Define how stocks, bonds and investments play a role in the financial future of a for profit and non profit organization?
Define how stocks, bonds and investments play a role in the financial future of a for profit and non profit organization? How does the overall market play into this? Using your company from previous(APPLE) and an additional company. There will need to be equations used, you decide which ones, show your math and explain why you chose those. Be very descriptive.
This paper will be no less than 3 pages and that should not include the title and reference section.
Essential Activities:
Reading Chapter 7 and 8 in the text will assist you in writing this discussion forum.
Watching the video Interest Rates will assist you in writing this discussion forum.
Notes:
This paper must be formatted in APA Style 7th edition.
Please refer to the written assignment rubric on the start here tab for this paper.
This paper is due Saturday.
https://www.investopedia.com/terms/i/interestrate….
Requirements: in-depth example
How do you even purchase a bond in the first place?226cor91411_ch07_226-263.indd 226 01/20/17 06:58 PMValuing Bonds7PART FOURviewpointsBusiness ApplicationYou are the chief financial officer (CFO) for Beach Sand Resorts. The firm needs $150 million of new capital to renovate a hotel property. As you discuss the firmÕs plans with a credit rating agency, you learn that if 15-year bonds are used to raise this capital, the bonds will be rated BB and will have to offer a 7 percent return. How many bonds will you have to issue to raise the necessary capital? What semiannual interest payments will Beach Sand have to make? (See the solution at the end of the chapter.)Personal ApplicationYou would like to invest in bonds. Your broker suggests two different bonds. The first, issued by Trust Media, will mature in 2023. 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 2023. This bondÕs 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 the solution at the end of the chapter.)Final PDF to printer
227cor91411_ch07_226-263.indd 227 01/20/17 06:58 PMLearning GoalsHow important are bonds and the bond market to a capital-ist economy? Those unfamil-iar with the financial markets may have the impression that the stock market dominates capital markets in the United States and in other coun-tries. Stock market performance appears constantly on 24-hour TV 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 stock market. At the end of 2015, the U.S. bond market represented roughly $39.6 trillion in outstanding debt obligations. At the same time, the market value of all common stock issues was worth just over half of the value of the bond market, at roughly $21.0 trillion.Bonds also trade in great volume and frequency. During 2015, the total average daily trading in all types of U.S. bonds reached over $730 billion. Investors are often attracted to the stock market because it offers the potential for high investor returnsÑbut great risks come with that high potential return. While some bonds offer safer and more stable returns than stocks, other bonds also offer high potential rewards and, conse-quently, higher risk.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 weÕve used in the preceding chapters. LG7-1 Describe bond characteristics. LG7-2 Identify various bond issuers and their motivation for issu-ing 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 riskÕs effects on bond yields. LG7-8 Assess bond market performance.© Royalty-Free/CorbisFinal PDF to printer
228 part four Valuing of Bonds and Stockscor91411_ch07_226-263.indd 228 01/20/17 06:58 PM7.1 ∙ Bond Market OverviewBond CharacteristicsBonds are debt obligation securities that corporations, 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 securi-ties because bondholders (investors) know both how much they will receive in inter-est payments and when their principal will be returned. From the bond issuerÕs point of view, the bond is a loan that requires regular interest payments and an eventual repay-ment of the borrowed principal. InvestorsÑoften pension funds, banks, and mutual fundsÑbuy 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 bondÕs main characteristics include: ¥ The date the principal will be repaid (the maturity date). ¥ The par value, or face value, of each bond, which is the principal loan amount that the borrower must repay. ¥ The coupon (interest) rate. ¥ A description of any property to be pledged as collateral. ¥ Steps that the bondholder can take in the event that the issuer fails to pay the inter-est or principal.Table 7.1 describes par value and other bond characteristics. Most bonds have a par value of $1,000. This is the amount of principal the issuer has promised to repay. Bonds have fixed lives. The bondÕs life ends when the issuer repays the par value to the buyer on the bondÕs maturity date. Although a bond will mature on a specific calendar date, 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 bonds together by their time to maturity and classifies them as short-term bonds, medium-term bonds, or long-term bonds, regardless of issuer. Long-term bonds carry 20 or 30 years to maturity. Of course, over time, the 30-year bond becomes a 20-year bond, 10-year bond, and eventually matures. But other time periods to maturity do exist. For example, in 2011, the railroad company Norfolk Southern Corp. issued $400 million of bonds with 100 years to maturity. The bonds have a coupon (inter-est) rate of 6 percent and mature in 2111.When interest rates economywide fall several percentage points (which often takes several years), homeowners everywhere seek to refinance their home mortgages. They want to make lower interest payments (and sometimes want to pay down their mortgage principal) every month. Corporations that have outstanding bond debt will also want to refinance those bonds. Sometimes the indenture contract (the legal contract between a bond issuer and bondholders) allows companies to do so; sometimes the indenture pro-hibits refinancing. Bonds that can be refinanced have a call feature, which means that the issuer can ÒcallÓ the bonds back and repay the principal before the maturity date. To com-pensate the bondholders for getting the bond called, the issuer pays the principal and a call premium. The most common call premium is one yearÕs worth of interest payments. In some indentures, the call premium declines over time.The bondÕs coupon rate determines the dollar amount of interest paid to bondhold-ers. 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 per-cent 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 issued with a coupon book. Every six months a bondholder would tear out a coupon and mail it to the issuer, who would then make the LG 7-1bondsPublicly traded form of debt.fixed-income securitiesAny securities that make fixed payments.principalFace amount, or par value, of debt.indenture agreementLegal contract describing the bond characteristics and the bondholder and issuer rights.maturity dateThe calendar date on which the bond principal comes due.par valueAmount of debt borrowed to be repaid; face value.time to maturityThe length of time (in years) until the bond matures and the issuer repays the par value.callAn issuer redeeming the bond before the scheduled maturity date.call premiumThe amount in addition to the par value paid by the issuer when calling a bond.coupon rateThe annual amount of inter-est paid expressed as a percentage of the bondÕs par value.Final PDF to printer
chapter 7 Valuing Bonds 229cor91411_ch07_226-263.indd 229 01/20/17 06:58 PMinterest payment. These are sometimes referred to as bearer bonds (often a feature of spy or mystery movies), because whoever held the coupon book could receive the payments. Nowadays, issuers register bond owners and automatically wire interest payments to the ownerÕs bank or brokerage account. Nevertheless, the term coupon persists today.At original issue, bonds typically sell at par value, unless interest rates are very volatile. Bondholders recoup the par value on the bondÕs maturity date. How-ever, at all times in between these two dates, bonds might trade among investors in the secondary bond market. The bondÕs price as it trades in the secondary market will not likely be the par value. Bonds trade for higher and lower prices than their par values. WeÕll thoroughly demonstrate the reasons for bond pricing in a later sec-tion of this chapter. Bond prices are quoted in terms of percent of par value rather than in dollar terms. Sources of trading information list a bond that traded at $1,150 as 115, and a bond that traded for $870 as 87.TABLE 7.1 Typical Bond FeaturesCharacteristicDescriptionCommon ValuesPar valueThe amount of the loan to be repaid. This is often referred to as the principal of the bond.$1,000Time to maturityThe number of years left until the maturity date.1 year to 30 yearsCallThe opportunity for the issuer to repay the principal before the maturity date, usually because interest rates have fallen or issuerÕs circumstances have changed. When calling a bond, the issuer commonly pays the principal and one year of interest payments.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.Coupon rateThe interest rate used to compute the bondÕs interest payment each year. Listed as a percentage of par value, the actual payments usually are paid twice per year.2 to 10 percentBond priceThe bondÕs market price reported as a percentage of par value.80 to 120 percent of par valuebond priceCurrent price that the bond sells for in the bond market.MATH COACH PERCENT-TO-DECIMAL CONVERSIONSWhen discussing interest rates or using them in calculator or spread-sheet time value of money functions, the value should be in percent (%) form, like 2.5%, 7%, and 11%. When using interest rates in formu-las, the value needs to be in decimal form, like 0.025, 0.07, and 0.11.To convert between the two forms of representing an interest rate, use Decimal = Percent ( % ) __________ 100 EXAMPLE 7-1Bond CharacteristicsConsider a bond issued 10 years ago with an at-issue time to maturity of 30 years. The bondÕs coupon rate is 8 percent and it currently trades in the bond market for 109. Assum-ing a par value of $1,000, what is the bondÕs current time to maturity, semiannual interest payment, and bond price in dollars?SOLUTION: Time to maturity = 30 years − 10 years = 20 years Annual payment = 0.08 × $1,000 = $80, so semiannual payment is $40 Bond price = 1.09 × 1,000 = $1,090 Similar to Problems 7-1, 7-2, 7-3, 7-4, Self-Test Problem 1LG7-1 Bond IssuersFor many years, bonds were considered stodgy, overly conservative investments. Not anymore! The fixed-income industry has seen tremendous innovation in the past couple LG7-2 For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.Final PDF to printer
230 part four Valuing of Bonds and Stockscor91411_ch07_226-263.indd 230 01/20/17 06:58 PMof decades. The financial industry has created and issued many new types of bonds and fixed-income securities, some with odd-sounding acronyms, like TIGRs, CATS, COU-GRs, 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, corpo-rate 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 Òfull-faith-and-creditÓ 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 pub-lic 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, Treasury securities issued with 1 to 10 years until maturity are Treasury notes. Securities issued with 10 to 30 years until maturity are Treasury bonds. Figure 7.1 shows that the number of new Treasuries being offered actually declined in the late 1990s as the federal budget deficit declined. However, this reversed in 2002 and then dramatically accelerated in 2009 after the global financial cri-sis and during the years of the FedÕs quantitative easing programs.CORPORATE BONDS Corporations raise capital to finance investments in inven-tory, plant and equipment, research and development, and general business expansion. As managers decide how to raise capital, corporations can issue debt, equity (stocks), or a mixture of both. The driving force behind a corporationÕs financing strategy is the 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 2015, corporations switched to raising capital by issuing bonds to take advantage of low interest rates and issued $17.1 trillion in new bonds. You can see this rise in capital reflected in Figure 7.1.05001,0001,5002,0002,50019901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012201320142015Annual Bond Issuance ($ Billions)MunicipalTreasuryCorporateFIGURE 7.1 Amount of Capital Raised Yearly from Bonds Issued by Local and Federal Government and CorporationsLocal or municipal governments, the U.S. Treasury, and corporations have issued many new types of bonds and fixed-income securities over the past two decades.Data source: Securities Industry and Financial Markets Association.Final PDF to printer
chapter 7 Valuing Bonds 231cor91411_ch07_226-263.indd 231 01/20/17 06:58 PMMUNICIPAL BONDS State and local governments borrow money to build, repair, or improve streets, highways, hospitals, schools, sewer systems, and so on. The interest and principal on these municipal bonds are repaid in two ways. Projects 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 rev-enue 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 SecuritiesTreasury Inflation-Protected Securities (TIPS) have proved one of the most success-ful 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. 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 infla-tion (measured by the consumer price index, CPI). As the bondÕs 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 prin-cipal amount will be substantially higher than the original $1,000. Consider a 10-year TIPS issued on January 15, 2009, that pays a 2⅛ 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 (= $1,000 × 230.22100 Ö 214.69971). Therefore, the 2⅛ percent coupon (paid semiannually) would be $11.39 = (0.02125 × $1,072.29 Ö 2). A TIPSÕ total return comes from both the interest payments and the inflation adjustment to the par value.Treasury Inflation- Protected SecuritiesTIPS are U.S. government bonds where the par value changes with inflation.EXAMPLE 7-2TIPS PaymentsA TIPS bond was issued on July 15, 2006, that pays a 2½ percent coupon. The reference CPI at issue was 201.95. The reference CPI for the following interest payments wereJanuary 2009214.70July 2009213.52January 2010216.25Given these numbers, what is the par value and interest payment of the TIPS on the three interest-payment dates? What is the total return from January 2009 to January 2010?SOLUTION:Compute the TIPS index ratio for each period as current CPI divided by the at-issue CPI: The par value for January 2009 is $1,000 × 214.70 Ö 201.95 = $1,063.13, so the interest pay-ment is 0.025 × $1,063.13 Ö 2 = $13.29. The answers for the next two dates are:July 2009Par value = $1,057.29Interest payment = $13.22January 2010Par value = $1,070.81Interest payment = $13.39The capital gain between January 2009 and January 2010 is $1,070.81 Ð $1,063.13 = $7.68. Adding the two interest payments together results in $26.61 (= $13.22 + $13.39). Thus, the total return is 3.23% = ($7.68 + $26.61 )/$ 1,063.13.Similar to Problems 7-7, 7-8, 7-19, 7-20, 7-33, 7-34LG7-2 For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.Final PDF to printer
232 part four Valuing of Bonds and Stockscor91411_ch07_226-263.indd 232 01/20/17 06:58 PMU.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 Admin-istration, among others, issue these agency bonds to support particular sectors of the economy. Agency securities do not carry the federal governmentÕs 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.U.S. government agencies invented one popular type of debt security: mortgage-backed securities (MBSs). Fannie Mae and Freddie Mac offer subsidies or mortgage guarantees for people who wouldnÕt otherwise qualify for mortgages, especially first-time homeown-ers. Fannie Mae started out as a government-owned enterprise in 1938 and became a pub-licly held corporation in 1968. Freddie Mac was chartered as a publicly held corporation at its inception in 1970. Since 2008, both have been in government conservatorship and run by the Federal Housing Finance Agency. To increase the amount of money available (liquidity) for the home mortgage market, Fannie Mae and Freddie Mac purchase home mortgages from banks, credit unions, and other lenders. They combine the mortgages into diversified portfolios of such loans and then issue mortgage-backed securities, which represent a share in the mortgage debt, to investors. As homeowners pay off or refinance the underlying portfolio of mortgage loans, MBS investors receive interest and principal payments. After selling mortgages to Fannie Mae or Freddie Mac, mortgage lenders have ÒnewÓ cash to pro-vide more mortgage loans. This process worked well for decades until the late 2000s, when subprime mortgages were given to people who couldnÕt afford them. As 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 bor-rowers pay off their consumer loans. The asset-backed securities market is one of the fastest-growing areas in the financial services sector.agency bondsBonds issued by U.S. gov-ernment agencies.Treasury bonds are U.S. government-issued debt securities that investors trade on secondary markets. The government also issues nonmarketable debt, called Òsavings bonds,Ó directly to investors. The common EE savings bonds, introduced in 1980, do not pay regular interest payments. Instead, interest accrues and adds to the bondÕs value. After a one-year holding period, they can be redeemed at many banks or credit unions. You can also purchase savings bonds and other Treasury securi-ties (bills, notes, bonds, and TIPS) electronically through the U.S. TreasuryÕs 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 pur-chased 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 BUY TREASURIES DIRECT!finance at work personal financesell 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 grandchil-dren. 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 ÒPatriot bondÓ on them. So EE savings bonds are now often called Patriot Bonds.mortgage-backed securitiesSecurities that represent a claim against the cash flows from a pool of mortgage loans.asset-backed securitiesDebt securities whose pay-ments originate from other loans, such as credit card debt, auto loans, and home equity loans.! want to know more?Key Words to Search for Updates: TreasuryDirect (go to www.treasurydirect.gov)Final PDF to printer
chapter 7 Valuing Bonds 233cor91411_ch07_226-263.indd 233 01/20/17 06:58 PMOn the bondÕs 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 company stock. The number of shares of stock for which the bond can be converted 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. Although the bondholder can convert to the stock shares anytime, investors tend to wait until the maturity date when the interest payments from the bond exceed the divi-dends that would be paid from the stock shares. Reading Bond QuotesTo those familiar with bond terminology, bond quotes provide all of the information needed to make informed investment decisions. The volume of Treasury securities traded each day is substantial. Treasury bonds and notes average more 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 and data can be found in The Wall Street Journal and online at places like Yahoo! Finance (finance.yahoo.com). Table 7.2 shows three bond quote examples.convertible bondA debt security that can be converted to shares of stock or another type of security.LG7-3 ! want to know more?Key Words to Search for Updates: subprime, MBS, financial crisisIn 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. Finan-cial 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 subprime MORTGAGE-BACKED SECURITIES AND FINANCIAL CRISISfinance at work marketsborrowers were charged higher interest rates. When these subprime mortgages were packed into the pool of mort-gages, 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 down-ward 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 bor-rowers 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.Further Reading: John W. Schoen, Ò7 years on from crisis, $150 billion in bank fines and penalties,Ó CNBC, April 30, 2015. http://www.cnbc .com/2015/04/30/7-years-on-from-crisis-150-billion-in-bank-fines-and- penalties.htmlFinal PDF to printer
234 part four Valuing of Bonds and Stockscor91411_ch07_226-263.indd 234 01/20/17 06:58 PMA typical listing for Treasury bonds appears first. Here, this Treasury bond pays bondholders a coupon of 2.750 percent. On a $1,000 par value bond, this interest income would be $27.50 annually, paid as $13.750 every six months per bond. The bond will mature in February of 2018Ñsince this is fairly soon, the bond is considered a short-term bond. Both the bid and the ask quotes for the bond appear, expressed as per-centages of the bondÕs par value of $1,000. The bid price is the price at which investors can sell the bond. A bid of 104.0156 means that an investor could sell for $1,040.156. Investors can buy this bond at the ask price of 104.0313, or $1,040.313. Since the price is higher than the par value of the bond, the bond is selling at a premium to par because its coupon rate is higher than current rates. Thus, investors call this kind of security a premium bond.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. Since the bond dealer takes the opposite side of the transaction, the dealer buys at the low price and sells at the higher price. The bid-ask spread is part of the dealerÕs compensation for taking on risk. An investor who bought this bond and held it to maturity would experi-ence a $40.31 (= $1,040.31 Ð $1,000) capital loss (Ð3.87 percent [= Ð$40.31/$1,040.31]). The bond lost 0.0234 percent of its value during the dayÕs tradingÑa change of Ð$0.23 for a $1,000 par value bond. Last, the bond is offering investors who purchase it at the ask price and hold it to maturity a 0.771 percent annual return.Corporate bond quotes provide similar information. The table shows the quote for a Boeing bond that offers bondholders a coupon of 2.60 percent, or $13.00 semiannually (= $1,000 × 0.026 Ö 2). The bond would be considered a mid-term bond (usually five years to maturity), since it matures in the year 2025. Corporate bonds are also quoted in percentage of par value. The price quote of 98.400 indicates that the last trade occurred at a price of $984.00 per bond. Since the bond is selling for a price lower than its $1,000 par value, itÕs called a discount bond. An investor who bought this bond would reap a $16.00 (= $1,000 – $984.00) capital gain if the bond were held to maturity. The Boeing bond represents an annual return of 2.79 percent for the investor who purchases the bond at $984.00.Companies set a bondÕs 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 premium bondA bond selling for greater than its par value.discount bondA bond selling for lower than its par value.Treasury SecuritiesCOUPON RATEMO/YRBIDASKEDCHGASK YLD2.750Feb 18104.0156104.0313−0.02340.771Corporate BondCOMPANYCOUPONMATURITYLAST PRICEYIELDBoeing Co2.60October 202598.4002.79Municipal BondISSUECOUPONMATURITYPRICEBID YLDNYC Muni Wtr Fin Auth4.50006-15-3797.5704.66TABLE 7.2 Bond Quote ExamplesFinal PDF to printer
chapter 7 Valuing Bonds 235cor91411_ch07_226-263.indd 235 01/20/17 06:58 PMbond issues many times may carry very different coupon rates 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 Munic-ipal 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, itÕs considered a long-term bond. According to Table 7.2, the bond is trading at a price just below par valueÑ97.57 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 dol-lar amount of $4,878.50 (= 0.9757 × $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.EXAMPLE 7-3Bond QuotesYou note the following bond quotes and wish to determine each bondÕs price, term, and interest payments.Treasury SecuritiesMATURITY RATEMO/YRBIDASKEDCHGASK YLD9.00Nov 20137.5938137.6250Ð0.15634.80Corporate BondCOMPANYCOUPONMATURITYLAST PRICELAST YIELDKohls Corp7.375Oct 15, 2023110.014.991Municipal BondISSUECOUPONMATURITYPRICEYLD TO MATFlorida St Aquis & Bridge Constr5.00July 1, 2025106.784.458SOLUTION: The Treasury bond matures in November of 2020 and pays 9 percent interest. Investors receive cash interest payment of $45 (= 0.09 × $1,000 Ö 2) semiannu-ally. Since the bond matures in less than 10 years but more than 1 year, we would consider it a mid-term bond. Since no ÒnÓ appears next to the maturity date, we can 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 (= 137.594 × $1,000) and buy it for $1,376.25 (= 1.37625 × $1,000). The price fell on this particular day by $1.56 (= Ð0.001 5625 × $1,000). The dealer earned $0.31 (× $1,376.25 Ð $1,375.94) on each trade of these premium bonds.The Kohls corporate bond pays a semiannual interest payment of $36.88 (= 0.07375 × $1,000 Ö 2) and its price is $1,100.10 (= 1.1001 × $1,000). This premium bondÕs 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 (= 0.05 × $5,000 Ö 2) every six months. The bonds are priced at $5,339.00 (= 1.0678 × $5,000).Similar to Problems 7-9, 7-10, Self-Test Problem 1LG7-3 For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.Final PDF to printer
236 part four Valuing of Bonds and Stockscor91411_ch07_226-263.indd 236 01/20/17 06:58 PM7.2 ∙ Bond ValuationPresent Value of Bond Cash FlowsAny bondÕs value computation directly applies time value of money concepts. Bondhold-ers know the interest payments that they are scheduled to receive and the repayment of the par value at maturity. The current price of a bond is, therefore, the present value of these future cash flows discounted at the prevailing market interest rate. The prevailing market interest rate will depend on the bondÕs term to maturity, credit quality, and tax 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 pay-ments. Instead, the bond pays only the par value payment at its maturity date. So a zero coupon bond sells at a substantial discount from its par value. For example, a bond with a par value of $1,000, maturing in 20 years, and priced to yield 6 percent, might be pur-chased 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) represents the interest income received over the 20 years based upon the discount rate of 6 percent. The time line for this zero coupon bond valuation appears as56%Cash ßowPeriod10020 years151,000PV = ?We compute the zeroÕs price by finding the present value of the $1,000 cash flow received in 20 years. However, to be consistent with regular coupon-paying bonds, zero coupon bonds are priced using semiannual compounding. So the formula and calculator valuation would use 40 semiannual periods at a 3 percent interest rate rather than 20 peri-ods at 6 percent. Using the present value equation of Chapter 4 results in PV = F V N _____ (1 + i ) N = $1,000 ______ 1. 03 40 = $1,000 ______ 3.262 = $306.56 So the zero coupon bondÕs 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 comparisonÕs 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 pay-ments 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 asLG7-4 zero coupon bondA bond that does not make interest payments but generally sells at a deep discount and then pays the par value at the maturity date.1Cash ßowPeriodPV = ?23703435383940Semiannual periods353535353535351,000. . .. . .3%TIME OUT 7-1 Describe the different reasons that the U.S. government, local governments, and corpo-rations would issue bonds. 7-2 What is the following bondÕs price and what dollar amount will the bond pay for its semiannual interest payment? COMPANYCOUPONMATURITYPRICEYIELDHome Depot Inc.5.40Mar 1, 2020100.065.391CALCULATOR HINTSN = 40 I = 3PMT = 0FV = 1000CPT PV = −306.56Final PDF to printer
