Chapter 5 – Bonds and Bond
Pricing
 Learning Objectives
 Apply the TVM Equations in bond pricing
 Understand the difference between annual
bonds and semi-annual bonds
 Differentiate between different types of bonds
 Calculate yields on bonds Bond Features
 Understand basic features of bonds
 Delineate Bond Ratings
Real vs. Financial Assets
 Real Assets have physical characteristics that
determine the value of the asset
 Size, Shape, Material, Color, etc.
 Price based on the benefits of the physical
characteristics
 Financial Assets physical characteristics are
inconsequential
 Value based on claim to promised or anticipated cash
flows
 TVM concepts used to price financial assets
Application of TVM – Bond Pricing
 Bond instrument is a long-term debt
instrument (long-term liability) of a
company
 Bond issuer promises a specific set of
cash payments in the future
 Coupon (interest) payments
 Principal repayment
 Timing and amount of future cash
payments stated on the bond…see Figure
5.2 for time line of cash flow promises
Application of TVM – Bond Pricing
 Timeline for promised cash flows
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Example, Patel Corporation Bond
$1,000 par value (principal)
8% annual coupon payments (interest)
Twenty year bond
 Principal $1,000 due 12/31/23 is lump sum
 Coupons of $80 annually are annuity
 What is the current value (present value)
of these promised future cash payments?
Application of TVM – Bond Pricing
 Steps to price a bond
 Determine annuity stream
 Coupon Rate times Par Value
 8% x $1,000 = $80
 Find PV of annuity stream
 Find PV of principal repayment
 Add PVs together for bond price
 Patel Corporation Bond
 PV of coupons is $917.59
 PV of principal is $311.80
 Price of Patel Corporation bond is $1,229.39
Application of TVM – Bond Pricing
Key Components of a Bond
 Par Value or Face Value or Principal
 Coupon Rate (annual interest rate
percent)
 Coupon (regular interest payment)
 Maturity Date or Expiration Date (bond is
totally repaid)
 Yield or Yield to Maturity or Discount Rate
Semi-Annual Bonds
 Corporations and governments elect how often
they will make coupon payments
 Most common choice is every six months
 Consistent with interest rates from chapter 4
 Coupon rate is stated annually
 Coupon payment = (Coupon Rate x Par Value) / 2
 Discount rate for TVM is the yield to maturity / 2
 Number of periods (n) is years x 2
 Timeline of promised cash flows, Figure 5.5
page 117
Semi-Annual Bond
Three Methods to Bond Pricing
 Equations or Formula
 Solve the two pieces separately and add them
up (coupons and principal present values)
 TVM Keys on a Calculator
 Note with TI BAII Plus…use of P/Y variable
 Compute price directly
 Spreadsheet
 Function is PV and variables require time
preference
 Compute price directly
Types of Bonds
 By Issuer
 Corporate Bonds – Companies
 Treasury Bonds – U.S. Government
 Municipal Bonds – State and Local
Governments
 By Features – Table 5.1, page 120
 Standard, Semi-Annual, Floating Rate
(coupon rate changes), Zero, Consol,
 Callable, Putable, Convertible
Pricing a Zero-Coupon Bond
 Special Pricing Feature of Zero-Coupon Bond
 No coupon payments
 Priced as Semi-Annual Bond for Principal repayment
 Also know as deep discount bond
 Price of bond is the initial principal
 Difference between price and final payment is interest
on bond
 Interest is implied each year as bond price
changes using the original yield to maturity
 Amortization schedule (Table 5.2) shows implied
interest payments each six months
Finding Yield to Maturity
 Yield to maturity – return on the bond if held to
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maturity
Discount rate for pricing the bond
If price and cash flows are known you can find
YTM
Iterative Process – can not isolate r in TVM
formula
Calculator or Spreadsheet fast and accurate
Relationship of Coupon Rate and YTM (see
Table 5.3)
Bond Features
 Variables
 Price, Principal, YTM, Coupon Rate, Maturity
Date, Frequency of Coupon Payments
 Need all but one variable to determine
missing variable
 Indenture or Deed of Trust (Bond Contract)
 Collateral or Security of Bond
 Real Property is Collateral – Mortgage Bond
 No Collateral - Debenture
Bond Features
 Senior Debt versus Junior Debt
 Older Issue is Senior
 Junior Debt paid off after Senior Debt
 Protective Covenants
 Prohibits actions of bond issuer
 Designed to protect bondholder
 Added Features to Bond (Options)
 Call, Put, Conversion
 Provides issuer or holder future choices
Bond Ratings
 Agencies Rate Bonds
 Ratings based on potential default
 Best rating AAA
 Categories based on ratings (Table 5.4)
 Investment Grade (AAA to BBB- or Baa3)
 Speculative Grade (BB+ or Ba1 to B- or B3)
 Also known as Junk Bonds
 Extremely Speculative (C rating group)
 Default (D rating by Standard and Poor’s)
Quoting Conventions and Markets
 Bonds usually trade in a dealer market
 Dealers state buying and selling prices
 Dealers usually in money center banks
 Some bonds listed on NYSE
 Bonds listed by issuing company
 Bond’s coupon rate and maturity date part of
the bond name
 Current yield
 Volume, Closing Price, and Net Change
Homework
 Problem 1 – Pricing with Annual Coupons
 Problem 2 – Pricing with Semi-Annual
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Coupons
Problem 6 – Yield on Semi-Annual Bonds
Problem 10 – Coupon Rates
Problem 12– Pricing Semi-Annual Bond
Problem 14 – Zero Coupon Bond
Appendix – Government Bonds
 Names of federal government bonds
based on maturity dates at issue:
 U.S. Treasury Bill, maturity less than one year
 U.S. Treasury Note, maturity between two and
ten years
 U.S. Treasury Bonds, maturity over ten years
 Pricing for Notes and Bonds…
 Semi-annual coupon bonds
 Another application of TVM equations
U.S. Treasury Bills
 Treasury Bills are short term pure discount
bills (pay no interest)
 Pricing formula discounts but ignores
compounding and conventional return
calculation methods
 Formula: