Financial Management: Principles & Applications Thirteenth Edition Chapter 9 Debt Valuation and Interest Copyright © 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved

Learning Objectives (1 of 2) Identify the key features of bonds and describe the difference between private and public debt markets. Calculate the value of a bond and relate it to the yield to maturity on the bond. Describe the four key bond valuation relationships.

Learning Objectives (2 of 2) Identify the major types of corporate bonds. Explain the effects of inflation on interest rates and describe the term structure of interest rates.

Principles Applied in This Chapter Principle 1: Money Has a Time Value. Principle 2: There is a Risk-Return Tradeoff. Principle 3: Cash Flows Are the Source of Value

9.1 OVERVIEW OF CORPORATE DEBT

Corporate Borrowings When a corporation borrows money to finance its operations, it has two main sources: Loan from a financial institution (known as private debt since it involves only two parties) Bonds (known as public debt since they can be traded in the public financial markets)

Borrowing Money in the Private Financial Market Financial Institutions provide loans to finance firm’s day-to-day operations (working capital loans) or it might be used for the purchase of equipment or property (transaction loans). Such a loan is considered a private market transaction because it involves only the two parties to the loan.

Private Debt Placements (1 of 2) Firms can raise money by selling debt securities directly to investors through a private placement. The major investors in private placements are large financial institutions, with the three most important investor groups being (1) Life insurance companies, (2) state and local retirement funds, and (3) private pension funds.

Private Debt Placements (2 of 2) Advantages of Private Debt Placement Speed Reduced costs Financing flexibility Disadvantages of Private Debt Placement Interest costs Restrictive covenants

Floating—Rate Loans (1 of 2) Loans made in the private financial market are typically floating-rate loans, which means that every month or every quarter the rate of interest charged by the lender adjusts up or down depending on the movement of an agreed-upon benchmark rate of interest. The most popular benchmark rate of interest is the London Interbank Offered Rate (LIBOR). This is the daily rate that is based on the interest rates at which banks offer to lend in the London wholesale or interbank market.

Floating—Rate Loans (2 of 2) For example, a corporation may get a 1-year loan with a rate of 300 basis points (or 3%) over LIBOR with a ceiling of 11% and a floor of 4%.

Table 9.1 Types of Bank Debt Blank (Panel A) Types of Bank Loans—Classified by Intended Use Working-capital Loans Typically, these loans set up a line of credit based on an open-ended credit agreement whereby the firm has prior approval to borrow up to a set limit. This type of credit agreement is similar to that of a personal credit card that provides a line of credit up to an agreed-on limit. The credit is then used to provide cash needed to support the firm’s day-to-day business needs. Transaction loans Firms use this type of loan to finance a specific asset. These loans typically call for installment payments designed to repay the principal amount of the loan, plus interest, with fixed monthly or annual payments. Home mortgage and automobile loans are examples of transaction loans that require installment payments. (Panel B) Types of Bank Loans—Classified by the Collateral Used to Secure the Loan Secured debt This type of debt acts as a promise to pay that is backed by granting the lender an interest in a specific piece of property, known as collateral. The property used to secure the loan can include virtually any tangible business asset, such as accounts receivable, inventory, plant and equipment, or real estate. Unsecured debt This type of debt acts as a promise to pay that is not supported by collateral, so the lender relies on the creditworthiness and reputation of the borrower to repay the debt when due.

CHECKPOINT 9.1: CHECK YOURSELF Calculating the Rate of Interest on a Floating-Rate Loan Consider the same loan period as above but change the spread over LIBOR from .25% to .75%. Is the ceiling rate or floor rate violated during the loan period?

Step 1: Picture the Problem (1 of 2) The graph on the next slide shows the LIBOR index (series 1), LIBOR plus the spread of 75 basis points (series 2), the ceiling rate (series 3), and the floor rate (series 4).

Step 1: Picture the Problem (2 of 2)

Step 2: Decide on a Solution Strategy (1 of 2) We have to determine the floating rate for every week and see if it exceeds the ceiling or falls below the floor. Floating rate on Loan = LIBOR for the previous week + spread of .75%

Step 2: Decide on a Solution Strategy (2 of 2) The floating rate on loan cannot exceed the ceiling rate of 2.5% or drop below the floor rate of 1.75%. If the floating rate falls below the floor, the rate will be reset at the floor rate. If the floating rate exceeds the ceiling, the rate will be reset at the ceiling rate.