chapter 7 Valuing Bonds 237cor91411_ch07_226-263.indd 237 01/27/17 07:20 PMThe 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 bondÕs maturity. Think through this: When bonds pay semiannual payments, the discount rate must be a semian-nual 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 pres-ent value equations for the annuity cash flows and the value of the par redemption appear in the bond valuation equation 7-1: Present value of bond = Present value of interest payments + Present value of par value = PMT × ⎡ ⎢ ⎣ 1 − 1 ______ (1 + i) N ___________ i ⎤ ⎥ ⎦ + $1,000 __________ (1 + i) N 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 denoted in semiannual periods. The price of this coupon bond should be Bond price = $35 × ⎡ ⎢ ⎣ 1 − 1 __________ (1 + 0.03) 40 ______________ 0.03 ⎤ ⎥ ⎦ + $1,000 ____________ (1 + 0.03) 40 = $809.017 + $306.557 = $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 payment ($306.557).Because equation 7-1 is quite complex, we usually compute bond prices using a finan-cial calculator or computer program. An investor would compute the bond value using a financial calculator by entering N = 40, I = 3, PMT = 35, FV = 1000, and computing the present value (PV). The calculator solution is $1,115.57.1CALCULATOR HINTSN = 40I = 3PMT = 35FV = 1000CPT PV = −1,115.57(7-1)1In order to focus on the valuation concepts, we present these examples with the full six months until the bondÕs 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 priceEXAMPLE 7-4Find the Value of a BondConsider 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 com-pounding (N = 2 × 15 = 30, i = 6.5 Ö 2 = 3.25, and PMT = 0.055 × $1,000 Ö 2 = $27.50) as Bond value = $27.50 × [ 1 − 1 ____________ (1 + 0.0325) 30 _____________ 0.0325 ] + $1,000 ___________ (1 + 0.0325) 30 = $522.00 + $383.09 = $905.09 So this bondÕs value is $905.09, which is less than the $940 price. The bond is overvalued in the market and you should not buy it.Similar to Problems 7-21, 7-22, 7-23, 7-24, Self-Test Problem 1LG7-4 For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.CALCULATOR HINTSN = 30I = 3.25PMT = 27.50FV = 1000CPT PV = −905.09Final PDF to printer
238 part four Valuing of Bonds and Stockscor91411_ch07_226-263.indd 238 01/20/17 06:58 PMBond Prices and Interest Rate RiskAt the time of purchase, the bondÕs interest payments and par value expected at maturity are fixed and known. Over time, economywide interest rates change, but the bondÕs coupon rate remains fixed. A rise in prevailing interest rates (also called increasing the discount rate) reduces all bondsÕ values. If interest rates fall, all bonds will enjoy rising values. Consider that when interest rates rise, newly issued bonds offer to pay higher interest rates than the rates offered on existing bonds. So to sell an existing bond with its lower coupon rate, its market price must fall so that the buyer can expect a profit similar to that offered by newly issued bonds. Similarly, when pre-vailing 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 7.47 percent coupon exactly matched prevailing interest rates when the bond was issued in 1986. Consequently, the bond sells for its par value of $1,000. Shortly thereafter, interest rates quickly rose to over 9 percent. As interest rates rose, bond prices had to decline. Then in 1988, interest rates started a prolonged descent to lows not seen for decades. 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. Note that since the bond will only pay $1,000 when it matures, the price must converge to $1,000 at the end. The determinants of market interest rate levels and changes are discussed in Chapter 6. Bondholders can incur large capital gains or capital losses.The fact that, as prevailing interest rates change, the prices of existing bonds will change has a specific name in the financial industryÑinterest rate risk. Interest rate risk means that during periods when interest rates change substantially (and quickly), bondholders experience distinct gains and losses in their bond inventories. But interest LG7-5 interest rate riskThe chance of a capital loss due to interest rate fluctuations.MATH COACH BOND PRICING AND PERIODSSince most bonds have semiannual interest payments, we must use semiannual periods to discount the cash flows. Most errors in com-puting a bond price occur in the adjustment for semiannual periods. The errors happen whether you are using either the bond pricing equation or a financial calculator. To convert to semiannual periods, be sure to adjust the three variables: number of periods, interest rate, and payments.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 a six-month rate. Divide the annual coupon payment by 2 for the six-month payment. Remember to adjust all three inputs for the semiannual periods.A coupon-paying bondÕs price should hover reasonably around the par value of the bond. For a $1,000 par value bond, we could expect a price in the range of $700 to $1,300. If you compute a price outside this range, check to see whether you made the semiannual period adjustments correctly.$0$200$400$600$800$1,000$1,200$1,400198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012201320142015Bond Price0%2%4%6%8%10%12%Interest RateInterest rateBond priceFIGURE 7.2A Demonstration of the Price and Market Interest Rate over Time of a 30-Year Treasury Bond Issued in 1986 with a Coupon of 7.47 PercentAs interest rates rise, bond prices fall. Here you can see great variance in the economy over 30 years. Long-term bondholders experience substantial inter-est rate risk.Data source: Yahoo! Finance, finance.yahoo.com.Final PDF to printer
chapter 7 Valuing Bonds 239cor91411_ch07_226-263.indd 239 01/20/17 06:58 PMrate risk does not affect all bonds exactly the same. Very short-term bonds experience little or no fluctuation in their prices, and thus 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.The first four rows show the prices and price changes for 30-year bonds with differ-ent coupon rates. Notice that the bonds with higher coupon rates also have higher prices. Bondholders as a rule find it more valuable to receive the large annuity payments. Also notice that a 1 percent increase in interest rates from 6 percent to 7 percent causes bond prices to fall. Bondholders with higher coupon 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, bondholdersÕ cash flowsÑboth periodic pay-ments and final payoff at maturityÑare discounted at a higher rate, decreasing a bondÕs 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 cou-pon 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 income payments and hold their lower coupon bonds to maturity to avoid locking in the capital loss. Either way, they lose money relative to those bondholders with higher coupon rates. You can see this illustrated in the 30-year bonds shown in Table 7.3. Reinvestment rates tend to help partially offset changing discount rates for higher coupon paying bonds.Another factor that influences the amount of reinvestment risk bondholders face is their bondsÕ time to maturity. The last four bonds in the table all have a 5 percent cou-pon but have different times to maturity. Note that when interest rates increase, the bond prices of longer-term bonds decline more than shorter-term bonds. This shows that bonds with longer maturities and lower coupons have the highest interest rate risk. Short-term bonds with high coupons have the lowest interest rate risk. High interest rate risk bonds experience considerable price declines when interest rates are rising. However, these bonds also experience dramatic capital gains when interest rates are falling. While a 1 percent change in market interest rates is not commonly seen on a daily or monthly basis, such a change is not unusual over the course of several months or a year.reinvestment rate riskThe chance that future interest payments will have to be reinvested at a lower interest rate. ABCDE1Time to MaturityCouponPrice at 6%Price at 7%Change23THE IMPACT OF THE COUPON RATE ON PRICE430 years 0%$ 169.73$ 126.93−25.2%530 years5 861.62 750.55−12.9 630 years71,138.381,000.00−12.2 730 years101,553.511,374.32−11.5 89THE IMPACT OF TIME TO MATURITY ON PRICE1020 years5884.43786.45−11.11110 years5925.61857.88−7.312 5 years5957.35916.83−4.213 2 years5981.41963.27−1.81415=PV(0.06/2,2*5,-B12*10/2,-1000)=(D12-C12)/C12TABLE 7.3 Interest Rate RiskFinal PDF to printer
240 part four Valuing of Bonds and Stockscor91411_ch07_226-263.indd 240 01/20/17 06:58 PMTIME OUT 7-3 Show the time line and compute the present value for an 8.5 percent coupon bond (paid semiannually) with 12 years left to maturity and a market interest rate of 7.5 percent. 7-4 Describe the relationship between interest rate changes and bond prices. 7.3 ∙ Bond YieldsCurrent YieldAlthough we speak about Òthe prevailing interest rate,Ó bond relationships reflect many interest rates (also called yields). Some rates are difficult to calculate but accu-rately reflect the return the bond is offering. Others, like the current yield, are easy to compute but only approximate the bondÕs true return. A bondÕs current yield is defined as the bondÕs annual coupon rate divided by the bondÕs current market price. Current yield measures the rate of return a bondholder would earn annually from the coupon interest payments alone if the bond were purchased at a stated price. Current yield does not measure the total expected return because it does not account for any capital gains or losses that will occur from purchasing the bond at a discount or pre-mium to par.Yield to MaturityYield 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 LG7-6 current yieldReturn from interest pay-ments; computed as the annual interest payment divided by the current bond price.yield to maturityThe total return the bond offers if purchased at the current price and held to maturity.Capital Gains in the Bond MarketSay that you anticipate falling long-term 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 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 Bond price = $32.50 × [ 1 − 1 __________ (1 + 0.03) 40 ___________ 0.03 ] + $1,000 _________ (1 + 0.03) 40 = $751.230 + $306.557 = $1,057.79 The price in one year would be Bond price = $32.50 × [ 1 − 1 ____________ (1 + 0.0275) 38 _____________ 0.0275 ] + $1,000 ___________ (1 + 0.0275) 38 = $760.276 + $356.690 = $1,116.97 So, the capital gain is $59.18 (= $1,116.97 − $1,057.79). The interest payment during the year is $65 (= 0.065 × $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 (= $124.18 Ö $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 5EXAMPLE 7-5LG7-5 CALCULATOR HINTSN = 40I = 3PMT = 32.50FV = 1000 CPT PV = −1,057.79 Then change N = 38I = 2.75 CPT PV = −1,116.97For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.Final PDF to printer
chapter 7 Valuing Bonds 241cor91411_ch07_226-263.indd 241 01/30/17 11:55 AMcurrent yield calculation, itÕs also more difficult to compute, because we must compute the bondÕs cash flowsÕ internal rate of return. This calculation seeks to equate the bondÕs current market price with the value of all anticipated future interest and par value pay-ments. In other words, it is the discount rate that equates the present value of all future cash flows with 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 = PV of annuity ( PMT, i, N ) + PV ( FV, i, N ) (7-2)Investors commonly compute the yield to maturity using financial calculators. For exam-ple, 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 = 16, PV = Ð1150, PMT = 35, and FV = 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 bondÕs yield to maturity is 4.73 percent (2 × 2.363 percent).EXAMPLE 7-6Computing Current Yield and Yield to MaturityYou have identified a 3.5 percent Treasury bond with four years left to maturity and a quoted price of 96.281. Calculate the bondÕs current yield and yield to maturity.SOLUTION:(1) First, identify that the bondÕs price is $962.81 (= 96.281% × $1,000 = 0.96281 × $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 (= $35 Ö $962.81).(3) The yield to maturity is computed using equation 7-2 and the financial calculator as N = 8, PV = −962.81, PMT = 17.50, and FV = 1,000. Computing the interest rate (I) results in 2.263 percent and multiplying by 2 gives the yield to 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 gain to be earned if held to maturity.Similar to Problems 7-13, 7-14, 7-27, 7-28, Self-Test Problem 2LG7-6 CALCULATOR HINTSN = 8PV = −962.81PMT = 17.50FV = 1000CPT I = 2.263SO YTM = 2.263 × 2= 4.53%Notice the link between a bondÕs yield to maturity and the prevailing market interest rates used to deter-mine a bondÕs price as we discussed in the previous section. We use the market interest rate to compute the bondÕs value. We use the actual bond price to compute its yield to maturity. If the bond is correctly priced at its economic value, then the market interest rate will equal the yield to maturity. Thus, the relationship that we previously identified between bond prices and mar-ket interest rates applies to yields as well. This shows the inverse relationship between bond prices and bond yields. As a bondÕs price falls, its yield to maturity increases and a rising bond price accompanies a fall-ing yield. Look back at Figure 7.2 and you will see this relationship clearly.MATH COACH BOND YIELDS AND FINANCIAL CALCULATORSPeople computing a bondÕs yield to maturity make three common mistakes. To avoid the first mistake, ensure that the bond price (PV) is a different sign than the interest and par value cash flows (PMT and FV). The second mistake: People forget to make the number of periods (N) and the per-period interest payment (PMT) consistent. Both should be in semiannual terms if the coupon payment is paid semiannually. Last, many people forget to multiply the resulting calculator interest rate (I) output by 2 to convert the semiannual rate back to an annual rate.For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.Final PDF to printer
242 part four Valuing of Bonds and Stockscor91411_ch07_226-263.indd 242 01/20/17 06:58 PMYield to CallThe 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 bondholderÕs par value prior to its scheduled maturity. Issuers often call bonds after large drops in market interest rates. In such cases, issuers commonly pay bondhold-ers the bondÕs 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 debtÑjust as homeowners doÑto reduce their interest payments.Issuers gain important advantages with call provisions because they allow refinanc-ing 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 inves-tors must seek equally profitable bonds to buy with the proceeds. You will recall that investors can face reinvestment riskÑthe available bonds arenÕt as profitable because interest rates have declined. Bonds are called away at the worst time for investors. In addition, bond prices will rise as market interest rates fall, which could provide issuers opportunities to sell the bonds at a profit. But the price increases will be limited by the fact that the bond will likely be called early. As partial compensation, bond investors receive the call price, which is the par value of the bond plus the call premium (typically one year of interest payments). The possibility that bonds can be called early dampens their upside price potential. We can even compute the price of a bond thatÕs likely to be called from the equation Price of a callable bond = Present value of interest payments to call date + Present value of call price = PMT × ⎡ ⎢ ⎣ 1 − 1 ______ (1 + i) N ___________ i ⎤ ⎥ ⎦ + Call price _________ (1 + i) N (7-3)In this case, N is the number of periods until the bond can be called and i is the pre-vailing market rate. The prevailing market interest rate will probably differ from the rate for a noncallable bond. The previous section demonstrated via the yield curve that bonds with different maturities have different yields. A bond that matures in 20 years, but is likely to be called in 5 years, will carry a yield appropriate for a five-year bond.Now, reconsider the 20-year bond with a 7 percent coupon that we discussed previ-ously (see pp. 236Ð237). If the bond can be called in five years with a call price of $1,070, the appropriate discount rate happens to be 5.75 percent annually at that time (instead of the 6 percent in the original problem). This time line would beThe 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 Bond price = $35 × [ 1 − 1 _____________ (1 + 0.02875) 10 _____________ 0.02875 ] + $1,070 ___________ (1 + 0.02875) 10 = $300.47 + $805.91 = $1,106.38 1Cash ßowPeriodPV = ?27034358910Semiannual periods353535353535351,070. . .. . .2.875%CALCULATOR HINTSN = 10I = 2.875PMT = 35FV = 1070CPT PV = −1,106.38Final PDF to printer
chapter 7 Valuing Bonds 243cor91411_ch07_226-263.indd 243 01/27/17 06:13 PMIn 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 eight years to maturity, which we examined previously. 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 = 6, PV = −1130, PMT = 35, and FV = 1070. The resulting interest rate (i) is 2.26 percent. The yield to call for this bond is thus 4.52 percent (= 2 × 2.26%).yield to callThe total return that the bond offers if purchased at the current price and held until the bond is called.MATH COACH SPREADSHEETS AND BOND PRICINGCommon spreadsheet programs have functions that can compute the price or yield to maturity of a bond. The functions areCompute a bond price = PRICE(settlement,maturity,rate,yld,redemption,frequency,basis)Compute a yield to maturity = YIELD(settlement,maturity,rate,pr,redemption,frequency,basis)Settlement is the bondÕs settlement date. This is the purchase date of the bond; typically it is today. Maturity is the bondÕs maturity date. Rate is the bondÕs annual coupon rate. Pr is the bondÕs price per $100 face value. Note that the par value of a bond is typically $1,000, so an adjustment is needed for this input. Redemption is the bondÕs redemption value per $100 face value. Frequency is the number of coupon payments per year. For semiannual, frequency = 2. Basis is the type of day count basis to use.Consider the bond valuation problem of Example 7-4. The spreadsheet solution is the same as the TVM calculator solution and the pricing equation.Also consider the yield to maturity problem in Example 7-6. This spreadsheet solves for the yield to maturity.See this textbookÕs 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.Final PDF to printer
244 part four Valuing of Bonds and Stockscor91411_ch07_226-263.indd 244 01/27/17 06:16 PMMunicipal Bonds and YieldMunicipal 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-exemptÑat 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 [=(1 − 0.35) × $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 taxable bonds is to convert the yield to maturity of the muni to a taxable equivalent yield, as shown in equation 7-4. Equivalent taxable yield = Muni yield ___________ 1 − Tax rate (7-4)For high-income investors (in the 35 percent marginal tax bracket) a 5 percent muni bond has an equivalent taxable yield of 7.69 percent [= 0.05 Ö (1 − 0.35)]. 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 tax-able yield is only 6.94 percent. The corporate bond provides more after-tax profit than the muni for this investor. ItÕs easy to see why muni bonds are popular among high-income investors (those with substantial marginal tax rates).taxable equivalent yieldModification of a municipal bondÕs yield to maturity used to compare muni bond yields to taxable bond yields.EXAMPLE 7-7LG7-6 Which Bond Has a Better After-Tax Yield?Imagine a time when you have a high income, placing you in the 31 percent marginal tax bracket. You are interested in investing some money in a bond issue and have three alterna-tives. The first is a corporate bond with a 6.4 percent yield to maturity. The second bond is a 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?SOLUTION: The Treasury and corporate bonds are both taxable, so we can compare them directly with each other. The yield of 6.4 percent on the corporate is clearly higher than the 5.7 percent yield offered by the Treasury bond. To include a comparison with the nontaxable municipal bond, compute its equivalent taxable yield as in equation 7-4: Equivalent taxable yield = 4.0% ______ 1 − 0.31 = 5.80% The municipal bondÕs 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 3For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.2States have differing rules bout whether they tax the income from a particular municipal bondÑthey 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 consesquences.Final PDF to printer
chapter 7 Valuing Bonds 245cor91411_ch07_226-263.indd 245 01/20/17 06:58 PMSummarizing YieldsIn this section, we have presented several different types of interest rates, or yields, associated with bonds. See a summary in Table 7.4. Many of these yields relate to one another. Consider the bonds and associated yields reported in Table 7.5. Treasury bonds (1) to (3) show how coupon rates, current yield, and yield to maturity relate. When a bond trades at its par value (usually $1,000), then the coupon rate, current yield, and yield to maturity are all the same. When that bond is priced at a premium (bond 2), then both the current yield and the yield to maturity will be lower than the coupon rate. They are both higher than the coupon rate when the bond trades at a discount. Notice that yield Interest RatePurposeDescriptionCoupon rateCompute bond cash interest paymentsThe coupon rate is reported as a bond characteristic. It is reported as a percentage and is multiplied by the par value of the bond to determine the annual cash interest payment. The coupon rate will not change through the life of the bond.Current yieldQuick assessment of the interest rate a bond is offeringComputed as the annual interest payment divided by the current price of the bond. It measures the return to be expected from just the interest payments if the bond was purchased at the current price. Since the bond price may change daily, the current yield will change daily.Yield to maturityAccurate measurement of the interest rate a bond is offeringThe return offered by the bond if purchased at the current price. This return includes both the expected income and capital gain/loss if held to the matu-rity date. The yield to maturity will change daily as the bond price changes.Yield to callInterest rate obtained if the bond is calledSame as the yield to maturity except that it is assumed that the bond will be called at the earliest date it can be called.Taxable equivalent yieldComparison of nontaxable bond yields to taxable bond yieldsInvestors must pay taxes on most types of bonds. However, municipal bonds are tax free. To compare the muniÕs nontaxable yield to maturity to that of taxable bonds, divide the yield by one minus the investorÕs marginal tax rate.Market interest rateComparison of prices of all bondsThe interest rate determined by the bond prices of actual trades between buyers and sellers. The market interest rate will be different for bonds of dif-ferent times to maturity and different levels of risk.Total returnDetermine realized performance of an investmentRealized return that includes both income and capital gain/loss profits.TABLE 7.4 Summary of Interest RatesABCDEFG1PriceCoupon RateCurrent YieldYield to MaturityYield to Call (in 5 Years)Taxable Equivalent Yield (35% Tax Rate)2(1) Treasury$1,0005.00%5.00%5.00%5.00%3(2) Treasury 1,1005.00 4.55 3.79 3.79 4(3) Treasury 9005.00 5.56 6.37 6.37 5(4) Corporate 1,000 6.00 6.00 6.00 6%6.00 6(5) Corporate 1,100 6.00 5.414.61 4.594.61 7(6) Corporate 900 6.00 6.677.44 9.527.44 8(7) Muni 1,000 4.00 4.00 4.00 6.159(8) Muni 1,100 4.00 3.64 2.84 4.3710(9) Muni 900 4.00 4.44 5.30 8.151112=C3*10/B3=2*RATE(10,C7*10/2,-B7,1000+C7*10)=E10/(1-0.35)13=2*RATE(10,C7*10/2,-B7,1000+C7*10)14TABLE 7.5 Price, Coupon, and Yield Relationships of a 10-Year BondCall price = Par value + One yearÕs interestFinal PDF to printer
