1、Chapter 7Chapter 7Interest Rates and Interest Rates and Bond ValuationBond ValuationMcGraw-Hill/IrwinCopyright 2013 by The McGraw-Hill Companies,Inc.All rights reserved.Key Concepts and Skills Know the important bond features and bond types Understand bond values and why they fluctuate Understand bo
2、nd ratings and what they mean Understand the impact of inflation on interest rates Understand the term structure of interest rates and the determinants of bond yields7-2Chapter Outline Bonds and Bond Valuation More about Bond Features Bond Ratings Some Different Types of Bonds Bond Markets Inflation
3、 and Interest Rates Determinants of Bond Yields7-3Bond Definitions Bond Par value(face value)Coupon rate Coupon payment Maturity date Yield or Yield to maturity7-4Present Value of Cash Flows as Rates Change Bond Value=PV of coupons+PV of par Bond Value=PV of annuity+PV of lump sum As interest rates
4、increase,present values decrease So,as interest rates increase,bond prices decrease and vice versa7-5Valuing a Discount Bond with Annual Coupons Consider a bond with a coupon rate of 10%and annual coupons.The par value is$1,000,and the bond has 5 years to maturity.The yield to maturity is 11%.What i
5、s the value of the bond?Using the formula:B=PV of annuity+PV of lump sum B=1001 1/(1.11)5/.11+1,000/(1.11)5 B=369.59+593.45=963.04 Using the calculator:N=5;I/Y=11;PMT=100;FV=1,000 CPT PV=-963.047-6Valuing a Premium Bond with Annual Coupons Suppose you are reviewing a bond that has a 10%annual coupon
6、 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?Using the formula:B=PV of annuity+PV of lump sum B=1001 1/(1.08)20/.08+1000/(1.08)20 B=981.81+214.55=1196.36 Using the calculator:N=20;I/Y=8;PMT=100;FV=1000 CPT PV=-1,196.367-7Grap
7、hical Relationship Between Price and Yield-to-maturity(YTM)Bond PriceYield-to-maturity(YTM)7-8Bond Prices:Relationship Between Coupon and Yield If YTM=coupon rate,then par value=bond price If YTM coupon rate,then par value bond price Why?The discount provides yield above coupon rate Price below par
8、value,called a discount bond If YTM coupon rate,then par value bond price Why?Higher coupon rate causes value above par Price above par value,called a premium bond7-9The Bond Pricing Equationttr)(1FVrr)(11-1C Value Bond7-10Example 7.1 Find present values based on the payment period How many coupon p
9、ayments are there?What is the semiannual coupon payment?What is the semiannual yield?B=701 1/(1.08)14/.08+1,000/(1.08)14=917.56 Or PMT=70;N=14;I/Y=8;FV=1,000;CPT PV=-917.567-11Interest Rate Risk Price Risk Change in price due to changes in interest rates Long-term bonds have more price risk than sho
10、rt-term 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 ris
11、k than low coupon rate bonds7-12Figure 7.27-13Computing Yield to Maturity Yield to Maturity(YTM)is the rate implied by the current bond price 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 If you have a f
12、inancial calculator,enter N,PV,PMT,and FV,remembering the sign convention(PMT and FV need to have the same sign,PV the opposite sign)7-14YTM with Annual Coupons Consider a bond with a 10%annual coupon rate,15 years to maturity and a par value of$1,000.The current price is$928.09.Will the yield be mo
13、re or less than 10%?N=15;PV=-928.09;FV=1,000;PMT=100 CPT I/Y=11%7-15YTM with Semiannual Coupons Suppose a bond with a 10%coupon rate and semiannual coupons,has a face value of$1,000,20 years to maturity and is selling for$1,197.93.Is the YTM more or less than 10%?What is the semiannual coupon paymen
14、t?How many periods are there?N=40;PV=-1,197.93;PMT=50;FV=1,000;CPT I/Y=4%(Is this the YTM?)YTM=4%*2=8%7-16Table 7.17-17Current Yield vs.Yield to Maturity Current Yield=annual coupon/price Yield to maturity=current yield+capital gains yield Example:10%coupon bond,with semiannual coupons,face value of
15、 1,000,20 years to maturity,$1,197.93 price Current yield=100/1,197.93=.0835=8.35%Price in one year,assuming no change in YTM=1,193.68 Capital gain yield=(1,193.68 1,197.93)/1,197.93=-.0035=-.35%YTM=8.35-.35=8%,which is the same YTM computed earlier7-18Bond Pricing Theorems Bonds of similar risk(and
16、 maturity)will be priced to yield about the same return,regardless of the coupon rate If you know the price of one bond,you can estimate its YTM and use that to find the price of the second bond This is a useful concept that can be transferred to valuing assets other than bonds7-19Bond Prices with a
17、 Spreadsheet There is a specific formula for finding bond prices on a spreadsheet PRICE(Settlement,Maturity,Rate,Yld,Redemption,Frequency,Basis)YIELD(Settlement,Maturity,Rate,Pr,Redemption,Frequency,Basis)Settlement and maturity need to be actual dates The redemption and Pr need to be input as%of pa
18、r value Click on the Excel icon for an example7-20Differences Between Debt and EquityDebt Not an ownership interest Creditors do not have voting rights Interest is considered a cost of doing business and is tax deductible Creditors have legal recourse if interest or principal payments are missed Exc
19、ess debt can lead to financial distress and bankruptcyEquity 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 not a liability of the firm,and stockholders have no leg
20、al recourse if dividends are not paid An all equity firm can not go bankrupt merely due to debt since it has no debt7-21The Bond Indenture Contract between the company and the bondholders that includes The basic terms of the bonds The total amount of bonds issued A description of property used as se
21、curity,if applicable Sinking fund provisions Call provisions Details of protective covenants7-22Bond Classifications Registered vs.Bearer Forms Security Collateral secured by financial securities Mortgage secured by real property,normally land or buildings Debentures unsecured Notes unsecured debt w
