Chapter 7 • Interest Rates and Bond Valuation Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved.
Chapter Outline v Bonds and Bond Valuation v More on Bond Features v Bond Ratings v Some Different Types of Bonds v Bond Markets v Inflation and Interest Rates v Determinants of Bond Yields 7 -1
Bond Definitions v Bond v Par value (face value) v Coupon rate v Coupon payment v Maturity date v Yield or Yield to maturity 7 -2
Terminology of Bond v A company issues a bond with par value $1, 000, 10% coupon rate, and 30 years of time to maturity. v Bond’s coupon = regular interest payments Ø The company has to pay $ 100 interest every year and $1, 000 in 30 years. v Par or face value = the amount that will be paid at the end of loan v Time to maturity = the number of years until face value is paid. 7 -3
Present Value of Cash Flows as Rates Change v Bond Value = PV of coupons + PV of par v Bond Value = PV of annuity + PV of lump sum v Remember, as discount rates (yield to maturity) increase, present values decrease. v So, as discount rates increase, bond prices decrease and vice versa. 7 -4
Valuing a Discount Bond with Annual Coupons v Consider a corporate bond with a coupon rate of 10% and annual coupons. The par value is $1000 and the bond has 5 years to maturity. The yield to maturity is 11%. What is the value of the bond? v Yield to Maturity = Discount rate required in the market on a bond Ø Using the formula: ü B = PV of annuity + PV of lump sum ü B = 100[1 – 1/(1. 11)5] /. 11 + 1000 / (1. 11)5 ü B = 369. 59 + 593. 45 = 963. 04 ü Discount Bond because Par value of Bond > Price of Bond ü It is always a discount bond when coupon rate < YTM. 7 -5
Valuing a Premium Bond with Annual Coupons v Suppose you are looking at a bond that has a 10% annual coupon and a face value of $1000. There are 20 years to maturity and the yield to maturity is 8%. What is the price of this bond? Ø Using the formula: ü B = PV of annuity + PV of lump sum ü B = 100[1 – 1/(1. 08)20] /. 08 + 1000 / (1. 08)20 ü B = 981. 81 + 214. 55 = 1196. 36 ü It is premium bond because Par value of Bond < Price of Bond ü Premium bond when coupon rate > YTM. 7 -6
Bond Price Graphical Relationship Between Price and Yield-tomaturity Yield-to-maturity v Bond characteristics: Coupon rate 8% with annual coupons, Maturity=10 yrs. 7 -7
Relationship between Present Value (Bond Price) and Discount Rate (YTM) v PV = Ø PV is bond price. r = YTM, C and Par are cash flows that bond generates with a coupon rate and Par value. v Inverse relationship between bond price and YTM is interpreted as inverse relationship between PV and discount rate. v Another name of a discount rate is an interest rate. v YTM is an annual interest rate when bondholders hold bonds until the maturity date. v Given the same cash flows which mean the same coupon rate and Par value, the cheaper bond price is, the higher YTM is. Note: Coupon payment is a kind of promised interest payment but it does not reflect the purchasing bond price. 7 -8
Relationship Between Coupon and Yield v TTM = T, Par Value = $1, 000 v Coupon Rate = YTM = 5% v What is Coupon Payment? Ø Coupon rate*1000 = $ 50 v What is Future Value of Cash Flows generated by Bond at time of T? v FV = FV(Coupon Payment)+ Par Value v FV = 7 -9
Coupon Rate = Yield To Maturity v FV at t=T = 1000(1. 05)T v PV at t=0 = FV/(1. 05)T =1000 v PV = 1, 000 = Par Value v Coupon Rate = Promised interest rate Ø The coupon rate does not reflect the purchasing price of a bond. v Yield to Maturity = Discount rate v Promised interest = Discount rate Ø Bond price = Par value v Promised interest rate > Discount rate Ø Bond price > Par value v Promised interest rate < Discount rate Ø Bond price < Par Value 7 -10
Bond Prices: Relationship Between Coupon and Yield v If YTM > coupon rate, then bond price < par value Ø Why? interest rate is lower than discount rate. Ø Selling at a discount, called a discount bond v If YTM < coupon rate, then par value < bond price Ø Why? Ø Selling at a premium, called a premium bond 7 -11
Coupon Rate and Yield v c = coupon rate, r = yield to maturity v If c=r, then Present value is equal to Par value. 7 -12