246 part four Valuing of Bonds and Stockscor91411_ch07_226-263.indd 246 01/20/17 06:58 PMto maturity is higher than current yield for discount bonds, and that yield to maturity is lower than current yield for premium bonds. In other words, the current yield always lies between the coupon rate and the yield to maturity. Both the current yield and the yield to maturity move in the opposite direction to the bondÕs price.Bonds (4) to (6) are callable corporate bonds. Recall that all the yields (current yield, yield to maturity, and yield to call) are identical when the bond trades at par value. When interest rates fall and bond prices increase, as with bond (5), the issuing corporation has a strong incentive to call the bond after five years, as allowed in the indenture agreement. So investors should base their purchase decisions on the yield to call. When interest rates increase, bond prices decline (as bond (6) shows). In this case, investors could compute the yield to call (as shown), but the information isnÕt useful because the company will not likely call the bond while interest rates are high.The last three bonds shown in the table are municipal bonds. Recall that these bonds typically offer lower yields because the income from munis is tax exempt. It is easier to compare municipal bonds with Treasuries and corporate bonds if you compute the municipal bondÕs taxable equivalent yield first. Here, we use a marginal tax rate of 35 percent in the calculation. The last column of the table shows that the taxable equiva-lent yield of the municipal bonds is really quite competitive with corporate bond yields. Any investor with income taxed at the 35 percent marginal tax bracket would prefer the municipal bond over the corporate bond if the muniÕs taxable equivalent yield is higher than the yield to maturity (or yield to call) of the corporate bond.The table also shows that Treasury securities offer lower yields than corporate bonds with similar terms to maturity. The difference (or spread) between Treasury and corpo-rate yields gives rise to a discussion of bond credit risk, which follows.credit quality riskThe chance that the issuer will not make timely interest payments or even default.bond ratingA grade of credit quality as reported by credit rating agencies.investment gradeHigh credit quality corpo-rate bonds.TIME OUT 7-5 Calculate the yield to maturity for a zero coupon bond with a price of $525 and 10 years left to maturity. 7-6 Which is higher for a discount bond, the yield to maturity or the coupon rate? Why? 7.4 ∙ Credit RiskBond RatingsWill a bond issuer make the promised interest and par value payments over the next 10, 20, or even 30 years? Credit quality risk is the chance that the bond issuer will not be able to make timely payments. To assess this risk, independent bond rating agencies, such as MoodyÕs and Standard & PoorÕs, monitor corporate, U.S. agency, or municipal developments during the bondÕs lifetime and report their findings as a grade or rating. The U.S. government issues the highest credit quality debt, though that consensus has recently come into doubt as the U.S. debt and budget deficit have ballooned.The primary Òbig threeÓ bond credit rating agencies in the United States include MoodyÕs Investors Service, Standard & PoorÕs Corporation, and Fitch IBCA Inc. Each of these credit analysis firms assigns similar ratings based on detailed analyses of issu-ersÕ financial condition, general economic and credit market conditions, and the eco-nomic value of any underlying collateral. The Standard & PoorÕs ratings are shown in Table 7.6. Their highest credit quality rating is AAA. Bonds rated AAA, AA, A, or BBB are considered investment grade bonds. The issuers of these securities have the highest chance of making all interest and par value payments promised in the indenture agreement.LG7-7 Final PDF to printer
chapter 7 Valuing Bonds 247cor91411_ch07_226-263.indd 247 01/20/17 06:58 PMThe investment community considers bonds rated BB and below to be below-investment grade bonds, and some investors, such as pension funds or other fiduciaries, cannot purchase these securities for their portfolios. These bonds are considered to be speculative because they carry a significant risk that the issuer will not make current or future payments. Speculative bonds are sometimes called junk bonds because of this risk. In order to attract buyers, issuers sell these bonds at a considerable discount from par and a high associated yield to maturity. Agencies often enhance ratings from ÒAAÓ to ÒCCCÓ with the addition of a plus (+) or minus (Ð) sign to show relative standing within the major rating categories. For example, the Greek government saw its bonds upgraded from CCC+ to BÐ by Standard & PoorÕs on January 22, 2016. The next week, Standard and PoorÕs downgraded Dutch Shell Plc from AAÐ to A+. These rating changes impact not only the current prices of these bonds, but also the interest rate Greece and Royal Dutch Shell would have to pay if they issued new bonds.Standard & PoorÕs signals that itÕs considering a rating change by placing an individ-ual bond, or all of a given issuerÕs bonds, on CreditWatch (S&P). Rating agencies make their ratings information available to the public through their ratings information desks. In addition to published reports, ratings are made available in many public libraries and over the Internet.Credit rating agencies conduct general economic analyses of companiesÕ business and analyze firmsÕ specific financial situations. A single company may carry several out-standing bond issues. If these issues feature fundamental differences, then they may have different credit level risks. For example, unsecured corporate bonds, or debentures, are backed only by the reputation and financial stability of the corporation. A senior bond has a priority claim over junior (more recently issued) securities in the event of default or bankruptcy. So, senior bonds carry less credit risk than junior bonds. Some bonds are secured with collateral. When you buy a car using a loan, the car is collateral for that loan. If you donÕt make the loan payments, the bank will repossess the car. Companies can also debenturesUnsecured bonds.senior bondsOlder bonds that carry a higher claim to the issuerÕs assets.junk bondsLow credit quality corporate bonds, also called specula-tive bonds or high-yield bonds.Credit RiskCredit RatingDescriptionInvestment GradeHighest qualityAAAThe obligorÕs (issuerÕs) capacity to meet its financial commitment on the obligation is extremely strong.High qualityAAThe obligorÕs capacity to meet its financial commitment on the obligation is very strong.Upper medium gradeAThe obligorÕs capacity to meet its financial commitment on the obligation is still strong, though somewhat susceptible to the adverse effects of changes in circumstances and economic conditions.Medium gradeBBBThe obligor exhibits adequate protection. However, adverse economic conditions or changing circumstances are more likely to lead to a weakened capacity to meet its financial commitment.Below Investment GradeSomewhat speculativeBBFaces major ongoing uncertainties or exposure to adverse business, financial, or economic conditions which could lead to the obligorÕs inadequate capacity to meet its financial commitment.SpeculativeBAdverse business, financial, or economic conditions will likely impair the obligorÕs capacity or willingness to meet its financial commitment.Highly speculativeCCCCurrently vulnerable to nonpayment, and is dependent upon favorable business, financial, and economic conditions for the obligor to meet its financial commitment.Most speculativeCCCurrently highly vulnerable to nonpayment.Imminent defaultCBankruptcy petition has been filed or similar action taken, but payments on this obligation are being continued.DefaultDObligations are in default or the filing of a bankruptcy petition has occurred and payments are jeopardized.TABLE 7.6 Standard & PoorÕs Bond Credit RatingsSource: Standard & PoorÕs web page.unsecured corporate bondsCorporate debt not secured by collateral such as land, buildings, or equipment.Final PDF to printer
248 part four Valuing of Bonds and Stockscor91411_ch07_226-263.indd 248 01/20/17 06:58 PMoffer collateral when issuing bonds. When a firm uses collateral such as real estate or fac-tory equipment, the bonds are called mortgage bonds or equipment trust certificates, respectively. Bonds issued with no collateral generally carry higher credit risk.Credit Risk and YieldInvestors will only purchase higher risk bonds if those securities offer higher returns. Therefore, issuers price bonds with high credit risk to offer high yields to maturity. So another common name for junk bonds is high-yield bonds. Differences in credit risk are a prime source of differences in yields between government and various corporate bonds. Figure 7.3 shows the historical average annual yields for long-term Treasury bonds and corporate bonds with credit ratings of Aaa and Baa since 1980. Riskier low-quality bonds always offer a higher yield than the higher quality bonds. However, the yield spread between high- and low-quality bonds varies substantially over time. The yield difference between Baa bonds and Treasuries was as high as 3.7 percent and 3.3 percent in 1982 and 2003, respectively. The spread has been as narrow as 1.3 percent and 1.4 percent in 1994 and 2006, respectively.How do some corporationsÕ debt obligations become junk bonds? Some companies that arenÕt economically sound or those that use a high degree of financial leverage issue junk bonds. In other cases, financially strong companies issue investment grade bonds and then, over time, begin to have trouble. Eventually a companyÕs bonds can be down-graded to junk status. For example, General Motors (GM) bonds were considered of the highest quality from the 1950s through the 1980s and much of the 1990s. On May 9, 2005, Standard & PoorÕs downgraded GM bonds to junk status. Junk bonds that were originally issued at investment grade status are called fallen angels. GM eventually filed for bankruptcy protection in June 2009. By 2016, its credit rating was at the lowest end of investment grade (BBBÐ).Bonds that experience credit-rating downgrades must offer a higher yield. As all the future cash flows are fixed, the bond price must fall to create a higher yield to maturity. Alternatively, bonds that are upgraded experience price increases and yield decreases. Bond upgrades often occur during strong economic periods because corporate issuers tend to perform better financially at these times. In a weak economy, high-yield bonds lose their luster because the default risk rises. More credit downgrades occur during mortgage bondsBonds secured with real estate as collateral.high-yield bondsBonds with low credit qual-ity that offer a high yield to maturity, also called junk bonds.024681012141618198019811982198319841985198719881990199119861989199219931994199619971995199819992000200120022003200420052006200720082009201020112012201320142015Yield to Maturity (%)Treasury bondsCorporate, AaaCorporate, BaaFIGURE 7.3Yield to Maturity on Long-Term Bonds of Different Credit Risk, 1980Ð2015Looking at the historical yields for long-term Trea-sury and corporate bonds, notice how the yield spread between high- and low- quality bonds varies substantially over time.equipment trust certificatesBonds secured with fac-tory and equipment as collateral.Final PDF to printer
chapter 7 Valuing Bonds 249cor91411_ch07_226-263.indd 249 01/20/17 06:58 PMTIME OUT 7-7 Explain why a change in a bondÕs credit rating will cause its price to change. 7-8 One company has issued two bond classes. One issue is a mortgage bond and the other is a debenture. Which issue will have a higher bond rating and which will offer a higher yield? ! want to know more?Key Words to Search for Updates: Greek bonds, Greek debt crisisGreece joined the European monetary union in 2000, which means the euro replaced drachmas as the national currency. The euro was a much stronger currency than the drachma because it was backed by the economic prosperity of the whole European Union. Hence, the Greek government was able to borrow from foreign investors at much lower interest rates. This contributed to the ensuing economic boom and expansion of government spending in Greece.The Greek government has long been operating on high budget deficits and borrowing. But the problems really began in the Fall of 2009 when the new elected government found that it had inherited a financial burden that was much larger than previously reported. The budget deficit was revised to be larger than 13 percent of the size of the economy. The revelation of these huge government deficits and debts cast enormous doubt on the ability of the Greek government to pay its debts.This increase in risk was reflected on December 8, 2009, by the downgrade to BBB (lowest in the Euro Zone) of the Sovereign bond of Greece by the Fitch credit rating firm. A GREEK TRAGEDY: DEBT CRISISfinance at work marketsStandard & PoorÕs and MoodyÕs both downgraded Greece Sovereigns to junk bond status in May and June of 2010. As a consequence, Greece found that it was difficult to borrow more money and had to offer lenders yields of as much as 12 percent and a financial crisis developed.In order to restore investor confidence, the Greek gov-ernment has pledged to an austerity plan that cuts spending and reduces the budget deficit. However, the success of the plans has been undermined by strong domestic opposition as illustrated by strikes and even riots. As a temporary solu-tion, the European Union and the International Monetary Fund together offered a large loan package to help out Greece. This calmed the bond market and Greek bond yields fell, but they are still high. Unfortunately, the severe economic depres-sion in Greece has caused further problems with its ability to pay its debt. In 2011 and 2012, Greece enacted several bond restructurings which mandated changes in the terms. They are considered selective bond defaults. In June of 2015, Greece became the first developed country to miss an Inter-national Monetary Fund loan repayment. economic recessions. In general, any event that impacts the likelihood of a firm paying back the interest payments and principle it owes will impact its credit risk. Credit risk is a determinant of the discount rate. The discount rate is also influenced by macroeco-nomic factors, like decisions by the Federal Reserve Board. A change in the discount rate directly changes the value of the bond. Therefore, company performance, strength of the economy, and monetary policy all affect bond values. 7.5 ∙ Bond MarketsThe majority of trading volume in the bond market occurs in a decentralized, over-the-counter market. Most trades occur between bond dealers and large institutions (like mutual funds, pension funds, and insurance companies). Dealers bid for bonds that inves-tors seek to sell and offer bonds from their own inventory when investors want to buy. This is especially true for the very active Treasury securities market. However, a small number of corporate bonds are listed on centralized exchanges.LG7-8 Final PDF to printer
250 part four Valuing of Bonds and Stockscor91411_ch07_226-263.indd 250 01/20/17 06:58 PMTIME OUT 7-9 Why can we use various interest rates to describe the performance of the entire bond market? 7-10 What bond segments are measured by which bond indexes? Credit RatingPriceIssuer Name (symbol)Coupon %MaturityMoody’sS.&P.FitchLastChangeYield %Anadarko Pete Corp APC.HMBaa2BBBBBBAt&t Inc T4332471Baa1BBB+AÐHome Depot Inc HD4333476A2An.a.Anheuser-busch Inbev Fin Inc BUD4327588NRAÐn.a.Anheuser-busch Inbev Fin Inc BUD4327481NRAÐn.a.Visa Inc V4319927A1A+n.a.JPMorgan Chase & Co. JPM4005051A3AÐA+Home Depot Inc HD4333469A2An.a.At&t Inc T43324706.38%4.13%3.00%4.90%3.65%3.15%1.63%2.00%3.60%Sep 15, 2017Feb 17, 2026Apr 01, 2026Feb 01, 2046Feb 01, 2026Dec 14, 2025May 15, 2018Apr 01, 2021Feb 17, 2023Baa1BBB+AÐ100.375101.385101.016105.629102.038102.49499.12100.032100.884Ð0.283+0.024+0.404+0.267Ð0.84Ð0.153Ð0.52Ð0.005+0.2536.12%3.96%2.88%4.55%3.40%2.85%2.02%1.99%3.46%FIGURE 7.4 Most Active Investment Grade Bonds, February 5, 2016This is an example of the most actively traded investment bonds for a given day.Source: The New York Times, http://markets.on.nytimes.com/research/markets/bonds/bonds.aspThe NYSE operates the largest centralized U.S. bond market. The majority of bond vol-ume at the NYSE is in corporate debt. The most actively traded investment grade bonds for the day are shown in Figure 7.4. Even the most active corporate bonds experience relatively low trading volume. Note that some of the bonds traded are short-term, like Anadarko Pete Corp and JPMorgan Chase & Co. Other bonds have many years to maturity, like the Anheuser-busch Inbev bond that matures in February 2046. Most of the ones shown are premium bonds (price greater than par value), while one is a discount bond. Following the Bond MarketThe entire bond market encompasses a wide variety of securities with varying credit quality from different issuers. Large differences also arise among bonds in terms of their characteristics such as term to maturity and size of the coupon. The biggest factor asso-ciated with changes in bond prices is changes in interest rates. So, one common way to describe the direction of bond prices is simply to report the change in interest rates, since we know that interest rate changes will affect all bonds the same way. The interest rate referenced is the yield to maturity and daily yield change for the 10-year Treasury. Know-ing how this interest rate changed today gives bond investors a good idea of the general price movement of all types of bonds.Bond indexes track specific segments of the bond market. Various securities firms, such as Barclays Capital or Merrill Lynch, maintain these indexes that capture bond price and yield changes in particular segments. You can find information about major bond indexes on the Internet and in publications like The Wall Street Journal (both in print and online). Figure 7.5 shows indexes that track bonds by type of issuer (federal government, corporation, local government, etc.) and time to maturity (short, intermediate, and long).Final PDF to printer
chapter 7 Valuing Bonds 251cor91411_ch07_226-263.indd 251 01/20/17 06:58 PMTracking Bond BenchmarksFriday, February 05, 2016IndexComposite (Price Return)Composite (Total Return)Intermediate (Price Return)Intermediate (Total Return)Close%ChgYTDtotal return52-wk% ChgSPREAD, 52-WEEK RANGE () LatestYIELD (%), 52-WEEKRANGELatestLowHighLatestLowHighClosing index values, return on investment and yields paid to investors compared with 52-week highs and lows for different types of bonds. Preliminary data and data shown as Òn.a.Ó will update around 12p.m. the following business day.Broad Market Barclays CapitalHourly Treasury Indexes Barclays capitalU.S. Government/CreditBarclays AggregateU.S. Corporate Indexes Barclays CapitalHigh Yield Bonds Merrill LynchU.S. Agency Indexes Barclays CapitalMortgage-Backed Barclays CapitalMortgage-Backed Merrill LynchTax-Exempt Merrill LynchLong-Tenn (Price Return)Long-Term (Total Return)U.S. CorporateIntermediateLong-termDouble-A-rated (AA)Triple-B-rated (Baa)High Yield Constrained*Triple-C-rated (CCC)High Yield 100U.S. Agency10Ð20 years20-plus yearsMortgage-BackedGinnie Mae (GNMA)Freddie Mac (FHLMC)Fannie Mae (FNMA)Ginnie Mae (GNMA)Fannie Mae (FNMA)Freddie Mac (FHLMC)Muni Master7Ð12 years12Ð12 years22-plus yearsBond Buyer 6% MuniGlobal High YieldConstrainedEurope High YieldConstrained201.0081.0066.00……………………….1.742.012.351.471.765.506.071.620.470.620.120.13Ð0.22Ð2.69Ð5.58Ð2.23Ð1.69Ð2.191.331.101.451.412.562.401.351.871.231.291.371.840.070.040.030.040.310.33Ð0.01Ð0.010.110.030.310.100.11Ð0.32Ð0.61Ð0.33Ð0.07Ð0.20Ð0.03Ð0.08Ð0.01Ð0.010.080.050.020.010.010.00Ð0.020.04Ð0.01Ð0.030.152.5402.6302.1302.1301.9901.9903.0903.0903.7103.1205.1202.7004.4009.77120.4668.6966.4129.2952.9002.8602.9302.9103.1482.0992.1442.6363.3514.5003.1862.9821.6801.4803.3701.8602.0001.2401.2401.0201.0202.3502.3502.8302.2304.1702.0703.3005.85310.0175.0163.5505.8942.3202.1802.3702.3702.4741.5191.4861.9752.6684.0302.5142.4191.1700.9802.7002.2602.3201.3201.3201.1201.1202.4502.4503.6303.0205.0602.5304.3509.46420.4667.9465.6428.9232.4602.3802.5102.4702.5581.5201.5081.9752.6684.0302.6172.5071.3601.1502.9404.841.181.582129.411478.3713944.021298.4411499.002303.8927546.352481.832432.663154.03525.41610.86321.85263.712321.09258.70297.241606.511446.273153.271932.541908.281740.611131.09702.07435.92739.20506.37391.12371.79355.01129.031856.621.383.642.044.170.14Ð2.480.08Ð8.11Ð0.19Ð4.69Ð8.68Ð20.53Ð8.30Ð2.39Ð5.492.092.132.042.092.903.434.474.304.751.152.892.991.461.580.27Ð0.07Ð3.080.5714.00Ð4.007.0016.00……………………….n.a.n.a.n.a.n.a.n.a.810.001934.00658.00585.00794.00n.a.16.0018.0021.00n.a.n.a.n.a.n.a.n.a.n.a.n.a.n.a.Ð1.00Ð1.0010.00Ð17.00122.0052.00……………………….42.0098.00176.0068.00159.00438.00872.00374.00358.00465.0012.006.0054.0013.00Ð2.00Ð5.00Ð2.00Ð15.00Ð10.003.00Ð33.001.0018.0016.00173.00265.00111.00265.00827.001934.00721.00639.00816.0021.0015.0074.0036.0028.0041.0038.0023.0024.0031.00FIGURE 7.5 Major Bond Indexes as Reported in The Wall Street Journal and on the Internet, February 5, 2016Here are indexes that track bonds by type of issuer (federal government, corporation, local government, etc.) and time to maturity (short, intermediate, and long).Source: The Wall Street Journal Online. Tracking Bond Benchmarks web page.Final PDF to printer
252cor91411_ch07_226-263.indd 252 01/20/17 06:58 PMviewpoints RevisitedBusiness Application SolutionTo raise $150 million, Beach Sand Resorts would need to issue 150,000 bonds at the customary $1,000 par value (= $150 million Ö $1,000). The bonds will have to offer a 7 percent coupon. This means that Beach Sand Resorts will pay $35 in interest every six months for each bond issued (= 0.07 × $1,000 Ö 2). So for all 150,000 bonds, they will pay $5.25 million semiannually (= $35 × 150,000).Personal Application SolutionYou can calculate that buying 10 of the Trust Media bonds at the quoted price of 96.21 will cost $9,621 (= 0.9621 × $1,000 × 10) and would generate $285 (= 0.057 × $1,000 × 10 Ö 2) in interest payments every six months. Buying the bond in 2017, it is priced to offer a 6.47 percent yield to maturity. Ten of the Abalon bonds would cost $10,194 (= 1.0194 × $1,000 × 10) and pay $268.75 (= 0.05375 × $1,000 × 10 Ö 2) in interest payments every six months. This bond is priced to offer a 5.0 percent yield to maturity. The Trust bonds cost less to purchase, pay more in interest, and offer a higher return than the Abalon bonds. This is because the Trust bonds have higher credit risk. You must decide if the higher return of the Trust bonds is worth taking the extra risk.CALCULATOR HINTSN = 12PV = –1019.40PMT = 26.875FV = 1000CPT I = 2.502.50 × 2 = 5.0summary of learning goalsThis chapter describes the bond market. Debt is an important source of capital for companies and governments. A well-functioning bond market contributes to a successful economy. Investors can benefit from bond ownership. Before buying bonds, people should understand how they work.Describe bond characteristics. Bonds are debt securities that pay a rate of interest called the coupon rate. The dollar amount of interest is based on the par value (typically $1,000) of the bond. Interest is usually paid semiannually throughout the time to maturity. At the bondÕs maturity date, the par value is repaid in full. The bondÕs legal contract, the indenture agreement, states whether the bond has a call provision that allows the issuer to redeem the bond prior to scheduled maturity. If the bond is called, the issuer pays the bondholder the par value and a call premium.Identify various bond issuers and their motivations for issuing debt. Treasury securities are obligations of the U.S. government. The U.S. government uses this debt to fund spending that exceeds its revenue. Treasury bills are extremely short term, usually 30 to 90 days until maturity. Treasury notes are issued with 1 to 10 years to maturity, while Treasury bonds are issued with 10 to 30 years. Corporations LG7-1LG7-2borrow money by issuing bonds as a source of capital to invest in expansion and new business opportunities. State and local governments borrow money by issuing municipal bonds. The interest income from municipal bonds is, for the most part, tax exempt and therefore appeals to investors in the highest tax brackets.?Read and interpret bond quotes. A bondÕs price and coupon rate are expressed as percentages of the bondÕs par value. The bid price is the price at which investors can sell the bond and the ask price is the price at which investors buy a bond. When a quoted price is higher than the par value of the bond, the bond can be referred to as a premium bond. A bond that carries a price lower than 100 percent of par value is called a discount bond.Compute bond prices using present value concepts. The current price of a bond is computed by discounting the future cash flows received: interest LG7-3LG7-4Final PDF to printer
253cor91411_ch07_226-263.indd 253 01/20/17 06:58 PMpayments and par value repayment. The prevailing market interest rate for a bond with similar term to maturity, credit quality, and tax status is used as the discount rate.Explain the relationship between bond prices and interest rates. As prevailing interest rates change in the economy, bond prices also change. Interest rates and bond prices move in opposite directions. A rise in interest rates increases the discount rate and thus reduces a bondÕs value. The value of a bond will rise when interest rates fall. Changes in interest rates create risk factors for bonds called reinvestment risk and interest rate risk.Compute bond yields. The simplest bond yield computation is the current yieldÑsimply one year of interest payments divided by the current bond price. Current yield measures the return earned from the interest payments of the bond. However, many bondholders will experience a capital gain or loss in addition to the return from interest payments. The total rate that would be earned if a bond is purchased and held to maturity is the bondÕs yield to maturity. If a LG7-5LG7-6bond is callable, investors may compute the yield to call to assess the return earned if the bond ends up being called. Since municipal bonds pay tax-exempt interest payments, investors commonly compute a taxable equivalent yield to properly compare municipal returns to taxable bond returns.Find bond ratings and assess credit riskÕs effects on bond yields. Credit quality risk measures the possibility that the bond issuer will fail to make timely interest and principal payments or that the issuer may even default on the debt. Credit rating agencies grade bond risks and report bond ratings. High-quality corporate bonds are considered investment grade, while higher credit risk bonds are speculative, also called junk bonds and high-yield bonds.Assess bond market performance. Investors can follow the bond market through prevailing market interest rates because interest rates and bond prices move in the opposite direction. Bond indexes track specific segments of the bond market. Popular bond segments are short-term bonds, long-term bonds, Treasuries, high-grade corporate bonds, high-yield bonds, and municipal bonds.LG7-7LG7-8chapter equations 7-1 Present value of bond = PMT × ⎡ ⎢ ⎣ 1 − 1 ______ (1 + i ) N _________ i ⎤ ⎥ ⎦ + $1,000 ______ (1 + i ) N 7-2 Bond price = PV of annuity ( PMT, i, N ) + PV ( FV, i, N ) 7-3 Price of acallable bond = PMT × ⎡ ⎢ ⎣ 1 − 1 ______ (1 + i ) N _________ i ⎤ ⎥ ⎦ + Call price ________ (1 + i ) N 7-4 Equivalent taxable yield = Muni yield _________ 1 − Tax rate key termsagency bonds Bonds issued by U.S. government agen-cies. p. 232asset-backed securities Debt securities whose payments originate from other loans, such as credit card debt, auto loans, and home equity loans. p. 232bond Publicly traded form of debt. p. 228bond price Current price that the bond sells for in the bond market. p. 229bond rating A grade of credit quality as reported by credit rating agencies. p. 246call An issuer redeeming the bond before the scheduled maturity date. p. 228Final PDF to printer