Step 3: Solve (1 of 2) Blank LIBOR LIBOR + Spread (.75%) Loan Rate 2/29/2008 1.98% 3/7/2008 1.66% 2.73% 2.50% 3/14/2008 1.52% 2.44% 2.41% 3/21/2008 1.35% 2.27% 3/28/2008 1.60% 2.10% 4/4/2008 1.63% 2.35% 4/11/2008 1.67% 2.38% 4/18/2008 1.88% 2.42% 4/25/2008 1.93% 2.63% 5/2/2008 2.68% Ceiling Violated

Step 3: Solve (2 of 2) The table shows the ceiling is violated during the first week and last two weeks of the loan period. The floor rate is never violated.

Step 4: Analyze The ceiling is the maximum rate charged on the loan while floor is the minimum rate charged on the loan. If the ceiling or floor rates are violated, the loan rate is reset to the ceiling rate or the floor rate. If there were no ceiling, the loan rate would have been 2.73% during the first week of the loan, and 2.63% and 2.68% during the last two weeks of the loan.

Borrowing Money in the Public Financial Market Corporations engage the services of an investment banker while raising long-term funds in the public financial market. The investment banker performs three basic functions: Underwriting: assuming risk of selling a security issued. The client is given the money before the securities are sold to the public. Distributing or selling securities to ultimate investors Advising such as on source of capital, timing of the sale of securities

Corporate Bonds Corporate bond is a security sold by corporation that has promised future payments and a maturity date. If the firm fails to make its promised interest and principal payments, then the bond trustee can classify the firm as insolvent and force it into bankruptcy.

Basic Bond Features The basic features of a bond include the following: Bond indenture Claims on assets and income Par or face value Coupon interest rate Maturity and repayment of principal Call provision and conversion features

Table 9.2 Bond Terminology (1 of 2) Indenture The indenture is the legal agreement between the firm issuing the bonds and the bond trustee, who represents the bondholders. It lists the specific terms of the loan agreement, including a description of the bonds, the rights of the bondholders, the rights of the issuing firm, and the responsibilities of the trustee. Priority of claims on assets and income In the case of insolvency, claims of debt in general, including bonds, are honored before those of both common stock and preferred stock. In addition, interest payments hold priority over dividend payments for common and preferred stock. Par value The par value of a bond, also known as its face value, is the principal that must be repaid to the bondholder at maturity. In general, corporate bonds are issued with par values in increments of $1,000. Also, when bond prices are quoted in the financial press, prices are generally expressed as a percentage of the bond’s par value. Maturity and repayment of principal The maturity date refers to the date on which the bond issuer must repay the principal or par value to the bondholder. Coupon interest Rate The coupon rate on a bond indicates the percentage of the par value of the bond that will be paid out annually in the form of interest and is quoted as an APR.

Table 9.2 Bond Terminology (2 of 2) Current yield The current yield on a bond refers to the ratio of the annual interest payment to the bond’s current market price. If, for example, we have a bond with an 8% coupon interest rate, a par value of $1,000, and a market price of $700, it has a current yield of 11.4%, calculated as follows: Current Yield= Annual Interest Payment Current Market Price of the Bond = 0.08×$1,000 $700 = $80 $700 =0.114, or 11.4% (9-1) Call provision The call provision provides the issuer of the bond with the right to redeem or retire a bond before it matures. Conversion feature Some bonds have a conversion feature that allows bondholders to convert their bonds into a set number of shares of common stock.

Bond Ratings and Default Risk Bond ratings indicate the default risk i.e. the probability that the firm will make the bond’s promised payments. Rating agencies use borrower’s financial statements, financing mix, profitability, variability of past profits, and make judgments about the quality of the firm’s management in order to determine ratings.

Table 9.3 Interpreting Bond Ratings Bond Rating Category Standard & Poor’s Moody’s Description Investment Grade: Blank Prime or highest strong AAA Aaa Highest quality; extremely strong capacity to pay High quality AA Aa Very strong capacity to pay Upper medium A A-1, A Upper medium quality; strong capacity to pay Medium BBB Baa-1, Baa Lower medium quality; changing circumstances could impact the firm’s ability to pay Not Investment Grade: Speculative BB Ba Speculative elements; faces uncertainties Highly speculative B, CCC, CC B, Caa, Ca Extremely speculative and highly vulnerable to nonpayment Default D C Income bond; doesn’t pay interest

9.2 VALUING CORPORATE DEBT

Valuing Corporate Debt The value of corporate debt is equal to the present value of the contractually promised principal and interest payments (the cash flows) discounted back to the present using the market’s required yield to maturity on bonds of similar risk.

