, T and computing the present value (PV). The calculator solution is $1,115.57.1 CALCULATOR HINTS N 5 40 I53 PMT 5 35 FV 5 1000 CPT PV 5 21,115.57 S Bond Prices and Interest Rate Risk LG7-5 At the time of purchase, the bond's interest payments and par value expected at maturity are fixed and known. Over time, economywide interest rates change, but the bond's coupon rate remains fixed. A rise in prevailing interest rates (also called increasing the discount rate) reduces all bonds' values. If interest rates fall, all bonds will enjoy rising values. Consider that when interest rates rise, newly 1 In order to focus on the valuation concepts, we present these examples with the full six months until the bond's next interest payment. However, bonds can be sold anytime between interest payments. When this occurs, we simply add the interest accrued since the last payment to the price. chapter 7 cor6168X_ch07_232-271.indd 243 Valuing Bonds 243 21/10/13 3:56 PM Final PDF to printer EXAMPLE 7-4 LG7-4 Find the Value of a Bond For interactive versions of this example visit www.mhhe.com/can3e Consider a 15-year bond that has a 5.5 percent coupon, paid semiannually. If the current market interest rate is 6.5 percent, and the bond is priced at $940, should you buy this bond? SOLUTION: Compute the value of the bond using equation 7-1. Use semiannual compounding (N 5 2 3 15 5 30, I 5 6.5 4 2 5 3.25, and PMT 5 0.055 3 $1,000 4 2 5 $27.50) as: CALCULATOR HINTS N 5 30 I 5 3.25 PMT 5 27.50 FV 5 1000 CPT PV 5 2905.09 12 Bond value 5 $27.50 3 D 1 (1 1 0.0325)30 $1,000 T1 5 $522.00 1 $383.09 5 $905.09 0.0325 (1 1 0.0325)30 S than the $940 price. The bond is overvalued in the market and you So this bond's value is $905.09, which is less should not buy it. T O7-24, self-test problem 1 Similar to Problems 7-21, 7-22, 7-23, U T , MATH COACH BOND PRICING AND PERIODS J Since most bonds have semiannual interest payments, we must use semiannual periods to discount the cash flows. Most errors in comI puting a bond price occur in the adjustment for semiannual periods. The errors happen whether you are using either the bond pricing L to adjust the three variables: number of periods, interest equation or a financial calculator. To convert to semiannual periods, be sure rate, and payments. L The number of years needs to be multiplied by 2 for the number of semiannual periods. The interest rate should be divided by 2 for I payment. Remember to adjust all three inputs for the semiana 6-month rate. Divide the annual coupon payment by 2 for the 6-month nual periods. A A coupon-paying bond's price should hover reasonably around the par value of the bond. For a $1,000 par value bond, we could N this range, check to see whether you made the semianexpect a price in the range of $700 to $1,300. If you compute a price outside nual period adjustments correctly. 9 5 issued bonds offer to pay higher 6 interest rates than the rates offered on existing bonds. So to sell an existing bond with its lower coupon rate, its market price T expect a profit similar to that offered by newly must fall so that the buyer can issued bonds. Similarly, whenS prevailing interest rates fall, market prices for outstanding bonds rise to bring the offered return on older bonds with higher coupon rates into line with new issues. So market interest rates and bond prices are inversely related. That is, they move in opposite directions. Figure 7.2 demonstrates how the price of a 30-year Treasury bond may change over time. The 10.69 percent coupon exactly matched prevailing interest rates when the bond was issued in 1983. Consequently, the bond sells for its par value of $1,000. Shortly thereafter, interest rates quickly rose to very high levels (over 15 percent) in the economy. As interest rates rose, bond prices had to decline. Then in 1984, interest rates started a prolonged descent to near 0 in 2009 and again in 2012. Note that while a bond is issued at $1,000 and returns $1,000 at maturity, its price can vary a great deal in between. Bond investors must be aware that bond prices fluctuate on a day-to-day basis as interest rates fluctuate. The determinates 244 part four Valuing of Bonds and Stocks cor6168X_ch07_232-271.indd 244 21/10/13 3:56 PM Final PDF to printer figure 7.2 $1,800 A Demonstration of the Price and Market Interest Rate over Time of a 30-Year Treasury Bond Issued in 1983 with a Coupon of 10.69 Percent 16% Bond Price $1,600 14% $1,400 12% 10% $1,000 8% $800 Interest Rate 6% Interest Rate Bond Price $1,200 $600 S T O U T , 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 $0 2% 0% J in Chapter 6. Bondholdof market interest rate levels and changes are discussed ers can incur large capital gains or capital losses. I The fact that, as prevailing interest rates change, the prices of existing bonds L will change has a specific name in the financial industryinterest rate risk. L interest rates change subInterest rate risk means that during periods when stantially (and quickly), bondholders experience distinct gains and losses in their I bond inventories. But interest rate risk does not affect all bonds exactly the same. A Very short-term bonds experience little or no fluctuation in their prices, and thus N expose the bondholder to little interest rate risk. Long-term bondholders experience substantial interest rate risk. Table 7.3 illustrates the impact of interest rate risk on bonds with different coupons and times to maturity. 9 The first four rows show the prices and price changes for 30-year bonds with 5 different coupon rates. Notice that the bonds with higher coupon rates also have higher prices. Bondholders as a rule find it more6valuable to receive the large annuity payments. Also notice that a 1 percent increase in interest rates from T 6 percent to 7 percent causes bond prices to fall. Bondholders with higher coupon S bonds are not affected as much by interest rate increases because they can take the large coupon payments and reinvest those cash flows in new bonds that offer higher returns. The price decline is greater for bonds with lower coupons because of reinvestment rate risk. When interest rates increase, bondholders' cash flowsboth periodic payments and final payoff at maturityare discounted at a higher rate, decreasing a bond's value. Because the cash flows from low-coupon bonds are smaller, the holder of such bonds will have less money available from interest payments to buy the new, higher coupon bonds. Thus bondholders of lower coupon bonds have their capital tied up in assets that are not making them as much money. They face a bad dilemma: They can sell their lower coupon bonds and take a greater capital loss, using the (smaller) proceeds to buy new bonds with higher coupon rates. Or they can continue to receive the small chapter 7 cor6168X_ch07_232-271.indd 245 Data source: Yahoo! Finance, finance.yahoo.com. 4% $400 $200 As interest rates rise, bond prices fall. Here you can see great variance in the economy over 30 years. Long-term bondholders experience substantial interest rate risk. interest rate risk The chance of a capital loss due to interest rate fluctuations. reinvestment rate risk The chance that future interest payments will have to be reinvested at a lower interest rate. Valuing Bonds 245 21/10/13 3:56 PM Final PDF to printer table 7.3 Interest Rate Risk 1 2 3 4 5 6 7 8 9 10 11 12 LG7-5 A Time to Maturity 30 years 30 years 30 years 30 years B C D Coupon Price at 6% Price at 7% THE IMPACT OF THE COUPON RATE ON PRICE 0% $ 169.73 $ 126.93 5 861.62 750.55 7 1,138.38 1,000.00 10 1,553.51 1,374.32 E Change 25.2% 12.9 12.2 11.5 20 years 10 years 5 years 2 years THE IMPACT OF TIME TO MATURITY ON PRICE 5 884.43 786.45 5 925.61 857.88 5 957.35 916.83 5 981.41 963.27 11.1 7.3 4.2 1.8 S income payments and hold their T lower coupon bonds to maturity to avoid locking in the capital loss. Either way, they lose money relative to those bondholders O with higher coupon rates. You can see this illustrated in the 30-year bonds shown U tend to help partially offset changing discount in Table 7.3. Reinvestment rates rates for higher coupon payingTbonds. Another factor that influences the amount of reinvestment risk bondholders , face is their bonds' time to maturity. The last four bonds in the table all have a 5 percent coupon but have different times to maturity. Note that when interest rates increase, the bond pricesJof longer-term bonds decline more than shorterterm bonds. This shows that bonds with longer maturities and lower coupons I Short-term bonds