Chapter 6
The Valuation and Characteristics of Bonds
VALUATION
A systematic process through which the price at which
a security should sell is established
The security's intrinsic value
THE BASIS OF VALUE
Real assets (houses, cars) have worth due to the services they provide
Financial assets are pieces of paper and depend for value on the present value of future
cash flows
Differences of opinion about the value of securities arise from different assumptions about
future cash flows and the interest rate for taking present values
Stock prices are hardest to pin down because future dividends and prices are never
guaranteed.
INVESTMENTS AND RETURNS
Investing: Using any resource in a way which generates future benefits rather than
immediate satisfaction
Financial Investing: Putting money to work to earn more money by entrusting it to an
organization which pays the owner for its use
Methods of entrusting money
lending - debt investment - bonds
ownership - equity investment - stock
Return on One Year Investments
Return is what the investor receives
Can be expressed as a dollar amount or as a rate
Rate of return (required rate of return) is what the investor receives divided by what was
invested
6-1
BONDS
Bonds represent a debt relationship:
The issuing company borrows and the bond buyer lends.
Bonds enable one company to borrow from many investors at once
Firms raise money through L-T securities therefore the value of these securities is
important to the financial manager.
The valuation of these securities is affected by investing, financing, and dividend decisions.
Terminology
Promissory note - Legal evidence of the debt
Term or Maturity - Time until repayment
Par or face value - Loan principal
Non-amortized debt - pays interest only until maturity
New issues, seasoned issues
Characteristics:
Type
(1) Classify by security behind it
Secured Bonds
Backed by the value of specific assets
Mortgage Bonds - Backed by real estate
Debentures
Unsecured bonds
Rely on general creditworthiness
Riskier than secured debt of the same company
Usually issued at higher coupon rates
Subordinated Debentures - Senior Debt
Priority in the event of failure
Junk Bonds:
High risk - High return
Issued by weak or new companies
Often used to finance acquisitions
(2) classify as to whether senior or junior
(3) Equipment Trust Certificates
(4) Collateral Trust Bonds
(5) Income bonds
(6) Pollution Control & Industrial Revolution
6-2
Features
(1) Indenture
(2) Trustee
(3) Call feature
(4) Bond refunding
(5) Sinking fund
(6) Equity Linked Debt
Convertible Bonds
Can be converted into stock
Exercise if the stock's price rises enough to make converted shares
worth more than the bond
"Sweetener"
Warrants
(7) Sizes of issue
(8) Coupon rates
(9) Maturities
(10) Bond ratings
Investment Grade (top 4 ratings)
BOND RATINGS
Ratings assess default risk based on analysis of issuing firm by rating agency
Main agencies: Moody's and S&P
Rating Symbols and Grades
Moody's
Aaa
Aa
A
S&P
AAA
AA
A
Implication
Highest quality,
extremely safe
Good quality,
Baa
Ba
B
BBB
BB
B
"Investment grade"
Poor quality,
risky
Caa
C
CCC
D
Low quality, very
risky
Investment grade: Above Baa/BBB
6-3
Why Ratings are Important
Investors require higher returns on riskier issues
Ratings measure default risk and are therefore a determinant of the rates investors
demand
A lower rating implies the firm's cost of borrowing is higher
The Significance of
the Investment Grade Rating
Most bonds are purchased by institutional investors
Required by law to make only conservative investments
Can deal only in investment grade bonds
This limits the market for lower rated debt
The Differential Over Time
The rate spread tends to be larger when rates are high
High rates are associated with tough economic times
when marginal companies tend to fail
The risk of default is greater so investors demand bigger differential in bad times
The spread itself is an economic indicator
A high differential is a signal that harder times
are coming
Bond Indentures
Agreements in bond contracts
Control default risk by prohibiting risky activity by the issuing company
Sinking Funds
Ensure funds are available for repayment of principal
Periodic deposits
Random calls
Serial bonds
6-4
Advantages of debt financing
(1) relatively low cost
(2) leverage affect on EPS
(3) owners maintain greater control
Disadvantages
(1) increase financial risk
(2) restrictions placed on firm by lenders
Corporate Bonds
most traded on OTC
large issues are traded on listed exchanges
Government Debt
T-bills
T-notes
T-bonds
Price Quotations of bonds (corporate and government):
Percentage of Par
INTERNATIONAL BOND MARKET
Eurobonds--bonds issued by U.S. Corporation denominated in dollars but sold to investors
outside the U.S. (Mainly bearer bonds)
Foreign Bonds--written by investment banking syndicates from a single country
denominated in the currency of the country and issued in another country
6-5
Bond Valuation
In terms of the time value of money:
Invest PV at rate k and receive future cash flows of
principal = PV, and
interest = kPV
at the end of a year, so
FV1 = PV + kPV
FV1 = PV(1+k)
Think of PV as the price of the security
with future cash flows FV1
Then the rate of return (k) is the interest rate which makes the present value of the future
cash flows equal to the price
The Return on Longer Term Investments
Usually involves a number of cash flows at different times
The concept remains the same
Return is the discount rate which makes the present value of
all future cash flows equal to the price.