Valuing Bonds by Discounting Future Cash Flows (1 of 3) Step 1: Determine bondholder cash flows, which are the amount and timing of the bond’s promised interest and principal payments to the bondholders. Annual Interest = Par value × coupon rate Example: The annual interest for a 10-year bond with coupon interest rate of 7% and a par value of $1,000 is equal to $70, (.07 × $1,000 = $70). This bond will pay $70 every year and $1,000 at the end of 10-years.

Valuing Bonds by Discounting Future Cash Flows (2 of 3) Step 2: Estimate the appropriate discount rate on a bond of similar risk. Discount rate is the return the bond will yield if it is held to maturity and all bond payments are made.

Calculating a Bond’s Yield to Maturity (YTM) We can think of YTM as the discount rate that makes the present value of the bond’s promised interest and principal equal to the bond’s observed market price.

Valuing Bonds by Discounting Future Cash Flows (3 of 3) Step 3: Calculate the present value of the bond’s interest and principal payments from Step 1 using the discount rate in step 2.

CHECKPOINT 9.2: CHECK YOURSELF Calculating the Yield to Maturity on a Corporate Bond Calculate the YTM on the Ford bond where the bond price rises to $900 (holding all other things equal).

Step 1: Picture the Problem YTM = ? Years 1 2 3 … Blank 11 Cash flow −$900 $65 $1,065 Purchase price = $900 Interest payments = $65 per year for years 1-11 Final payment = $1,000 in year 11 of principal.

Step 2: Decide on a Solution Strategy We can use equation 9-2a to find YTM. YTM is the rate that makes the present value of all future expected cash flows equal to the current market price. We can also solve for YTM using a calculator and a spreadsheet.

Step 3: Solve (1 of 2) Using a Mathematical Equation It is cumbersome to solve for YTM by hand using the equation. It is more practical to use the financial calculator or the spread sheet.

Step 3: Solve (2 of 2) Using a Financial Calculator N = 11 I/Y = 7.89 PV = −900 PMT = 65 FV = 1,000 Using an Excel Spreadsheet = RATE(nper, pmt,pv,fv) = RATE (11,65,−900,1000) = 7.89%

Step 4: Analyze The yield to maturity on the bond is 7.89%. The yield is higher than the coupon rate of interest of 6.5%. Since the coupon rate is lower than the yield to maturity, the bond is trading at a price below $1,000. We call this a discount bond.

Using Market—Yield—to—Maturity Data (1 of 2) Market-yield-to-maturity data are regularly reported by a number of investor services and are often quoted in terms of credit spread, or yield spread, or spread over Treasury bonds. Table 9-4 contains some example yield to maturity by credit rating – this directly provides us with the yield to maturity on bonds with different levels of risk.

Table 9.4 Corporate Bond Yields: Bond Yields by Bond Rating and Term to Maturity (1 of 2) 1 year 2 years 3 years 5 years 7 years 10 years 30 years Aaa/AAA 0.22 0.31 0.42 0.76 1.26 2.00 3.41 Aa1/AA+ 0.26 0.43 0.58 0.96 1.46 2.17 3.62 Aa2/AA 0.29 0.55 0.74 1.16 1.66 2.35 3.83 Aa3/AA– 0.77 1.20 1.70 2.39 3.88 A1/A+ 0.32 0.60 0.80 1.23 1.73 2.43 3.93 A2/A 0.98 1.40 1.89 2.57 4.03 A3/A– 0.62 0.95 1.18 2.19 2.92 4.51 Baa1/BBB+ 0.83 1.19 1.42 1.91 2.45 3.18 4.80 Baa2/BBB 1.00 1.39 1.65 2.73 3.48 5.17