with high coupons have the have the highest interest rate risk. lowest interest rate risk. HighLinterest rate risk bonds experience considerable price declines when interest rates L are rising. However, these bonds also experience dramatic capital gains when interest rates are falling. While a 1 percent change in market interest ratesI is not commonly seen on a daily or monthly basis, such a change is not unusual over A the course of several months or a year. N EXAMPLE 7-5 For interactive versions of this example visit www.mhhe.com/can3e 9 LG7-5 5 Capital Gains in the Bond 6 Market Say that you anticipate falling long-term T interest rates from 6 percent to 5.5 percent during the next year. If this occurs, what will be the total return for a 20-year, 6.5 percent coupon S bond through the interest rate decline? SOLUTION: To determine the total return, compute the capital gain or loss and the interest paid over the year. The capital gain or loss is determined from the change in price. The current bond price is: 12 Bond price 5 $32.50 3 D 246 1 (1 1 0.03)40 $1,000 5 $751.230 1 $306.557 5 $1,057.79 T1 0.03 (1 1 0.03)40 part four Valuing of Bonds and Stocks cor6168X_ch07_232-271.indd 246 21/10/13 3:56 PM Final PDF to printer The price in one year would be: CALCULATOR HINTS 12 Bond price 5 $32.50 3 D 1 (1 1 0.0275)38 $1,000 5 $760.276 1 $356.690 5 $1,116.97 T1 0.0275 (1 1 0.0275)38 N 5 40 I53 PMT 5 32.50 FV 5 1000 CPT PV 5 21,057.79 So, the capital gain is $59.18 (5 $1,116.97 2 $1,057.79). The interest payment during the year is $65 (5 0.065 3 $1,000). If interest rates fall to 5.5 percent, then this bond should provide a total return of $124.18, which would be an 11.74 percent return (5 $124.18 4 $1,057.79). Of course, this is only an anticipated interest rate change and it may not occur. Similar to Problems 7-25, 7-26, 7-35, 7-36, self-test problem 5 S T O U TIME OUT T for an 8.5 percent coupon 7-3 Show the time line and compute the present value bond (paid semiannually) with 12 years left to maturity and a market interest , Then change N 5 38 I 5 2.75 CPT PV 5 21,116.97 rate of 7.5 percent. Describe the relationship between interest rate changes and bond prices. 7-4 J I L L 7.3 Bond Yields I Current Yield A Although we speak about \"the prevailing interest rate,\" bond relationships reflect many interest rates (also called yields). SomeN rates are difficult to calculate LG7-6 but accurately reflect the return the bond is offering. Others, like the current yield, are easy to compute but only approximate the bond's true return. A bond's 9 rate divided by the bond's current yield is defined as the bond's annual coupon current market price. Current yield measures the5rate of return a bondholder would earn annually from the coupon interest payments alone if the bond were 6 purchased at a stated price. Current yield does not measure the total expected T or losses that will occur return because it does not account for any capital gains S to par. from purchasing the bond at a discount or premium current yield Yield to Maturity LG7-6 Yield to maturity is a more meaningful equation for investors than the simple current yield calculation. The yield to maturity calculation tells bond investors the total rate of return that they might expect if the bond were bought at a particular price and held to maturity. While the yield to maturity calculation provides more information than the current yield calculation, it's also more difficult to compute, because we must compute the bond's cash flows' internal rate of return. This calculation seeks to equate the bond's current market price with the value of all anticipated future interest and par value payments. In other words, it is the discount rate that equates the present value of all future cash flows with yield to maturity Return from interest payments; computed as the annual interest payment divided by the current bond price. The total return the bond offers if purchased at the current price and held to maturity. chapter 7 Valuing Bonds cor6168X_ch07_232-271.indd 247 247 21/10/13 3:56 PM Final PDF to printer the current price of the bond. To calculate yield to maturity, investors must solve for the interest rate, i, in equation 7-2, or solve for i in: Bond price 5 PV of annuity (PMT, i, N) 1 PV(FV, i, N) (7-2) Investors commonly compute the yield to maturity using financial calculators. For example, consider a 7 percent coupon bond (paid semiannually) with eight years to maturity and a current price of $1,150. The return that the bond offers investors, the yield to maturity, is computed as N 5 16, PV 5 21150, PMT 5 35, and FV 5 1000. Computing the interest rate (I) gives us 2.363 percent. We must remember, however, that 2.363 percent is only the return for six months because the bond pays semiannually. Yield to maturity always means an annual return. So, this bond's yield to maturity is 4.73 percent (2 3 2.363 percent). EXAMPLE 7-6 For interactive versions of this example visit www.mhhe.com/can3e CALCULATOR HINTS N=8 PV = 2962.81 PMT = 17.50 FV = 1000 CPT I = 2.263 so YTM = 2.263 2 = 4.53% LG7-6 S T and Yield to Maturity Computing Current Yield O bond with four years left to maturity and a quoted You have identified a 3.5 percent Treasury price of 96:09. Calculate the bond's U current yield and yield to maturity. T SOLUTION: , (1) First, identify that the bond's price is $962.81 (5 96 09/32% 3 $1,000 5 0.9628125 3 $1,000). (2) The annual $35 in interest payments is paid in two $17.50 semiannual payments. Therefore, the current yield of the bond is 3.64 percent (5 $35 4 J $962.81). (3) The yield to maturity is computed using equation 7-2 and the financial calculator as I FV 5 1,000. Computing the interest rate (I) results in 2.263 N 5 8, PV 5 2962.81, PMT 5 17.50, and percent and multiplying by 2 gives the yieldLto maturity of 4.53 percent. (4) Note that the current yield is less than the yield to maturity because it does not account for the capital L gain to be earned if held to maturity. I A N Similar to Problems 7-13, 7-14, 7-27, 7-28, self-test problem 2 9 5 6 T S Notice the link between a bond's yield to maturity and the prevailing market interest rates used to determine a bond's price as we BOND YIELDS AND FINANCIAL CALCULATORS discussed in the previous section. We use the People computing a bond's yield to maturity make three common market interest rate to compute the bond's mistakes. To avoid the first mistake, ensure that the bond price (PV) value. We use the actual bond price to comis a different sign than the interest and par value cash flows (PMT pute its yield to maturity. If the bond is corand FV). The second mistake: People forget to make the number of rectly priced at its economic value, then the periods (N) and the per-period interest payment (PMT) consistent. market interest rate will equal the yield to Both should be in semiannual terms if the coupon payment is paid semiannually. Last, many people forget to multiply the resulting maturity. Thus, the relationship that we precalculator interest rate (I) output by 2 to convert the semiannual viously identified between bond prices and rate back to an annual rate. market interest rates applies to yields as well. This shows the inverse relationship between bond prices and bond yields. As a bond's price falls, its yield to maturity increases and a rising bond price accompanies a falling yield. Look back at Figure 7.2 and you will see this relationship clearly. MATH COACH 248 part four Valuing of Bonds and Stocks cor6168X_ch07_232-271.indd 248 21/10/13 3:56 PM Final PDF to printer Yield to Call The yield to maturity computation assumes that the bondholder will hold the bond to its maturity. But remember that some bonds have call provisions that allow the issuers to repay the bondholder's par value prior to its scheduled maturity. Issuers often call bonds after large drops in market interest rates. In such cases, issuers commonly pay bondholders the bond's par value plus one year of interest payments. The reasons behind early bond redemptions are obvious. When interest rates fall, issuers can sell new bonds at lower interest rates. Companies want to refinance their debtjust as homeowners doto reduce their interest payments. Issuers gain important advantages with call provisions because they allow refinancing opportunities. Of course, the same provisions are disadvantages for bond investors. When bonds are called, investors receive the par value and call premium, but then investors must seek equally profitable bonds to