254cor91411_ch07_226-263.indd 254 01/31/17 07:24 PMcall premium The amount in addition to the par value paid by the issuer when calling a bond. p. 228convertible bond A debt security that can be converted to shares of stock or another type of security. p. 233coupon rate The annual amount of interest paid expressed as a percentage of the bondÕs par value. p. 228credit quality risk The chance that the issuer will not make timely interest payments or even default. p. 246current yield Return from interest payments; computed as the annual interest payment divided by the current bond price. p. 240debentures Unsecured bonds. p. 247discount bond A bond selling for lower than its par value. p. 234equipment trust certificates Bonds secured with factory and equipment as collateral. p. 248fixed-income securities Any securities that make fixed payments. p. 228high-yield bonds Bonds with low credit quality that offer a high yield to maturity, also called junk bonds. p. 248indenture agreement Legal contract describing the bond characteristics and the bondholder and issuer rights. p. 228interest rate risk The chance of a capital loss due to interest rate fluctuations. p. 238investment grade High credit quality corporate bonds. p. 246junk bonds Low credit quality corporate bonds, also called speculative bonds or high-yield bonds. p. 247maturity date The calendar date on which the bond prin-cipal comes due. p. 228mortgage-backed securities Securities that represent a claim against the cash flows from a pool of mortgage loans. p. 232mortgage bonds Bonds secured with real estate as col-lateral. p. 248par value Amount of debt borrowed to be repaid; face value. p. 228premium bond A bond selling for greater than its par value. p. 234principal Face amount, or par value, of debt. p. 228reinvestment rate risk The chance that future interest payments will have to be reinvested at a lower interest rate. p. 239senior bonds Older bonds that carry a higher claim to the issuerÕs assets. p. 247taxable equivalent yield Modification of a municipal bondÕs yield to maturity used to compare muni bond yields to taxable bond yields. p. 244time to maturity The length of time (in years) until the bond matures and the issuer repays the par value. p. 228Treasury Inflation-Protected Securities TIPS are U.S. government bonds where the par value changes with inflation. p. 231unsecured corporate bonds Corporate debt not secured by collateral such as land, buildings, or equipment. p. 247yield to call The total return that the bond offers if pur-chased at the current price and held until the bond is called. p. 243yield to maturity The total return the bond offers if pur-chased at the current price and held to maturity. p. 240zero 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. p. 236self-test problems with solutionsPriceCoupon(%)MaturityYTM (%)Current Yield (%)Fitch RatingsCallable101.575.2001-Mar-20214.7775.119AANo1 Bond Quotes and Value SheilaÕs broker has given her the following bond quote for a bond issued by Delvin Hardware. What is the price she would pay to buy this bond? Before buying the bond, Sheila notices that other bonds with the same time to maturity and credit rating are offering a 5.08 yield to maturity. What is the bond price at the 5.08 yield? Should Sheila buy this bond? The date is March 2, 2017.Solution:Sheila knows that the bond quote means that it would cost her $1,015.70 (= 1.0157 × $1,000) to purchase now. However, this bond is priced to offer a lower yield to maturity (4.777%) than that offered by similar bonds (5.08%), so it appears mispriced. The value LG7-1, 7-3, 7-4Final PDF to printer
255cor91411_ch07_226-263.indd 255 01/20/17 06:58 PMof this bond using the 5.08 percent market interest rate can be computed using equation 7-1. The semiannual interest payment is $26 (= 0.052 × $1,000 Ö 2) and will be paid eight more times. The bondÕs value is Bond value = $26.00 × [ 1 − 1 _____________ (1 + 0.0254) 8 _____________________ 0.0254 ] + $1,000 ___________ (1 + 0.0254 ) 8 = $186.10 + $818.19 = $1,004.29 Since the bondÕs value is $1,004.29 and the price is $1,015.70, it appears to be overpriced by $11.41. Sheila may want to consider other bonds that offer an appropriate yield for their level of risk.2 Yield to Maturity and Yield to Call Kaito is considering a bond issued from All Satellite Radio. The bond has a 9.625 percent coupon and will mature on August 1, 2023. The current market price for the bond is 101.50 and the date is February 2, 2017. Kaito wants to know the current yield and yield to maturity that the bond is offering. In addition, the bond can be called on August 1, 2019, at a price of 104.813. So he wants to know the yield to call as well.Solution:The Radio bond pays $48.125 ( = 0.09625 × $1,000 Ö 2) in interest every six months and has 6½ years until it matures. At a price of 101.50, the bondÕs current yield is 9.48 percent ($96.25 Ö $1,015.00). The yield to maturity can be found with equation 7-2 and the financial calculator as N = 13, PV = Ð1015, PMT = 48.125, and FV = 1000. Computing the interest rate (I) results in 4.656 percent and multiplying by 2 gives the yield to maturity of 9.31 percent. Kaito knows that Radio could call the bond early. To compute the yield to call, the number of periods and the future price need to be changed. In that case, the yield to call would be computed as N = 5, PV = Ð1015, PMT = 48.125, and FV = 1048.13 Computing the interest rate (I) results in 5.33 percent and multiplying by 2 gives the yield call of 10.66 percent.3 Municipal Bonds and Income Tax Brackets Shane is a securities broker with many clients. His company has acquired a large number of municipal bonds issued for the Atlanta, Georgia, airport. These bonds pay a coupon of 5 percent, mature on January 1, 2039, have an AAA credit rating, and carry a price of 107.091. Assume that it is January 2, 2018, and that the par value of the bond is $5,000. As an alternative, corporate bonds with similar risk and time to maturity offer a 6.35 percent yield to maturity. Shane is trying to determine which of his clients these bonds would benefit the most. Solution:Since these municipal bonds are issued in the state of Georgia, the bondholders in Georgia will not have to pay either federal or state income tax on the interest payments. Therefore, Shane should focus on his clients who live in Georgia. This bond offers investors a yield to maturity that can be computed using equation 7-2. Using the financial calculator, enter N = 44, PV = Ð 5354.55, PMT = 125, and FV = 5000. Computing the interest rate (I) results in 2.245 percent and multiplying by 2 gives the yield to maturity of 4.49 percent. The tax savings provide a larger benefit for people in a higher marginal tax bracket. Investors in the 35 percent tax bracket can compare the muni bond yield to a taxable corporate yield by converting the muni to an equivalent taxable yield as in equation 7-4: Equivalent taxable yield = 4.49% _______ 1 − 0.35 = 6.91% So people in the highest tax bracket will prefer this municipal bond to the similar corporate bonds offering only 6.35 percent. The following table shows the equivalent taxable yield for the marginal tax brackets of 2009. Shane notes that in this case, his LG7-6LG7-6CALCULATOR HINTSN = 8I = 2.54PMT = 26.00FV = 1000 CPT PV = − 1004.29Final PDF to printer
256cor91411_ch07_226-263.indd 256 01/20/17 06:58 PMclients in the upper two marginal tax brackets would benefit from these municipal bonds. Investors in the lower brackets would do better purchasing the corporate bonds.Marginal Tax Bracket (%)101525283335Equivalent Taxable Yield (%)4.995.285.996.196.706.914 Credit Risk and Bond Costs Monica is CFO of a manufacturing company that wants to raise capital for several new business projects. The firmÕs current bonds are rated A. Monica is working closely with the credit rating agencies to determine what the credit rating would be on new bonds issued under two different circumstances. In the first case, the firm would issue $50 million in new bonds to fund a project. In the second case, the firm would issue $150 million to fund two new projects. The credit rating agency says that the first alternative would result in a BBB rating and the second case would result in a BB rating. Monica uses the following current market yield table to assess the interest cost of the two alternatives. What would the interest rate cost (in dollars) be in each case?Credit RatingAAAAAABBBBBB20-Year Average Yield5.75.96.16.57.18.4Solution:If Monica goes with the first case and raises $50 million with a bond issue, the bonds will be rated BBB, the lowest investment grade rating. She would issue the bonds with the market rate 6.5 percent as the coupon rate. This means that she will have to pay $3.25 million ( = 0.065 × $50 million) every year in interest payments. If she decides to issue $150 million in bonds instead, they will be rated BB and be known as junk bonds. She will need to offer the higher interest rate of 7.1 percent as the coupon rate. Therefore, she will have to pay $10.65 million ( = 0.071 × $150 million) every year in interest payments. The difference in the two options is due to both the difference in coupon rate and the amount of money borrowed. One other issue Monica may want to consider is the reputation impact of having bonds rated in the junk bond range. Other people in the industry often use bond ratings as a signal about the financial stability of the firm. Her suppliers may begin to worry about the firm if it has a BB rating and may not be willing to extend credit. In other words, the second case may create some financial problems in other parts of the company.5 Capital Gains and Losses in Bonds Microcasm, Inc., a pharmaceutical company, has issued bonds that now have 15 years to maturity. The bonds have a coupon rate of 4.4 percent and a recent bond quote of 102.35. The bond has a credit rating of BBB and is priced to provide a 4.187 yield to maturity. A news announcement today discloses that Microcasm has been named in a lawsuit that could become a serious problem for the firm. As a response, Standard & PoorÕs lowered its credit rating to BB+. The bonds with this credit rating and maturity have a yield to maturity of 5.08. What is the price change experienced by the bonds (in dollars and percentage)? Solution:The bond price before the announcement can be computed from the bond quote of 102.35, which indicates a price of $1,023.50. The price after the announcement can be computed using semiannual compounding: Bond Price = $22 × [ 1 − 1 _____________ (1 + 0.0254) 30 _____________________ 0.0254 ] + 1,000 ___________ (1 + 0.0254 ) 30 = $458.02 + $471.19 = $929.21 Therefore, the bond changed Ð $94.29 [ = $1,023.50 Ð $929.21], or Ð 9.21 percent [ = Ð $94.29/$1,023.50] of its value.LG7-7CALCULATOR HINTSN = 30I = 2.54PMT = 22FV = 1000 CPT PV = − 929.22LG7-5Final PDF to printer
257cor91411_ch07_226-263.indd 257 01/20/17 06:58 PMquestions 1. What does a call provision allow issuers to do, and why would they do it? (LG7-1) 2. List the differences between the new TIPS and tradi-tional Treasury bonds. (LG7-2) 3. Explain how mortgage-backed securities work. (LG7-2) 4. Provide the definitions of a discount bond and a pre-mium bond. Give examples. (LG7-3) 5. Describe the differences in interest payments and bond price between a 5 percent coupon bond and a zero coupon bond. (LG7-4) 6. All else equal, which bondÕs price is more affected by a change in interest rates, a short-term bond or a longer-term bond? Why? (LG7-5) 7. All else equal, which bondÕs price is more affected by a change in interest rates, a bond with a large cou-pon or a small coupon? Why? (LG7-5)? 8. Explain how a bondÕs interest rate can change over time even if interest rates in the economy do not change. (LG7-5) 9. Compare and contrast the advantages and disadvan-tages of the current yield computation versus yield to maturity calculations. (LG7-6) 10. What is the yield to call and why is it important to a bond investor? (LG7-6) 11. What is the purpose of computing the equivalent taxable yield of a municipal bond? (LG7-6) 12. Explain why high-income and wealthy people are more likely to buy a municipal bond than a corporate bond. (LG7-6) 13. Why does a Treasury bond offer a lower yield than a corporate bond with the same time to maturity? Could a corporate bond with a different time to maturity offer a lower yield? Explain. (LG7-7) 14. Describe the difference between a bond issued as a high-yield bond and one that has become a Òfallen angel.Ó (LG7-7) 15. What is the difference in the trading volume between Treasury bonds and corporate bonds? Give examples and/or evidence. (LG7-8)problems 7-1 Interest Payments Determine the interest payment for the following three bonds: 3½ percent coupon corporate bond (paid semiannually), 4.25 percent coupon Treasury note, and a corporate zero coupon bond maturing in 10 years. (Assume a $1,000 par value.) (LG7-1) 7-2 Interest Payments Determine the interest payment for the following three bonds: 4½ percent coupon corporate bond (paid semiannually), 5.15 percent coupon Treasury note, and a corporate zero coupon bond maturing in 15 years. (Assume a $1,000 par value.) (LG7-1) 7-3 Time to Maturity A bond issued by Ford on May 15, 1997, is scheduled to mature on May 15, 2097. If today is November 16, 2014, what is this bondÕs time to maturity? (LG7-1) 7-4 Time to Maturity A bond issued by IBM on December 1, 1996, is scheduled to mature on December 1, 2096. If today is December 2, 2015, what is this bondÕs time to maturity? (LG7-1) 7-5 Call Premium A 6 percent corporate coupon bond is callable in five years for a call premium of one year of coupon payments. Assuming a par value of $1,000, what is the price paid to the bondholder if the issuer calls the bond? (LG7-1) 7-6 Call Premium A 5.5 percent corporate coupon bond is callable in 10 years for a call premium of one year of coupon payments. Assuming a par value of $1,000, what is the price paid to the bondholder if the issuer calls the bond? (LG7-1)basic problemsFinal PDF to printer
258cor91411_ch07_226-263.indd 258 01/20/17 06:58 PM 7-7 TIPS Interest and Par Value A 2¾ percent TIPS has an original reference CPI of 185.4. If the current CPI is 210.7, what is the current interest payment and par value of the TIPS? (LG7-2) 7-8 TIPS Interest and Par Value A 3⅛ percent TIPS has an original reference CPI of 180.5. If the current CPI is 206.8, what is the current interest payment and par value of the TIPS? (LG7-2) 7-9 Bond Quotes Consider the following three bond quotes: a Treasury note quoted at 97.844, a corporate bond quoted at 103.25, and a municipal bond quoted at 101.90. If the Treasury and corporate bonds have a par value of $1,000 and the municipal bond has a par value of $5,000, what is the price of these three bonds in dollars? (LG7-3) 7-10 Bond Quotes Consider the following three bond quotes: a Treasury bond quoted at 106.438, a corporate bond quoted at 96.55, and a municipal bond quoted at 100.95. If the Treasury and corporate bonds have a par value of $1,000 and the municipal bond has a par value of $5,000, what is the price of these three bonds in dollars? (LG7-3) 7-11 Zero Coupon Bond Price Calculate the price of a zero coupon bond that matures in 20 years if the market interest rate is 3.8 percent. (LG7-4) 7-12 Zero Coupon Bond Price Calculate the price of a zero coupon bond that matures in 15 years if the market interest rate is 5.75 percent. (LG7-4) 7-13 Current Yield WhatÕs the current yield of a 3.8 percent coupon corporate bond quoted at a price of 102.08? (LG7-6) 7-14 Current Yield WhatÕs the current yield of a 5.2 percent coupon corporate bond quoted at a price of 96.78? (LG7-6) 7-15 Taxable Equivalent Yield WhatÕs the taxable equivalent yield on a municipal bond with a yield to maturity of 3.5 percent for an investor in the 33 percent mar-ginal tax bracket? (LG7-6) 7-16 Taxable Equivalent Yield WhatÕs the taxable equivalent yield on a municipal bond with a yield to maturity of 2.9 percent for an investor in the 28 percent mar-ginal tax bracket? (LG7-6) 7-17 Credit Risk and Yield Rank from highest credit risk to lowest risk the following bonds, with the same time to maturity, by their yield to maturity: Treasury bond with yield of 5.55 percent, IBM bond with yield of 7.49 percent, Trump Casino bond with yield of 8.76 percent, and Banc One bond with a yield of 5.99 percent. (LG7-7) 7-18 Credit Risk and Yield Rank the following bonds in order from lowest credit risk to highest risk all with the same time to maturity, by their yield to maturity: Treasury bond with yield of 4.65 percent, United Airlines bond with yield of 9.07 percent, Bank of America bond with a yield of 6.25 percent, and Hewlett-Packard bond with yield of 6.78 percent. (LG7-7)intermediate problems 7-19 TIPS Capital Return Consider a 3.5 percent TIPS with an issue CPI reference of 185.6. At the beginning of this year, the CPI was 193.5 and was at 199.6 at the end of the year. What was the capital gain of the TIPS in dollars and in percent-age terms? (LG7-2) 7-20 TIPS Capital Return Consider a 2.25 percent TIPS with an issue CPI reference of 187.2. At the beginning of this year, the CPI was 197.1 and was at 203.8 at the end of the year. What was the capital gain of the TIPS in dollars and in percent-age terms? (LG7-2) 7-21 Compute Bond Price Compute the price of a 3.8 percent coupon bond with 15 years left to maturity and a market interest rate of 6.8 percent. (Assume interest payments are semiannual.) Is this a discount or premium bond? (LG7-4)Final PDF to printer
259cor91411_ch07_226-263.indd 259 01/20/17 06:58 PM 7-22 Compute Bond Price Compute the price of a 5.6 percent coupon bond with 10 years left to maturity and a market interest rate of 7.0 percent. (Assume interest payments are semiannual.) Is this a discount or premium bond? (LG7-4) 7-23 Compute Bond Price Calculate the price of a 5.2 percent coupon bond with 18 years left to maturity and a market interest rate of 4.6 percent. (Assume interest payments are semiannual.) Is this a discount or premium bond? (LG7-4) 7-24 Compute Bond Price Calculate the price of a 5.7 percent coupon bond with 22 years left to maturity and a market interest rate of 6.5 percent. (Assume interest payments are semiannual.) Is this a discount or premium bond? (LG7-4) 7-25 Bond Prices and Interest Rate Changes A 5.75 percent coupon bond with 10 years left to maturity is priced to offer a 6.5 percent yield to maturity. You believe that in one year, the yield to maturity will be 5.8 percent. What is the change in price the bond will experience in dollars? (LG7-5) 7-26 Bond Prices and Interest Rate Changes A 6.5 percent coupon bond with 14 years left to maturity is priced to offer a 7.2 percent yield to maturity. You believe that in one year, the yield to maturity will be 6.8 percent. What is the change in price the bond will experience in dollars? (LG7-5) 7-27 Yield to Maturity A 5.65 percent coupon bond with 18 years left to maturity is offered for sale at $1,035.25. What yield to maturity is the bond offering? (Assume interest payments are semiannual.) (LG7-6) 7-28 Yield to Maturity A 4.30 percent coupon bond with 14 years left to maturity is offered for sale at $943.22. What yield to maturity is the bond offering? (Assume interest payments are semiannual.) (LG7-6) 7-29 Yield to Call A 6.75 percent coupon bond with 26 years left to maturity can be called in 6 years. The call premium is one year of coupon payments. It is offered for sale at $1,135.25. What is the yield to call of the bond? (Assume interest pay-ments are semiannual.) (LG7-6) 7-30 Yield to Call A 5.25 percent coupon bond with 14 years left to maturity can be called in 4 years. The call premium is one year of coupon payments. It is offered for sale at $1,075.50. What is the yield to call of the bond? (Assume interest pay-ments are semiannual.) (LG7-6) 7-31 Comparing Bond Yields A client in the 39 percent marginal tax bracket is com-paring a municipal bond that offers a 4.5 percent yield to maturity and a similar-risk corporate bond that offers a 6.45 percent yield. Which bond will give the client more profit after taxes? (LG7-6) 7-32 Comparing Bond Yields A client in the 28 percent marginal tax bracket is com-paring a municipal bond that offers a 4.5 percent yield to maturity and a similar-risk corporate bond that offers a 6.45 percent yield. Which bond will give the client more profit after taxes? (LG7-6)advanced problems 7-33 TIPS Total Return Reconsider the 3.5 percent TIPS discussed in problem 7-19. It was issued with CPI reference of 185.6. The bond is purchased at the begin-ning of the year (after the interest payment), when the CPI was 193.5. For the interest payment in the middle of the year, the CPI was 195.1. Now, at the end of the year, the CPI is 199.6 and the interest payment has been made. What is the total return of the TIPS in dollars and in percentage terms for the year? (LG7-2) 7-34 TIPS Total Return Reconsider the 2.25 percent TIPS discussed in problem 7-20. It was issued with CPI reference of 187.2. The bond is purchased at the beginning of the year (after the interest payment), when the CPI was 197.1. For the interest payment in the middle of the year, the CPI was 200.1. Now, at the end of the year, Final PDF to printer
260cor91411_ch07_226-263.indd 260 01/20/17 06:58 PMthe CPI is 203.8 and the interest payment has been made. What is the total return of the TIPS in dollars and in percentage terms for the year? (LG7-2) 7-35 Bond Prices and Interest Rate Changes A 6.25 percent coupon bond with 22 years left to maturity is priced to offer a 5.5 percent yield to maturity. You believe that in one year, the yield to maturity will be 6.0 percent. If this occurs, what would be the total return of the bond in dollars and percent? (LG7-5) 7-36 Bond Prices and Interest Rate Changes A 7.5 percent coupon bond with 13 years left to maturity is priced to offer a 6.25 percent yield to maturity. You believe that in one year, the yield to maturity will be 7.0 percent. If this occurs, what would be the total return of the bond in dollars and percentage terms? (LG7-5) 7-37 Yields of a Bond A 2.50 percent coupon municipal bond has 12 years left to maturity and has a price quote of 98.45. The bond can be called in four years. The call premium is one year of coupon payments. Compute and discuss the bondÕs current yield, yield to maturity, taxable equivalent yield (for an investor in the 35 percent marginal tax bracket), and yield to call. (Assume interest pay-ments are semiannual and a par value of $5,000.) (LG7-6) 7-38 Yields of a Bond A 3.85 percent coupon municipal bond has 18 years left to maturity and has a price quote of 103.20. The bond can be called in eight years. The call premium is one year of coupon payments. Compute and discuss the bondÕs current yield, yield to maturity, taxable equivalent yield (for an investor in the 35 percent marginal tax bracket), and yield to call. (Assume interest pay-ments are semiannual and a par value of $5,000.) (LG7-6) 7-39 Bond Ratings and Prices A corporate bond with a 6.5 percent coupon has 15 years left to maturity. It has had a credit rating of BBB and a yield to maturity of 7.2 percent. The firm has recently gotten into some trouble and the rating agency is downgrading the bonds to BB. The new appropriate discount rate will be 8.5 percent. What will be the change in the bondÕs price in dollars and percentage terms? (Assume interest payments are semiannual.) (LG7-7) 7-40 Bond Ratings and Prices A corporate bond with a 6.75 percent coupon has 10 years left to maturity. It has had a credit rating of BB and a yield to maturity of 8.2 percent. The firm has recently become more financially stable and the rating agency is upgrading the bonds to BBB. The new appropriate discount rate will be 7.1 percent. What will be the change in the bondÕs price in dollars and per-centage terms? (Assume interest payments are semiannual.) (LG7-7) 7-41 Spreadsheet Problem Say that in June of this year, a company issued bonds that are scheduled to mature three years from now in June. The coupon rate is 5.75 percent and is semiannually. The bond issue was rated AAA. a. Build a spreadsheet that shows how much money the firm pays for each inter-est rate payment and when those payments will occur if the bond issue sells 50,000 bonds. b. If the bond issue rating would have been BBB, then the coupon rate would have been 6.30 percent. Show the interest payments with this rating. Explain why bond ratings are important to firms issuing capital debt. c. Consider that interest rates in the economy increased in the first half of this year. If the firm would have issued the bonds in January of this year, then the coupon rate would have only been 5.40 percent. How much extra money per year is the firm paying because it issued the bonds in June instead of January? 7-42 Spreadsheet Problem You have a portfolio of three bonds. The long bond will mature in 19 years and has a 5.5% coupon rate. The midterm bond matures in 9 years and has a 6.6% coupon rate. The short bond matures in only 2 years and has a 4% coupon rate. Final PDF to printer
261cor91411_ch07_226-263.indd 261 01/20/17 06:58 PM a. Construct a spreadsheet that shows the value of these three bonds and the portfo-lio when the discount rate is 5%. The spreadsheet can look something like this: ABCDE1NowChange to2Interest rate =5.00%5.50%3BondsBond Price NowPrice After ChangeChange in $Change in %4Long bond5Midterm bond6Short bond7 Total =$0.00$0.00 b. Illustrate what happens when the discount rate increases by 0.5%. What do you notice about the changes in price between the three bonds? c. Show the bond prices when the discount rate decreases by 0.5% from the dis-count rate in part a. What do you notice about the price change between parts b and c?research it! Bond Information OnlineInformation on the bond market is widely available in papers like The Wall Street Journal and BarronÕs. Bond information can also be found online at financial websites like finance.yahoo.com and www.finra.org. The bond credit rating agencies also maintain websites with their own bond market news.You can follow the bond market easily at places like the Yahoo! Finance website. Click on the Bond link in the menu to go to their Bond Center. Bond yields for various maturity Treasury securities are shown for today and for previous days. The Bond Composite Rates link shows similar comparisons for municipal and corporate bonds too.Bond calculators are also available free on the Web. Compare a bond price result from your calculator or the price equation with the online bond calculator result at Investopedia. (www.investopedia.com/calculator/BondPrice.aspx)integrated mini-case Corporate Bond Credit Risk Changes and Bond PricesLandÕoÕToys is a profitable, medium-sized, retail company. Several years ago it issued a 6½ percent coupon bond, which pays interest semiannually. The bond will mature in 10 years and is currently priced in the market as $1,037.19. The average yields to maturity for 10-year corporate bonds are reported in the following table by bond rating.Bond RatingYield (%)Bond RatingYield (%)AAA5.4BB 7.3AA5.7B 8.2A6.0CCC 9.2BBB6.5CC10.5C12.0D14.5Periodically, one company will purchase another by buying all of the target firmÕs stock. The bonds of the target firm continue to exist. The debt obligation is assumed Final PDF to printer