Semiannual Coupons (Ex. 7. 1) v Bonds issued in the US usually make coupon payments twice a year. v If an ordinary bond has a coupon rate of 16%, $80 are paid twice a year v Coupon rate and YTM are also quoted like APRs Ø 16% quoted coupon rate ü 8% rate per six months Ø YTM = 14% ü Semiannual YTM = 7 % Ø Which value is higher, par value or bond price? 7 -13
Example 7. 1 v A corporate bond with 14% coupon rate and semi-annual coupon payment. TTM=7 yrs. YTM is quoted as 16%. v Find present values based on the payment period Ø Ø How many coupon payments are there? 14 What is the semiannual coupon payment? 7% What is the semiannual yield? 8% B = 70[1 – 1/(1. 08)14] /. 08 + 1000 / (1. 08)14 = 917. 56 v What should we know to price a bond? Ø YTM, Par value, Coupon Rate, Time to maturity 7 -14
Computing Yield-to-maturity v In Reality, we know bond price but do not know YTM. v Yield-to-maturity is the rate implied by the current bond price. v Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity. 7 -15
YTM with Annual Coupons v Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $928. 09. Ø Ø Ø Will YTM be more or less than 10%? Try 11% PV= 100(1 -(1/1. 11)15)/0. 11+1000/(1. 11)15 If PV>928. 09, then raise r If PV<928. 09, then reduce r 7 -16
YTM with Semiannual Coupons v Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $1197. 93. Ø Is YTM more or less than 10%? Ø What is the semiannual coupon payment? Ø How many periods are there? Ø YTM = 4%*2 = 8% v Current Yield == annual coupon / price Ø 100/1197. 93 =. 0835 Ø If you buy this bond at 1197. 93, you will earn 8. 35% interests, when bond price is regarded as investment. 7 -17
Table 7. 1 7 -18
Useful Concept of YTM v YTM is an interest rate when bondholders hold bonds up to the maturity date. Ø YTM reflects bond price which can be a purchasing price. v Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate. Ø Highly risky bond will have higher YTM. Ø Negative relation between bond risk and YTM. v If you know the price of one bond, you can estimate its YTM and use that to find the price of the second bond. 7 -19
Why is YTM an actual interest? v Coupon rate is c % and YTM is r. v Present Value is the bond price. v Bond price x (1+r)T = Future value Ø If you buy bond at the bond price and hold it to the maturity, then you will earn r % interests annually. Ø YTM on a bond is the interest rate you will earn if you hold the bond to maturity. 7 -20
Differences Between Debt and Equity • Debt • Not an ownership interest • Creditors do not have voting rights. • Interest is considered a cost of doing business and is tax deductible. • Interest or principal payments are liability of the company. • Excess debt can lead to financial distress and bankruptcy. • Equity • Ownership interest • Common stockholders vote for the board of directors, M&A decision • Dividends are not considered a cost of doing business and are not tax deductible. • Dividends are not a liability of the firm and stockholders have no legal recourse if dividends are not declared to be paid. • An all equity firm can not go bankrupt. 7 -21
The Bond Indenture v Contract between the company and the bondholders and includes Ø Ø Ø The basic terms of the bonds The total amount of bonds issued A description of property used as security, if applicable Repayment Arrangement: Sinking Fund Call provisions if any. Details of protective covenants 7 -22
Bond Classifications v Registered vs. Bearer Forms v Security Ø Ø Collateral – secured by (financial) assets Mortgage – secured by real property, normally land or buildings Debentures – unsecured with maturity of 10 years or more Notes – unsecured debt with original maturity less than 10 years v Seniority: Senior vs. subordinated debt 7 -23
Bond Characteristics and Required Returns v The yield to maturity depends on the risk characteristics of the bond when issued. v Which bonds will be riskier to bondholders? Ø Ø Secured debt versus a debenture Subordinated debenture versus senior debt A bond with a sinking fund versus one without it A callable bond versus a non-callable bond v The risker bond is, the higher YTM is. 7 -24
