KEY CONCEPTS AND SKILLS

Chapter 5 INTEREST RATES AND BOND VALUATION 5-1 KEY CONCEPTS AND SKILLS Know the important bond features and bond types Comprehend bond values (prices) and why they fluctuate Compute bond values and fluctuations Appreciate bond ratings, their meaning, and relationship to bond terms and value Understand the impact of inflation on interest rates Grasp the term structure of interest rates and the determinants of bond yields 5-2 1

CHAPTER OUTLINE 5.1 Bonds and Bond Valuation 5.2 More on Bond Features 5.3 Bond Ratings 5.4 Some Different Types of Bonds 5.5 Bond Markets 5.6 Inflation and Interest Rates 5.7 Determinants of Bond Yields 5-3 5.1 BONDS AND BOND VALUATION A bond is a legally binding agreement between a borrower and a lender that specifies: Par (face) value Coupon rate (which determines coupon payment) Maturity date Bondholders have a required rate of return on the bond Do not confuse the coupon rate with the required rate of return in the market The yield to maturity (YTM) is the expected rate of return on the bond Almost always, YTM = the required return 5-4 2

BOND VALUATION Primary Principle: (Fundamental) Value of any financial security = Present value of that security s expected future cash flows Bond value is, therefore, determined by the present value of the coupon payments plus the present value of the par, or face, value Present values (i.e., bond values) are inversely related to market interest rates, which themselves affect bondholders required rates of return. 5-5 CONCEPTUAL CASH FLOW OF A 10 YEAR BOND Xanth Co. has issued a 10 year bond with an 8% annual coupon. The cash flows from the bond would be paid as follows: 5-6 3

THE BOND-PRICING EQUATION Notice that: The first term is the present value of the coupon payments (an annuity) The second term is the present value of the face-value payment 5-7 FREQUENCY OF COUPON PAYMENTS Bond terms dictate the frequency of coupon payments The coupon rate is expressed in annual terms If the rate is expressed annually and the payments are more frequent, calculation of bond value requires: Dividing the annual coupon payment by the number of compounding periods per year to arrive at the value of each periodic coupon payment (C); Dividing the annual required rate of return by the number of compounding periods per year to arrive at the desired periodic required return (or desired periodic yield) (i.e., r); Multiplying the remaining years of the bond s life by the number of compounding periods per year to arrive at the remaining number of coupon payments (T). 5-8 4

BOND EXAMPLE On 1-1-16, consider a US government bond with a 63/8% coupon that expires in Dec. 2020. The Par Value of the bond is $1,000. Coupon payments are made semi-annually (June 30 and Dec. 31 for this particular bond). Coupon payment is $31.875: 63/8% x 1000 / 2 Using Jan. 1, 2010 as today, the timeline showing the sizes and timing of cash flows is this: 5-9 BOND EXAMPLE On Jan. 1, 2016, the required yield is 5%/year. The size and timing of the cash flows are: 5-10 5

BOND EXAMPLE: CALCULATOR Find the present value (as of January 1, 2016), of a 6 3/8% coupon bond with semi-annual payments, and a maturity date of December 2020 if the current required return is 5%. N 10 I/Y PV PMT FV 2.5 1,060.17 31.875 = 1,000 1,000 0.06375 2 5-11 BOND EXAMPLE Now assume that the required yield is 11%. For this new req d return, calculate the bond s price. 5-12 6

REQUIRED RETURN & BOND VALUE Bond Value 1300 1200 1100 When the required return < coupon rate, the bond trades at a premium. When the required ret. = coupon rate, the bond trades at par. When the required ret. > coupon rate, the bond trades at a discount. 1000 800 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 6 3/8% Discount Rate (Required Ret.) 5-13 BOND CONCEPTS Bond prices and market interest rates (i.e., required returns) move in opposite directions. When required return > coupon rate, price < face (or par) value The bond is a discount bond When required return = coupon rate, price = face value The bond sells at par value When required return < coupon rate, price > face value The bond is a premium bond 5-14 7

INTEREST-RATE RISK Price Risk Change in price due to changes in market interest rates, which affect bondholders required returns Long-term bonds have more price risk than shortterm bonds Low-coupon-rate bonds have more price risk than high-coupon-rate bonds Reinvestment Rate Risk Uncertainty concerning rates at which cash flows can be reinvested Short-term bonds have more reinvestment rate risk than long-term bonds High-coupon-rate bonds have more reinvestment rate risk than low-coupon-rate bonds 5-15 MATURITY AND BOND PRICE VOLATILITY Bond Value Consider two otherwise identical bonds. The long-maturity bond will have much more volatility with respect to changes in the discount rate. Par Short-Maturity Bond C Long-Maturity Bond Discount Rate (Req d Ret.) 5-16 8

