Principles of Managerial Finance. Lawrence J. Gitman Chad J. Zutter

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1 Global edition Principles of Managerial Finance Fourteenth edition Lawrence J. Gitman Chad J. Zutter

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3 278 Part 3 Valuation of Securities Figure 6.2 Impact of Inflation Relationship between annual rate of inflation and 3-month U.S. Treasury bill average annual returns, Annual Rate (%) Treasury Bill Rates and Inflation T-bills a 2 2 Inflation b Year a Average annual rate of return on 3-month U.S. Treasury bills. b Annual percentage change in the consumer price index. Sources: Data from selected Federal Reserve Bulletins and U.S. Department of Labor Bureau of Labor Statistics. Term Structure of Interest Rates term structure of interest rates The relationship between the maturity and rate of return for bonds with similar levels of risk. yield curve A graphic depiction of the term structure of interest rates. yield to maturity (YTM) Compound annual rate of return earned on a debt security purchased on a given day and held to maturity. inverted yield curve A downward-sloping yield curve indicates that short-term interest rates are generally higher than long-term interest rates. normal yield curve An upward-sloping yield curve indicates that long-term interest rates are generally higher than short-term interest rates. The term structure of interest rates is the relationship between the maturity and rate of return for bonds with similar levels of risk. A graph of this relationship is called the yield curve. A quick glance at the yield curve tells analysts how rates vary between short-, medium-, and long-term bonds, but it may also provide information on where interest rates and the economy in general are headed in the future. Usually, when analysts examine the term structure of interest rates, they focus on Treasury securities because they are generally considered to be free of default risk. Yield Curves A bond s yield to maturity (YTM) (discussed later in this chapter) represents the compound annual rate of return that an investor earns on the bond, assuming that the bond makes all promised payments and the investor holds the bond to maturity. In a yield curve, the yield to maturity is plotted on the vertical axis and time to maturity is plotted on the horizontal axis. Figure 6.3 shows three yield curves for U.S. Treasury securities: one at May 22, 1981, a second at September 29, 1989, and a third at May 20, Observe that both the position and the shape of the yield curves change over time. The yield curve of May 22, 1981, indicates that short-term interest rates at that time were above longer-term rates. For reasons that a glance at the figure makes obvious, this curve is described as downward sloping. Interest rates in May 1981 were also quite high by historical standards, so the overall level of the yield curve is high. Historically, a downward-sloping yield curve, which is sometimes called an inverted yield curve, occurs infrequently and is often a sign that the economy is weakening. Most recessions in the United States have been preceded by an inverted yield curve. Usually, short-term interest rates are lower than long-term interest rates, as they were on May 20, That is, the normal yield curve is upward sloping. Notice that the May 2013 yield curve lies entirely beneath the other two curves

4 Chapter 6 Interest Rates and Bond Valuation 279 Figure 6.3 Treasury Yield Curves Yield curves for U.S. Treasury securities: May 22, 1981; September 29, 1989; and May 20, 2013 Yield to Maturity May 22, 1981 September 29, 1989 May 20, Time to Maturity (years) Sources: Data from U.S. Department of the Treasury, Office of Domestic Finance, Office of Debt Management. flat yield curve A yield curve that indicates that interest rates do not vary much at different maturities. shown in Figure 6.3. In other words, interest rates in May 2013 were unusually low, largely because at that time the economy was still recovering from a deep recession, and the Federal Reserve was exerting downward pressure on interest rates to stimulate the economy. Sometimes, a flat yield curve, similar to that of September 29, 1989, exists. A flat yield curve simply means that rates do not vary much at different maturities. The shape of the yield curve may affect the firm s financing decisions. A financial manager who faces a downward-sloping yield curve may be tempted to rely more heavily on cheaper, long-term financing. However, a risk in following this strategy is that interest rates may fall in the future, so long-term rates that seem cheap today may be relatively expensive tomorrow. Likewise, when the yield curve is upward sloping, the manager may believe that it is wise to use cheaper, short-term financing. Relying on short-term financing has its own risks. Firms that borrow on a short-term basis may see their costs rise if interest rates go up. Even more serious is the risk that a firm may not be able to refinance a short-term loan when it comes due. A variety of factors influence the choice of loan maturity, but the shape of the yield curve is something that managers must consider when making decisions about short-term versus long-term borrowing. Matter of fact Bond Yields Hit Record Lows On July 25, 2012, the 10-year Treasury note and 30-year Treasury bond yields reached all-time lows of 1.43% and 2.46%. That was good news for the housing market. Many mortgage rates are linked to rates on Treasury securities. For example, the traditional 30-year mortgage rate is typically linked to the yield on 10-year Treasury notes. With mortgage rates reaching new lows, potential buyers found that they could afford more expensive homes, and existing homeowners were able to refinance their existing loans, lowering their monthly mortgage payments and leaving them with more money to spend on other things. This kind of activity is precisely what the Federal Reserve hoped to stimulate by keeping interest rates low during the economic recovery.