buy with the proceeds. You will recall that investors can face reinvestment riskthe available bonds aren't as profitable because interest rates have declined. Bonds are called away at the worst time for investors. In addition, bond prices will rise S as market interest rates fall, which could provide issuers opportunities to sell the bonds at a profit. But the price T increases will be limited by the fact that the bond will likely be called early. As partial compensation, bond investors receive the callO price, which is the par value of the bond plus the call premium (typically one year of Uinterest payments). The possibility that bonds can be called early dampens their upside price potential. We can T even compute the price of a bond that's likely to be called from the equation: LG7-6 , Price of a callable bond 5 Present value of interest payments to call date 1 Present value of call price 12 5 PMT 3 D 1 (1 1 i)N J Call price TI 1 i (1 1 i)N (7-3) L L bond can be called and i is In this case, N is the number of periods until the the prevailing market rate. The prevailing market interest rate will probably difI fer from the rate for a noncallable bond. The previous section demonstrated via A the yield curve that bonds with different maturities have different yields. A bond Nfive years, will carry a yield that matures in 20 years, but is likely to be called in appropriate for a 5-year bond. Now, reconsider the 20-year bond with a 7 percent coupon that we discussed 9 previously (see pp. 242-243). If the bond can be called in five years with a call price 5 5.75 percent annually at that of $1,070, the appropriate discount rate happens to be time (instead of the 6 percent in the original problem). 6 This time line would be Period Cash flow 0 1 2 3 PV5? 35 35 35 T S 2.875% ... 4 7 35 ... 35 8 35 LG7-6 Semiannual periods 9 10 35 35 1,070 The changes in this time line are only 10 semiannual payments of $35 (rather than 40 such semiannual payments), a 2.875 percent semiannual discount rate, and the call price payment of $1,070. The price of this callable bond would be: 1 12 (1 1 0.02875)10 $1,070 T1 Bond price 5 $35 3 D 0.02875 (1 1 0.02875)10 5 $300.47 1 $805.91 5 $1,106.38 chapter 7 cor6168X_ch07_232-271.indd 249 CALCULATOR HINTS N 5 10 I 5 2.875 PMT 5 35 FV 5 1070 CPT PV 5 21,106.38 Valuing Bonds 249 21/10/13 3:56 PM Final PDF to printer yield to call The total return that the bond offers if purchased at the current price and held until the bond is called. In this example, the callable bond would be priced at $1,106.38, which is slightly lower than an identical bond that was not callable, priced at $1,115.57. If a bond is likely to be called, then the yield to maturity calculation does not give investors a good estimate of their return. Bondholders can use instead a yield to call calculation, which differs from the yield to maturity only in that its calculation assumes that the investor will receive the par value and call premium at the earliest call date. For example, reconsider the 7 percent coupon bond (paid semiannually) with 8 years to maturity, which we examined previously (see p. 248). The current bond price is $1,130 (which is slightly lower than the yield to maturity bond price of $1,150). If the bond can be called in three years at a specific call price of the par value plus one annual coupon, then what is the yield to call? The yield to call is computed as N 5 6, PV 5 21130, PMT 5 35, and FV 5 1070. The resulting interest rate (I) is 2.26 percent. The yield to call for this bond is thus 4.52 percent (5 2 3 2.26%). S T SPREADSHEETS AND BOND PRICING O Common spreadsheet programs have functions that can compute the price or yield to maturity of a U bond. The functions are: T Compute a bond price 5 PRICE(settlement,maturity,rate,yld,redemption,frequency,basis) , MATH COACH Compute a yield to maturity 5 YIELD(settlement,maturity,rate,pr,redemption,frequency,basis) J date. This is the purchase date of the bond; typically it is Settlement is the bond's settlement today. Maturity is the bond's maturityI date. Rate is the bond's annual coupon rate. Pr is the bond's price per $100 face value. Note that the par value of a bond is typically $1,000, so an adjustment is the bond's redemption value per $100 face