Example: If pay $363 for a guarantee of $200 next year and $250 the following year, the
return is (approximately) 15% because:
0
1
2
$200
$250
PV=$363
6-6
Bond Cash Flows: The Coupon Rate and Payment
The interest rate paid on the bond's face amount ($1000)
Generally fixed for the life of the bond
Coupon payment - dollar amount of interest paid, usually semiannually
BOND VALUATION - BASIC IDEAS
Coupon rates are fixed for bond's life and are
chosen close to market rates at the time of issue.
But market rates change constantly.
In order to be salable among investors after their initial issue, bonds must offer new
investors the market return.
Accomplished by market price changes
E.g.: If market rate goes up, bond's price goes down. Price drop increases a new buyer's
yield because bond's cash flows are fixed
Price drops until yield = new market rate
6-7
Fundamental rule: Bond prices and interest rates move in opposite directions
As interest rates rise, bond prices lower, but this is not 1-1 relationship.
Coupon Rate Relationship
YTM
6-8
Kd < Coupon Rate  Premium
Kd > Coupon Rate  Discount
Kd = Coupon Rate  Par
DETERMINING THE PRICE OF A BOND
PB = PV interest payments + PV principal repayment
Annuity
+
Single Amount
Two time value problems together
0
1
2
3
n-2
PMT PMT PMT
n-1
n
PMT PMT PMT
Annuity
FV
(for bonds the par value
or selling price)
Amount
PVA=PMT[PVFAk,n]
PV=FV[PVFk,n]
PB = PMT[PVFAk,n] + FV[PVFk,n]
THE BOND PRICING FORMULA
m
Ct
Price of Bond = 
(1 + i )t
t=1
6-9
Two Cash Streams
Annuity (interest)
1 - (1 +
PV a = A [
i - nm
)
m
]
i
m
Single Sum
PV s =
S
i
(1 + )nm
m
Interest paid semiannually therefore need to adjust interest rate and period.
Most bonds pay interest semiannually, so periods along the time line are half years
PB = PMT[PVFAk,n] + FV[PVFk,n]
PMT (the interest payment) is calculated by applying the coupon rate to
the face value and dividing by two
k = market rate divided by two
n = years from now until maturity times two
6-10
Bond Interest Rates
Coupon rate determines PMT
Coupon Rate = Interest in dollars
Par Value
The current yield is the annual interest payment divided by the bond's
current price.
Not used in pricing calculations
Current Yield = Interest in dollars
Price of Bond
k = the current market rate the bond must yield k to new investors
Rate at which PV is taken
k = YTM – Yield to Maturity
YTM= Capital gain (loss) + income from interest payments
YTM (Exact)
Bond Price =
C1
C2
C + Par
+
+ ....+ m
1
2
(1 + YTM ) (1 + YTM )
(1 + YTM )m
YTM (approximate)
Par - Price
number of yrs maturity
Price + Par
2
Annual Interest dollars +
YTM app =
6-11
Solve for Price
The Emory Corporation issued an 8%, 25 year bond 15 years ago at its $1,000 par
value. Comparable bonds are yielding 10% today. What must Emory's bond sell
for to yield 10% (YTM) to the buyer? Interest is paid semiannually.