5 280 Part 3 Valuation of Securities Theories of Term Structure Three theories are frequently cited to explain the general shape of the yield curve: the expectations theory, the liquidity preference theory, and the market segmentation theory. expectations theory The theory that the yield curve reflects investor expectations about future interest rates; an expectation of rising interest rates results in an upwardsloping yield curve, and an expectation of declining rates results in a downward-sloping yield curve. Expectations Theory One theory of the term structure of interest rates, the expectations theory, suggests that the yield curve reflects investor expectations about future interest rates. According to this theory, when investors expect short-term interest rates to rise in the future (perhaps because investors believe that inflation will rise in the future), today s long-term rates will be higher than current short-term rates, and the yield curve will be upward sloping. The opposite is true when investors expect declining short-term rates: Today s short-term rates will be higher than current long-term rates, and the yield curve will be inverted. To understand the expectations theory, consider this example. Suppose that the yield curve is flat. The rate on a 1-year Treasury note is 4 percent, and so is the rate on a 2-year Treasury note. Now, consider an investor who has money to place into a low-risk investment for 2 years. The investor has two options. First, he could purchase the 2-year Treasury note and receive a total of 8 percent (ignoring compounding) in 2 years. Second, he could invest in the 1-year Treasury earning 4 percent, and then when that security matures, he could reinvest in another 1-year Treasury note. If the investor wants to maximize his expected return, the decision between the first and second options above depends on whether he expects interest rates to rise, fall, or remain unchanged during the next year. If the investor believes that interest rates will rise, it means next year s return on a 1-year Treasury note will be greater than 4 percent (that is, greater than the 1-year Treasury rate right now). Let s say the investor believes that the interest rate on a 1-year note next year will be 5 percent. If the investor expects rising rates, his expected return is higher if he follows the second option, buying a 1-year Treasury note now (paying 4 percent) and reinvesting in a new security that pays 5 percent next year. Over 2 years, the investor would expect to earn about 9 percent (ignoring compounding) in interest, compared to just 8 percent earned by holding the 2-year bond. If the current 1-year rate is 4 percent and investors generally expect that rate to go up to 5 percent next year, what would the 2-year Treasury note rate have to be right now to remain competitive? The answer is 4.5 percent. An investor who buys this security and holds it for 2 years would earn about 9 percent interest (again, ignoring compounding), the same as the expected return from investing in two consecutive 1-year bonds. In other words, if investors expect interest rates to rise, the 2-year rate today must be higher than the 1-year rate today, and that in turn means that the yield curve must have an upward slope. Example 6.2 Suppose that a 5-year Treasury note currently offers a 3% annual return. Investors believe that interest rates are going to decline, and 5 years from now, they expect the rate on a 5-year Treasury note to be 2.5%. According to the expectations theory, what is the return that a 10-year Treasury note has to offer today? What does this imply about the slope of the yield curve?