value. Frequency is needed for this input. Redemption is L the number of coupon payments per L year. For semiannual, frequency 5 2. Basis is the type of day count basis to use. I Consider the bond valuation problem of Example 7-4. The spreadsheet solution is the same as the A equation. TVM calculator solution and the pricing N 9 5 6 T Also consider the yield to maturity problem in Example 7-6. This spreadsheet solves for the yield S to maturity. See this textbook's online student center to watch instructional videos on using spreadsheets. Also note that the solutions for all the examples in the book are illustrated using spreadsheets in videos that are also available on the textbook website. 250 part four Valuing of Bonds and Stocks cor6168X_ch07_232-271.indd 250 21/10/13 3:56 PM Final PDF to printer Municipal Bonds and Yield LG7-6 Municipal bonds (munis) seem to offer low yields to maturity compared to the return that corporate bonds and Treasury securities offer. Munis offer lower rates because the interest income they generate for investors is tax-exemptat least at the federal level.2 Specifically, income from municipal bonds is not subject to taxation by the federal government or the state government where the bonds are issued. As a result, municipal bond investors willingly accept lower yields than those they can obtain from taxable bonds. Generally speaking, investors compare the after-tax interest income earned on taxable bonds against the return earned on municipal bonds. For example, suppose an investor in the 35 percent marginal income tax bracket has $100,000 to invest in either corporate or municipal bonds. The $100,000 investment would earn a taxable $7,000 annually from 7 percent corporate bonds or $5,000 from tax-exempt 5 percent municipal bonds. After taxes, the corporate bond leaves the investor with $4,550 [5(1 2 0.35) 3 $7,000]. Obviously, this is less than the tax-free income of $5,000 generated by the muni bond. A common way to compare yields from muni bonds versus those from taxS able bonds is to convert the yield to maturity of the muni to a taxable equivalent T yield, as shown in equation 7-4. taxable equivalent yield O (7-4) Equivalent taxable yield 5 U 1 2 Tax rate T tax bracket) a 5 percent For high-income investors (in the 35 percent marginal muni bond has an equivalent taxable yield of 7.69 ,percent [5 0.05 4 (1 2 0.35)]. Modification of a municipal bond's yield to maturity used to compare muni bond yields to taxable bond yields. Muni yield The 5 percent muni is more attractive for this investor than a 7 percent corporate bond. However, for an investor with lower income (in the 28 percent marginal tax bracket) the equivalent taxable yield is only 6.94Jpercent. The corporate bond I L LG7-6 L Which Bond Has a Better After-Tax Yield? I Imagine a time when you have a high income, placing you in the 31 percent marginal tax A bracket. You are interested in investing some money in a bond issue and have three alternatives. The first is a corporate bond with a 6.4 percent yield N to maturity. The second bond is a EXAMPLE 7-7 For interactive versions of this example visit www.mhhe.com/can3e Treasury that offers a 5.7 percent yield. The third choice is a municipal bond priced at a yield to maturity of 4.0 percent. Which bond gives you the highest after-tax yield? 9 5 The Treasury and corporate bonds are both taxable, so we can compare them directly with each other. The 6 yield of 6.4 percent on the corporate is clearly higher than the 5.7 percent yield offered by the Treasury bond. Tits equivalent taxable yield as in To include a comparison with the nontaxable municipal bond, compute equation 7-4: S SOLUTION: Equivalent taxable yield 5 4.0% 5 5.80% 1 2 0.31 The municipal bond's equivalent taxable yield of 5.80 percent is higher than the Treasury but lower than the corporate bond. Similar to Problems 7-15, 7-16, 7-31, 7-32, 7-37, 7-38, self-test problem 3 2 States have differing rules about whether they tax the income from a particular municipal bond they will generally tax income from munis issued out of state. Further, capital gains arising from municipal bond sales may be taxed, and the income from municipal bonds must be added to overall income when determining the Alternative Minimum Tax