Table 9.4 Corporate Bond Yields: Bond Yields by Bond Rating and Term to Maturity (2 of 2) 1 year 2 years 3 years 5 years 7 years 10 years 30 years Baa3/BBB– 1.49 1.87 2.11 2.62 3.16 3.91 5.56 Ba1/BB+ 2.27 2.64 2.90 3.41 3.98 4.75 6.37 Ba2/BB 3.04 3.68 4.21 4.79 5.58 7.19 Ba3/BB– 3.82 4.18 4.47 5.00 5.61 6.42 8.00 B1/B+ 4.60 4.95 5.25 5.79 7.26 8.82 B2/B 5.38 5.72 6.04 6.59 7.24 8.10 9.63 B3/B– 6.15 6.49 6.82 7.38 8.06 8.93 10.45 Caa/CCC+ 6.93 7.61 8.17 8.87 9.77 11.26 U.S. Treasury Yield 0.18 0.25 0.32 0.60 1.00 1.59 2.76

Using Market Yield to Maturity Data (2 of 2) A credit or yield spread represents the difference in the number of basis points (with 100 basis points equal to 1 percent) that a corporate bond yields over a U.S. Treasury security of the same maturity as the corporate bond. For example, if the credit or yield spread for a 30- year Aaa1/BBB1-rated corporate bond is 204 basis points, then this bond should yield 2.04 percent over the yield earned on a similar 30-year U.S. Treasury bonds.

Promised versus Expected Yield to Maturity The yield to maturity calculation assumes that the bond performs according to the terms of the bond contract or indenture. Since corporate bonds are subject to risk of default, the promised yield to maturity may not be equal to expected yield to maturity. The financial press quotes promised yields and not expected rates of return.

CHECKPOINT 9.3: CHECK YOURSELF Valuing a Bond Issue Calculate the present value of the AT&T bond if the market’s required yield to maturity for comparable-risk bonds rises to 9% (holding all other things equal).

Step 1: Picture the Problem Years 1 2 3 … Blank 20 Cash flow $85 $1,085 k PV of all Cash flows =? $85 interest + $1,000 Principal $85 annual interest

Step 2: Decide on a Solution Strategy Here we know the following: Annual interest payments = $85 Principal amount or par value = $1,000 Time = 20 years YTM or discount rate = 9% We can use the above information to determine the value of the bond by discounting future interest and principal payment to the present.

Step 3: Solve (1 of 2) Using a Mathematical Formula = $ 85{[1−(1/(1.09)20] ÷ (.20)} + $1,000/(1.09)20 = $85 (9.128) + $178.43 = $954.36

Step 3: Solve (2 of 2) Using a Financial Calculator N = 20 1/y = 9.0 PMT = 85 FV = 1000 PV = 954.36 Using an Excel Spreadsheet = PV (rate, nper, pmt, fv) = PV (.09,20,85,1000) = $954.36

Step 4: Analyze The value of AT&T bond falls to $954.36 when the yield to maturity rises to 9%. The bonds are now trading at a discount as the coupon rate on AT&T bonds is lower than the market yield. An investor who buys AT&T bonds at its current discounted price will earn a promised yield to maturity of 9%.

Semiannual Interest Payments In general, Corporate bonds pay interest on a semiannual basis. We can adapt Equation (9-2a) from annual to semiannual payments as follows:

CHECKPOINT 9.4: CHECK YOURSELF Valuing a Bond Issue That Pays Semiannual Interest Calculate the present value of the AT&T bond if the yield to maturity on comparable-risk bonds rises to 9% (holding all other things equal).

Step 1: Picture the Problem 40 6-month periods i = 9% Periods 1 2 3 … Blank 40 Cash flow $42.5 $1,042.50 PV=? $42.50 Semiannual interest $42.5 interest + $1,000 Principal

Step 2: Decide on a Solution Strategy Here we know the following: Semiannual interest payments = $42.50 Principal amount or par value = $1,000 Time = 20 years or 40 periods YTM or discount rate = 9% or 4.5% for 6-months We can use the above information to determine the value of the bond by discounting future interest and principal payment to the present.

Step 3: Solve (1 of 2) Using a Mathematical Formula = $ 42.5{[1−(1/(1.045)40] ÷ (.20)} + $1,000/(1.045)40 = $42.5 (18.40) + $171.93 = $954

Step 3: Solve (2 of 2) Using a Financial Calculator N = 40 1/y = 4.50 PMT = 42.50 FV = 1000 PV = 954 Using an Excel Spreadsheet = PV (rate, nper, pmt, fv) = PV (.045,40,42.5,1000) = $954

Step 4: Analyze Using semi-annual compounding we get a value of $954 for AT&T bonds. This is very close to the value of $954.26 found using annual compounding. However, for a large investor buying thousands of bonds, this can certainly add up over time.