262cor91411_ch07_226-263.indd 262 01/20/17 06:58 PMANSWERS TO TIME OUT 7-1 The federal government issues bonds to fund its annual spending deficit and to refund old bonds that are maturing. Local governments and corporations issue bonds to raise the capital needed to fund projects. For local governments, those projects might be the building of roads, bridges, sewer systems, schools, airports, etc. For companies, the projects tend to be expansions of their businesses, which might entail a large fac-tory, new facilities in different geographical locations, and even the purchase of exist-ing business lines from other companies. 7-2 The current price is 100.06 percent of $1,000, which is $1,000.60. It will pay a semian-nual payment of 5.40% × $1,000 Ö 2 = $27. 7-3 Bondprice = $42.50 × ⎡ ⎢ ⎣ 1 − 1 ___________ (1 + 0.0375) 24 ______________ 0.0375 ⎤ ⎥ ⎦ + $1,000 ___________ (1 + 0.0375) 24 = $664.90 + $413.32 = $1,078.22 7-4 The relationship is one of opposite directions. Increases in market interest rates are associated with decreases in the price of existing bonds. Decreases in interest rates accompany increases in bond prices. 7-5 Using the calculator with settings of N = 20, PV = Ð525, PMT = 0, FV = 1000, solving for I gives 3.274 percent. Multiplying this semiannual yield by 2 gives a 6.55 percent yield to maturity. 7-6 The yield to maturity is higher than the coupon rate for a discount bond. By definition, bonds become discount bonds when the market interest rate (known as the yield to maturity for a bond) rises above the fixed coupon rate. 7-7 A credit rating change will change the appropriate discount for the bond. An increase in the rating calls for a lower discount rate to be used while a decrease in the rating calls for a higher discount rate. This change in the discount rate directly impacts the bond price. 7-8 The mortgage bond has real estate collateral whereas the debenture has no collateral. Therefore, the mortgage bond is considered a safer security for investors and will be given a higher rating. With the lower bond rating, the debenture will have to offer a higher yield.1Cash ßowPeriod?20213442.5222324Semiannual periods42.542.542.542.542.542.542.51,000. . .. . .3.75%by the new firm. The credit risk of the bonds often changes because of this type of an event.Suppose that the firm Treasure Toys makes an announcement that it is purchasing LandÕoÕToys. Due to Treasure ToysÕ projected financial structure after the purchase, Standard & PoorÕs states that the bond rating for LandÕoÕToys bonds will change to BB. a. Compute the yield to maturity of LandÕoÕToys bonds before the purchase announcement and use it to determine the likely bond rating. b. Assume the bondÕs price changes to reflect the new credit rating. What is the new price? Did the price increase or decrease? c. What is the dollar change and percentage change in the bond price? d. How do the bond investors feel about the announcement?Final PDF to printer
263cor91411_ch07_226-263.indd 263 01/20/17 06:58 PM 7-9 Since bond prices move in the opposite direction to interest rates, the change in inter-est rates provides much of the information for knowing the change in bond prices. 7-10 Figure 7.5 illustrates many of the popular bond indexes. For example, Barclays Capital reports various broad market and U.S. Treasury bond indexes. For corporate bonds, Merrill Lynch reports indexes for medium-term investment grade, long-term investment grade, and speculative grade. Merrill Lynch also has municipal bond indexes.Final PDF to printer
264cor91411_ch08_264-295.indd 264 01/20/17 04:39 PMviewpointsPART FOURBusiness ApplicationAs CEO of your firm, Dawa Tech, which makes computer components, you have been able to grow its dividends by 8 percent per year to a recent $2 per share. You expect this growth to continue. As a result, the stock price has risen to $65 and has a P/E ratio of 16.25.Tomorrow, you are scheduled to meet with some stockholders and financial analysts. To prepare for the meeting, you should know what return the shareholders seem to expect and estimate where the Dawa stock price may be in three years. How will you go about preparing for this meeting? (See the solution at the end of the chapter.)Personal ApplicationYou are impressed with the news and entertainment firm CBC Newscorp. The per-share dividends have increased from $1.25 per year three years ago to the recent $1.68 annual dividend. Then you discover that 15 analysts are following the firm and that their mean growth estimate for the future is 10.1 percent. Now you want to know if the current selling price of $54 seems like a good deal if the appropriate required return for the stock is 13.5 percent. (See the solution at the end of the chapter.)Who are these Òanalysts,Ó and where can you find their opinions?Valuing Stocks8Final PDF to printer
265cor91411_ch08_264-295.indd 265 01/20/17 04:39 PMan investment is that they know that they can sell the stock during any trading day. Investors buy and sell stocks among themselves in stock markets. Well-functioning stock mar-kets are critical to any capitalistic economy. In this chapter, weÕll dis-cuss stock market operations and stock valuation.and Larry Page of Google to take their companies public so that their businesses can become large corpo-rations. Both the company founders and the new owners (stock investors) have amassed much wealth over the years under this arrangement. One very important reason that investors are willing to buy company stock as Businesses need capital to start up operations, expand product lines and services, and serve new markets. In the last chapter, we discussed debt, which is one source of financial capital upon which busi-nesses can draw. Their other source of capital is called equity, or business ownership. Public corporations share business ownership and raise money by issuing stocks to investors. When the company sells this form of equity ownership to raise money, it gives up some ownershipÑand thus some controlÑover the business. Investors buy stock to receive the benefits of business ownership. Most citizens do not have the time or expertise to operate their own businesses. Buying stock allows them to participate in the profits of economic activities. Access to equity capital has allowed entre-preneurs like Bill Gates of Microsoft Learning Goals LG8-1 Understand the rights and returns that come with com-mon stock ownership. LG8-2 Know how stock exchanges function. LG8-3 Track the wider stock market with stock indexes and dif-ferentiate among the kinds of information each index provides. LG8-4 Know the terminology of stock trading. LG8-5 Compute stock values using dividend discount and constant- growth models. LG8-6 Calculate the stock value of a variable-growth-rate company. LG8-7 Assess relative stock values using the P/E ratio model.© Sherab/AlamyFinal PDF to printer
266 part four Valuing of Bonds and Stockscor91411_ch08_264-295.indd 266 01/20/17 04:39 PM8.1 ∙ Common StockEquity securities (stocks) represent ownership shares in a corporation. Common stock offers buyers the potential for current income from dividends and capital appreciation from any stock price increases. Over time, some corporate profits are reinvested in the firm, which increases the value of each shareholderÕs stake in the business. At any point in time, the market value of a firmÕs common stock depends on many factors, including ¥ The companyÕs profitability. ¥ Growth prospects for the future. ¥ Current market interest rates. ¥ Conditions in the overall stock market.Over periods of 30 to 40 years, stocks have offered investors the best opportunities to increase wealth. Since stocks are also susceptible to price declines and stock price fluctuations can be very volatile over short periods of time, stock investing requires a longer-term outlook.Virtually any business firm that is organized as a corporation (see Chapter 1) may choose to issue publicly traded stock. Common stockholders vote to elect the board of directors; they also vote on various other proposals requested by other shareholders or the management team. As owners of the firm, common stockholders are considered to be residual claimants. This means that common stockholders have the right to claim any cash flows or value after all other claimants have received what they are owed. As a company earns cash flows, it must pay suppliers, employees, expenses, taxes, and debt interest payments. Stockholders claim the leftover (or residual) cash flow. These profits can be used to reinvest in the firm to foster growth, pay dividends to shareholders, or a combination of the two.Stocks of growing firms are valuable. Stocks in firms that pay dividends to sharehold-ers are also valuable. Stocks issued by firms that have greater amounts of residual cash flow are more valuable. The value is reflected in the stock price. Therefore, stock price values arise from the companyÕs underlying business success. Many different inves-tors and analysts may estimate a stockÕs fundamental value based upon some outlook or theory. But the actual stock price is determined on stock exchanges when investors seek to trade with one another. LetÕs discuss this trading process and then explore how stocks are valued.8.2 ∙ Stock MarketsIn general, people will invest significant amounts of their wealth in stocks only if they know that they can convert their shares into cash at any time. Stock exchanges provide this liquidity, allowing buyers and sellers the means to transact stock trades with each other. This liquidity gives many people the confidence to invest in the first place and makes stocks (as well as bonds) attractive investments relative to less-liquid assets like real estate or fine collectiblesÑwhich can be difficult to sell quickly at full value.The most well-known stock exchange in the world is the New York Stock Exchange (NYSE). The New York Stock Exchange, located in New York City on the corner of Wall Street and Broad Street, is the largest U.S. stock exchange as measured by the value of companies listed and the dollar value of trading activity. The NYSE is the largest equi-ties marketplace in the world and is home to approximately 2,800 companies (many with multiple securities listed). While other exchanges may boast more companies listed, the largest companies in the world tend to list in New York. The holding company that owns the NYSE, Intercontinental Exchange, also operates Euronext, a Europe-based electronic exchange market. For decades, the American Stock Exchange, located just down the street, competed with the NYSE. However, in 2008, the NYSE acquired this exchange. Now, smaller companies trade at this location, which is referred to as AMEX.LG8-1common stockAn ownership stake in a corporation.residual claimantsOwnership of cash flows and value after other claim-ants are paid.LG8-2New York Stock Exchange (NYSE)Large and prestigious stock exchange with a trading floor.Final PDF to printer
P/E Ratio:DeÞned as currentprice divided bylast four quartersof earnings.Dividend Yield:DeÞned as annualdividends dividedby current stockprice. (%)Dividend: Pershare amount ofdividends paid inlast 12 months. ($)Last Price andChange: Lasttraded price andthe change fromthe prior day. ($)Prev Close:Open:Bid:Ask:1y Target EstBeta:Next Earnings Date:117.01118.02116.56 X 100117.46 X 100126.000.56211522-Apr-16 DayÕs Range:52wk Range:Volume:Avg Vol (3m):Market Cap:P/E (ttm):EPS (ttm):Div & Yield117.26 – 118.5387.50 – 124.835,726,2986,924,000107.93B24.514.803.56 (3.08%)118.5118.0117.5117.010amMCD12pm1d5d1m3m6m1y2y5ymax2pm4pmStock Name andTicker Symbol: Thecorporate name andunique symbol usedfor trading andquotes.McDonaldÕs Corp. (MCD)117.540.53(0.45%)Watchlist- NYSEFeb 10, 4.00pm ESTPrevious Close4:00PM ESTMcDonaldÕs Corporation Common S52-Week Range:The highest andlowest price thestock has traded forin the past 12months. ($)© Yahoo!Volume ofTrading: Totalnumber of sharestraded during theprevious day. chapter 8 Valuing Stocks 267cor91411_ch08_264-295.indd 267 01/20/17 04:39 PMMuch of the stock buying and selling at the NYSE occurs at 17 stations, called trading posts, on the trading floor. Each post is staffed by a designated market maker (formerly known as specialists), who oversees the orderly trading of the specific stocks assigned to that post. Brokers, located around the perimeter of the floor, act as agents for those buying and selling stocks. Brokers execute orders by matching buy and sell orders. Once the buy and sell orders match, the transaction is completed and the trade appears on trading screens viewed by people all over the world.Consider this scenario. You decide to buy shares of McDonaldÕs stock because of new menu items and other initiatives. You place a buy order for 100 shares with your brokerÑ either with a simple phone call or through an online brokerage service. The broker then sends the order to the NYSE electronically to the trading post assigned for McDonaldÕs stock. At the trading post, the specialist makes sure the transaction is executed in a fair and orderly manner. Your buy order competes with other orders at the point of sale for the best price and an on-floor broker executes your purchase. You will receive a trade confirmation from your broker describing the trade and noting the exact amount you owe for the 100 shares of McDonaldÕs plus any applicable commissions. The NYSE reports the transaction and it appears within seconds on displays across the country and around the world. Note that buy and sell orders are electronically routed from all over the world to the NYSE, which then routes trade results back. Since most of the trade orders are already in electronic form, why not electronically match buy and sell orders and bypass any human intervention in floor trading? Indeed, the NYSE has joined many other exchanges in becoming increasingly electronic. Some floor market-maker firms can see a time when no human intervention will be a part of floor trading at the NYSE. The NYSE will trade millions of McDonaldÕs stock shares in a given day. A stock quote for McDonaldÕs stock, ticker symbol MCD, is shown in Figure 8.1. On February 10, 2016, more than 5.7 million McDonaldÕs shares traded. The stock closed at $117.54 per share, which was $0.53 higher than the closing price of the previous day. At this price, McDonaldÕs stock is currently closer to its 52-week high of $124.83 than to its 52-week low of $87.50.trading postsTrading location on the floor of a stock exchange.brokersFloor traders who execute orders for others and themselves.ticker symbolUnique code for a company consisting of one to five letters.FIGURE 8.1Read a Stock Quote, February 10, 2016, Yahoo! FinanceIf you know what to look for, reading a stock quote is not as complicated as it first may appear. Final PDF to printer
268 part four Valuing of Bonds and Stockscor91411_ch08_264-295.indd 268 01/20/17 04:39 PMTo list its stock on the NYSE, a company must meet minimum requirements for its ¥ Total number of stockholders. ¥ Level of trading volume. ¥ Corporate earnings. ¥ Firm size.The exchange also charges an initial list fee and an annual fee. Listing standards and fees are higher for the NYSE than for other stock exchanges, so many firms cannot (or choose not to) list their stocks there. Another popular stock trading system is the NASDAQ Stock Market, an electronic stock market without a physical trading floor. Today, NASDAQ features many of the big-name high-tech companies investors have come to know, like Apple Computer (ticker: AAPL), Intel (ticker: INTC), Microsoft (ticker: MSFT), and Qualcomm (ticker: QCOM). Many newer high-tech companies like Google (ticker: GOOG), Netflix (ticker: NFLX), and Adobe Systems Inc. (ticker: ADBE), are also listed on NASDAQ. In 2007, NASDAQ purchased OMX, which owned seven Nordic and Baltic stock exchanges, and became NASDAQ OMX. NASDAQ ranks second, behind the NYSE, among the worldÕs equity markets in terms of total dollar volume. NASDAQ lists approximately 3,100 domestic and foreign companies.Instead of having a trading floor, NASDAQ uses a vast electronic trading system that executes trades via computer rather than in person. Instead of one designated market maker overseeing the process for an individual stock on a trading floor, NasdaqÕs system uses multiple market makers, or dealers. Market makers use their own stock inventory and capital to compete with other dealers to buy and sell the stocks they represent. When an investor places an order through a stockbroker for a NASDAQ-listed stock, the elec-tronic system routes the order and the investor buys shares from the dealer offering the best (lowest) price. Typical NASDAQ stocks support 10 market makers actively compet-ing with one another for investor trades.Table 8.1 shows trading activity on the three main stock exchanges for one day in February 2016. Note that all three exchanges traded more than 1 billion shares during the day.The business of providing platforms or forums for investors and speculators to trade stocks and other financial assets has been changing rapidly. Many exchanges that previ-ously used physical floor trading systems with specialists and open outcry to establish stock prices are shifting to electronic systems with no trading floors. Long-standing, traditional exchanges are also merging with other domestic and international exchanges to create fewer, but larger, forums that focus not just on U.S. securities but on many more internationally focused financial assets. The wider range of represented securities allows traders new opportunities to explore trading relationships among securities traded across the world. This worldwide trading will establish economically sound prices and addi-tional financial stability around the world.NASDAQ Stock MarketLarge electronic stock exchange.market makersDealers and specialists who oversee an orderly trading process.dealersNASDAQ market makers who use their own capital to trade with investorsNYSEAMEXNASDAQAdvancing issues1,624 (52%)744 (53%)1,269 (48%)Declining issues1,426 (46%)607 (44%)1,298 (49%)Unchanged issues78 (2%)42 (3%)94 (4%)New highs44206New lows15667201Total volume4,428,773,6811,042,526,8642,388,659,663Source: Yahoo! FinanceTABLE 8.1 Trading on the NYSE, NASDAQ, and AMEX, February 10, 2016Final PDF to printer
chapter 8 Valuing Stocks 269cor91411_ch08_264-295.indd 269 01/20/17 04:39 PMTracking the Stock MarketWith thousands of stocks trading every minute, many stock prices rise while others fall. Table 8.1 also shows that, throughout the trading day, 1,624 stocks increased in price on the NYSE while 1,426 stocks decreased in price. While the AMEX also expe-rienced more stocks with increases in price than declines, the NASDAQ saw more declines. In addition to the number of stocks advancing and declining, the table also shows the number of stocks that hit new 52-week price highs (44 listed on the NYSE) and new lows (156 on the NYSE) on that day. So, was this a good day or a bad day in the stock market?To say anything about the general direction of the stock market, stock indexes are useful. Dozens of stock indexes are designed to track the overall market; many more track different market segments. The three most recognized indexes are the Dow Jones Industrial Average (DJIA), the Standard & PoorÕs 500 Index (S&P 500), and the NASDAQ Composite Index.Charles H. Dow invented the first stock average in 1884. At the turn of the 20th century, railroads were the first major corporations. So he began with 11 stocks, mostly railroads. Dow created a price average by simply adding up 11 stock prices and dividing by the number 11. Two years later, Dow began tracking a 12-stock industrial average. This industrial average would eventually evolve into the modern DJIA, which is a price average of 30 large, industry-leading stocks that together represent roughly 30 percent of the total stock value of all U.S. equities. DJIA level changes describe how the largest companies that participate in the stock market performed over a given period. The DJIA was at 15,914.74, a change of −99.64 (or −0.62 percent), on the day illustrated in Table 8.1.The Standard & PoorÕs Corp. introduced its 500-stock index in 1957. Standard & PoorÕs chooses companies to include in the S&P 500 Index to represent the 10 sectors of the economy: 1. Financial 2. Information technology 3. Health care 4. Industrials 5. Consumer discretionary 6. Consumer staples 7. Energy 8. Telecom services 9. Utilities 10. MaterialsS&P uses market capitalization (a measure of company size using stock price times shares outstanding), not just stock prices, of the largest 500 U.S. firms to compute the index. These 500 firms represent roughly 80 percent of the overall stock market capital-ization (number of shares times share price). Although the DJIA is a long-time favorite LG8-3stock indexIndex of market prices of a particular group of stocks. The index is used to measure those stocksÕ performance.Dow Jones Industrial Average (DJIA)A popular index of 30 large, industry-leading firms.Standard & PoorÕs 500 Index (S&P 500)A stock index of 500 large companies.NASDAQ Composite IndexA technology-firm weighted index of stocks listed on the NASDAQ Stock Exchange.market capitalizationThe size of the firm mea-sured as the current stock price multiplied by the num-ber of shares outstanding.TIME OUT 8-1 What are three primary stock exchanges in the United States and where are they located? For which of the exchanges does physical location matter? Why? 8-2 Describe differences in trading procedures on the NYSE versus the NASDAQ. Which do you think is most fair to investors? Why? Final PDF to printer
chapter 8 Valuing Stocks 271cor91411_ch08_264-295.indd 271 01/20/17 04:39 PMThe DJIA fully recovered in early 2013 and closed above 15,000 for the first time on May 7, 2013, and above 18,000 on February 13, 2015. This massive stock market rise coincides with the quantitative easing programs implemented by the U.S. Federal Reserve.TIME OUT 8-3 Discuss why the dayÕs market return may be different when measured by the DJIA, S&P 500 Index, and NASDAQ Composite taken separately. 8-4 Why might the Òmarket bubbleÓ phenomenon appear more dramatic because it occurred in the NASDAQ Composite rather than by the DJIA or S&P 500 Index? 8-5 If you followed the market regularly, to which index would you give the most credence? Why? Trading StocksPeople who wish to buy and sell stocks need to open stock brokerage accounts. Tra-ditional, full-service stockbrokers (e.g., Morgan Stanley Smith Barney, Merrill Lynch, UBS, Edward Jones) provide clients with research and advice in addition to executing trades. Their clients pay for this research and advice: Commission fees for these ser-vices may run well over $100 per trade. Discount brokerage firms (e.g., Charles Schwab, E-trade, Scottrade, TD Ameritrade) charge a much lower commission, $5 to $30 per trade, but do not provide the additional services. Investors at discount brokerages usually place trades through the brokerageÕs Internet sites.Buy and sell orders go through the brokerage firm to a market maker (a dealer or a specialist) at a stock exchange. The quoted bid is the highest price at which the market maker offers to pay for the stock. Investors have little choice but to accept this selling price, because regardless of the broker used, the market maker offers the only place to sell the stock. The quoted ask price is the lowest price at which a market maker will sell a stockÑso investors buy at the ask price. The difference between the bid and the ask price may be only $0.01 for high-volume stocks and can be as high as $0.20 for less-often traded companies. The spread between the bid and the ask price is a cost to the investor and a profit for the market maker. This profit compensates the market maker for provid-ing a market and liquidity for that stock.Investors can place a buy or sell market order. A market order to buy stock will be filled immediately at the current ask price when routed to the stock exchange. A sell market order will be filled at the current bid price. The advantage of a market order is that it exe-cutes immediately at the best available price. The disadvantage of a market order is that the investor does not know in advance what that fill price will be. Investors can name their own prices by using limit orders, in which investors specify the price at which they are willing to execute the buy or sell order. With a buy limit order, a trade is executed if the ask quote is at or below the price target. For a sell limit order, a trade is executed if the bid quote moves through the specified price. If the current quote does not meet the price cited in the limit order, the trade is not executed. The advantage of a limit order is that the investor makes the trade at the desired price; the disadvantage is that the trade might not be executed at all.Consider a quote of McDonaldÕs stock with a bid price of $117.00 and an ask price of $117.05. An investor placing a market buy order would purchase the stock at $117.05. A market sell order would execute as the price rises through $117.00. Note that an investor who simul-taneously bought and sold 100 shares would pay $11,705 and receive $11,700Ñlosing $5. An investor who places a buy limit order at $116.75 will only purchase the shares if the ask price falls to $117.75 or lower. If the ask does not fall, the order will not execute. Bid and ask prices tell investors at what prices the stock can currently be traded in general. But being able to buy at the ask price does not guarantee that the stock should be valued at that price. WeÕll discuss various ways to arrive at reasonable per-share stock values in the next section.LG8-4bidThe quoted price investors are likely to receive when they sell stock.askThe quoted price investors are likely to pay when they buy stock.market orderA stock buy or sell order to be immediately executed at the current market price.limit orderA stock buy or sell order at a specific price. It will only be executed if the market price meets the specified price.Final PDF to printer
