CHAPTER 7: INTEREST RATES AND BOND VALUATION

7-3 KEY CONCEPTS AND SKILLS

• Define important bond features and types of bonds.

• Explain bond values and yields and why they fluctuate.

• Describe bond ratings and what they mean.

• Outline the impact of inflation on interest rates.

• Illustrate the term structure of interest rates and the determinants of bond yields.

7-4 CHAPTER 7 OBJECTIVES

Part 1

• Define important bond features and types of bonds.

• Explain bond values and yields and why they fluctuate.

• Describe bond ratings and what they mean.

Part 2

• Outline the impact of inflation on interest rates.

• Illustrate the term structure of interest rates and the determinants of bond yields.

7-5 CHAPTER OUTLINE

• Bonds and Bond Valuation

• More about Bond Features

• Bond Ratings

• Some Different Types of Bonds

• Bond Markets

• Inflation and Interest Rates

• Determinants of Bond Yields

7-6 BOND DEFINITIONS

• Par Value (Face Value): Principal amount, repaid at maturity.

• Coupon: Stated interest payment.

• Coupon Rate: Annual coupon divided by face value.

• Maturity Date: Date when the bond will be repaid.

• Yield or Yield to Maturity (YTM): Rate of return required in the market for the bond.

  • Note: The Coupon Rate is only used to determine the amount of Annual Interest the bond pays: $ext{Par Value} imes ext{Coupon Rate ext{(in percent)}} = ext{Annual Interest}$

  • Yield to maturity, required return, and market rate are used interchangeably.

7-7 PRESENT VALUE OF CASH FLOWS AS RATES CHANGE

• Bond Value Formula:

  • $ext{Bond Value} = ext{PV of coupons} + ext{PV of par value}$

  • This can be simplified to:

  • $ext{Bond Value} = ext{PV of annuity} + ext{PV of lump sum}$

• As interest rates increase, present values decrease. Thus, bond prices are inversely related to changes in interest rates.

7-8 VALUING A DISCOUNT BOND WITH ANNUAL COUPONS

• Example:

  • Consider a bond with a coupon rate of 10%, annual coupons, par value of $1,000, with 5 years to maturity and a YTM of 11%.

  • Using the formula:

  • $B = ext{PV of annuity} + ext{PV of lump sum}$

  • $B = 100 rac{1 - [1/(1.11)^5]}{0.11} + rac{1,000}{(1.11)^5}$

  • Calculate:

  • $B = 369.59 + 593.45 = 963.04$

• Calculator Method:

  • Enter:

  • N = 5; I/Y = 11; PMT = 100; FV = 1,000; CPT PV = -963.04

7-9 VALUING A PREMIUM BOND WITH ANNUAL COUPONS

• Example:

  • Review a bond with a 10% annual coupon and a face value of $1,000. 20 years to maturity, and YTM is 8%.

  • Using the formula:

  • $B = ext{PV of annuity} + ext{PV of lump sum}$

  • Calculate:

  • $B = 100 rac{1 - [1/(1.08)^{20}]}{0.08} + rac{1,000}{(1.08)^{20}}$

  • Solve:

  • $B = 981.81 + 214.55 = 1,196.36$

• Calculator Method:

  • Enter:

  • N = 20; I/Y = 8; PMT = 100; FV = 1,000; CPT PV = -1,196.36

  • A Premium Bond sells for more than par value.

7-10 BOND PRICES: RELATIONSHIP BETWEEN COUPON AND YIELD

• If the YTM equals the coupon rate, then the par value equals the bond price.

• If YTM > Coupon Rate:

  • Price < Par Value (Discount Bond)

• If YTM < Coupon Rate:

  • Price > Par Value (Premium Bond)

7-11 BOND PRICING EQUATION

• Present Value of Annuity

• Present Value of Singe Sum

7-12 EXAMPLE 7.1: SEMI-ANNUAL PAYMENTS

• If an ordinary bond has a coupon rate of 14 percent, the owner will get a total of $140 per year, paid in two payments of $70 each, with a YTM of 16% and a maturity of 7 years.