9.3 BOND VALUATION: FOUR KEY RELATIONSHIPS

Relationship 1 First Relationship The value of bond is inversely related to changes in the market’s required yield to maturity. Blank YTM = 12% YTM rises to 15% Par value $1,000 Coupon rate 12% Maturity date 5 years Bond Value $899 Bond Value Drops

Figure 9-1 Bond Value and the Market’s Required Yield to Maturity (5—Year Bond, 12% Coupon Rate)

Relationship 2 The market value of a bond will be less than the par value (discount bond) if the market’s required yield to maturity is above the coupon interest rate and will be more than the par valued if the market’s required yield to maturity is below the coupon interest rate.

Relationship 3 As the maturity date approaches, the market value of a bond approaches its par value. Figure 9.2 clearly demonstrates the value of a bond, whether a premium or a discount bond, approaches its par value as the maturity date becomes closer in time.

Table 9-5 Bond Prices Relative to Maturity Date Blank Years to Maturity 12% Coupon Bond 5 4 3 2 1 12% yield scenario $1,000.00 Discount bond 15% yield scenario $ 899.44 $ 914.35 $ 931.50 $ 951.23 $ 973.91 Premium bond 9% yield scenario $1,116.69 $1,097.19 $1,075.94 $1,052.77 $1,027.52

Figure 9-2 Value of a 12% Coupon Bond during the Life of the Bond

Relationships 4 Long term bonds have greater interest-rate risk than short-term bonds. While all bonds are affected by a change in interest rates, the prices of longer-term bonds fluctuate more when interest rates change than do the prices of shorter-term bonds (see Table 9.6)

Table 9.6 Bond Price Fluctuations for Bonds with Different Maturities Blank Years to Maturity 5 10 15 20 25 30 15% (increased yield) $899.44 $849.44 $824.58 $812.22 $806.08 $803.02 % price decrease −10.1% −15.1% −17.5% −18.8% −19.4% −19.7% $1,000.00 % price increase 11.7% 19.3% 24.2% 27.4% 29.5% 30.8% 9% (decreased yield) $1,116.69 $1,192.53 $1,241.82 $1,273.86 $1,294.68 $1,308.21

9.4 TYPES OF BONDS

Types of Bonds Table 9.7 contains a list of the major types of corporate bonds. The differences among the various types of bonds are a function of how each of the following bond attributes are defined: Secured versus unsecured Priority of claims Initial offering market Abnormal risk Coupon level Amortizing or non-amortizing Convertibility

Table 9.7 Types of Corporate Bonds (1 of 3) Debentures A debenture is any unsecured debt instrument. Because they are unsecured, the earning ability of the issuing corporation is of great concern to the bondholder. They are riskier than secured bonds and as a result must provide investors with a higher yield than secured bonds provide. Often the issuing firm attempts to provide some protection to the holder of the bond by committing not to issue more secured long-term debt that would further tie up the firm’s assets and leave the bondholders less protected. To the issuing firm, the major advantage of debentures is that no property has to be committed to secure them. This allows the firm to issue debt and still preserve some future borrowing power. Subordinated debentures The claims of subordinated debentures are honored only after the claims of secured debt and unsubordinated debentures have been satisfied. Mortgage bonds A mortgage bond is secured by a lien on real property. Typically, the value of the real property is greater than that of the bonds issued. This provides the mortgage bondholders with a margin of safety in the event the market value of the secured property declines. In the case of foreclosure, the bondholders get the proceeds from the sale of the secured property. If the proceeds from this sale do not cover the bonds, the bondholders become general creditors, similar to debenture bondholders, for the unpaid portion of the debt.