272 part four Valuing of Bonds and Stockscor91411_ch08_264-295.indd 272 01/20/17 04:39 PM!want to know more?Key Words to Search for Updates: irrational exuberance, price bubble, maniaTo us today, it may seem ludicrous that in the years 1634 to 1636, the people of Holland were in the midst of ÒTulip Mania,Ó and the price for a single rare tulip bulb approached the equivalent of $35,000. Then the bubble burst and tulip prices quickly plunged to less than the equivalent of $1. We may call those people who invested in a $35,000 tulip bulb irrational or even Òcrazy.ÓBut this type of story seems to repeat itself throughout history. Investors paid extremely high prices for the new computer stocks in the 1960s, the Ònifty fiftyÓ companies in the 1970s, Japanese stocks during the 1980s, and Inter-net stocks during the late 1990s. The mania for stocks like Iomega drove its price from an equivalent of $1 per share in January of 1995 to over $75 in just 16 months. When the bubble burst, the price fell hard. Many years later, in 2008, the company was purchased by EMC Corporation for dollars per share. But thatÕs just one company. A portfolio full of Inter-net stocks experienced a similar price mania followed by a severe fall. Investors created a stock index (TheStreet.com Internet Index) designed to track Internet stocks in late 1998, but by that time, part-time investors and veterans alike were already well into the craze. The Internet index started at 250, quickly rose to 1,270 by March of 2000, and subsequently fell to a low of 63 in October of 2002. Of course, the tech stock INVESTOR PSYCHOLOGYfinance at work behavioralbubble was followed by the real estate bubble. In retrospect, irrational bubble-like prices are not confined to tulips and the 17th century in Holland.Seemingly irrational behavior may not occur only dur-ing highly emotional periods of a price bubble. Recently, a growing recognition has arisen that ÒnormalÓ investors often behave in a way that might not be described as fully rational. Investors, being human, are subject to cognitive biases and emotions. Studies of investor behavior have discovered that investors commonly succumb to psychological biases and ¥ Trade too much. ¥ Sell winners too soon. ¥ Refuse to realize losses. ¥ Become overconfidentÑespecially when trading online. ¥ Seek stocks that have already increased in priceÑ perhaps up to their full potential price. ¥ Consider and react to whatÕs happening with each stock in isolation, rather than remembering the purpose for forming an overall portfolio.Investors who succeed in the long run are those who learn to avoid these psychological biases.TIME OUT 8-6 Explain how the difference in the bid and ask prices might be considered a hidden cost to the investor. 8-7 The bid and ask prices for Amazon.com are $37.79 and $37.85. If these quotes occur when a trade order is made, at what price would a market buy order execute? Would a limit sell order execute with a target price of $37.75? 8.3 ∙ Basic Stock ValuationCash FlowsIn the previous chapter, we showed how we value bonds by finding the present value of the future interest payments and the future par value. Stock valuation uses the same concept of finding the present value of future dividends and the future selling price. But of course uncertainty about both price appreciation and future dividend payment streams complicate stock valuation. Consider the simple case of valuing a stock to be held for one year shown in the time line. 0i1 yearPeriodCash ßowPV = ?D1 + P1The value of such a stock today, P0, is the present value of the dividend to be received in the first year, D1, plus the present value of the expected sales price in one year, P1. LG8-5Final PDF to printer
chapter 8 Valuing Stocks 273cor91411_ch08_264-295.indd 273 01/20/17 04:39 PMThe interest rate used to discount the cash flows is shown as i. Using the present value equation from Chapter 4 results in TodayÕs value = Present value of next yearÕs dividend and price P 0 = D 1 + P 1 _______ 1 + i (8-1)Whenever investors deal with future stock prices and future dividend payments, they must use expected values, not certain ones. Companies rarely decrease their dividends; most companiesÕ dividends either remain constant or slowly grow. Examining a firmÕs dividend history over the past few years will give clues to that companyÕs future dividend policy. For example, The Coca-Cola Company (ticker: KO) paid a $0.155 per share divi-dend for each quarter in 2006. The firm then raised the quarterly dividend to $0.17 for each quarterly dividend in 2007. The company paid quarterly dividends in 2008, 2009, 2010, 2011, and 2012 of $0.19, $0.205, $0.22, $0.235, and $0.255, respectively. For 2013 through 2015, Coca-Cola raised its quarterly dividend 2.5 cents every year. So the quar-terly dividend was $0.33 in 2015, for an annual dividend of $1.32. This dividend growth seems fairly stable and predictable.Stock prices, though, show much more volatility than dividend histories do. We face much uncertainty in trying to predict stock prices in the short term. Using a longer hold-ing period to estimate stock value reduces some, but by no means all, of the uncertainty. A 2-year holding period appears like this:Cash ßowPV = ? D2 + P2D1012 yearsPeriodiThe present value of the cash flows in years 1 and 2 is todayÕs stock value:TodayÕs value = Present value of next yearÕs dividend, the second yearÕs dividend, and the future price P 0 = D 1 ____ 1 + i + D 2 + P 2 ______ (1 + i) 2 (8-2)Notice that the divisor for the second term on the right-hand side of equation 8-2 is raised to the second power. This reflects the two years over which those cash flows must be discounted. You can do this analysis over any holding period. For a holding period of n years, the value of a stock is measured by the present value of dividends over the n years, and the eventual sale price, Pn. P 0 = Sum of the present value of each payment received P 0 = D 1 ____ 1 + i + D 2 ______ (1 + i) 2 + . . . + D n + P n ______ (1 + i) n (8-3)This formula incorporates both dividend income and capital appreciation or capital loss. It fully includes both major components of the investorÕs total return from investment.EXAMPLE 8-1 LG8-5Valuing Coca-Cola StockIn February 2016, you are valuing Coca-Cola stock to compare its value to its market price. The current market price is $43.01. Given the history of Coca-ColaÕs dividends, you believe that the company will pay total dividends in 2016 of $1.42 (= 4 ×$0.355). Your analysis indicates that the total dividends in 2017 and 2018 will be $1.54 and $1.66, respectively. In addition, you believe that the price of Coca-Cola stock at the end of 2015 For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.Final PDF to printer
274 part four Valuing of Bonds and Stockscor91411_ch08_264-295.indd 274 01/20/17 04:39 PMAs is often the case in finance, implementing equation 8-3 presents problems for some firms in practical terms. What will the future dividends of the firm be? What will the stock price be in 3, 5, or 10 years? While it seems that the dividend growth of Coca-Cola will be constant, consider the actual dividends and stock price of McDonaldÕs Corp. since 2000 shown in Figure 8.3.McDonaldÕs paid an annual dividend from 2000 to 2007. Some increases were small, like the $0.01 increase from 2000 to 2001 and again to 2002. Other increases were quite large, like the $0.50 increase between 2006 and 2007. Then McDonaldÕs changed to the more common quarterly dividend in 2008. Since the change to quarterly payments, will be $54.10 per share. If the appropriate discount rate is 11.0 percent, what is the value of Coca-Cola stock?SOLUTION: To organize your data, you first create the following timeline:Case ßowPV = ?Period0123years$1.66 + $54.10$1.54$1.4211.0%Using equation 8-3, you compute the stock value as P 0 = $1.42 _______ 1 + 0.11 + $1.54 _________ (1 + 0.11) 2 + $1.66 + $54.10 _____________ (1 + 0.11) 3 = $1.279 + $1.250 + $40.771 = $43.30 Since your analysis shows that Coca-ColaÕs stock should be valued at $43.30 while itÕs sell-ing for only $43.01, the stock appears to be slightly undervalued. You believe that this might be a good time to buy some Coca-Cola stock.Similar to Problems 8-15, 8-16, 8-27, 8-28, Self-Test Problem 1CALCULATOR HINTS1ST CASH FLOW:N = 1, I = 11.0PMT = 0, FV = 1.42CPT PV = −1.2792ND CASH FLOW:N = 2, I = 11.0PMT = 0, FV = 1.54CPT PV = −1.2503RD CASH FLOW:N = 3, I = 11.0PMT = 0, FV = 55.76CPT PV = −40.771VALUE = $1.279 + $1.250 + $40.771 = $43.3002040601201408010020002001200220032004200520062007200820092010201120122013201420152016McDonaldÕs Stock Price ($)Date PaidDividend PaidFebruary 25, 2011May 27, 2011August 30, 2011November 29, 2011February 28, 2012May 31, 2012August 30, 2012November 29, 2012February 27, 2013May 30, 2013August 29, 2013November 27, 2013$0.61$0.61$0.61$0.70$0.70$0.70$0.70$0.77$0.77$0.77$0.77$0.81November 13, 2000November 13, 2001November 13, 2002November 12, 2003November 10, 2004November 10, 2005November 13, 2006November 13, 2007February 28, 2008June 5, 2008August 28, 2008November 26, 2008February 26, 2009June 4, 2009August 28, 2009November 27, 2009February 25, 2010May 27, 2010August 30, 2010November 29, 2010$0.22$0.23$0.24$0.40$0.55$0.67$1.00$1.50$0.38$0.38$0.38$0.50$0.50$0.50$0.50$0.55$0.55$0.55$0.55$0.61Date PaidDividend PaidFebruary 27, 2014May 29, 2014August 28, 2014November 26, 2014February 26, 2015May 28, 2015August 28, 2015November 27, 2015$0.81$0.81$0.81$0.85$0.85$0.85$0.85$0.89Date PaidDividend PaidFIGURE 8.3Dividends and Stock Price of McDonaldÕs since 2000Dividends rarely decline, but stock prices often do!Final PDF to printer
chapter 8 Valuing Stocks 275cor91411_ch08_264-295.indd 275 01/20/17 04:39 PMMcDonaldÕs dividend growth has been more stable and predictable through 2015. The figure also shows that McDonaldÕs stock price has been very volatile. The price fell from a split adjusted $25 in 2000 to $9.50 in 2003 and then steadily climbed to $45 in 2007. The stock went sideways during the financial crisis and then shot up to $88 in late 2011. The stock again went mostly sideways from 2012 to 2014 and then shot up again in 2015. An investor in 2000 would have had a very difficult time accurately forecasting these future dividends and stock prices. Indeed, short-term stock price changes seem almost random. Stock valuation can really only be viewed from a long-term perspective. Because predicting future dividends is uncertain at best, itÕs better to project valuation as a likely range of prices under reasonable assumptions rather than as a single price. After all, this computed price is an estimate of the firmÕs intrinsic value. This intrinsic value may differ from the stock price trading in the market. This possibility is discussed as a market efficiency topic in Chapter 10.Dividend Discount ModelsWe can extend the discounted cash flow approach in equation 8-3 for an infinite stream of dividends, n→∞, and no final future selling price. If stockholders receive all future cash flows as future dividends, the stockÕs value to the investor is the present value of all these future dividends. In other words, embedded in any stock price is the value of all future dividends. We can demonstrate this value as P 0 = D 1 ____ 1 + i + D 2 ______ (1 + i) 2 + D 3 ______ (1 + i) 3 + . . . (8-4)This equation shows the general case of the dividend discount model. The dividend discount model provides a useful theoretical basis because it illustrates the importance of dividends as a fundamental stock price determinant.But, again, finance professionals find it difficult to apply the dividend discount model because it requires that they estimate an infinite number of future dividends. To use the model in practice, analysts make simplifying assumptions to make the model workable. One common assumption: The firm has a constant dividend growth rate, g. If this is the case, next yearÕs dividend is simply this yearÕs dividend that grew one year at the growth rate, that is, D1 = D0 × (1 + g). In fact, we can express each dividend as a function of D0 and we can rewrite equation 8-4 as P 0 = D 0 (1 + g) ________ 1 + i + D 0 (1 + g) 2 _________ (1 + i) 2 + D 0 (1 + g) 3 _________ (1 + i) 3 + . . . (8-5)So, with this version of the model, we need not forecast an infinite string of dividends; D0 and g take care of that. However, we must still compute an infinite sum of numbers. Luckily, mathematicians know equations like these; they are known as power series. This power series can be simplified to the constant-growth model, and it assumes that the growth rate is smaller than the discount rate (i.e., for g < i): Stock value = Next yearÕs dividend Ö (Discount rate − Growth rate)Constant growth model = P 0 = D 0 (1 + g) ________ i − g = D 1 ____ i − g (8-6)If g ≥ i, then the denominator would be zero or negative. Economically and math-ematically, this is a nonsensical result. In the short run, a firm can grow very quickly. In the long run, no company can grow faster than the overall economic growth rate forever. You may hear the constant-growth model referred to as the Gordon growth model, after financial economist Myron J. Gordon.Investors use several methods to estimate a firmÕs growth rate for this model. They can project the dividend trend into the future and determine the implied growth rate, com-pute the past growth rate, or even consider a financial analystÕs growth rate predictions. dividend discount modelA valuation approach based on future dividend income.constant-growth modelA valuation method based on constantly growing dividends.Final PDF to printer
276 part four Valuing of Bonds and Stockscor91411_ch08_264-295.indd 276 01/20/17 04:39 PMConsider Coca-ColaÕs dividend behavior. If the 2015 dividend was $1.34 and the pro-jected dividends will grow to $1.66 in 2018, the implied projected dividend growth rate is therefore 7.94 percent (N = 3, PV = −1.34, PMT = 0, FV = 1.66, CPT I = 7.94) annually. The growth rate in dividend changes from 2008 to 2012 was 7.63 percent (N = 4, PV = −0.76, PMT = 0, FV = 1.02, CPT I = 7.63) per year. You can find analyst forecasts many places online. The Yahoo! Finance web page for Coca-Cola has an Ana-lyst Estimates link, which shows the average analystsÕ forecast for the firmÕs growth in the next five years at 8.95 percent.Preferred StockA special case of the constant-growth model occurs when the dividend does not grow but is the same every year. This zero-growth rate case describes a preferred stock. The term preferred comes from the fact that this type of stock takes preference over common stock in bankruptcy proceedings. Preferred stockholders have a higher priority for receiving proceeds from bankruptcy proceedings than do common stockholders. Preferred stock is largely owned by other companies, rather than by individual investors, because its divi-dends are mostly nontaxable income (70 percent of the income is exempt from taxes) to other corporations. Preferred stockholders do not have voting rights like common stock-holders, though, which prevents one company from controlling another through preferred stock ownership.preferred stockA hybrid security that has characteristics of both long-term debt and common stock.Constant Growth and Coca-Cola StockAssume that you are valuing Coca-Cola stock again. This time you are using the constant growth model, assuming a discount rate of 11.0 percent.SOLUTION: You have a choice of three growth rates to use. The implied projected dividend growth rate is 7.94 percent. Past dividend growth has been 7.63 percent and analysts forecast an 8.95 percent growth. Compute the stock value using all three growth rates.Using a dividend growth rate of 7.94 percent and equation 8-6, the stock value is $47.27: P 0 = $1.34 × (1 + 0.0794) __________________ 0.110 − 0.0794 = $47.27 Using a dividend growth rate of 8.95 percent, the stock value is $71.22: P 0 = $1.34 × (1 + 0.0895) __________________ 0.11 − 0.0895 = $71.22 Using a dividend growth rate of 7.63 percent, the stock value is $42.80: P 0 = $1.34 × (1 + 0.0763) __________________ 0.11 − 0.0763 = $42.80 Notice how a small change in the growth rate has a large impact on the stock value in this model. At a current price of $43.01 per share, Coca-Cola could be considered undervalued or overvalued depending on the growth rate used.Similar to Problems 8-19, 8-20, 8-29, 8-30, 8-31, 8-32, Self-Test Problem 2EXAMPLE 8-2LG8-3 An interesting characteristic of preferred stock is that it pays a constant dividend. Because the dividend does not change, the preferred stock can be valued using the constant-growth-rate model with a zero growth rate expressed as P = D/i. What would Coca-ColaÕs stock be worth if its dividend stayed at $1.34 and never grew? Using the same 11.0 percent For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.Final PDF to printer
chapter 8 Valuing Stocks 277cor91411_ch08_264-295.indd 277 01/20/17 04:39 PMdiscount rate, the stock would be valued at $12.18 (= $1.34 Ö 0.110). Given Coca-ColaÕs current stock price of $43.01, over 71.6 percent [= ($43.01 − $12.18)/$43.01] of its stock value comes from the expectation that Coca-ColaÕs dividend will grow. In other words, inves-tors highly value a growing firm.Most companies issue only common stock, but nearly 1,000 preferred stock issues still exist. Table 8.2 compares the common stock and preferred stock for 10 firms. Many of the preferred stocks come from the finance, energy, and real estate sectors. Notice that the dividend yield for preferred stock is higher than for the common stock, because preferred stock investors should expect a return from dividend payments only. Common stockholders will also expect a return from capital appreciation over time. Com-mon stocks also trade much more frequently than preferred stocks do.The zero-growth-rate version of the constant-growth valuation model shows that, since dividends are fixed, a preferred stockÕs price changes because of changes in the discount rate, i. When interest rates throughout the economy change, the discount rate also changes. Pre-ferred stock prices thus tend to act like bond prices. When interest rates rise, preferred stock prices fall. When interest rates decline, preferred stock prices rise. Preferred stock is usually categorized with bonds in the fixed-income security group because it acts so much like debt securities, even though a preferred stock represents equity ownership, like common stock.Expected ReturnStock valuation models require a discount rate, i, in order to compute the present value of the future cash flows. The discount rate used should reflect the investment risk level. Higher risk investments should be evaluated using higher interest rates. For example, the previous chapter on bonds demonstrated that higher risk bonds, such as junk bonds, offer higher rates of return. Similarly, investors demand higher returns from higher risk stocks than they do from lower risk stocks. We discuss stock risk measurement and appropriate expected returns in the next section of this book.However, one method for determining what return stock investors require from a stock is to use the constant-growth-rate model. If the current stock price fairly reflects its value, then the discount rate, i, in equation 8-6 should be the expected return for the stock. Solv-ing for this expected return results in equation 8-7: Expected return = i = D 1 ___ P 0 + g = Dividend yield + Capital gain (8-7)dividend yieldLast four quarters of divi-dend income expressed as a percentage of the current stock price.MATH COACH USING THE CONSTANT-GROWTH-RATE MODELThe distinction between the recent yearÕs dividends, D0, and next yearÕs dividends, D1, can be confusing in the constant growth-rate model. The modelÕs equation presents two different numerators. If you are given information about dividends last year or just paid, use the D0(1 + g) version of the equation. If you have information about expected dividends or next yearÕs dividend, use the D1 version of the equation.COMMON STOCKPREFERRED STOCKCompanyTickerPriceAnnual Dividend (Yield%)VolumeTickerPriceAnnual Dividend (Yield%)VolumeAlcoa Inc.AA$ 7.69$0.12(1.2) 26,021,380AAPRB$26.74$2.69(8.1)49,122El Du Pont de Nemours & Co.DD$ 58.48$1.72(2.6)5,397,520DDPRA$79.75$3.50(4.5)200Ford Motor Co.F$ 11.55$0.60(4.3)28,080,850FPRA$25.55$1.88(7.3)97,959National HealthcareNHC$ 61.29$1.54(2.5)23,484NHCA$15.52$0.80(5.1)634PG&E Corp.PCG $ 55.21 $1.82(3.4) 2,877,339PCG.PRA$30.57$0.75(2.6)3,247Public Storage Inc.PSA$233.61$6.50(2.6)1,040,665PSAPRW$24.74$1.30(5.7)51,329Source: New York Stock Exchange (www.nyse.com)TABLE 8.2 Common and Preferred Stock, February 12, 2016Final PDF to printer
278 part four Valuing of Bonds and Stockscor91411_ch08_264-295.indd 278 01/20/17 04:39 PMNote that the expected return comes again from two sources: dividend yield and expected appreciation of the stock price, or capital gain. For example, consider that Coca-ColaÕs dividend in 2016, D1, is expected to be $1.42 per share. At a current price of $43.01, Coca-Cola offers a dividend yield of 3.30 percent (= $1.42 Ö $43.01). Since analysts believe that the firmÕs stock price will grow at 8.95% percent in the future, investors expect a total return of 12.25 percent (= 3.30% + 8.95%). Dividend yield can represent a substantial por-tion of the profits for an investor. Many people get too enamored of high growth stocks that do not pay dividends and therefore miss out on an important source of stable returns.Corporate managers conduct an important application of the expected return concept to determine the return that their shareholders expect of them. We will discuss this appli-cation in detail in Part Six: Capital Budgeting.growth stocksCompanies expected to have above-average rates of growth in revenue, earn-ings, and/or dividends.TIME OUT 8-8 Explain how valuable a firmÕs (and therefore its stockÕs) growth is. Demonstrate this with growth and no-growth examples. 8-9 What proportion of the 12.25 percent of Coca-ColaÕs expected return above comes from dividend yield? Financial analysts examine a firmÕs business and financial suc-cess and assess long-term prospects and management effec-tiveness. They combine this microeconomic analysis with a macroeconomic view of the conditions of the economy, finan-cial markets, and industry outlooks. Their evaluation results in earnings predictions, stock price targets, and opinions about whether investors should buy the stock. Such recommenda-tions can help investors decide whether to buy, hold, or sell the stock.Analysts hired by brokerage firms and investment banks are called sell-side analysts because their firms make money by selling stocks and bonds. These analysts publicize their predictions and opinions publicly and in company Òtip sheetsÓ that are passed along to clients. Keep in mind that sell-side analysts often have incentives to be optimistic. Pension funds and mutual funds often hire analysts to give fund managers private opinions about securities. These analysts are referred to as buy-side analysts because they are hired by invest-ment firms looking for advice on what stocks to buy for their FINANCIAL ANALYSTSÕ PREDICTIONS AND OPINIONSfinance at work investmentsportfolios. Because this is private, little buy-side research is made public.Consider the 26 sell-side analystsÕ predictions reported for Coca-Cola on the Yahoo! Finance website. The average five-year share price growth prediction from these analysts is 8.95 percent. This is lower than the growth prediction for the industry (12.96 percent) and sector (12.79 percent). Last, analysts give opinions on whether investors should buy, sell, or hold Coca-Cola stock. Recommendations come in five levels: Strong Buy, Buy, Hold, Underperform, and Sell. Of the 26 analysts, 4 recommend a Strong Buy, 9 recommend a Buy, and 10 recommend a Hold. Note that even though the ana-lysts predict lower than average growth for the industry and sector, and that the analysts provide meager price targets, only three of the analysts recommend an Underperform and none a Sell. This optimism in analystsÕ opinions is common. Knowledgeable investors know that a ÒholdÓ recommenda-tion is as negative as most public or sell-side analysts get, and therefore a ÒholdÓ may actually represent a signal to sell.!want to know more?Key Words to Search for Updates: analyst opinion, financial analyst bias8.4 ∙ Additional Valuation MethodsVariable-Growth TechniquesSome companies grow at such a high rate that we cannot use the constant-growth-rate model to forecast their value. High growth rates might be sustainable for several years, but cannot continue forever. Consider what happens to a high-growth firm. Other com-panies will surely notice the market potential for high-growth rates and will enter those product markets to compete with the high-growth firm. The competition will soon drive LG8-6Final PDF to printer
Stage 1, high growth rate, g1Stage 2, stable growth rate, g2DividendsD0D1D2D3DnDn+1Dn+2ÉÉ→ ∞Period0123nn+1n+2 yearStage 1, high growth rate, g1Stage 2, stable growth rate, g2DividendsD0D0(1+g1)D0(1+g1)2D0(1+g1)3D0(1+g1)nDn+1Dn+2ÉÉ→ ∞Period0i123nn+1n+2 yearStage 1, high growth rate, g1Stage 2, stable growth rate, g2DividendsD0D0(1+g1)D0(1+g1)2D0(1+g1)3D0(1+g1)nD0(1+g1)n×(1+g2)D0(1+g1)n×(1+g2)2ÉÉ→ ∞Period0i123nn+1n+2 year chapter 8 Valuing Stocks 279cor91411_ch08_264-295.indd 279 01/20/17 04:39 PMdown the growth rates for all companies in that product market. Companies that experi-ence unusually high-growth tend to see that growth become only average in the future unless they possess some kind of entry barrier such as a patent or government regulation due to economies of scale.Remember that the constant-growth-rate model does not work for companies where g > i. And of course, we do not really expect the growth rate for these fast-growing firms to remain constant. To value these firms, we must use a variable-growth-rate technique. The variable-growth-rate method combines the present-value cash flow from equation 8-3 and the constant-growth-rate model from equation 8-6.First, the investor chooses two different growth rates for two stages of the analysis. The first and higher growth rate, g1, is the current growth rate, which we expect to last only a few years. A few years from now, we expect the firm to grow at a slower but more sustain-able rate of growth, g2. Figure 8.4 shows the cash flow time line when the first growth rate applies for the first n years, followed by the second growth rate, which applies forever.When we analyze a variable-growth-rate stock like the one in the figure, we know the recent dividend, D0, and the two expected growth rates. Therefore, we can calculate each of the dividends shown in general terms (i.e., D1). For example, the dividend in the first year (D1) is the year zero dividend that grows at g1, specifically D1 = D0 × (1 + g1 ). The dividend then grows at g1 again for the second year dividend, D2 = D0 × (1 + g1 )2. The div-idend continues to grow through the first stage to year n at Dn = D0 × (1 + g1 )n. Figure 8.5 shows the first-stage dividends.At this point, the company starts to move into stage 2 at the more modest growth rate, g2, and the dividends reflect that slower growth rate. So Dn+1 is the dividend Dn that grew at the rate g2, or Dn+1 = D0 × (1 + g1 )n × (1 + g2 ). Similarly, the dividend in year n + 2 is Dn+2 = D0 × (1 + g1 )n × (1 + g2 )2. We can now substitute the known dividends as presented in Figure 8.5 into Figure 8.6.variable growth rateA valuation technique used when a firmÕs current growth rate is expected to change some time in the future.FIGURE 8.4Variable Dividend GrowthDivide into two stages at the first year of the new growth rate.FIGURE 8.5Stage 1 DividendsCalculate the dividends in the first stage.FIGURE 8.6Details of the Variable Growth DividendsCompute the dividends in the second stage.Final PDF to printer
