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Bonds and Their Valuation
Chapter 7 Bonds and Their Valuation Key Features of Bonds Bond Valuation Measuring Yield Assessing Risk 7‐1 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. What is a bond? • A long‐term debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond. 7‐2 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Bond Markets • Primarily traded in the over‐the‐counter (OTC) market. • Most bonds are owned by and traded among large financial institutions. • The Wall Street Journal reports key developments in the Treasury, corporate, and municipal markets. Online edition lists trading for each day the most actively‐traded investment‐grade, high‐yield, and convertible bonds. 7‐3 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Key Features of a Bond • Par value: face amount of the bond, which is paid at maturity (assume $1,000). • Coupon interest rate: stated interest rate (generally fixed) paid by the issuer. Multiply by par value to get dollar payment of interest. • Maturity date: years until the bond must be repaid. • Issue date: when the bond was issued. • Yield to maturity: rate of return earned on a bond held until maturity (also called the “promised yield”). 7‐4 © 2012 Cengage Learning. -
Bond Valuation Reading
Bond valuation A reading prepared by Pamela Peterson Drake ___________________________________________________________ O U T L I N E 1. Valuation of long-term debt securities 2. Issues 3. Summary ___________________________________________________________ 1. Valuation of long-term debt securities Debt securities are obligations to repay an amount borrowed, along with some compensation for the time value of money and risk. The borrowers may be corporations, the government, or governmental agencies. The lenders may be corporations, governments, pension funds, mutual funds, or individual investors. Long-term debt securities, such as notes and bonds, are promises by the borrower to repay the principal amount. Notes and bonds may also require the borrower to pay interest periodically, typically semi- annually or annually, and generally stated as a percentage of the face value of the bond or note. We refer to the interest payments as coupon payments or coupons and the percentage rate as the coupon rate. If these coupons are a constant amount, paid at regular intervals, we refer to the security paying them as having a straight coupon. A debt security that does not have a promise to pay interest we refer to as a zero-coupon note or bond. The value of a debt security today is the present value of the promised future cash flows -- the interest and the maturity value.1 Therefore, the present value of a debt is the sum of the present value of the interest payments and the present value of the maturity value: Present value of a bond = present value of interest payments + present value of maturity value To calculate the value of a debt security, we discount the future cash flows -- the interest and maturity value -- at some rate that reflects both the time value of money and the uncertainty of receiving these future cash flows. -
Teaching Bond Valuation: a Differential Approach Demonstrating Duration and Convexity
JOURNAL OF ECONOMICS AND FINANCE EDUCATION • Volume 7 • Number 2 • Winter 2008 13 Teaching Bond Valuation: A Differential Approach Demonstrating Duration and Convexity TeWahn Hahn, David Lange 1 ABSTRACT A traditional bond pricing scheme used in introductory finance texts is simple enough but not necessarily intuitive. The differential approach suggested here presents premiums (discounts) as coupon interest over- (under-) payments to make bond pricing dynamics more intuitive. The primary pedagogic benefit is the differential approach demonstrates the more sophisticated bond valuation concepts of duration and convexity. Introduction The basic bond valuation formula is traditionally presented as a straight forward discounted cash flow application. The relationship between required yield and price is generally stated as “Bond prices and yields are inversely related: as yields increase, bond prices fall; as yields fall, bond prices rise” (Bodie, Kane and Marcus 2009. pg. 514). A second bond pricing observation is “An increase in a bond’s yield to maturity results in a smaller price change than a decrease in yield of equal magnitude” (Bodie, Kane and Marcus 2009. pg. 514). Both observations are attributable to Malkiel (1962). A pedagogic difficulty is students may be able to solve for the bond price given a change in interest rates, but may not fully understand the financial dynamics for bond price premiums and discounts. Further, the differential impact of an increase (decrease) in yield to maturity on bond price may be even more unclear. This paper first demonstrates the traditional bond valuation approach. Second, a differential bond price premium and discount conceptual approach is described. Third, the traditional and differential approaches are compared. -
1 Bond Valuation