Table 9.7 Types of Corporate Bonds (2 of 3) Eurobonds Eurobonds are bonds issued in a country different from the one in whose currency the bonds are denominated. For example, a bond that is issued in Europe or Asia by an American company and that pays interest and principal to the lender in U.S. dollars is considered a Eurobond. Thus, a Eurobond does not have to be issued in Europe; it merely needs to be issued in a country different from the one in whose currency it is denominated to be considered a Eurobond. Zero-coupon and very-low-coupon bonds These bonds require either no coupon interest payments (these are called zeroes) or very low coupon interest payments. Consequently, bondholders receive all or most of their return at maturity. Because these bonds pay little or no interest, they must sell at a deep discount. For the investor, a zero-coupon bond is like a U.S. savings bond. The obvious appeal of zero-coupon bonds is to those investors who need a lump sum of money at some future date but don’t want to be concerned about reinvesting interest payments. Today, zero-coupon bonds are infrequently issued by corporations. The dominant player in this market is the U.S. government, with the government’s zero-coupon bonds called STRIPS.

Table 9.7 Types of Corporate Bonds (3 of 3) Junk (high-yield) bonds Junk bonds are high-risk debt that has a below-investment-grade bond rating (see the earlier discussion of bond ratings). They are also called high-yield bonds because they pay interest rates that are 3 to 5% higher than those of the highest-rated bonds. Floating-rate bonds A floating- or variable-rate bond is simply one whose coupon rate fluctuates according to the level of current market interest rates. These bonds are quite popular with municipalities and foreign governments but are far less common among corporations. Convertible bonds Convertible bonds are debt securities that can be converted to a firm’s stock at a prespecified price.

9.5 DETERMINANTS OF INTEREST RATES

Determinants of Interest Rates Bond prices vary inversely with interest rates; therefore, we need to understand what determines interest rates if we want to understand how bond prices fluctuate.

Inflation and Real versus Nominal Interest Rates Interest rate quotes in the financial press are commonly referred to as the nominal (or quoted) interest rates and are the interest rates unadjusted for inflation. Real rate of interest adjusts for the expected effects of inflation.

Fisher Effect: The Nominal and Real Rate of Interest The relationship between the nominal rate of interest, rnominal , the anticipated rate of inflation, rinflation , and the real rate of interest is known as the Fisher effect.

CHECKPOINT 9.5: CHECK YOURSELF Solving for the Real Rate of Interest Assume now that you expect that inflation will be 5% over the coming year and want to analyze how much better off you will be if you place your savings in an account that also earns just 5%. What is the real rate of return in this circumstance?

Step 1: Picture the Problem (1 of 2) Let us assume that the prices of goods and services today is $1.00 per unit. With a 5% inflation, these goods and services will cost $1.05. Thus, $10,500 expected in the savings account at the end of the year will buy you only 10,000 units (10,500/1.05) at the end of the year.

Step 1: Picture the Problem (2 of 2) Blank Year 0 Year 1 Savings Account Balance $10,000.00 $10,500.00 Price Index (5% inflation) $1.00 $1.05 Purchasing Power (units) 10,000.00

Step 2: Decide on a Solution Strategy Step 3: Solve We can estimate the real rate of interest by using equation 9-4b. rreal = {(1+.05) ÷ (1+.05)} – 1 = 0%

Step 4: Analyze Here the nominal rate of interest is equal to the expected rate of inflation. Therefore, the real rate of return is equal to zero i.e. there is no increase in purchasing power from investing the savings at 5%.

CHECKPOINT 9.6: CHECK YOURSELF Solving for the Nominal Rate of Interest If you anticipate that the rate of inflation will now be 4% next year, holding all else the same, what rate of return will you need to earn on your savings in order to achieve a 2% increase in purchasing power?

Step 1: Picture the Problem (1 of 2) Let us assume that the prices of goods and services today is $1.00 per unit. If the expected rate of inflation is 4% and you want to be able to purchase 2% more, you will need to earn a nominal rate of interest on your savings that will allow you to buy 10,200 units at $1.04 each.

Step 1: Picture the Problem (2 of 2) Blank Year 0 Year 1 Savings Account Balance $10,000.00 $10,608 Price Index (5% inflation) $1.00 $1.04 Purchasing Power (units) 10,000.00 10,200.00 Real rate (% increase in purchasing power) 2% Interest rate of 6.08% solved in step 3

Step 2: Decide on a Solution Strategy Step 3: Solve We can use the Fisher model found in equation 9-4a to determine the nominal rate of interest.

Step 4: Analyze In order to achieve a 2% increase in purchasing power in the face of a 4% rate of inflation, you must earn a 6.08% rate on your savings.

