Lecture 5:

Bond Valuation
Professor Chiyoung Cheong
 Debt versus Equity
• Debt • Equity
• Not an ownership interest • Ownership interest
• No voting rights • Common stockholders vote to
• Interest is tax-deductible elect the board of directors and
• Creditors have legal recourse on other issues
if interest or principal • Dividends are not tax deductible
payments are missed • Dividends are not a liability of the
• Excess debt can lead to firm until declared. Stockholders
financial distress and have no legal recourse if dividends
bankruptcy are not declared
• An all-equity firm cannot go
bankrupt
 Bond Definitions
• Bond
• Debt contract
• Interest-only loan
• Par value (face value)
~ $1,000
• Coupon rate
• Coupon payment
• Maturity date
• Yield to maturity
Key Features of a Bond
• Par value:
• Face amount
• Re-paid at maturity
• Assume $1,000 for corporate bonds
• Coupon interest rate:
• Stated interest rate
• Usually = YTM at issue
• Multiply by par value to get coupon
payment
Key Features of a Bond
• Maturity:
• Years until bond must be repaid
• Yield to maturity (YTM):
• The market required rate of return for bonds of
similar risk and maturity
• The discount rate used to value a bond
• Return if bond held to maturity
• Usually = coupon rate at issue
• Quoted as an APR
The Bond Indenture “Deed of Trust”
Contract between issuing company and bondholders includes:
–Basic terms of the bonds
–Total amount of bonds issued
–Secured versus Unsecured
–Sinking fund provisions
–Call provisions
•Deferred call
•Call premium
–Details of protective covenants
Bond Ratings and Bond Quality
•High Grade
–Moody’s Aaa and S&P AAA –capacity to pay is extremely strong
–Moody’s Aa and S&P AA –capacity to pay is very strong
•Medium Grade
–Moody’s A and S&P A –capacity to pay is strong, but more susceptible to changes in
circumstances
–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
•Low Grade: Considered speculative
–Moody’s Ba, B, Caa and Ca and S&P BB, B, CCC, CC
–The “B” ratings are the lowest degree of speculation.
•Very Low Grade: C and below
Government Bonds
• Treasury Securities = Federal government debt
• Treasury Bills (T-bills)
• Pure discount bonds
• Original maturity of one year or less
• Treasury notes
• Coupon debt
• Original maturity between one and ten years
• Treasury bonds
• Coupon debt
• Original maturity greater than ten years
Bond Markets
• Primarily over-the-counter transactions with dealers
connected electronically
• Extremely large number of bond issues, but generally
low daily volume in single issues
• Getting up-to-date prices difficult, particularly on
small company or municipal issues
• Treasury securities are an exception
Bond Value
• Bond Value = PV(coupons) + PV(par)
• Bond Value = PV(annuity) + PV(lump sum)
• Remember:
• As interest rates increase present values decrease
( r → PV  )
• As interest rates increase, bond prices decrease
and vice versa
Valuation of Coupon Bonds:
•A typical example: What is the market price of a corporate bond
that has a coupon rate of 9%, a face value of $1,000 and matures
exactly 10 years from today if the interest rate is 10% compounded
semiannually?
•Timeline of coupons and face value repayment looks like this

• The cash flow from the bond look like:

• a) an annuity: 20 identical payments of $45 for 10 years (or 20
semi-annual payments)
• b) Plus a lump-sum amount of $1000 at the end of the period
The Bond-Pricing Equation
 1 
 1- (1+ YTM )t  F
Bond Value = C +
 (1+ YTM )
t
 YTM
 
PV(Annuity) PV(lump sum)

C = Coupon payment; F = Face value

r=discount rate (yield-to-maturity)

Current yield=Coupon/Bond Value

Texas Instruments BA-II Plus
N = number of periods to maturity
I/Y = period interest rate = YTM
PV = present value = bond value
PMT = coupon payment
FV = future value = face value = par value
Bond Prices:
Relationship Between Coupon and Yield