Structure of fixed income securities • A Fixed Income Security promises to pay fixed coupon payments at a prespecified dates and a fixed principal amount Bond Valuation (the face value) at the maturity date. • When there are no coupon payments then the bond is called a •The Structure of fixed income securities zero coupon bond or a pure discount bond. •Price & yield to maturity (ytm) •Term structure of interest rates Payments of a “N” year bond with annual coupon C and face value F •Treasury STRIPS •No-arbitrage pricing of coupon bonds payments: C C …………… C C+F Time: 0 1 2 ………….. N-1 N Coupon Bonds The U.S. government issues bonds • The coupon payments on coupon bonds are typically stated as a Default free bonds issued by the government: percentage of the principal (or face value) paid per year. Treasury bills have an initial maturity less than one year and are all • If coupon payments are made n times per year, then the coupon discount bonds amount is (c x F)/n, where c is the coupon rate and F is the face Treasure notes have initial maturities between one and ten years and value. pay coupons Treasury bonds have initial maturities longer than ten years and pay Understanding the terms: U.S. Treasury Notes and Bonds are coupons typically issued with face value of $10,000, and pay semi-annual coupons. Assume a 30 year coupon rate of 7.5%. What payments Default free bonds issued by government sponsored agencies do you receive from buying this bond? Fannie Mae: Federal National Mortgage Association Ginnie Mae: Government National Mortgage Association You receive a coupon payment of (0.075 x $10,000)/2 = $375 twice a Freddie Mac: Federal Home Loan Mortgage Corporation year and on the maturity date you will receive the coupon of $375 Federal Home Loan Bank plus the principal of $10,000. -
Bond Valuation and Analysis
BOND VALUATION AND ANALYSIS Bond Valuation and Analysis Bond Valuation & Analysis The Fixed Income Market Is Large… $45,000 $40,000 ) $40 trillion $35,000 billions $30,000 $32 trillion $25,000 $25 trillion $20 trillion $20,000 $15,000 $10,000 US Fixed Income Market $5,000 Oustanding Debt / Market Capitalization (US $ in US Stock Market $0 2007 2008 2009 2010 2011 2012 2013 2014 2015 Sources: Bond data from the Securities Industry and Financial Markets Association; Stock data from the World Bank. Bond Valuation & Analysis Layout of the Course ● Chapter 1: Bond Valuation ● Chapter 2: Estimating Yield to Maturity ● Chapter 3: Duration and Convexity ● Chapter 4: Comprehensive Example Bond Valuation & Analysis What You Should Know ● Introduction to R ● Intermediate R ● No prior experience with financial analysis necessary! Bond Valuation & Analysis About me ● Advise clients on valuation and other financial issues primarily related to litigation ● Previously taught investments, investment management, and corporate finance ● Author of Analyzing Financial Data and Implementing Financial Models Using R BOND VALUATION AND ANALYSIS See you in the course! BOND VALUATION AND ANALYSIS Welcome to the Course! Bond Valuation & Analysis About me ● Advise clients on valuation and other financial issues related to litigation ● Author of Analyzing Financial Data and Implementing Financial Models Using R Bond Valuation & Analysis Bonds ● Debt instrument ● Repay borrowed amount + interest ● Allows us to focus on fundamental concepts of bond valuation Bond Valuation -
Bond Valuation-14 Bond Valuation
All India Satellite Classes: CA AadityaCA Aaditya Jain Jain 011-47665500 BOND VALUATION-14 BOND VALUATION 1. INTRODUCTION/WHY BOND VALUATION? Bond valuation is the process of determining the fair price of a bond. As with any security or capital investment, the fair value of a bond is the present value of the Future cash flows it is expected to generate. Bonds or Debentures are long term loan which pay periodical interest and principal amount upon maturity. Determining the value of the bond is an application of the present value concept . 2. BASIC BOND RELATED TERM Value of Bond : The amount which the investor will pay today to purchase the bond.It is also known as Current Value Of Bond / Present Value Of Bond / Intrinsic Value Of Bond / Theoretical Value Of Bond / Equilibrium Value Of Bond Coupon Rate : The annual interest rate on a bond.It is the rate at which company pays interest. Coupon Amount: The amount of interest which is paid by the company . Amount Of Interest = Face Value Of Debenture Coupon Rate Years to Maturity : The year on which the principal amount of a bond is fully repaid is known as years to maturity Note :If the question is silent about the maturity period of any investment say preference shares , bonds , debentures etc then we will assume such investmet as irredeemable or perpetual . Yield: The rate of return required by the investor of a bond.It is also known as Yield To Maturity / Cost Of Debt / Discount Rate for debentureholder / Kd / Going Rate Of Interest /Market Interest Rate Face Value : It is also called Par Value.Interest is paid on face value.Unless otherwise stated bond is assumed to be issued at Face Value or Par Value . -