Interest—Rate Determinants (1 of 3) We can think of the interest rate for a particular note or bond as being composed of five basic components:

Interest—Rate Determinants (2 of 3) The inflation premium = premium for the expected rate of increase in the prices of goods and services in the economy over the terms of the bond or note. Default–risk premium = a premium to reflect the risk of default by the borrower.

Interest—Rate Determinants (3 of 3) Maturity-risk premium = a premium that reflects the additional return required by investors in longer-term securities to compensate them for the greater risk of price fluctuation on those securities caused by interest rate changes. Liquidity-risk premium = a premium required by investors for securities that cannot quickly be converted to cash at a reasonably predictable price

The Maturity—Risk Premium and the Term Structure of Interest Rates The relationship between interest rates and time to maturity, with default risk held constant is known as the term structure of interest rates or the yield curve. Figure 9.3 illustrates a hypothetical term structure of U.S. Treasury Bonds. We observe that the rate of interest on a 5-year note or bond is 11.5 percent, and the comparable rate on a 20-year bond is 13 percent. Generally, the yield curve rises for longer maturities.

Figure 9.3 The Term Structure of Interest Rates or Yield Curve

The Shape of the Yield Curve (1 of 2) By reviewing equation 9-4, we can gain an understanding of why a yield curve takes on one shape or another. For example, for Treasury security, the default-risk premium and the liquidity- risk premium would both be zero. Accordingly, the shape of the yield curve is driven by real risk-free rate of interest, inflation premium and maturity risk premium.

The Shape of the Yield Curve (2 of 2) During periods when inflation is expected to subside, the inflation premium should decrease over longer maturities, resulting in a downward sloping Treasury yield curve as shown in Figure 9.5. The reverse is also true as shown in Figure 9.4

Figure 9.4 Treasury Yield Curve during Period of Increasing Inflation Maturity Real Risk-Free Rate Inflation Premium Maturity-Risk Premium Yield 90 days 1.00% 1.75% 0.01% 2.76% 2 years 2.15% 0.11% 3.26% 5 years 2.56% 0.57% 4.13% 10 years 3.05% 0.97% 5.02% 20 years 3.42% 1.32% 5.74% 30 years 3.60% 1.50% 6.10%

Figure 9.5 Treasury Yield Curve during Period of Decreasing Inflation Maturity Real Risk-Free Rate Inflation Premium Maturity-Risk Premium Yield 90 days 1.00% 3.80% 0.01% 4.81% 2 years 3.71% 0.08% 4.79% 5 years 3.42% 0.25% 4.67% 10 years 2.85% 0.42% 4.27% 20 years 2.38% 0.63% 4.01% 30 years 2.19% 0.75% 3.94%

Shifts in the Yield Curve (1 of 2) The term structure of interest rates, or the yield curve, changes over time as expectations regarding each of the four factors that underlie interest rates. Figure 9.6 shows the yield curve one day before 911 attack and again two weeks later. Investors shifted their funds to the safety of short-term Treasury securities, which pushed up prices and pushed down yields on short-term securities relative to long-term securities.

Figure 9-6 Changes in the Term Structure of Interest Rates around September 11, 2001

Shifts in the Yield Curve (2 of 2) The yield curve is most often upward-sloping but it can assume different shapes i.e. downward sloping or flat. Figure 9-7 illustrates different shapes of yield curves at different dates, observed within a span of only 13 months.

Key Terms (1 of 6) Amortizing bond Basis point Bond indenture Bond rating Call provision Clean price Collateral Conversion feature

Key Terms (2 of 6) Convertible bond Corporate bond Coupon interest rate Credit spread Current yield Debenture Default-risk premium

Key Terms (3 of 6) Dirty price Discount bond Eurobonds Fisher effect Floating rate Floating-rate bond Inflation premium Interest rate risk

Key Terms (4 of 6) Junk (high-yield) bond London Interbank Offered Rate (LIBOR) Liquidity-risk premium Maturity-risk premium Mortgage bond Nominal (or quoted) interest rate Non-amortizing bond

Key Terms (5 of 6) Par or face value of a bond Private market transaction Premium bond Real rate of interest Recovery rate Secured bond Spread over Treasury bonds or yields

Key Terms (6 of 6) Subordinated debentures Syndicate Term structure of interest rates Transaction loan Unsubordinated debenture Yield curve Yield to maturity Yield Spread Zero-coupon bond

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