COUPON RATES AND BOND PRICES Bond Value Consider two otherwise identical bonds. The low-coupon bond will have more volatility with respect to changes in the discount rate. Par High-Coupon Bond C Low-Coupon Bond Discount Rate (Req d Ret.) 5-17 COMPUTING YIELD TO MATURITY Mechanically, yield to maturity (YTM) is the rate that sets the present value of a bond s future cash flows equal to the bond s current price YTM is implied by the bond s price and cash flows YTM can be thought of as the return expected by the bondholders (i.e., as the expected return) Finding YTM requires trial and error if you do not not have a financial calculator, an Excel sheet, or mult.-choice answers from which to choose. If you have a financial calculator, enter PV, PMT, N, and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign). Then, compute R (or I/Y). 5-18 9

YTM WITH ANNUAL COUPONS Consider a bond with a 10% annual coupon rate, 15 years to maturity, and a par value of $1,000. Current price is $928.09. Calculate YTM. Possible answers are: 9%, 10%, 11%, 12%, 13%. Financial calculator: N = 15; PV = 928.09; FV = 1,000; PMT = 100 CPT I/Y = 11% Math: 100 / 0.13 ( 1 1/1.13 15 ) + 1000 / 1.13 15 = 806.12 100 / 0.12 ( 1 1/1.12 15 ) + 1000 / 1.12 15 = 863.78 100 / 0.11 ( 1 1/1.11 15 ) + 1000 / 1.11 15 = 928.09 11% is the yield to maturity 5-19 YTM WITH SEMIANNUAL COUPONS Consider a bond with 10% coupon rate, semiannual coupons, $1000 face value, and maturity in 20 years. Price = $1,197.93. Calculate YTM. Will the YTM be more or less than 10%? What s the semi-annual coupon pmt.? ( 10% / 2 ) x $1K How many periods (half-years) are there? 20 x 2 So, N = 40; PV = -1,197.93; PMT = 50; FV = 1,00 CPT I/Y = 4% (Is this the Annual YTM?) YTM = 4% (per half-year) * 2 = 8% per year Math supposing 8%/yr. is one mult.-ch. answer. Convert the potential answer to a semi-annual rate: 4% Then do the usual math & confirm the answer: 50 / 0.04 ( 1 1/1.04 40 ) + 1000 / 1.04 40 = 1197.93 5-20 10

CURRENT YIELD VS. YIELD TO MATURITY Current yield = annual coupon / price Yield to maturity = current yield + capital gains yield Example: 10% coupon bond, with semi-annual coupons, face value of 1,000, 20 years to maturity, $1,197.93 price Current yield = $100 / 1197.93 =.0835 = 8.35% Price in 1 yr., assuming no change in required return, = 1,193.68 calculated using 19 years to maturity Capital gain yield = (1193.68 1197.93) / 1197.93 = 0.0035, or 0.35% YTM = 8.35% 0.35% = 8.00%, same as the YTM that we computed earlier for this same bond 5-21 BOND PRICING THEOREMS Bonds of same risk (and maturity) should be priced to yield about the same return, regardless of the coupon rate. Call these Bonds A and B. If you know the price of Bond A, you can calculate A s YTM. In turn, this YTM (i.e., the expected return on A) is a reasonable required rate of return for B, given that A & B have the same risk. Next, use this rate as the required return to calculate PV of B s cash flows and, hence, B s price. This is a useful concept that can be transferred to valuing assets other than bonds. 5-22 11

BOND PRICING WITH A SPREADSHEET Excel offers formulas for finding prices and YTMs. PRICE(Settlement,Maturity,Rate,Yld,Redemption,Frequency,Basis) YIELD(Settlement,Maturity,Rate,Pr,Redemption,Frequency,Basis) Settlement & maturity need to be actual dates Redemption & Pr are entered as % of par value Click on the Excel icon for an example. Alternately, PV(Rate,Nper,Pmt,FV) works pretty decently, too, for Price Additionally, RATE(Nper,PV,FV) works pretty decently, too, for Yield to Maturity 5-23 5.2 MORE ON BOND FEATURES There are two kinds of securities issued by corporations: Equity Represents Ownership Interest Debt Represents Short- or Long-Term Borrowing by the Firm Bonds are classified as Debt 5-24 12