ÉPeriodn yearDividendsD0D0(1+g1)D0(1+g1)2D0(1+g1)3D0(1+g1)n+Terminal value0i123280 part four Valuing of Bonds and Stockscor91411_ch08_264-295.indd 280 01/20/17 04:39 PMOnce we have calculated all of the dividends, we can begin finding the value of the variable-growth stock by focusing on Stage 2 of the problem. Assume that the dividends in Stage 2 are growing at a modest rate, g2, forever. As long as g2 < i, Stage 2 can use the constant-growth model, equation 8-6. Remember that the constant-growth model, P0 = D1/(i − g), replaces all future dividends with one value in the previous period. In pre-vious applications, the growth began in year 1, so the value used for all future dividends came from the year 0 dividend. In this case, the change in the dividend rate occurs in year n + 1, so we will use the value from year n. So, using the constant-growth model, we can replace all the cash flows in Stage 2 with one value from year n, as P n = D n+1 _____ i − g 2 = D 0 (1 + g 1 ) n (1 + g 2 ) _______________ i − g 2 The cash flows from Figure 8.6 now appear as shown in Figure 8.7.By replacing all the Stage 2 cash flows that continued indefinitely with one terminal price in year n, we reduce the problem to a fixed number of cash flows. The value of this variable-growth stock is finally computed as the present value of these cash flows, as solved with equation 8-3. Substituting the cash flows shown in Figure 8.7 into equation 8-3 gives us the general formula for finding the value of a variable-growth stock:General two-stage growth valuation model: Stock value = Present value of each dividend during the firstgrowth stage + Present value of the second stage growth P 0 = D 0 (1 + g 1 ) _________ 1 + i + D 0 (1 + g 1 ) 2 _________ (1 + i) 2 + D 0 (1 + g 1 ) 3 _________ (1 + i) 3 + . . . + D 0 (1 + g 1 ) n + Terminal value _______________________ (1 + i) n (8-8)where Terminal value = D 0 (1 + g 1 ) n (1 + g 2 ) _______________ i − g 2 The practical application of the variable-growth valuation technique requires the inves-tor to decide how long the current high-growth rate will last before declining to a more stable rate.The constant-growth-rate model is most useful for large, mature companies that grow in a stable manner. The variable-growth-rate model works well for dividend-paying companies that have an unusually fast rate of growth in the near future but are expected to enter a more stable growth rate environment soon. But there are still many firms that do not fit these two descriptions of firm growth. For example, many firms pay no dividends. To value firms with no dividends, replace the dividends in the models with cash flows. When you do this, you are valuing the entire firm, not just the stock value, because cash flows go to both stockholders and debt holders. In the case where a firm has low or even negative cash flows, the valuation techniques in the next section can be employed.FIGURE 8.7New Stage 1 of the Variable Growth Dividend TechniqueReplace all of the dividends to infinity with the price ( terminal value) in year n. Stage 2 disappears.Final PDF to printer
chapter 8 Valuing Stocks 281cor91411_ch08_264-295.indd 281 01/20/17 04:39 PMThe P/E ModelThe valuation models that weÕve presented thus far help investors attempt to compute a stockÕs fundamental value based upon its cash flows to the investor. Another common approach is to assess a stockÕs relative value. This approach compares one compa-nyÕs stock valuation to other firmsÕ stock values to evaluate whether your target companyÕs stock is appropriately priced. The price of a stock taken in isolation doesnÕt give us a good measure of how expensive it is. LetÕs use an analogy: At the grocery store, we are less concerned with the total price of a bag of sugar than we are with the price per pound. Similarly, the price of the stock matters less than its price per one dollar of earnings.Consider one company that earned $5 per share in profits for the year. Its stock sells for $100. Another company earned $2 per share and its stock price is $50 per share. LG8-7relative valueA stockÕs priceyness mea-sured relative to other stocks.EXAMPLE 8-3Variable Growth and Stock ValueThe dividend has grown from $1.00 per share on November 13, 2009, to $2.80 during 2015. This represents an annual growth rate of 18.7 percent (N = 6, PV = −1.00, PMT = 0, FV = 2.80, CPT I = 18.7). You think this growth rate will continue for three years and then fall to the long-term growth rate of 9.29 percent predicted by analysts. You assume a 13 per-cent discount rate.SOLUTION: Figure 8.3 shows a $2.80 (= 4 × $0.70) per share recent annual dividend. Modify equation 8-8 for a Stage 1 length of three years and then substitute i = 0.13, g1 = 0.187, g2 = 0.0929, and D0 = $2.80. The valuation equation and solution becomes12Period30Dividends× (1.187)× (0.0929) Ö (0.14 Ð 0.0929)× (1.187)2× (1.187)3D0 = $2.80D1 = $2.80D2 = $2.80P3 = $2.80 × (1.187)3D3 = $2.80 P 0 = $2.80 (1 + 0.187) ______________ 1 + 0.13 + $2.80 (1 + 0.187) 2 _______________ (1 + 0.13) 2 + $2.80 (1 + 0.187) 3 + Terminal value _____________________________ (1 + 0.13) 3 where Terminal value = $2.80 (1 + 0.187) 3 (1 + 0.0929) _________________________ 0.13 − 0.0929 = $137.95 = $2.94 + $3.09 + $4.68 + $137.95 ______________ 1.443 = $104.88 Given these parameters, the companyÕs stock is worth nearly $105 per share. Similar to Problems 8-33, 8-34, Self-Test Problem 3LG8-6 TIME OUT 8-10 Explain how the variable-growth-rate technique could be used for a firm whose dividend is not expected to grow for three years and then will grow at 5 percent indefinitely. 8-11 Set up and solve the McDonaldÕs valuation problem assuming that the first stage growth will last only two years. For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.Final PDF to printer
0102030405060701997199819992000200120022003200420052006200720082009201220132014201520102011P/E RatioDJIACoca-ColaMcDonaldÕs282 part four Valuing of Bonds and Stockscor91411_ch08_264-295.indd 282 01/20/17 04:39 PMAt first glance, the first stock appears to be more expensive because its price is a high $100 compared to the lower $50 price of the second stock. However, the first company generated higher per-share profits than did the second company. Buying the first stock means that you purchase $5 in earnings. The $100 stock price implies a cost of $20 for every $1 in earnings (= $100 Ö $5) generated. The $50 price of the second stock implies a cost of $25 for every $1 in earnings (= $50 Ö $2). So in this regard, the second company becomes more expensive. The price-earnings (P/E) ratio represents the most common valuation yardstick in the investment industry; it allows investors to quickly compare the cost of earnings. The P/E ratio is simply the current price of the stock divided by the last four quarters of earnings per share: P/E = Current stock price _______________________________ Per-share earnings for last 12 months (8-9)More accurately, this figure is the trailing P/E ratio and it is often denoted as P/E0, where the 0 subscript denotes the past (or trailing) earnings.Figure 8.8 shows two companiesÕ trailing P/E ratios: Coca-Cola and McDonaldÕs, as well as the Dow Jones Industrial AverageÕs trailing P/E ratio over a 16-year period. The P/E ratio for the DJIA changes slowly and mostly stays in the 18 to 27 range until the recent drop to 15. Historically, the DJIAÕs P/E ratio has fallen as low as single digits and climbed to over 30. The figure also shows that the P/E ratio for McDonaldÕs has varied more than has the indexÕs P/E ratio. The P/E ratio for Coca-Cola has experienced wild changesÑas high as 63 and as low as 18. Figure 8.8 shows that investors valued Coca-Cola more than McDonaldÕs in the late 1990s, but valued them nearly the same by the beginning of 2008.Variations in P/E ratios between popular companies can be quite large. For example, in February of 2016, the P/E ratio for Alphabet (the parent company of Google) was 28.7, while the ratio for Boeing Company was only 14.6. Alphabet stock is much more expensive than Boeing. But this does not mean that Boeing stock is a better deal than Alphabet stock. Investors are willing to pay much more in relative terms for Alphabet because they expect Alphabet will grow much faster than Boeing. Indeed, analysts predict an annual growth rate of 16.7 percent per year for Alphabet over the next five years, while they expect a growth rate of only 11.9 percent for Boeing. Remember that Example 8-2 shows how small changes in growth can result in large stock value changes. The large difference in expected growth between Alphabet and Boeing causes a large difference in their relative value.We can more directly see the impact that growth can have on the P/E ratio by modi-fying the constant-growth model. Begin with the model, P0 = D1 Ö (i − g). Dividing price-earnings (P/E) ratioCurrent stock price divided by four quarters of earnings per share.trailing P/E ratioThe P/E ratio computed using the past four quarters of earnings per share.FIGURE 8.8Historical P/E Ratio of the DJIA, Coca-Cola, and McDonaldÕsP/E ratios of large, successful companies can vary consid-erably over time. Here, you see that investors valued Coca-Cola over McDonaldÕs for much of the period, but there were periods when McDonaldÕs was valued higher.Source: Dow Jones and Company.Final PDF to printer
chapter 8 Valuing Stocks 283cor91411_ch08_264-295.indd 283 01/20/17 04:39 PMboth sides by the firmÕs earnings results in P0/E0 = (D1/E0) Ö (i − g). Note that the divi-dend payout ratio of the firm (D/E), the discount rate (i ), and the growth rate (g), taken together, determine the P/E ratio. All else held equal, larger growth rates will lead to larger P/E ratios. Also, firms that have higher payout ratios will have higher P/E ratios. Of course, if a firm pays out a high portion of its earnings as dividends, then it may not have the cash to fund high growth. Thus, high dividend payout firms tend not to be priced the same as high growth firms.The value of a stock, and thus its price, relates directly to its future success. Note that valuation models use estimates of future dividends and growth rates. Because of this focus on the future, many people prefer to use a P/E ratio that also looks forward rather than trailing. A forward P/E ratio uses analyst estimates of the earnings in the next 12 months instead of the past 12 months and can be denoted as P/E. The forward P/E ratio has the advantage over the trailing P/E ratio in that it incorporates investorsÕ expectations of the firmÕs upcoming profits. A disadvantage is that expected earnings are harder to estimate and thus less accurate than past earnings. The media uses the trailing P/E ratio, while financial managers and investors use the forward P/E ratio more.Knowledgeable investors who use the P/E ratio as a relative measure of value com-pare it to the firmÕs expected growth rate. Table 8.3 shows the forward P/E ratio and analystsÕ expected growth rates for the 30 Dow Jones Industrial Average firms. Investors consider companies with high P/E ratios and high growth rates to be appropriately priced. Companies with low P/E ratios and low growth also seem to be appropriately priced. Inves-tors should be concerned about firms with high P/E ratios and only single-digit growth rates. As such, Procter & Gamble, Coca-Cola, McDonaldÕs, and Chevron, among others, may be too expensive for their expected growth rates. Many investors like to buy growth stocks. They seek companies with high growth rates. But growth stock investors are also concerned about paying too much for a stock. While examining growth stocks, they can use the P/E ratio to assess how expensive the stock is. On the other hand, investors con-sider companies with low P/E ratios and high expected growth to be undervalued, and they are often referred to as value stocks. Apple and Boeing would qualify as value stocks. Many investors like to buy value stocks because they feel they are getting a bar-gain price for a stable company.There are some cases when a P/E ratio is not useful for relative valuation. For example, sometimes, a firm will lose money. That is, the earnings are negative. In other cases, a firm will take a large Òwrite-offÓ that will temporarily suppress earnings. In these cases, the P/E ratio would be negative or temporarily large. Therefore, other common relative value techniques are to utilize cash flow (CF) or book value (B) instead of earnings. The P/CF ratio is useful when firms take accounting write-offs that temporarily and dramati-cally impact earnings. The P/B ratio is useful in all cases but is particularly useful when a firm loses money and has negative cash flows. The book value of a firm is a very stable measure of accounting value, and it is therefore useful when earnings are volatile.Estimating Future Stock PricesWe can often find it useful to estimate a stockÕs future price. Consider equation 8-3Õs cash flow discount valuation model. The model requires estimates of future dividends and a future price. How can investors estimate this future price? They can use the P/E ratio model for this purpose. Upon reflection, you will see that multiplying the P/E ratio by earnings results in a stock price. So, in order to estimate a future price, simply mul-tiply the expected P/E ratio by the expected earnings. This concept is captured in the following equation: Future price = Future P/E ratio × Future earnings per share P n = ( P Ú E ) n × E n = ( P Ú E ) n × E 0 × (1 + g) n (8-10)forward P/E ratioThe P/E ratio computed using the estimated next four quarters of earnings per share.value stocksCompanies consid-ered to be temporarily undervalued.Final PDF to printer
284 part four Valuing of Bonds and Stockscor91411_ch08_264-295.indd 284 01/20/17 04:39 PMAs the formula shows, we can use assumptions about the earnings growth rate to estimate earnings in year n. Many investors believe the firmÕs P/E ratio in year n is best estimated using todayÕs P/E ratio. However, if todayÕs P/E ratio seems unusual compared with similar firms or even compared with a stock index, then adjustments might be wise.TIME OUT 8-12 Consider two firms with the same P/E ratio. Explain how one could be described as expensive compared to the other. 8-13 Compute the stock price for Goldman Sachs in five years if you expect the P/E ratio to decline to 6 and the earnings per share is $18.58. ABCDE1TickerCompany NameStock PriceForward P/E RatioNext 5 YearÕs Growth (%)2HDHome Depot$116.3218.8814.393PGProcter & Gamble80.9920.006.954KOCoca-Cola Company43.1120.838.955MCDMcDonaldÕs Corporation117.9319.569.506VZVerizon Communication50.1112.314.517DISWalt Disney91.1514.6811.858MMM3M Company153.9617.268.109JNJJohnson & Johnson101.8214.765.3210AAPLApple, Inc.93.999.3911.9311UTXUnited Technologies85.9512.249.0712GEGeneral Electric28.2615.967.9713WMTWalmart Stores66.1815.870.8714AXPAmerican Express52.669.378.1015PFEPfizer29.3611.655.4416MRKMerck & Company49.0312.874.2417XOMExxon Mobil81.0318.5826.4018IBMInternational Business Machines121.048.557.2519TRVThe Travelers Company107.4910.792.9420DDE.I. du Pont de Nemours58.4016.889.0021BABoeing Company108.6311.5311.9222NKENike, Inc.56.4222.8412.6223CSCOCisco Systems25.1110.518.2424INTCIntel Corporation28.6410.7710.0025CATCaterpillar63.1517.210.4326CVXChevron Corporation85.4318.18−23.8627UNHUnitedHealth Group111.8212.7414.0328MSFTMicrosoft Corporation50.5016.459.5129GSGoldman Sachs Group146.137.544.3130JPMJPMorgan Chase57.498.597.8931VVisa, Inc.70.4221.6716.62TABLE 8.3 P/E Ratios and Analyst Growth Estimates of DJIA Firms, February 12, 2016Source: Yahoo! Finance ScreenerFinal PDF to printer
chapter 8 Valuing Stocks 285cor91411_ch08_264-295.indd 285 01/20/17 04:39 PMviewpoints REVISITEDBusiness Application SolutionYou can compute the expected return using equation 8-7 as, i = $2 × (1 + 0.08) _____________ $65 + 0.08 = 0.0332 + 0.08 = 0.1132 Investors expect an 11.32 percent return.The P/E ratio of 16.25 and the stock price of $65 indicates that earnings were $4.00 per share (= $65 Ö 16.25). If the P/E ratio of 16.25 continues, then the price of the stock in three years may be $81.88 [= 16.25 × $4 × (1.08)3]. However, a P/E ratio of 16.25 may seem a little high for a firm with an 8 percent growth rate. So the P/E ratio might decline a bit to 15. If so, the stock price in three years would be $75.58. On the other hand, P/E ratios in the stock market may increase in general, thereby inflating this firmÕs ratio to 17. In this case, the price would be $85.66.You should report an expected stock price range of $75.58 to $85.66 with a target of $81.88.Personal Application SolutionThe information provided allows for two growth rate estimates for stock valuation. The dividend growth from $1.25 to $1.68 in three years implies a 10.36 percent historical growth rate (N = 3, PV = −1.25, PMT = 0, FV = 1.68, CPT I = 10.36). Since analystsÕ mean growth estimate is 10.1 percent, you can use either, or both, rates in the constant-growth-rate model using a 13.5 percent discount rate: P 0 = $1.68 × (1 + 0.1036) __________________ 0.135 − 0.1036 = $59.05 P 0 = $1.68 × (1 + 0.101) _________________ 0.135 − 0.101 = $54.40 Both valuation estimates exceed the current price of $54. The current stock price does not appear overvalued, so you can consider the purchase.EXAMPLE 8-4The P/E Ratio Model for CaterpillarLook at Table 8.3 and notice that the P/E ratio for Caterpillar seems high at 17.21 relative to the growth (0.43 percent) that analysts expect. Caterpillar earned $3.50 per share and paid a $3.08 dividend last year. You decide to explore this apparent anomaly and figure out what CaterpillarÕs stock price might reach in five years.SOLUTION: Compute the expected future price in five years under two different scenarios. The first assumption is that CaterpillarÕs P/E ratio will be the same in five years as it is today. But since this P/E ratio seems a bit high, the second scenario allows for a decline in the P/E ratio to 13. Under these two scenarios, the future price estimates are P 5 = ( P Ú E ) n × E 0 × (1 + g) n = 17.21 × $3.50 × (1 + 0.043) 5 = $74.35 P 5 = ( P Ú E ) n × E 0 × (1 + g) n = 13 × $3.50 × (1 + 0.043) 5 = $56.16 Note that if the P/E ratio decreases from 17.21 to 13 in five years, the future price could be much lower than analysts expect without the change.Similar to Problems 8-25, 8-26, 8-35, 8-36LG8-7 For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.Final PDF to printer
286cor91411_ch08_264-295.indd 286 01/20/17 04:39 PMsummary of learning goalsThis chapter describes stock ownership and discusses why efficient and fair stock markets are vital in capitalist economies. Investors can benefit from owning common stock. The existence of the stock exchanges allows for easy transfer of stock from one investor to another, providing much more liquidity than would investments with similar returns on investment. The media commonly reports stock market performance using stock indexes. Before buying or selling a stock, investors should determine the stockÕs value. Many stock valuation methods apply time value of money principles.Understand the rights and returns that come with common stock ownership. Common stockholders own the corporations in which they hold stock. Stockholders earn investment returns from receiving dividends and from stock price appreciation. As residual claimants, common stockholders claim any cash flows to the firm that remain after the firm pays all other claimsÑcreditors, bondholders, and preferred stockholders. When residual cash flows are high (low), stock values will be high (low).Know how stock exchanges function. Stock exchanges allow investors to quickly and inexpensively buy and sell thousands of stock shares. Trading at physical exchanges like the New York Stock Exchange and the American Stock Exchange takes place at brokersÕ trading posts on the floor by open outcry. Specialists and/or market makers oversee brokers and trades to ensure smooth trading in the stocks for which the specialists or dealers are responsible. Dealers create market liquidity in the NasdaqÕs electronic stock market; the AMEX and the NYSE process increasing percentages of their trades electronically as open outcry trading becomes increasingly rare. Billions of shares of stock trade every day on each of the exchanges.Track the wider stock market with stock indexes, and differentiate among the kinds of information each index provides. General stock market performance is measured with popular stock indexes like the Dow Jones Industrial Average, the Standard & PoorÕs 500 Index, and the NASDAQ Composite. The DJIA includes 30 of the largest (market capitalization) and most active companies in the U.S. economy. The S&P 500 Index combines the 500 firms that are the largest in their respective economic sectors. The NASDAQ Composite includes all the stock listed on the NASDAQ Stock Exchange. Because so many very large technology firms trade on the NASDAQ, investors consider this indexÕs performance a bellwether of the tech sector.Know the terminology of stock trading. Investors buy stock at the quoted ask price and sell at the LG8-1LG8-2LG8-3LG8-4bid price. The difference between the bid and ask price is the spreadÑusually a small amount that reimburses the specialist or dealer for expenses. A market order will be immediately executed at quoted prices when the order arrives at the exchange. A limit order will be executed only if the orderÕs price conditions are met; if the price conditions donÕt materialize, a limit order will not be executed and the trade will not take place.Compute stock values using dividend discount and constant-growth models. We can estimate a stockÕs value by discounting the future dividends and future stock price appreciation using an appropriate required rate of return as the discount rate. Because future dividends and future stock prices are highly uncertain, we simplify the models if we can reasonably assume conditions such as a constant-dividend-growth rate. We value preferred stock as a special zero-growth case of the constant-growth model. Valuation model dynamics make clear that lower discount rates lead to higher valuations. Higher growth rates also lead to higher valuations.Calculate the stock value of a variable-growth-rate company. Many companies grow very fast at first; we can expect slower future growth. We call such companies Òvariable-growth-rateÓ firms. We value these firms using a two-stage process with both the constant-growth model and the discounted cash flow model.Assess relative stock values using the P/E ratio model. Many investors use the P/E ratio as the most popular relative stock valuation measure. Both individual firm and overall market P/E ratios fluctuate over time. High P/E ratios are associated with high-growth stocks. Firms with high P/E ratios but low growth rates are considered relatively expensive. However, firms with low P/E ratios and high growth are considered cheap and we thus refer to them as value stocks. We often use the P/E ratio model with the firmÕs growth rate to estimate a stockÕs future price.LG8-5LG8-6LG8-7Final PDF to printer
287cor91411_ch08_264-295.indd 287 01/27/17 06:24 PMchapter equations 8-1 P 0 = D 1 + P 1 ______ 1 + i 8-2 P 0 = D 1 ____ 1 + i + D 2 + P 2 ______ (1 + i) 2 8-3 P 0 = D 1 ____ 1 + i + D 2 ______ (1 + i) 2 + ⋅ ⋅ ⋅ + D n + P n ______ (1 + i) n 8-4 P 0 = D 1 ____ 1 + i + D 2 ______ (1 + i) 2 + D 3 ______ (1 + i) 3 + ⋅ ⋅ ⋅ 8-5 P 0 = D 0 (1 + g) ________ 1 + i + D 0 (1 + g) 2 _________ (1 + i) 2 + D 0 (1 + g) 3 _________ (1 + i) 3 + ⋅ ⋅ ⋅ 8-6 Constant growth model = P 0 = D 0 (1 + g) ________ i − g = D 1 ____ i − g 8-7 Expected return = i = D 1 ___ P 0 + g = Dividend yield + Capital gain 8-8 P 0 = D 0 (1 + g 1 ) _________ 1 + i + D 0 (1 + g 1 ) 2 _________ (1 + i) 2 + D 0 (1 + g 1 ) 3 _________ (1 + i) 3 + ⋅ ⋅ ⋅ + D 0 (1 + g 1 ) n + D 0 (1 + g 1 ) n (1 + g 2 ) _______________ i − g 2 _________________________ (1 + i) n 8-9 P/E = Current stock price _______________________________ Per-share earnings for last 12 months 8-10 P n = ( P Ú E ) n × E n = ( P Ú E ) n × E 0 × (1 + g) n key termsask The quoted price investors are likely to pay when they buy stock. p. 271bid The quoted price investors are likely to receive when they sell stock. p. 271brokers Floor traders who execute orders for others and themselves. p. 267common stock An ownership stake in a corporation. p. 266constant-growth model A valuation method based on constantly growing dividends. p. 275dealers NASDAQ market makers who use their own cap-ital to trade with investors p. 268dividend discount model A valuation approach based on future dividend income. p. 275dividend yield Last four quarters of dividend income expressed as a percentage of the current stock price. p. 277Dow Jones Industrial Average (DJIA) A popular index of 30 large, industry-leading firms. p. 269forward P/E ratio The P/E ratio computed using the estimated next four quarters of earnings per share. p. 283growth stocks Companies expected to have above-average rates of growth in revenue, earnings, and/or dividends. p. 278limit order A stock buy or sell order at a specific price. It will only be executed if the market price meets the speci-fied price. p. 271market capitalization The size of the firm measured as the current stock price multiplied by the number of shares outstanding. p. 269market makers Dealers and specialists who oversee an orderly trading process. p. 268market order A stock buy or sell order to be immedi-ately executed at the current market price. p. 271NASDAQ Composite Index A technology-firm weighted index of stocks listed on the NASDAQ Stock Exchange. p. 269NASDAQ Stock Market Large electronic stock exchange. p. 268New York Stock Exchange (NYSE) Large and presti-gious stock exchange with a trading floor. p. 266Final PDF to printer