Firm and Corporate Bond Valuation: a Simulation Dynamic Programming Approach*
CUADERNOS DE ECONOMÍA , VOL. 41 (D ICIEMBRE), PP .345-360, 2004 FIRM AND CORPORATE BOND VALUATION: A SIMULATION DYNAMIC PROGRAMMING APPROACH* AUGUSTO CASTILLO* Pontificia Universidad Católica de Chile This paper analyzes corporate bond valuation of a straight bond, and the convertibility feature, when interest rates are stochastic and the firm value is determined by the interaction of a series of stochastic variables. The sensitivity of the corporate debt value to some key parameters is also explored. The methodology applied here is based on a hybrid of simulation and dynamic programming proposed by Raymar and Zwecher in 1997 to value financial American-type options. This methodology proves to be extremely efficient to value American-type options when the sources of uncertainty are numerous. JEL: C15, G13, C32 Keywords: Valuation, Options, Bond, Equity 1. INTRODUCTION This paper is concerned with the valuation of different types of corporate bonds, in an scenario characterized by many stochastic variables interacting to determine the value of the assets of a company, and where interest rates are also assumed to follow a stochastic process. The valuation methodology proposed here is a hybrid of simulation and dynamic programming and corresponds to an extension of the method proposed by Raymar and Zwecher in 1997 to value financial American-type options. The main advantage of the proposed methodology is that it proves to be extremely efficient to value American-type options when the sources of uncertainty are numerous. The paper is organized as follows: In Section 2 a review of the related literature in options valuation methodologies and corporate bond valuation methods are presented. -
Fixed Rate Bond Valuation and Risk
Fixed Rate Bond Valuation and Risk FinPricing Fixed Rate Bond Summary ▪ Fixed Rate Bond Introduction ▪ The Use of Fixed Rate Bond ▪ Valuation: Yield-to-Maturity Approach ▪ Valuation: Credit Spread Approach ▪ Practical Guide ▪ A Real World Example Fixed Rate Bond Fixed Rate Bond Introduction ▪ A bond is a debt instrument in which an investor loans money to the issuer for a defined period of time. ▪ The investor will receive coupons paid by the issuer at a predetermined interest rate at specified dates before bond maturity. ▪ The bond principal will be returned at maturity date. ▪ A fixed rate bond is usually a long term paper. ▪ Bonds are usually issued by companies, municipalities, states/provinces and countries to finance a variety of projects and activities. Fixed Rate Bond The Use of Fixed Rate Bond ▪ Fixed rate bonds generally pay higher coupons than interest rates. ▪ An investor who wants to earn a guaranteed interest rate for a specified term can choose fixed rate bonds. ▪ The benefit of a fixed rate bond is that investors know for certain how much interest rate they will earn and for how long. ▪ Due to the fixed coupon, the market value of a fixed rate bond is susceptible to fluctuation in interest rate and therefore has a significant interest rate risk. ▪ The long maturity schedule and fixed coupon rate offers an investor a solidified return. ▪ The real value of a fixed rate bond is also susceptible to inflation rate given its long term Fixed Rate Bond Valuation: Yield-to-Maturity Approach ▪ There are two types of bond valuation approaches in the market: yield-to-maturity approach and credit spread approach. -
Fabozzi Course.Pdf
Asset Valuation Debt Investments: Analysis and Valuation Joel M. Shulman, Ph.D, CFA Study Session # 15 – Level I CFA CANDIDATE READINGS: Fixed Income Analysis for the Chartered Financial Analyst Program: Level I and II Readings, Frank J. Fabozzi (Frank J. Fabozzi Associates, 2000) “Introduction to the Valuation of Fixed Income Securities,” Ch. 5 “Yield Measures, Spot Rates, and Forward Rates,” Ch. 6 “Introduction to Measurement of Interest Rate Risk,” Ch. 7 © 2002 Shulman Review/The Princeton Review Fixed Income Valuation 2 Learning Outcome Statements Introduction to the Valuation of Fixed Income Securities Chapter 5, Fabozzi The candidate should be able to a) Describe the fundamental principles of bond valuation; b) Explain the three steps in the valuation process; c) Explain what is meant by a bond’s cash flow; d) Discuss the difficulties of estimating the expected cash flows for some types of bonds and identify the bonds for which estimating the expected cash flows is difficult; e) Compute the value of a bond, given the expected cash flows and the appropriate discount rates; f) Explain how the value of a bond changes if the discount rate increases or decreases and compute the change in value that is attributable to the rate change; g) Explain how the price of a bond changes as the bond approaches its maturity date and compute the change in value that is attributable to the passage of time; h) Compute the value of a zero-coupon bond; i) Compute the dirty price of a bond, accrued interest, and clean price of a bond that is between coupon -