6 Chapter 6 Interest Rates and Bond Valuation 281 Consider an investor who purchases a 5-year note today and plans to reinvest in another 5-year note in the future. Over the 10-year investment horizon, this investor expects to earn about 27.5%, ignoring compounding (that s 3% per year for the first 5 years and 2.5% per year for the next 5 years). To compete with that return, a 10-year bond today could offer 2.75% per year. That is, a bond that pays 2.75% for each of the next 10 years produces the same 27.5% total return that the series of two 5-year notes is expected to produce. Therefore, the 5-year rate today is 3% and the 10-year rate today is 2.75%, and the yield curve is downward sloping. liquidity preference theory Theory suggesting that longterm rates are generally higher than short-term rates (hence, the yield curve is upward sloping) because investors perceive short-term investments to be more liquid and less risky than long-term investments. Borrowers must offer higher rates on long-term bonds to entice investors away from their preferred short-term securities. market segmentation theory Theory suggesting that the market for loans is segmented on the basis of maturity and that the supply of and demand for loans within each segment determine its prevailing interest rate; the slope of the yield curve is determined by the general relationship between the prevailing rates in each market segment. Liquidity Preference Theory Most of the time, yield curves are upward sloping, which, according to the expectations theory, means that investors expect interest rates to rise. An alternative explanation for the typical upward slope of the yield curve is the liquidity preference theory. This theory holds that, all else being equal, investors generally prefer to buy short-term securities, while issuers prefer to sell long-term securities. For investors, short-term securities are attractive because they are highly liquid and their prices are not particularly volatile. 1 Hence, investors will accept somewhat lower rates on short-term bonds because they are less risky than long-term bonds. Conversely, when firms or governments want to lock in their borrowing costs for a long period of time by selling long-term bonds, those bonds have to offer higher rates to entice investors away from the short-term securities that they prefer. Borrowers are willing to pay somewhat higher rates because long-term debt allows them to eliminate or reduce the risk of not being able to refinance short-term debts when they come due. Borrowing on a long-term basis also reduces uncertainty about future borrowing costs. Market Segmentation Theory The market segmentation theory suggests that the market for loans is totally segmented on the basis of maturity and that the supply of and demand for loans within each segment determine its prevailing interest rate. In other words, the equilibrium between suppliers and demanders of short-term funds, such as seasonal business loans, would determine prevailing short-term interest rates, and the equilibrium between suppliers and demanders of long-term funds, such as real estate loans, would determine prevailing long-term interest rates. The slope of the yield curve would be determined by the general relationship between the prevailing rates in each market segment. Simply stated, an upward-sloping yield curve indicates greater borrowing demand relative to the supply of funds in the long-term segment of the debt market relative to the short-term segment. All three term structure theories have merit. From them, we can conclude that at any time the slope of the yield curve is affected by (1) interest rate expectations, (2) liquidity preferences, and (3) the comparative equilibrium of supply and demand in the short- and long-term market segments. Upward-sloping yield curves result from expectations of rising interest rates, lender preferences for shorter-maturity loans, and greater supply of short-term loans than of long-term loans relative to demand. The opposite conditions would result in a downwardsloping yield curve. At any time, the interaction of these three forces determines the prevailing slope of the yield curve. 1. Later in this chapter, we demonstrate that debt instruments with longer maturities are more sensitive to changing market interest rates. For a given change in market rates, the price or value of longer-term debts will be more significantly changed (up or down) than the price or value of debts with shorter maturities.

7 282 Part 3 Valuation of Securities Risk Premiums: Issuer and Issue Characteristics So far, we have considered only risk-free U.S. Treasury securities. We now reintroduce the risk premium and assess it in view of risky non-treasury issues. Recall Equation 6.1: r 1 = r* + IP + RP 1 risk-free rate, R F risk premium In words, the nominal rate of interest for security 1 (r 1 ) is equal to the risk-free rate, consisting of the real rate of interest (r*) plus the inflation expectation premium (IP), plus the risk premium (RP 1 ). The risk premium varies with specific issuer and issue characteristics. Example 6.3 MyFinanceLab Solution Video The nominal interest rates on a number of classes of long-term securities in May 2013 were as follows: Security Nominal interest rate U.S. Treasury bonds (average) 3.18% Corporate bonds (by risk ratings): High quality (Aaa Aa) 3.94% Medium quality (Baa Baa) 4.76% Speculative (Ba C) 5.46% Because the U.S. Treasury bond would represent the risk-free, long-term security, we can calculate the risk premium of the other securities by subtracting the riskfree rate, 3.18%, from each nominal rate (yield): Security Risk premium Corporate bonds (by ratings): High quality (Aaa Aa) 3.94% % % Medium quality (A Baa) 4.76% % % Speculative (Ba C) 5.46% % % These risk premiums reflect differing issuer and issue risks. The lower-rated (speculative) corporate issues have a higher risk premium than that of the higherrated corporate issues (high quality and medium quality), and that risk premium is the compensation that investors demand for bearing the higher default risk of lower quality bonds. The risk premium consists of a number of issuer- and issue-related components, including business risk, financial risk, interest rate risk, liquidity risk, and tax risk, as well as the purely debt-specific risks default risk, maturity risk, and contractual provision risk briefly defined in Table 6.1. In general, the highest risk premiums and therefore the highest returns result from securities issued by firms with a high risk of default and from long-term maturities that have unfavorable contractual provisions.

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