Questions:

1. How many coupon payments are there?

2. What is the semiannual coupon payment?

3. What is the semiannual yield?

4. What is the bond price?

Calculation for Semi-Annual Payments:

• Coupon Payments = 7 years x 2 = 14 payments

• Semiannual Coupon Payment = $rac{1,000 imes 0.14}{2} = 70$

• Semiannual Yield = rac{16 ext{%}}{2} = 8 ext{%}

• Bond Price Calculation:

  • $B = 70 rac{1 - [1/(1.08)^{14}]}{0.08} + rac{1,000}{(1.08)^{14}} = 917.56$

7-16 INTEREST RATE RISK

• Price Risk:

  • Change in price due to changes in interest rates.

  • Long-term bonds have more price risk than short-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 risk than low coupon rate bonds.

7-29 THE BOND INDENTURE

• Contract between the issuer and bondholders:

  • Basic terms of the bonds.

  • Total amount of bonds issued.

  • Description of property used as security (if applicable).

  • Provisions related to sinking funds, calls, and protective covenants.

7-30 BOND CLASSIFICATIONS

• Registered vs. Bearer Forms:

• Security Types:

  • Collateral: Secured by financial securities.

  • Mortgage: Secured by real property.

  • Debentures: Unsecured.

  • Notes: Unsecured debt with an original maturity less than 10 years.

7-35 BOND CHARACTERISTICS AND REQUIRED RETURNS

• Secured Debt vs. Debentures: Secured debt has priority in payment.

• Subordinated Debenture vs. Senior Debt: Subordinated will be paid last.

• Callable Bonds: Face the risk of being called early.

7-36 BOND RATINGS – INVESTMENT QUALITY

• High Grade Bonds:

  • Moody’s Aaa and S&P AAA: Extremely strong capacity to pay.

  • Moody’s Aa and S&P AA: Very strong capacity to pay.

• Medium Grade:

  • Moody’s A and S&P A: Strong capacity but susceptible to changes.

  • Moody’s Baa and S&P BBB: Adequate capacity, sensitive to adverse conditions.

7-38 GOVERNMENT BONDS

• Treasury Securities: Federal government debt.

  • T-bills: Pure discount bonds with maturity of one year or less.

  • T-notes: Coupon debt with maturity between one and ten years.

  • T-bonds: Coupon debt with maturity greater than ten years.

• Municipal Securities: Debt of state and local governments with tax-exempt interest at the federal level.

7-40 ZERO COUPON BONDS

• Bonds that make no periodic interest payments (coupon rate = 0%).

• Yield-to-maturity comes from the difference between purchase price and par value.

• Cannot sell for more than par value.

• Examples include Treasury Bills and principal-only Treasury strips.

7-41 FLOATING-RATE BONDS

• Coupon rates float based on some index value, with less price risk.

• Examples include adjustable-rate mortgages and inflation-linked Treasuries.

7-42 OTHER BOND TYPES

• Include catastrophe bonds, income bonds, convertible bonds, and put bonds.

• Each bond type can have various provisions impacting required returns.

7-44 BOND MARKETS

• Primarily over-the-counter transactions with low daily volume in small issues.

• Treasury securities are liquid exceptions.

7-49 INFLATION AND INTEREST RATES

• Real Rate of Interest: Change in purchasing power.

• Nominal Rate of Interest: Quoted rate of interest changes in dollars.

• Ex Ante Rate: Includes real rate + adjustment for expected inflation.

7-50 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

  • $h$ = expected inflation rate

7-57 FACTORS AFFECTING BOND YIELDS

• Components of bond yield:

  • Real rate of interest ($r^*$)

  • Expected future inflation premium (IP)

  • Interest rate risk premium (MRP)

  • Default risk premium (DRP)

  • Taxability premium (TXP)

  • Liquidity premium (LRP)

7-66 COMPREHENSIVE PROBLEM

• Calculate the price of a $1,000 par value bond with a 6% coupon rate paid semiannually, if:

  • Priced to yield 5%: S = $1,071.77

  • Yield rises to 7%: S = $934.05

  • Current yield at 7% YTM: ext{CY} = 6.42 ext{%}

7-68 END OF CHAPTER 7

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