22、ith original maturity less than 10 years Seniority7-23Bond Characteristics and Required Returns The coupon rate depends on the risk characteristics of the bond when issued Which bonds will have the higher coupon,all else equal?Secured debt versus a debenture Subordinated debenture versus senior debt
23、 A bond with a sinking fund versus one without A callable bond versus a non-callable bond7-24Bond Ratings Investment Quality High Grade Moodys Aaa and S&P AAA capacity to pay is extremely strong Moodys Aa and S&P AA capacity to pay is very strong Medium Grade Moodys A and S&P A capacity to pay is st
24、rong,but more susceptible to changes in circumstances Moodys Baa and S&P BBB capacity to pay is adequate,adverse conditions will have more impact on the firms ability to pay7-25Bond Ratings-Speculative Low Grade Moodys Ba and B S&P BB and B Considered possible that the capacity to pay will degenerat
25、e.Very Low Grade Moodys C(and below)and S&P C(and below)income bonds with no interest being paid,or in default with principal and interest in arrears7-26Government Bonds Treasury Securities Federal government debt T-bills pure discount bonds with original maturity of one year or less T-notes coupon
26、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 level7-27Exa
27、mple 7.4 A taxable bond has a yield of 8%,and a municipal bond has a yield of 6%.If you are in a 40%tax bracket,which bond do you prefer?8%(1-.4)=4.8%The after-tax return on the corporate bond is 4.8%,compared to a 6%return on the municipal At what tax rate would you be indifferent between the two b
28、onds?8%(1 T)=6%T=25%7-28Zero Coupon Bonds Make no periodic interest payments(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 b
29、onds(OIDs)Treasury Bills and principal-only Treasury strips are good examples of zeroes7-29Floating-Rate Bonds Coupon rate floats depending on some index value Examples adjustable rate mortgages and inflation-linked Treasuries There is less price risk with floating rate bonds The coupon floats,so it
30、 is less likely to differ substantially from the yield-to-maturity Coupons may have a“collar”the rate cannot go above a specified“ceiling”or below a specified“floor”7-30Other Bond Types Disaster bonds Income bonds Convertible bonds Put bonds There are many other types of provisions that can be added
31、 to a bond and many bonds have several provisions it is important to recognize how these provisions affect required returns7-31Sukuk Sukuk are bonds have been created to meet a demand for assets that comply with Shariah,or Islamic law Shariah does not permit the charging or paying of interest Sukuk
32、are typically bought and held to maturity,and are extremely illiquid7-32Bond 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,particula
33、rly on small company or municipal issues Treasury securities are an exception7-33Work the Web Example Bond quotes are available online One good site is FINRAs Market Data Center Click on the web surfer to go to the site Choose a company,enter it in the search bar,choose Bond in the drop-down,and see
34、 what you can find!7-34Treasury Quotations Highlighted quote in Figure 7.4 15 Nov 24 7.5 137.29 137.31 3.9133 What is the coupon rate on the bond?When does the bond mature?What is the bid price?What does this mean?What is the ask price?What does this mean?How much did the price change from the previ
35、ous day?What is the yield based on the ask price?7-35Clean vs.Dirty Prices Clean price:quoted price Dirty price:price actually paid=quoted price plus accrued interest Example:Consider a T-bond with a 4%semiannual yield and a clean price of$1,282.50:Number of days since last coupon=61 Number of days
36、in the coupon period=184 Accrued interest=(61/184)(.04*1000)=$13.26 Dirty price=$1,282.50+$13.26=$1,295.76 So,you would actually pay$1,295.76 for the bond7-36Inflation and Interest Rates Real rate of interest change in purchasing power Nominal rate of interest quoted rate of interest,change in actua
37、l number of dollars The ex ante nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation7-37The 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 r=real rate
38、h=expected inflation rate Approximation R=r+h7-38Example 7.5 If we require a 10%real return and we expect inflation to be 8%,what is the nominal rate?R=(1.1)(1.08)1=.188=18.8%Approximation:R=10%+8%=18%Because the real return and expected inflation are relatively high,there is significant difference
39、between the actual Fisher Effect and the approximation.7-39Term Structure of Interest Rates Term structure is the relationship between time to maturity and yields,all else equal It is important to recognize that we pull out the effect of default risk,different coupons,etc.Yield curve graphical repre
40、sentation of the term structure Normal upward-sloping;long-term yields are higher than short-term yields Inverted downward-sloping;long-term yields are lower than short-term yields7-40Figure 7.6 Upward-Sloping Yield Curve7-41Figure 7.6 Downward-Sloping Yield Curve7-42Figure 7.7Insert new Figure 7.7
41、here7-43Factors Affecting Bond Yields Real rate of interest Expected future inflation premium Interest rate risk premium Default risk premium Taxability premium Liquidity premium7-44Quick Quiz How do you find the value of a bond,and why do bond prices change?What is a bond indenture,and what are som
42、e 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?7-45Ethics Issues In 1996,allegations were made against Moodys that it was issuing ra
43、tings on bonds it had not been hired to rate,in order to pressure issuers to pay for their service.The government conducted an inquiry,but charges of antitrust violations were dropped.Even though no legal action was taken,does an ethical issue exist?7-46Comprehensive Problem What is the price of a$1,000 par value bond with a 6%coupon rate paid semiannually,if the bond is priced to yield 5%and it has 9 years to maturity?What would be the price of the bond if the yield rose to 7%.What is the current yield on the bond if the YTM is 7%?7-47End of Chapter7-48
