As noted in Chapter 2, financial institutions and markets create the mechanism through which funds flow between savers (funds suppliers) and borrowers (funds demanders). All else being equal, savers would like to earn as much interest as possible, and borrowers would like to pay as little as possible. The interest rate prevailing in the market at any given time reflects the equilibrium between savers and borrowers.
INTEREST RATE FuNdAMENTALS
The interest rate or required return represents the cost of money. It is the com- pensation that a supplier of funds expects and a demander of funds must pay.
Usually the term interest rate is applied to debt instruments such as bank loans or bonds, whereas the term required return may be applied to almost any kind of investment, including common stock, which gives the investor an ownership stake in the issuer. In fact, the meaning of these two terms is quite similar because in both cases the supplier is compensated for providing funds to the demander.
A variety of factors can influence the equilibrium interest rate. One factor is inflation, a rising trend in the prices of most goods and services. Typically, savers demand higher returns (that is, higher interest rates) when inflation is high be- cause they want their investments to more than keep pace with rising prices. A second factor influencing interest rates is risk. When people perceive that a par- ticular investment is riskier, they will expect a higher return on that investment as compensation for bearing the risk. A third factor that can affect the interest rate is a liquidity preference among investors. The term liquidity preference refers to the general tendency of investors to prefer short-term securities (that is, securities that are more liquid). If, all other things being equal, investors would prefer to buy short-term rather than long-term securities, interest rates on short-term in- struments such as Treasury bills will be lower than rates on longer-term securi- ties. Investors will hold these securities, despite the relatively low return that they offer, because they meet investors’ preferences for liquidity.
interest rate
Usually applied to debt instruments such as bank loans or bonds; the compensation paid by the borrower of funds to the lender; from the borrower’s point of view, the cost of borrowing funds.
required return Usually applied to equity instruments such as common stock; the cost of funds obtained by selling an ownership interest.
inflation
A rising trend in the prices of most goods and services.
liquidity preference A general tendency for investors to prefer short-term (that is, more liquid) securities.
Matter of fact
Near the height of the financial crisis in December 2008, interest rates on Treasury bills briefly turned negative, meaning that investors paid more to the Treasury than the Treasury prom- ised to pay back. Why would anyone put their money into an investment that they know will lose money? Remember that 2008 saw the demise of Lehman Brothers, and fears that other commer- cial banks and investments banks might fail were rampant. Evidently, some investors were willing to pay the U.S. Treasury to keep their money safe for a short time.
Fear Turns T-Bill Rates Negative
The Real Rate of Interest
Imagine a perfect world in which there is no inflation, in which investors have no liquidity preferences, and in which there is no risk. In this world, there would be one cost of money: the real rate of interest. The real rate of interest real rate of interest
The rate that creates equilibrium between the supply of savings and the demand for investment funds in a perfect world, without inflation, where suppliers and demanders of funds have no liquidity preferences and there is no risk.
LG1
creates equilibrium between the supply of savings and the demand for funds. It represents the most basic cost of money. Historically, the real rate of interest in the United States has averaged about 1 percent per year, but that figure does fluc- tuate over time. This supply–demand relationship is shown in Figure 6.1 by the supply function (labeled S0) and the demand function (labeled D). An equilibrium between the supply of funds and the demand for funds (S0 = D) occurs at a rate of interest r0*, the real rate of interest.
Clearly, the real rate of interest changes with changing economic conditions, tastes, and preferences. To combat a recession, the Board of Governors of the Federal Reserve System might initiate actions to increase the supply of credit in the economy, causing the supply function in Figure 6.1 to shift to, say, S1. The result could be a lower real rate of interest, r1*, at equilibrium (S1 = D). With a lower cost of money, firms might find that investments that were previously unat- tractive are now worth undertaking, and as firms hire more workers and spend more on plant and equipment, the economy begins to expand again.
Nominal or Actual Rate of Interest (Return)
The nominal rate of interest is the actual rate of interest charged by the supplier of funds and paid by the demander. Throughout this book, interest rates and re- quired rates of return are nominal rates unless otherwise noted. The nominal rate of interest differs from the real rate of interest, r*, as a result of two factors, infla- tion and risk. When people save money and invest it, they are sacrificing con- sumption today (that is, they are spending less than they could) in return for higher future consumption. When investors expect inflation to occur, they believe that the price of consuming goods and services will be higher in the future than in the present. Therefore, they will be reluctant to sacrifice today’s consumption un- less the return they can earn on the money they save (or invest) will be high enough to allow them to purchase the goods and services they desire at a higher future price. That is, investors will demand a higher nominal rate of return if they expect inflation. The additional return that investors require to compensate them for inflation is called the expected inflation premium (IP).