DEBT VERSUS EQUITY Debt Not an ownership interest Creditors do not have voting rights Interest paid on debt is considered a cost of doing business and is taxdeductible on a firm s income statement Creditors have legal recourse if interest or principal pmts. are missed Excess debt can lead to financial distress and bankruptcy Equity Ownership interest Common stockholders vote for the board of directors and other issues Dividends are not considered a cost of doing business and are not tax-deductible Dividends are neither a liability nor an obligation of the firm; stockholders have no legal recourse if dividends are not paid An all-equity firm cannot go bankrupt 5-25 THE BOND INDENTURE Indenture A contract between the issuing company and the bondholders that includes: The basic terms of the bonds (Face Value, Coupon Rate, Maturity Date, Frequency of Coupon Pmts.) The total amount of bonds issued A description of property used as security, if applicable Sinking fund provisions (if applicable) Call provisions (if applicable) Details of protective debt covenants 5-26 13

SAMPLE BOND FEATURES Features of a recent CSX bond issue demonstrate the range of items covered in the bond indenture: 5-27 BOND CHARACTERISTICS Security Collateral secured by financial securities Mortgage secured by real property, normally land or buildings Debentures unsecured debt Notes unsecured debt with original maturity less than 10 years Seniority A firm will often have multiple different bonds outstanding at once In many cases, a hierarchy exists among bonds 5-28 14

BOND CHARACTERISTICS (CONT.) Sinking Funds Funds into which firm makes payments (as security) these funds are used (by a trustee) to reduce a firm s overall bond obligation periodically, across time Call Provisions (if applicable) Deferred Call date after which a callable bond can be called Call Premium difference between the stated call price (per bond) and the actual price of the bond 5-29 BOND CHARACTERISTICS (CONT.) Protective Covenants Rules and restrictions written into the indenture Place constraints on the firm Often written in terms of ratios For example, a firm cannot issue additional long-term debt might be expressed as the debt/equity ratio cannot exceed, say, 0.6 See page 141 of textbook for representative examples of debt covenants 5-30 15

REQUIRED YIELDS The coupon rate depends on the risk characteristics of the bond when issued. Which bonds will have the higher coupon rate, all else equal? Secured debt versus a debenture (unsecured debt) Subordinated debenture versus senior debt A bond with a sinking fund versus one without A callable bond versus a non-callable bond A bond with protective covenants versus a bond without any such covenants 5-31 5.3 BOND RATINGS INVESTMENT QUALITY High-Grade Moody s Aaa and Standard & Poors (S&P) AAA: Capacity to make payments is extremely strong Moody s Aa and S&P AA: Capacity to make payments is very strong Medium-Grade Moody s A and S&P A: Capacity to pay is strong, but more susceptible to changes in circumstances Moody s Baa and S&P BBB: Capacity to pay is adequate, adverse conditions will have more impact on the firm s ability to pay 5-32 16

BOND RATINGS - SPECULATIVE Low-Grade Moody s Ba and B; S&P BB and B Considered speculative investments, with respect to capacity to pay. Very-Low-Grade Moody s C and S&P C and D Considered to have highly uncertain repayment and, in many cases, already in default with principal and interest in arrears. 5-33 5.4 SOME DIFFERENT TYPES OF BONDS There are many types of bonds Some common bonds include: Government Bonds Federal State and Municipal Zero-Coupon Bonds (a.k.a., Pure-Discount Bonds) Floating-Rate Bonds Each is discussed below 5-34 17

GOVERNMENT BONDS Treasury Securities Federal government debt Treasury bills (T-bills) pure discount bonds with original maturity less than one year T-notes coupon debt with original maturity between one and ten years T-bonds coupon debt with original maturity greater than ten years Municipal Securities Debt of state and local governments Varying degrees of default risk, rated similar to corporate debt Interest received is tax-exempt at the federal level 5-35 AFTER-TAX YIELDS Example: A taxable (corporate) bond s YTM is 8.0% & a municipal bond s yield is 6.0%. If you are in a 40% tax bracket, which bond do you prefer? 8.0% (1 40%) = 4.8% The after-tax return on the corp. bond is 4.8%, compared to a 6.0% after-tax return on the muni bond At what tax rate would you be indifferent between the two bonds? 8.0% (1 T) = 6.0% Solve for T = 25% 5-36 18