288cor91411_ch08_264-295.indd 288 01/27/17 07:26 PMpreferred stock A hybrid security that has characteristics of both long-term debt and common stock. p. 276price-earnings (P/E) ratio Current stock price divided by four quarters of earnings per share. p. 282relative value A stockÕs priceyness measured relative to other stocks. p. 281residual claimants Ownership of cash flows and value after other claimants are paid. p. 266Standard & PoorÕs 500 Index (S&P 500) A stock index of 500 large companies. p. 269stock index Index of market prices of a particular group of stocks. The index is used to measure those stocksÕ performance. p. 269ticker symbol Unique code for a company consisting of one to five letters. p. 267trading posts Trading location on the floor of a stock exchange. p. 267trailing P/E ratio The P/E ratio computed using the past four quarters of earnings per share. p. 282value stocks Companies considered to be temporarily undervalued. p. 283variable growth rate A valuation technique used when a firmÕs current growth rate is expected to change some time in the future. p. 279self-test problems with solutions1 Discounting Dividends and Future Price You are checking a financial analystÕs recommendation. The analyst projects a companyÕs stock price to be $72 per share in three years. The most recent annual dividend was $1.68 per share. The analyst expects that dividend to grow at 9.8 percent annually. Given a 13.5 percent required return, the analyst claims the stock is undervalued at the current price of $54; thus he strongly urges investors to buy it. Using these assumptions, is the stock really undervalued? Solution:Using the $72 target price and expected dividends, you can use equation 8-3 to value the cash flows. Since the dividends grow at 9.8 percent, the next three annual dividends will be D1 = $1.84 (= $1.68 × 1.098), D2 = $2.03 (= $1.84 × 1.098), and D3 = $2.22 (= $2.03 × 1.098). Discounting these cash flows results in a value of $53.96: P 0 = $1.84 ________ 1 + 0.135 + $2.03 __________ (1 + 0.135) 2 + $2.22 + $72 __________ (1 + 0.135) 3 = $1.63 + $1.58 + $50.76 = $53.96 At the current $54 per share price, the stock does not appear undervalued. It appears fairly valued.2 Growth Rates, Required Return, and Value Consider that a company is about to embark on a large high-risk project. You believe that when this news is publicly announced, shareholders will react by requiring a higher return from the company and by expecting faster growth. The company is expected to pay a $1.75 per share dividend next year. You think that the current price of $70 is fair, given the expected 9 percent growth rate. However, after the announcement investors will expect a 10 percent growth rate and increase the required return by 1.2 percent. If this occurs as you predict, how will the stock price change because of the announcement? Solution:ItÕs not initially clear whether this will be good or bad news for the stock price. A rise in the growth rate increases the stockÕs value. But a higher required return lowers the value. The two changes somewhat offset one another. Since the current $70 stock price is fair, investors require a return of 11.5 percent (= $1.75 Ö $70 + 0.09) before the LG8-5LG8-5Final PDF to printer
289cor91411_ch08_264-295.indd 289 01/20/17 04:39 PMannouncement. After the announcement, investors will require a 12.7 percent return (= 0.115 + 0.012) and expect a 10 percent growth rate. Therefore, the new stock price should be $64.81 per share, a decline of $5.19 (−7.4 percent). P 0 = $1.75 __________ 0.127 − 0.10 = $64.81 This was bad news for the stock price.3 Variable Growth Rates Years Young Match is an online dating firm that finds matches for active people over 55. It has seen substantial growth in revenue and profits as the baby-boom generation ages. The firm will pay its first-ever dividend of $0.20 per share ($0.05 per quarter) next year. The dividend is expected to grow at 20 percent per year for the next four years. In the fifth year and afterwards, the Years Young dividend will grow at a steady 9.5 percent per year. If the appropriate discount rate for Years Young is 11 percent, what is the value of the stock? Solution:The variable-growth-rate technique should be used to value this stock. First, calculate the dividends for the first four years. The first dividend is given as D1 = $0.20. Using the 20 percent growth rate, the rest of the first stage dividends are D2 = $0.24 (= $0.20 × 1.20), D3 = $0.288 (= $0.24 × 1.20), and D4 = $0.346 (= $0.288 × 1.20). The first dividend in the second growth stage is D5 = $0.378 (= $0.346 × 1.095). Next, use the constant-growth-rate model and the 11 percent discount rate to convert the rest of the dividends to a terminal price in year four: Terminal value = P 4 = $0.378 __________ 0.11 − 0.095 = $25.23 Finally, equation 8-3 can be used to discount all the cash flows as P 0 = $0.20 _______ 1 + 0.11 + $0.24 _________ (1 + 0.11 ) 2 + $0.288 _________ (1 + 0.11 ) 3 + $0.346 + $25.23 _____________ (1 + 0.11 ) 4 = $0.180 + $0.195 + $0.211 + $16.847 = $17.43 The stock for the Years Young Match company is valued at $17.43.4 The P/E Ratio and Relative Value Home Shop (HS) has a stock price of $31.79 and is expected to grow at 14.1 percent per year. HSÕs P/E ratio is 14.3. Three other firms are also expected to grow at a similar rate: General Electronic, Almo, and Cisko. The P/E ratios of these firms range from 11.16 to 12.91, with an average of 12.0. If investors decided that HS should be equally expensive as these other firms, what price would the stock fall to in order for it to have a P/E ratio of 12.0? What return would result from this change in price? Solution:Since the price of HS is $31.79 and the P/E ratio is 14.3, then the expected earnings of HS are $2.22 per share (= $31.79 Ö 14.3). For the P/E ratio to be 12.0, the price would have to fall to $26.64 (= 12.0 × $2.22). The $5.15 decrease would represent a 16.2 percent (= Ð$5.15 Ö $31.79) capital loss in the price.1LG8-6LG8-71An alternative solution is to recognize that a change in the P/E ratio from 14.3 to 12.0 represents a −16.1 percent change. Thus the price would have to change by the same proportion.Final PDF to printer
290cor91411_ch08_264-295.indd 290 01/20/17 04:39 PMquestions 1. As owners, what rights and advantages do share-holders obtain? (LG8-1) 2. Describe how being a residual claimant can be very valuable. (LG8-1) 3. Obtain a current quote of McDonaldÕs (MCD) from the Internet. Describe what has changed since the quote in Figure 8.1. (LG8-2) 4. Get the trading statistics for the three main U.S. stock exchanges. Compare the trading activity to that of Table 8.1. (LG8-2) 5. Why might the Standard & PoorÕs 500 Index be a better measure of stock market performance than the Dow Jones Industrial Average? Why is the DJIA more popular than the S&P 500? (LG8-3) 6. Explain how it is possible for the DJIA to increase one day while the NASDAQ Composite decreases during the same day. (LG8-3) 7. Which is higher, the ask quote or the bid quote? Why? (LG8-4) 8. Illustrate through examples how trading commission costs impact an investorÕs return. (LG8-4) 9. Describe the difference in the timing of trade execu-tion and the certainty of trade price between market orders and limit orders. (LG8-4) 10. What are the differences between common stock and preferred stock? (LG8-5) 11. How important is growth to a stockÕs value? Illus-trate with examples. (LG8-5) 12. Under what conditions would the constant-growth model not be appropriate? (LG8-5) 13. The expected return derived from the constant-growth-rate model relies on dividend yield and capital gain. Where do these two parts of the return come from? (LG8-5) 14. Describe, in words, how to use the variable-growth-rate technique to value a stock. (LG8-6) 15. Can the variable-growth-rate model be used to value a firm that has a negative growth rate in Stage 1 and a stable and positive growth in Stage 2? Explain. (LG8-6) 16. Explain why using the P/E relative value approach may be useful for companies that do not pay divi-dends. (LG8-7) 17. How is a firmÕs changing P/E ratio reflected in the stock price? Give examples. (LG8-7) 18. Differentiate the characteristics of growth stocks and value stocks. (LG8-7) 19. WhatÕs the relationship between the P/E ratio and a firmÕs growth rate? (LG8-7) 20. Describe the process for using the P/E ratio to esti-mate a future stock price. (LG8-7)problems 8-1 Stock Index Performance On March 5, 2013, the Dow Jones Industrial Average set a new high. The index closed at 14,253.77, which was up 125.95 that day. What was the return (in percent) of the stock market that day? (LG8-3) 8-2 Stock Index Performance On March 9, 2009, the Dow Jones Industrial Average reached a new low. The index closed at 6,547.05, which was down 79.89 that day. What was the return (in percent) of the stock market that day? (LG8-3) 8-3 Buying Stock with Commissions Your discount brokerage firm charges $7.95 per stock trade. How much money do you need to buy 200 shares of Pfizer, Inc. (PFE), which trades at $31.40? (LG8-4) 8-4 Buying Stock with Commissions Your discount brokerage firm charges $9.50 per stock trade. How much money do you need to buy 300 shares of Time War-ner, Inc. (TWX), which trades at $22.62? (LG8-4) 8-5 Selling Stock with Commissions Your full-service brokerage firm charges $140 per stock trade. How much money do you receive after selling 200 shares of Nokia Corporation (NOK), which trades at $20.13? (LG8-4)basic problemsFinal PDF to printer
291cor91411_ch08_264-295.indd 291 01/20/17 04:39 PM 8-6 Selling Stock with Commissions Your full-service brokerage firm charges $135 per stock trade. How much money do you receive after selling 250 shares of International Business Machines (IBM), which trades at $96.17? (LG8-4) 8-7 Buying Stock with a Market Order You would like to buy shares of Sirius Satellite Radio (SIRI). The current ask and bid quotes are $3.96 and $3.93, respectively. You place a market buy order for 500 shares that executes at these quoted prices. How much money did it cost to buy these shares? (LG8-4) 8-8 Buying Stock with a Market Order You would like to buy shares of Coldwa-ter Creek, Inc. (CWTR). The current ask and bid quotes are $20.70 and $20.66, respectively. You place a market buy order for 200 shares that executes at these quoted prices. How much money did it cost to buy these shares? (LG8-4) 8-9 Selling Stock with a Limit Order You would like to sell 200 shares of Xenith Bankshares, Inc. (XBKS). The current ask and bid quotes are $4.66 and $4.62, respectively. You place a limit sell order at $4.65. If the trade executes, how much money do you receive from the buyer? (LG8-4) 8-10 Selling Stock with a Limit Order You would like to sell 100 shares of Echo Global Logistics, Inc. (ECHO). The current ask and bid quotes are $15.33 and $15.28, respectively. You place a limit sell order at $15.31. If the trade executes, how much money do you receive from the buyer? (LG8-4) 8-11 Value of a Preferred Stock A preferred stock from Duquesne Light Company (DQUPRA) pays $3.55 in annual dividends. If the required return on the pre-ferred stock is 6.7 percent, whatÕs the value of the stock? (LG8-5) 8-12 Value of a Preferred Stock A preferred stock from Hecla Mining Co. (HLPRB) pays $3.50 in annual dividends. If the required return on the preferred stock is 6.8 percent, what is the value of the stock? (LG8-5) 8-13 P/E Ratio and Stock Price Ultra Petroleum (UPL) has earnings per share of $1.56 and a P/E ratio of 32.48. WhatÕs the stock price? (LG8-7) 8-14 P/E Ratio and Stock Price JPMorgan Chase Co. (JPM) has earnings per share of $3.53 and a P/E ratio of 13.81. What is the price of the stock? (LG8-7)intermediate problems 8-15 Value of Dividends and Future Price A firm is expected to pay a dividend of $1.35 next year and $1.50 the following year. Financial analysts believe the stock will be at their price target of $68 in two years. Compute the value of this stock with a required return of 10 percent. (LG8-5) 8-16 Value of Dividends and Future Price A firm is expected to pay a dividend of $2.05 next year and $2.35 the following year. Financial analysts believe the stock will be at their price target of $110 in two years. Compute the value of this stock with a required return of 12 percent. (LG8-5) 8-17 Dividend Growth Annual dividends of ATTA Corp grew from $0.96 in 2005 to $1.76 in 2017. What was the annual growth rate? (LG8-5) 8-18 Dividend Growth Annual dividends of Generic Electrical grew from $0.66 in 2012 to $1.03 in 2017. What was the annual growth rate? (LG8-5) 8-19 Value a Constant Growth Stock Financial analysts forecast Safeco Corp.Õs (SAF) growth rate for the future to be 8 percent. SafecoÕs recent dividend was $0.88. What is the value of Safeco stock when the required return is 12 percent? (LG8-5) 8-20 Value a Constant Growth Stock Financial analysts forecast Limited Brands (LTD) growth rate for the future to be 12.5 percent. LTDÕs recent dividend was $0.60. What is the value of Limited Brands stock when the required return is 14.5 percent? (LG8-5) 8-21 Expected Return Ecolap Inc. (ECL) recently paid a $0.46 dividend. The dividend is expected to grow at a 14.5 percent rate. At a current stock price of $44.12, what is the return shareholders are expecting? (LG8-5)Final PDF to printer
292cor91411_ch08_264-295.indd 292 01/20/17 04:39 PM 8-22 Expected Return Paychex Inc. (PAYX) recently paid an $0.84 dividend. The dividend is expected to grow at a 15 percent rate. At a current stock price of $40.11, what is the return shareholders are expecting? (LG8-5) 8-23 Dividend Initiation and Stock Value A firm does not pay a dividend. It is expected to pay its first dividend of $0.20 per share in three years. This dividend will grow at 11 percent indefinitely. Using a 12 percent discount rate, compute the value of this stock. (LG8-6) 8-24 Dividend Initiation and Stock Value A firm does not pay a dividend. It is expected to pay its first dividend of $0.25 per share in two years. This dividend will grow at 10 percent indefinitely. Using an 11.5 percent discount rate, com-pute the value of this stock. (LG8-6) 8-25 P/E Ratio Model and Future Price Kellogg Co. (K) recently earned a profit of $2.52 earnings per share and has a P/E ratio of 13.5. The dividend has been grow-ing at a 5 percent rate over the past few years. If this growth rate continues, what would be the stock price in five years if the P/E ratio remained unchanged? What would the price be if the P/E ratio declined to 12 in five years? (LG8-7) 8-26 P/E Ratio Model and Future Price New York Times Co. (NYT) recently earned a profit of $1.21 per share and has a P/E ratio of 19.59. The dividend has been growing at a 7.25 percent rate over the past six years. If this growth rate continues, what would be the stock price in five years if the P/E ratio remained unchanged? What would the price be if the P/E ratio increased to 22 in five years? (LG8-7)advanced problems 8-27 Value of Future Cash Flows A firm recently paid a $0.45 annual dividend. The dividend is expected to increase by 10 percent in each of the next four years. In the fourth year, the stock price is expected to be $80. If the required return for this stock is 13.5 percent, what is its value? (LG8-5) 8-28 Value of Future Cash Flows A firm recently paid a $0.60 annual dividend. The dividend is expected to increase by 12 percent in each of the next four years. In the fourth year, the stock price is expected to be $110. If the required return for this stock is 14.5 percent, what is its value? (LG8-5) 8-29 Constant Growth Stock Valuation Waller Co. paid a $0.137 dividend per share in 2000, which grew to $0.55 in 2012. This growth is expected to continue. What is the value of this stock at the beginning of 2013 when the required return is 13.7 percent? (LG8-5) 8-30 Constant Growth Stock Valuation Campbell Supper Co. paid a $0.632 divi-dend per share in 2013, which grew to $0.76 in 2016. This growth is expected to continue. What is the value of this stock at the beginning of 2017 when the required return is 8.7 percent? (LG8-5) 8-31 Changes in Growth and Stock Valuation Consider a firm that had been priced using a 10 percent growth rate and a 12 percent required return. The firm recently paid a $1.20 dividend. The firm just announced that because of a new joint ven-ture, it will likely grow at a 10.5 percent rate. How much should the stock price change (in dollars and percentage)? (LG8-5) 8-32 Changes in Growth and Stock Valuation Consider a firm that had been priced using an 11.5 percent growth rate and a 13.5 percent required return. The firm recently paid a $1.50 dividend. The firm has just announced that because of a new joint venture, it will likely grow at a 12 percent rate. How much should the stock price change (in dollars and percentage)? (LG8-5) 8-33 Variable Growth A fast-growing firm recently paid a dividend of $0.35 per share. The dividend is expected to increase at a 20 percent rate for the next Final PDF to printer
293cor91411_ch08_264-295.indd 293 01/20/17 04:39 PMthree years. Afterwards, a more stable 12 percent growth rate can be assumed. If a 13 percent discount rate is appropriate for this stock, what is its value? (LG8-6) 8-34 Variable Growth A fast-growing firm recently paid a dividend of $0.40 per share. The dividend is expected to increase at a 25 percent rate for the next four years. Afterwards, a more stable 11 percent growth rate can be assumed. If a 12.5 percent discount rate is appropriate for this stock, what is its value? (LG8-6) 8-35 P/E Model and Cash Flow Valuation Suppose that a firmÕs recent earnings per share and dividend per share are $2.50 and $1.30, respectively. Both are expected to grow at 8 percent. However, the firmÕs current P/E ratio of 22 seems high for this growth rate. The P/E ratio is expected to fall to 18 within five years. Compute a value for this stock by first estimating the dividends over the next five years and the stock price in five years. Then discount these cash flows using a 10 percent required rate. (LG8-5, LG8-7) 8-36 P/E Model and Cash Flow Valuation Suppose that a firmÕs recent earnings per share and dividend per share are $2.75 and $1.60, respectively. Both are expected to grow at 9 percent. However, the firmÕs current P/E ratio of 23 seems high for this growth rate. The P/E ratio is expected to fall to 19 within five years. Compute a value for this stock by first estimating the dividends over the next five years and the stock price in five years. Then discount these cash flows using an 11 percent required rate. (LG8-5, LG8-7) 8-37 Spreadsheet Problem Spreadsheets are especially useful for computing stock value under different assumptions. Consider a firm that is expected to pay the following dividends:Year 123456$1.20$1.20$1.50$1.50$1.75$1.90and grow at 5% thereafter a. Using an 11 percent discount rate, what would be the value of this stock? b. What is the value of the stock using a 10 percent discount rate? A 12 percent discount rate? c. What would the value be using a 6 percent growth rate after year 6 instead of the 5 percent rate using each of these three discount rates? d. What do you conclude about stock valuation and its assumptions? 8-38 Spreadsheet Problem Design a spreadsheet similar to the one below to compute the value of a variable growth rate firm over a five-year horizon.ABCDEF1Inputs2Current dividend =3First-stage growth =4Second-stage growth =5Discount rate =67Year123458Projected dividend 9Terminal price =10Present value = a. What is the value of the stock if the current dividend is $1.30, the first stage growth is 18 percent, the second stage growth is 9 percent, and the discount rate is 11 percent?Final PDF to printer
294cor91411_ch08_264-295.indd 294 01/20/17 04:39 PM b. What is the value of the stock if the current dividend is $1.30, the first stage growth is 2 percent, the second stage growth is 8 percent, and the discount rate is 9.5 percent? c. What is the value of the stock if the current dividend is $2.50, the first stage growth is 15 percent, the second stage growth is 7 percent, and the discount rate is 10 percent?research it! Stock ScreenerInvestors can choose from many thousands of stocks. The large number to choose from can be quite daunting to new investors. Fortunately, some good stock screeners are available for free on the Internet that will find only the kinds of companies the investor is looking for. Looking for small value companies? A stock screen at Yahoo! Finance will show all the stocks that meet the three criteria of (1) market capitalization between $250 million and $500 million, (2) P/E ratio less than or equal to 10, and (3) an estimated five-year growth of greater than or equal to 20 percent. In February of 2016, 39 firms met all three of these criteria. Yahoo! Finance provides many screens like this one to choose from. Pick one of these preset screens. Discuss the kinds of stocks the screen will find and report on those companies. (https://finance.yahoo.com/screener)integrated mini-case: Valuing Carnival CorporationCarnival Corp. (CCL) provides cruises to major vacation destinations. Carnival operates 99 cruise ships in North America, Europe, Australia, and Asia. The company also operates hotels, sightseeing motor coaches and rail cars, and luxury day boats. These activities generated earnings per share of $2.26 for 2015. The stock price at the end of 2015 was $54.48. The previous stock prices and dividends are shown in the following table:20082009201020112012201320142015Annual dividend$ 1.20$ 0.00$ 0.40$ 1.00$ 1.00$ 1.50$ 1.00$ 1.10Stock price at the end of the year$20.77$27.06$39.81$28.97$34.07$38.29$44.31$54.48Key StatisticCarnivalGeneral EntertainmentServices SectorP/E ratio20.2619.75 18.60 Dividend yield 2.67% 3.17% 1.57%Next 5-year growth18.00%17.65%14.72%Carnival is a firm in the General Entertainment industry, which is in the Services sector. The following table shows some key statistics for Carnival, the industry, and the sector:Use the various valuation models and relative value measures to assess whether Carnival stock is correctly valued. Compute value estimates from multiple models. The appropriate required rate of return is 11 percent.ANSWERS TO TIME OUT 8-1 The New York Stock Exchange (NYSE) has a physical location in New York City near the American Exchange. NASDAQ is an electronic network and therefore does not have a specific location per se.Final PDF to printer
295cor91411_ch08_264-295.indd 295 01/20/17 04:39 PM 8-2 The NYSE uses a specialist at each trading post on the floor to manage the trading in the stocks assigned to that post. Orders come to the floor through stockbrokers worldwide. The trades are executed through an auction system with the floor brokers. NASDAQ uses an electronic network that ties together many dealers that are inter-ested in trading the stock. These dealers compete with each other to offer the best price. Orders come in from stockbrokers and are executed with the dealer that has the best price. Both of these systems are good and each exchange works diligently to make their system effective and efficient for investors. 8-3 First, these indexes are composed of different stocks. Second, the type of stocks in each index may be weighted toward different industries. Last, the indexes are com-puted using different methodologies. 8-4 The bubble mostly occurred in the Internet and other technology-oriented firms. These firms, especially the smaller ones, made up a much larger portion of the NASDAQ Composite than the DJIA or the S&P 500. Therefore, the dramatic price rise and fall for these companies had a bigger impact on NASDAQ. This is visually seen in the figure. 8-5 Of the popular indexes, the S&P 500 Index includes the largest portion of the market capitalization and therefore gives the best indication of what is happening in the stock market. 8-6 An investor buys at the higher ask price and sells at the lower bid price. Thus, the difference between the bid and ask price is a cost to the trader. If the bid-ask spread is $0.05, this cost seems small for an $80 stock and high for a $5 stock. 8-7 A market buy order would execute at the ask price of $37.85. Yes, the limit sell order at $37.75 executes if the bid is at $37.75 or higher. So, the order would execute at the bid of $37.79. 8-8 Firm growth is very valuable to the value of a stock. Consider three firms with the same $1 dividend and 12 percent discount rate but with growth of 10 percent, 5 percent, and 0 percent, respectively. Using the Gordon growth model, the stock price estimates are P 0 = $1 × (1 + 0.1) ____________ 0.12 − 0.10 = $55; P 0 = $1 × (1 + 0.05) _____________ 0.12 − 0.05 = $15; P 0 = $1 × (1 + 0) __________ 0.12 − 0 = $8.33 Note how dramatically different the price estimates are. 8-9 The dividend yield for Coca-Cola was 2.84 percent. This is a 26.94 percent (= 3.30 Ö 12.25) proportion of the total expected return. The rest comes from growth expectations. 8-10 The variable-growth model was demonstrated using an initially high growth rate that reduced to a long-term growth rate. However, it is valid with any initial growth rate (high, low, zero, and even negative). The key is that it must settle into a long-term constant-growth rate that is lower than the discount rate. 8-11 P 0 = $2.20 (1 + 0.218) ______________ 1 + 0.14 + $2.20 (1 + 0.218) 2 + $2.20 (1 + 0.218) 2 (1 + 0.102) ________________________ 0.14 − 0.102 ________________________________________ (1 + 0.14) 2 = $2.351 + $3.264 + $94.649 _______________ 1.2996 = $77.69 8-12 Rearranging the Gordon growth model, P0/E0 = (D1/E0) Ö (i − g), we see that the P/E ratio is related to the firmÕs growth rate. Higher P/E ratios are expected for firms with higher growth rates. If two firms have the same P/E ratio, the one with the higher growth rate might be described as cheap compared to the firm with the lower growth rate. 8-13 P 5 = (P/E) × E 0 × (1 + g) 5 = 6 × $18.58 × (1 + 0.043) 5 = $137.60 Final PDF to printer
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