Funds Supplied/Demanded
Real Rate of Interest
r*1 r*0
S1 = D S0 = D
D
S1
S1
S0
S0
D F I G u R E 6 . 1
Supply–Demand Relationship
Supply of savings and demand for investment funds
nominal rate of interest The actual rate of interest charged by the supplier of funds and paid by the demander.
Similarly, investors generally demand higher rates of return on risky invest- ments as compared to safe ones. Otherwise, there is little incentive for investors to bear the additional risk. Therefore, investors will demand a higher nominal rate of return on risky investments. The additional return that investors require to compensate them for bearing risk is called the risk premium (RP). Therefore, the nominal rate of interest for security 1, r1, is given by
r1 = r* + IP + RP1
¯ ˘˙ ¯˘˙
risk-free rate, RF
risk premium
(6.1)
As the horizontal braces below the equation indicate, the nominal rate, r1, can be viewed as having two basic components: a risk-free rate of return, RF, and a risk premium, RP1:
r1 = RF + RP1 (6.2)
For the moment, ignore the risk premium, RP1, and focus exclusively on the risk-free rate. Equation 6.1 says that the risk-free rate can be represented as
RF = r* + IP (6.3)
The risk-free rate (as shown in Equation 6.3) embodies the real rate of interest plus the expected inflation premium. The inflation premium is driven by inves- tors’ expectations about inflation: The more inflation they expect, the higher will be the inflation premium, and the higher will be the nominal interest rate.
Three-month U.S. Treasury bills (T-bills) are short-term IOUs issued by the U.S. Treasury, and they are widely regarded as the safest investments in the world. They are as close as we can get in the real world to a risk-free investment.
To estimate the real rate of interest, analysts typically try to determine what rate of inflation investors expect over the coming 3 months. Next, they subtract the expected inflation rate from the nominal rate on the 3-month T-bill to arrive at the underlying real rate of interest. For the risk-free asset in Equation 6.3, the real rate of interest, r*, would equal RF - IP. A simple personal finance example can demonstrate the practical distinction between nominal and real rates of interest.
Marilyn Carbo has $10 that she can spend on candy costing
$0.25 per piece. She could buy 40 pieces of candy ($10.00 ,
$0.25) today. The nominal rate of interest on a 1-year investment is currently 7%, and the expected rate of inflation over the coming year is 4%. Instead of buying the 40 pieces of candy today, Marilyn could invest the $10. After 1 year, she would have $10.70 because she would have earned 7% interest—an additional $0.70 (0.07 * $10.00)—on her $10 investment. During that year, inflation would have increased the cost of the candy by 4%—an additional $0.01 (0.04 * $0.25)—to
$0.26 per piece. As a result, at the end of the 1-year period Marilyn would be able to buy about 41.2 pieces of candy ($10.70 , $0.26), or roughly 3% more (41.2 , 40.0 = 1.03). The 3% increase in Marilyn’s buying power represents her real rate of return. The nominal rate of return on her investment (7%) is partly eroded by inflation (4%), so her real return during the year is the difference be- tween the nominal rate and the inflation rate (7, - 4, = 3,).
Personal Finance Example 6.1▶
MyFinancelab Solution Video
The value of bonds, as fixed-income security, is negatively related to changes in the nominal interest rate. One component of interest rate under the control of the government is real interest rate, which is determined by the Federal Reserve or the central bank of a country. The other component of interest rate is determined by the market prices, and measured through the Consumer Price Index (infla- tion). Over time, the real interest rate does not fluctuate sharply, but inflation usually does, resulting in a higher or lower nominal interest rate.
Saving and Loans Bank (S&LB) is a governmental social bank located in Kuwait with paid-up capital of $8,850 million, and more than $12,500 million in outstanding loans. Recently, the S&LB finalized an in-depth plan to securitize the $12,500 million in outstanding loans. Backed by the full
focus on PRACTICE
in practice To avoid the reinvestment risk, it was
planned to issue the bonds as deeply dis- counted bonds with a zero coupon rate.