ZERO-COUPON BONDS Make no periodic interest payments (i.e., have a coupon rate = 0%) The entire yield to maturity comes from the difference between the purchase price and the par value Cannot sell for more than par value Sometimes called zeroes, deep-discount bonds, or original-issue discount bonds (OIDs or OID bonds) Treasury Bills and principal-only Treasury STRIPS (or strips ) are good examples of zeroes 5-37 PURE-DISCOUNT BONDS Information needed for valuing pure discount bonds: Time to maturity (T) = Maturity date - today s date Face value (F) Discount rate (r) Present value of a pure-discount bond s single cash flow: 5-38 19

PURE DISCOUNT BONDS: EXAMPLE Find the value of a 30-year zero-coupon bond with a $1,000 par value and a YTM of 6%. 5-39 FLOATING-RATE BONDS On this type of bond, the coupon rate floats depending on some index value Examples adjustable-rate mortgage bonds & inflation-linked Treasury bills, notes, bonds There is less price risk with floating-rate bonds. The coupon floats, so it is less likely to differ substantially from required return. Coupons may have a collar the rate cannot go above a specified ceiling or below a specified floor. 5-40 20

5.5 BOND MARKETS Primarily over-the-counter transactions with dealers connected electronically Extremely large number of bond issues, but generally low daily volume in single issues Makes getting up-to-date prices difficult, particularly on small-company or municipal issues Treasury securities are an exception 5-41 TREASURY QUOTATIONS (Fig. 5.4) 11/15/39 4.375 130.1250 130.2031 1.4063 2.779 What is the coupon rate on the bond? 43/8% per yr. When does the bond mature? 2039 What is the bid price? 1301/8% of $1000, or $1301.150 What is the ask price? 130.2031% of $1K: $1302.031 How much did the price change from the previous day? Down by 1.4063% of $1K, or $14.063 What is the current yield based on the ask price? 2.779% 5-42 21

5.6 INFLATION AND INTEREST RATES Real rate of interest change in purchasing power Nominal rate of interest quoted (or stated) rate of interest, includes change in purchasing power and inflation The ex ante nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation Fisher notes that investors realize inflation reduces purchasing power and insist on high returns during inflationary times: A rise in the rate of inflation causes the nominal rate to rise just enough so that the real rate of interest is unaffected. 5-43 THE FISHER EFFECT The Fisher Effect defines the relationship between real rates, nominal rates, and inflation. (1 + R) = (1 + r) (1 + h), where R = nominal rate, or stated rate on an investment r = real rate h = expected inflation rate Approximation R r + h Another approximation r R h (1+R) = (1+r) (1+h) 1+R = 1+ r + h + r h 1+R 1+ r + h R r + h 5-44 22

THE FISHER EFFECT: EXAMPLE If an investment states an 18.0% nominal rate and we expect inflation to be 8.0%, what is the underlying real rate of return? (1 + R) = (1 + r) (1 + h) 1.180 = (1 + r) (1.080) Solve for r = 0.0926, or 9.26% Approximation: r 18.0% 8.0% = 10.0% Because the expected inflation is relatively high, there is a significant difference between the actual Fisher Effect and the approximation.. nearly 3/4 percent! 5-45 5.7 DETERMINANTS OF BOND YIELDS Term structure (of interest rates) is the relationship between yields and time to maturity, all else equal. It is important to recognize that we pull out the effect of default risk, different coupons, etc. Yield curve graphical representation of the term structure (see Figure 5.6) Normal upward-sloping, long-term yields are higher than short-term yields Inverted downward-sloping, long-term yields are lower than short-term yields 5-46 23

SAMPLE YIELD CURVE (Fig. 5.7) 5-47 FACTORS AFFECTING REQUIRED RETURN Default-risk premium remember bond ratings Taxability premium remember municipal versus taxable Liquidity premium bonds that have more frequent trading will generally have lower required returns Anything else that affects the risk of the cash flows to the bondholders will affect the required returns. 5-48 24

QUICK QUIZ How do you find the value of a bond, and why do bond prices change? What is a bond indenture, and what are some of the important features? What are bond ratings, and why are they important? How does inflation affect interest rates? What is the term structure of interest rates? What factors determine the required return on bonds? 5-49 25