• Coupon rate = YTM  Price = Par

• Coupon rate < YTM  Price < Par
• “Discount bond” … Why?
• Coupon rate > YTM  Price > Par
• “Premium bond” … Why?
 The Bond-Pricing Equation
Adjusted for Semi-annual Coupons

 1 
 1- 
C (1+ YTM /2)2t F
Bond Value =  +
2 YTM /2  (1 + YTM 2t
/2)
 
C = Annual coupon payment  C/2 = Semi-annual coupon
YTM = Annual YTM (as an APR)  YTM/2 = Semi-annual YTM
t = Years to maturity  2t = Number of 6-month
periods to maturity
 Zero Coupon Bonds
• Make no periodic interest payments (coupon rate = 0%)
• Entire yield-to-maturity comes from the difference
between the purchase price and the par value (capital
gains)
• Cannot sell for more than par value
• Sometimes called zeroes, or deep discount bonds
• Treasury Bills and U.S. Savings bonds are good examples
of zeroes
The Yield to Maturity (YTM)

•The Yield to maturity (YTM) of a bond is the discount rate

that equates the today’s bond price with the present value of
the future cash flows of the bond.
•The yield to maturity is the average annual rate of return that
a bondholder will earn if bond held to maturity
•Usually coupon rate at issue equals YTM
•We use YTM as the discount rate to value a bond
Computing Yield-to-Maturity (YTM)
• Yield-to-maturity (YTM) = the market required
rate of return implied by the current bond price
• With a financial calculator,
• Enter N, PV, PMT, and FV
• Remember the sign convention
• PMT and FV need to have the same sign (+)
• PV the opposite sign (-)
• CPT I/Y for the yield
Yield to Maturity of a Zero-Coupon Bond
–The yield to maturity for a zero-coupon bond is the return
you will earn as an investor by buying the bond at is current
market price, holding the bond to maturity, and receiving the
promised face value payment.
–Yield to Maturity of an n-Year Zero-Coupon Bond
Graphical Relationship Between
Price and Yield-to-maturity
1500
1400
1300
Bond Price

1200
1100
1000
900
800
700
600
0% 2% 4% 6% 8% 10% 12% 14%

Yield-to-maturity
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
Interest Rate Risk
• 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
 Bond Value ($) vs Years
remaining to Maturity
Premium CR>YTM

YTM = CR M
1,000

CR<YTM
Discount

30 25 20 15 10 5 0
Figure 6.2
Bond Characteristics and
Required Returns
• Coupon rate
• (risk characteristics of the bond when issued)
• Usually ≈ yield at issue
• Which bonds will have the higher coupon,
all else equal?
• Secured debt versus a debenture
• Subordinated debenture versus senior debt
• A bond with a sinking fund versus one without
• A callable bond versus a non-callable bond
 Corporate Bond Quotations
ABC 8.375 Jul 15, 2033 100.641 8.316 362 30 763,528

• What company are we looking at?

• What is the coupon rate? If the bond has a $1000 face
value, what is the coupon payment each year?
• When does the bond mature?
• What was the trading volume on that day?
• What is the quoted price? (Ask price)
• How does the bond’s yield compare to a comparable
Treasury note/bond?
Treasury Quotations
Treasury Quotations
• Highlighted quote in Figure 6.3

5/15/2030 6.250 150.7188 150.7500 .8906 2.713

• When does the bond mature?

• What is the coupon rate on the bond?
• 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 previous day?
• What is the YTM based on Ask price?
 Factors Affecting Required Return

• Default risk premium – bond ratings

• Taxability premium – municipal versus taxable
• Liquidity premium – bonds that have more frequent trading
will generally have lower required returns
• Maturity premium – longer term bonds will tend to have
higher required returns.
Anything else that affects the risk of the cash flows to the
bondholders will affect the required returns