Bond Ratings – Investment Quality v Moody and S&P: Bond rating firms v Their evaluation is based on how likely the firm is to default and the protection of creditors in the event of a default. v Risk of change in bond prices: 1) market interest change 2) possibility of default v Bond rating firms only consider the possibility of default. 7 -25
Bond Ratings – Investment Quality v High Grade Ø Moody’s Aaa and S&P AAA – capacity to pay is extremely strong Ø Moody’s Aa and S&P AA – capacity to pay is very strong v Medium Grade Ø Moody’s A and S&P A – capacity to pay is strong, but more susceptible to changes in circumstances Ø 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 7 -26
Bond Ratings - Speculative v Low Grade Ø Moody’s Ba, B, Caa and Ca Ø S&P BB, B, CCC, CC Ø Considered speculative with respect to capacity to pay. The “B” ratings are the lowest degree of speculation. v Very Low Grade Ø Moody’s C and S&P C – bonds with no interest being paid Ø Moody’s D and S&P D – in default with principal or interests in arrears 7 -27
Investment vs. Junk Bond v Investment-grade bond: at least BBB or Baa v Junk Bond: below BBB or Baa v Junk Bond’ price movement is similar to that of an ordinary stock. Ø High volatility of bond price 7 -28
Government Bonds v Treasury Securities Ø Federal government debt Ø T-bills – pure discount bonds with original maturity of one year or less Ø T-notes – coupon debt with original maturity between one and ten years Ø T-bonds coupon debt with original maturity greater than ten years v Municipal Securities Ø Debt of state and local governments Ø Varying degrees of default risk, rated similar to corporate debt Ø Interest received is usually tax-exempt at the federal level 7 -29
Ex. 7. 4 v Taxable bonds: 8% yield v Municipal bond of comparable risk and maturity : 6% yield v For an investor in a 40% tax bracket, which bond are preferred? Ø 8 (1 -0. 4) = 4. 8% Ø Municipal bond is preferred. v What is break-even tax rate? Ø 8 (1 -t) = 6 Ø t =. 25 7 -30
Zero-Coupon Bonds v Make no periodic interest payments (coupon rate = 0%) v The entire yield-to-maturity comes from the difference between the purchase price and the par value. v Cannot sell for more than par value v Sometimes called zeroes, deep discount bonds, or original issue discount bonds (OIDs) v Treasury Bills are good examples of zeroes 7 -31
Floating Rate Bonds v Coupon rate floats depending on some index value such as Treasury Bill interest rate or the 30 year Treasury bond rate. Ø Examples – adjustable rate mortgages and inflationlinked Treasuries v There is less price risk with floating rate bonds Ø The market interest is negatively related to bond prices. Ø A coupon rate is positively related to bond prices. Ø The coupon floats, so it is less likely to differ substantially from the yield-to-maturity. v Coupons may have a “collar” – the rate cannot go above a specified “ceiling” or below a specified “floor” 7 -32
Other Bond Types v Convertible bonds: exchange these bonds for stocks before maturity at holder’s option. Ø In what situation, do bondholders want to convert bonds into stocks? increase in the stock price or decrease? v Disaster (catastrophe) bonds: Pay interest and principal as usual unless claims reach a certain threshold for a single disaster. v Income bonds: Coupons are paid to bondholders only if the firm’s income is sufficient. Ø Price of an ordinary bond vs price of an income bond if others are same. 7 -33
Other Bond Types v Callable bond: allows the company to repurchase or “call” part or all of the bond issue at stated prices over a specific period. v Put bonds: allow bondholder to force the issuer to buy the bond at the stated price. Ø Bondholders have rights to sell put bonds at the stated price. v There are many other types of provisions that can be added to a bond and many bonds have several provisions – it is important to recognize how these provisions affect required returns (or risk). 7 -34
Bond Markets v Primarily over-the-counter transactions with dealers connected electronically § Not as transparent as stock market § No centralized reporting of transaction v Extremely large number of bond issues are traded but generally low daily volume in single issues § Retail bond trading is now allowed. v Getting up-to-date prices are difficult, particularly on small company or municipal issues. v Treasury securities are an exception. Ø Large trading volume of Treasury securities. 7 -35
Treasury Quotations v Highlighted quote in Figure 7. 4 Ø Ø Ø Ø 8 Nov 21 132: 23 132: 24 -12 5. 14 What is the coupon rate on the bond? 8% When does the bond mature? 2021 Nov. What is the bid price? 132 and 23/32 % What is the ask price? 132 and 24/32 % How much did the price change from the previous day? – 12/32 What is the yield based on the ask price? 5. 14% v Bid price means the price that investors can sell. Ø In other words, a bid price is the price that a dealer offers for his buying. v Ask price does the price that investors can buy. Ø An ask price is the price that a dealer offers for his selling. 7 -36
Clean vs. Dirty Prices v Clean price: quoted price = net of accrued interest v Dirty price: price actually paid = quoted price plus accrued interest v Example: Consider T-bond in previous slide, assume today is July 15, 2005 Ø Number of days since last coupon = 61 Ø Number of days in the coupon period = 182 Ø Accrued interest = (61/182)(. 04*100, 000) = 1340. 07 v Prices (based on ask): Ø Clean price = 132, 750 Ø Dirty price = 132, 750 + 1, 340. 07 = 134, 090. 07 v So, you would actually pay $134, 090. 07 for the bond 7 -37
Inflation and Interest Rates v Real rate of interest – change in purchasing power v Nominal rate of interest – quoted rate of interest, change in purchasing power and inflation v The ex-ante nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation 7 -38
The Fisher Effect v The Fisher Effect defines the relationship between real rates, nominal rates and inflation v (1 + R) = (1 + r)(1 + h), where Ø R = nominal rate Ø r = real rate Ø h = expected inflation rate v Approximation ØR≈r+h 7 -39
Example 7. 6 v If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate? v R = (1. 1)(1. 08) – 1 =. 188 = 18. 8% v Approximation: R ≈ 10% + 8% = 18% 7 -40
Term Structure of Interest Rates v Term structure is the relationship between time to maturity and yields, all else equal. v It is important to recognize that we pull out the effect of default risk, different coupons, etc. Ø Term structure is based on pure discount bonds. v Yield curve – graphical representation of the term structure Ø Normal – upward-sloping, long-term yields are higher than shortterm yields Ø Inverted – downward-sloping, long-term yields are lower than short-term yields 7 -41
Figure 7. 6 – Upward-Sloping Yield Curve 7 -42
Figure 7. 6 – Downward-Sloping Yield Curve 7 -43
Factors Affecting Required Return (YTM) v Default risk premium – remember bond ratings v Taxability premium – remember municipal versus taxable v Liquidity premium – bonds that have more frequent trading will generally have lower required returns v Anything else that affects the risk of the cash flows to the bondholders will affect the required returns 7 -44
YTM and Risk of Bond A Bond B Coupon 10% TTM 20 yrs 20 yrs Price ($) 1197. 93 849. 515 u YTM= 2*4 = 8% for Bond A and YTM=2*6 =12% for Bond B. u Why is YTM of bond A different from YTM of bond B? u Are YTMs discount rates? u Can we also regard YTM as interest rates? u The market requires a higher return (YTM) to hold Bond B than Bond A. 7 -45
YTM and Risk of Bond v FV of Bond A in year 20 = 50[(1. 04)40 -1]/0. 04 +1000 = 5, 751. 3 v FV of Bond B in year 20 = 50[(1. 06)40 -1]/0. 06+1000 = 7, 738 v 1197. 93 (1+r)40 = 5, 751. 3 -> r = 4% v 849. 515 (1+r)40 =7, 738 -> r = 6% v When you buy Bond A and B respectively at $ 1197. 93 and $ 849. 515, you will earn 8% and 12% YTM for 20 years. v YTM is the interest rate that bondholders can earn when they hold the bond by the maturity date. 7 -46
Quick Quiz v How do you find the value of a bond and why do bond prices change, given a fixed coupon rate and Par value? v What is a bond indenture and what are some of the important features? Ø YTM is included in a bond indenture? v What are bond ratings and why are they important? v How does inflation affect interest rates? v What is the term structure of interest rates? v What factors determine the required return on bonds? 7 -47
Chapter 7 • End of Chapter Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved.
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