PB = PMT[PVFAk,n] + FV[PVFk,n]
PMT = (Coupon Rate  Face Value)/2
= (.08  $1,000)/2
= $40.00
n = 10 years  2 = 20
k = 10%/2 = 5%
FV = $1,000
PB = $40[PVFA5,20] + $1,000[PVF5,20]
A-4: PVFA5,20 = 12.4622
A-2: PVF5,20 = .3769
PB = $40[12.4622] + $1,000[.3769]
= $498.49 + $376.90
= $875.39
Double Check for reasonableness: Estimate the answer first based on whether the
market rate is above or below the coupon rate.
MATURITY RISK REVISITED
Maturity risk arises from the fact that bond prices vary (inversely)
with interest rates. Also called price risk and interest rate risk.
Longer term bond prices change more in response to interest rate movements than
shorter term bond prices, so maturity risk implies the degree of risk is related to the
maturity (term) of the bond.
6-12
Interest Rate Increase from 8% to 10% Assume all bonds were originally priced at
1000 and had an 8% coupon.
Time to Maturity
2 yrs
5 yrs
10 yrs
20 yrs
Price
$964.54
$922.77
$875.39
$828.36
Drop from $1,000
$35.46
$77.23
$124.61
$171.64
AS TIME GOES BY
What would happen to the price of the Emory bond if interest rates didn't change
again for the remainder of its life?
FINDING THE YIELD AT A GIVEN PRICE
PB = PMT[PVFAk,n] + FV[PVFk,n]
PB is given and k is the unknown
Can't solve algebraically - two tables at once
Trial and error (iterative) approach
Annual Interest + [ P m Po ]
n
YTM =
Po + P m
2
Approximate formula indicates an approximate yield.
Plug approximate YTM into formula and check to see if calculated Po = actual Po
if not:
(1) Try higher rate if a calculated price is greater than actual price or vice versa.
(2) Bracket the actual rate with one calculated higher and one calculated lower
rate than the actual rate, then interpolate.
i.e. Coupon = 7%
Po = 840 N = 10 years (Interest paid annually)
70 +
YTM A =
1000 - 840
10
= 9.35%
1840
2
6-13
.09 = 871.26
x = 840
.10 = 816.15
.01
.1 - x
=
816.15 - 871.26 816.15 - 840
.01
.1 - x
=
- 55.11 - 23.85
9.56%
Zero Coupon Bonds
Pay no interest
Price is present value of principal repayment
Interest is taxable even though not received
Zero Coupon Bonds
(Zero, Bullet, Discount)
Po =
Pm
(1 + r )m
= Pm ( PVIF x% m, )
i.e.
