Chapter 12
Principles of Bond
Valuations and
Investments
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
Principles of Bond Valuation and
Investment

Fundamentals of the Bond Valuation Process

Rates of Return

The Movement of Interest Rates


Investment Strategy: Interest Rate
Considerations
Bond Swaps
12-2
Fundamentals of the Bond
Valuation Process

The price of a bond represents the
present value of future interest
payments plus the present value of
the par value of the bond at
maturity
12-3
Fundamentals of the Bond
Valuation Process
n
Ct
Pn
V 

n
1  i 
t 1 1  i 
V=
n=
t=
Ct =
Pn =
i=
Market value or price of the bond
Number of periods
Each period
Coupon or interest payment for each period, t
Par or maturity value
Interest rate in the market
12-4
Fundamentals of the Bond
Valuation Process



Assume a bond pays 10% interest or $100 for 20
years and has a par or maturity value of $1,000.
The interest rate in the marketplace is assumed
to be 12%.
The present value of the bond, using annual
compounding, is:
12-5
Fundamentals of the Bond
Valuation Process



Assume a bond pays 10% interest or $100 for 20
years and has a par or maturity value of $1,000.
The interest rate in the marketplace is assumed
to be 12%.
The present value of the bond, using annual
compounding, is:
12-6
Present Value of an Annuity of $1
(coupon payments)
12-7
Present Value of an Single Amount of $1
(par or maturity value)
12-8
Calculating Bond Prices Using Tables
t n
Ct
Pn
V 

t
n
(1  i)
t 1 (1  i )








Present Value of Coupon Payments (Ct)
(from Table 12-1 or Appendix D)
Present value of Maturity Value (Pn)
(from Table 12-2 or Appendix C)
n = 20, i = 12 %
n = 20, i = 12%
$100 x 7.469 = $746.90
$1,000 x 0.104 = $104.00
Present value of coupon payments = $746.90
Present value of maturity value
= $104.00
Value of bond
= $850.90
12-9
Calculating Bond Prices
Using Excel
Please click on the Excel icon
12-10
Other Methods of Calculating
Bond Prices


Using financial calculator
Using the Internet (Online bond
calculations)
12-11
Fundamentals of the Bond
Valuation Process



Assume a bond pays 10% interest (5%
semiannually, or $50 every six months, for 20
years and has a par or maturity value of $1,000.
The interest rate in the marketplace is assumed
to be 12%.
The present value of the bond, using semiannual
compounding, is:
12-12
Fundamentals of the Bond
Valuation Process



Assume a bond pays 10% interest (5%
semiannually, or $50 every six months, for 20
years and has a par or maturity value of $1,000.
The interest rate in the marketplace is assumed
to be 12%.
The present value of the bond, using semiannual
compounding, is:
12-13
Excerpts from Bond Value Table
12-14
Rates of Return





Current Yield
Yield to Maturity
Yield to Call
Anticipated Realized Yield
Reinvestment Assumption
12-15
Current Yield

Annual interest payment divided by
price of bond

Example:
• 10% coupon rate $1,000 par value bond
selling at $950
$100
Current yield 
 10.53%
$950

Ignores capital gains or losses
12-16
Yield to maturity (YTM)

Measure of return that considers
• Annual interest rate received
• Difference between current bond price and maturity
value
• Number of years to maturity

The interest rate at which you can discount the
• Future coupon payments and
• Maturity value
• To arrive at quoted price of the bond

Assumption: all coupons are reinvested at the same
(YTM) rate.
12-17
Yield to Maturity Example


Assume the market price of the bond is $850.90,
coupon or interest payment is $100, maturity
value is $1,000 and number of periods is 20.
What interest rate will force the future cash
inflows to equal $850.90?
12-18
The Formula for Approximate
Yield to Maturity
Y 
Y 

Pn-V
n
C(0.6)
t
V+ (0.4) Pn
+++
Approximare yield to maturity
V = Market value or price of the bond
n = Number of periods
Ct = Coupon or interest payment for each period, t
Pn = Par or maturity value
12-19
Yield to Call


To the extent a debt instrument may
be called in before maturity, a
separate calculation for yield to call
may be necessary
Yield to call value is determined by:
• the coupon rate,
• the length of time to the call date,
• the call price, and
• the market price.
12-20
Yield to Call Example