The investors of the treasury bonds will have to hold them until maturity to get the maximum benefits. This, in turn, will re- duce the liquidity of the bonds in the sec- ondary market, resulting in lower market value. The idea was to sell each issue to one major institutional investor who could strip the issue by selling securities with dif- ferent maturities to increase the liquidity of the issues.
▶ Which method do you think is the best to adjust bond income and in- terest rate from the issuer’s and the bondholder’s points of view?
▶ Is it better to issue deeply dis- counted bonds to the public or to sell the issue to a major financial institution, which in turn can strip them?
faith of the Kuwaiti government, the bank plans to issue bonds against the outstanding loans. The treasury bonds will be free of default risk but not free of inflation, or reinvestment risk. Based on a regional market’s survey, the maturity will range between 5, 7, and 10 years. To avoid the negative effect of inflation on the bond value, S&LB plans to index the bonds to inflation or to an equity index. If issued bonds are indexed to inflation, the periodic coupon will be equal to the inflation level plus 150 to 200 basis points. If they are equity indexed, the coupon rate will be equal to the equity index minus 100 to 150 basis points.
Another proposed method of indexing these bonds is to adjust their par value to the inflation or equity index.
Therefore, the issued bonds will not be viewed as fixed income securities but treated as floating income securities.
Bond Valuation and Interest Rate Risk
The premium for expected inflation in Equation 6.3 represents the average rate of inflation expected over the life of an investment. It is not the rate of infla- tion experienced over the immediate past, although investors’ inflation expecta- tions are undoubtedly influenced by the rate of inflation that has occurred in the recent past. Even so, the inflation premium reflects the expected rate of inflation.
The expected inflation premium changes over time in response to many factors, such as changes in monetary and fiscal policies, currency movements, and inter- national political events. For a discussion of a U.S. debt security whose interest rate is adjusted for inflation, see the Focus on Practice box above.
Figure 6.2 illustrates the annual movement of the rate of inflation and the risk-free rate of return from 1961 through 2012. During this period, the two rates tended to move in a similar fashion. Note that T-bill rates were slightly above the inflation rate most of the time, meaning that T-bills generally of- fered a small positive real return. Between 1978 and the early 1980s, inflation and interest rates were quite high, peaking at more than 13 percent in 1980–
1981. Since then, rates have gradually declined. To combat a severe recession, the Federal Reserve pushed interest rates down to almost 0% in 2009 and kept them there for several years. Note that over this entire period, the infla- tion rate was negative only once (in 2009). Even though the economy experi- enced a positive inflation rate each year from 2010 to 2012, the Fed kept in- terest rates near zero, so the real interest rate in those years was actually negative.
deflation
A general trend of falling prices.
TERM STRuCTuRE OF 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 informa- tion 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 matu- rity. 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, 2013.
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 ob- vious, 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, 2013. That is, the normal yield curve is upward sloping.
Notice that the May 2013 yield curve lies entirely beneath the other two curves
1964 1970 1976 1982 1988 1994 2000 2006 2012
Year 14
18
10
6
2
Annual Rate (%)
–2
Treasury Bill Rates and Inflation 1961–2012
Inflationb T-billsa F I G u R E 6 . 2
Impact of Inflation Relationship between annual rate of inflation and 3-month U.S.
Treasury bill average annual returns, 1961–2012
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.
aAverage annual rate of return on 3-month U.S. Treasury bills.
bAnnual percentage change in the consumer price index.
Sources: Data from selected Federal Reserve Bulletins and U.S. Department of Labor Bureau of Labor Statistics.
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 fi- nancial 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.
18 16 14 12 10 8 6 4 2 0 5
10 15 20 25 30
Yield to Maturity
Time to Maturity (years) May 22, 1981
September 29, 1989
May 20, 2013
Data from U.S. Department of the Treasury, Office of Domestic Finance, Office of Debt Management.
Sources:
F I G u R E 6 . 3 Treasury Yield Curves Yield curves for U.S.
Treasury securities: May 22, 1981; September 29, 1989; and May 20, 2013
flat yield curve
A yield curve that indicates that interest rates do not vary much at different maturities.
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 mort- gage payments and leaving them with more money to spend on other things. This kind of activ- ity is precisely what the Federal Reserve hoped to stimulate by keeping interest rates low during the economic recovery.