Pm = 1000
Po = 352
m = 10
352 = 1000(PVIFx%,10)
.352 = (PVIFx%,10)
11% = x
Console - Perpetual bonds
CALL PROVISIONS (FEATURES)
6-14
Allow bond issuing firms to "call in" and pay off bonds
Protects company against a drop in interest rates
Refunding debt
Pay off high interest bond with new low rate borrowing
A call premium (penalty) included to compensate
investors for loss of high interest
Premium usually declines as maturity approaches
In problems, state premium in terms of coupon rate
Bond's early life is usually call protected
THE EFFECT OF A CALL PROVISION ON PRICE
Bonds may appear certain to be called when protected period is over
Usually due to a large drop in interest rates
Traditional bond valuation includes cash flows which aren't likely to happen after the protected period
Special procedure is required
6-15
Bond's Life
0
1
2
3
4
5
6
7
8
9
10
PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT
FV
Now
End
of Call
Protect
FV
+
Call Premium
Maturity
Unlikely
to Occur
Valuation
to Call
Valuation to Maturity
Figure 6-5 Valuation of a Bond Subject to Call
TM 6-10 Slide 2 of 3
6-16
Valuing The Sure-To-Be-Called Bond
Solve for YTC
Rate
Maturity
Yld
2000-05* May
81/4s
Bid
Ask
Bid Chg
105:25
106:1
+4
7.53*
* May 2000-05 Bond matures on 2005 but is callable starting in 2000
** Yld
For callable bonds the YTM is calculated in one of two ways
a. to first call date when the asked price is above par
b. to maturity date when the asked price is equal to or below par
YTC
1. Substitute the Call Price for Par
2. Substitute the number of years to first call for maturity years
Use a Modified Formula
PB(call) = PMT[PVFAk,m] +CP[PVFk,m]
where
m = number of periods to call
CP = Call Price
= Face Value + Call Premium
6-17
Example 6-4
Northern Timber issued a callable, $1,000, 25-year bond five years ago at an
18% coupon rate. Call protected for first 10 years; Call premium is one
year's interest at coupon rate; Market rate is now 8%. What is bond's price
with and without the call?
Solution:
Normal valuation to maturity
n = 20yrs  2 = 40
Now
0
10
FV = $1,000
20
30
40
50
Semiannual
Periods
Now Call
CP = FV + Call Prem = $1,180
Valuation to call
m = 5yrs  2 = 10
TM 6-11 Slide 1 of 3
Without call:
PB = PMT[PVFAk,n] + FV[PVFk,n]
PMT = (.18  $1,000)/2 = $90
n = 20  2 = 40, k = 8%/2 = 4%
FV = $1,000
PB = $90[PVFA4,40] + $1,000[PVF4,40]
= $90[19.7928] + $1,000[.2083]
= $1,781.35 + $208.30
= $1989.65
The price represents the present value of the issuer's cash flow commitment if the
bond isn't called.
6-18
With call:
PB(call) = PMT[PVFAk,m] + CP[PVFk,m]
PMT = .18  $1,000 / 2 = $90
m = 5  2 = 10, k = 8% / 2 = 4%
CP = $1,000 + .18($1,000) = $1,180
PB(call) = $90[PVFA4,10] + $1,180[PVF4,10]
= $90[8.1109] +$1,180[.6756]
= $729.98 + $797.21
= $1,527.19
The Refunding Decision
Compare the interest savings from calling with the cost of making the call and
issuing a new bond
Dangerous Bonds With Surprising Calls
Obscure call features buried in contract terms,
e.g., sinking funds
Risky Issues
Sometimes bonds sell for prices far below those indicated by valuation techniques
Implies the company that issued the bond is in financial trouble
THE INSTITUTIONAL CHARACTERISTICS OF BONDS
Bearer bonds or registered bonds
Transfer agent
Owners of record
6-19
Treasury Bill Yields
Money market instruments sold on a discount basis are sensitive to changes in interest
rates but not to the same degree as bonds with coupon payments.
Discount Yield =
360 100 - P
[
]
n
100
Treasury Bill Yields
Equivalent Yield =
365 100 - P
[
]
n
P
i.e. Discount yield on bill 8.6% with 80 days till maturity.
.086 =
360 100 - Price
80
100
.086 =
365 100 - Price
80
Price
8.6 = 4.5 [ 100 - Price ]
4.5 [Price] = 447.4
P = 98.48
Equivalent Yield = 8.6%
.0188 = 100 - Price
Price
1.0188 [Price] = 100
Price = 98.15
6-20
Factors Affecting Overall Interest Rates and Bond Prices
Strong economic growth tends to place upward pressure on interest rates (drop in bond
prices)
Weak economic growth tends to place downward pressure on interest rates (increase in
bond prices)
Money supply increase (demand not affected) downward pressure on rates
Money supply increase (demand increases for funds) upward pressure--inflation
Oil prices have major impact upon prices
drop in oil prices--lower interest rates
Weaker dollar (everything else constant) increase inflationary expectations (prices of
imports increase); thus increase in rates
6-21