20-year bond was initially issued at 11.5% interest
rate, and was callable at $1,090 five years after issue

Two years later, the yield to maturity on the bond is
9.48%, and the bond is selling for $1,180


An investor who buys the bond two years after issue
can have his bond called back after three more years at
$1,090
To compute yield to call, determine the approximate
interest rate that will equate a $1,180 investment
today with $115 (11.5%) per year for the next three
years plus a payoff or call price value of $1,090 at the
end of three years.
12-21
Yield to Call Example continued

Yield to call = 7.43%
• 205 basis points less than yield to
maturity

If market price is equal to or greater
than call price, investor should do a
separate calculation for yield to call
12-22
Yield to Call Calculation An Alternative Method Click on the Bonds icon
Y = yield to maturity expressed in %
R = coupon rate (or i)
P = price of the bond.
M = the number of years to Call date.
The relation is:
M
P
R
i 1 



Y 

1
100 
i
100








Y 

1
100 
M
12-23
Anticipated Realized Yield

Return over the expected holding
period
12-24
The Formula for Approximate
Anticipated Realized Yield
= Coupon payment
Yr
=
Pr  V
Ct 
nr
(0.6)V  (0.4) Pr
= Realized price
V = Market price
Yr = Anticipated realized yield
Ct = Coupon payment
Pr = Realized price
V = Market price
nr = Number of periods to realization
12-25
Reinvestment Assumption
Yield to Maturity
 Yield to Call
 Anticipated Realized Yield

Assume that the determined rate also
represents an appropriate rate for
reinvestment of funds.
12-26
Computing Bond Yields
Yield Measure
Purpose
Nominal Yield
Current yield
Measures the coupon rate
Measures current income rate
Promised yield to
maturity
Promised yield to
call
Measures expected rate of return
for bond held to maturity
Measures expected rate of return
for bond held to first call date
Realized
(horizon) yield
Measures expected rate of return
for a bond likely to be sold prior to
maturity.
12-27
The Movement of Interest Rates



Investors wishing to make substantial
profit in bond market must try to
anticipate direction of interest rates
Short-term rates may not move in the
same direction as long-term rates
Interest rates — coincident indicator
12-28
Factors Influencing Interest Rates


Inflationary expectations
Demand for funds by:
• Individuals
• Businesses
• Government


Desire for savings
Federal Reserve policy
12-29
Term Structure of Interest Rates


Depicts the relationship between
maturity and interest rates
Sometimes called the yield curve
12-30
Figure 12-1 Term Structure of Interest
Rates
Yield
Yield
Inverted
Normal
a
b
Maturity
Maturity
Yield
Yield
Humped
c
Maturity
Flat
d Maturity
12-31
Investment Strategy: InterestRate Considerations
Bond-Pricing Rules
 Example of Interest-Rate Change
 Deep Discount verses Par Bonds
 Yield Spread Considerations

12-32
Expectations Hypothesis

Any long-term rate is an average of
the expectations of future short-term
rates over the applicable time
horizon
12-33
Liquidity Preference Theory


The shape of the term structure
curve tends to be upward sloping
more than any other pattern.
Reflects recognition that long
maturity obligations are subject to
greater price-change movements
when interest rates change
• Investors demand higher return for
holding longer-term maturities
12-34
Market Segmentation Theory



Banks prefer short-term liquid
securities
Life insurance companies prefer
long-term bonds
These two institutions often put
pressure on short-term and longterm rates
12-35
Relative Volatility of Short-Term
and Long-Term Interest Rates
12-36
Investment Strategy: Interest Rate
Considerations

When investor believes interest rates
will fall
• Buy long-terms bonds to maximize price
movement with rate change
12-37
Change in Market Prices of Bonds for Shifts in
Yields to Maturity
12 Percent Coupon Rate
6 Percent Coupon Rate
12-38
Bond Pricing Rules
1. Bond prices and interest rates are
inversely related.
2. Prices of long-term bonds are more
sensitive to change in YTM than shortterm bonds.
3. Bond price sensitivity increases at a
decreasing rate as maturity increases.
12-39
Bond Pricing Rules continued
4. Bond prices are more sensitive to a
decline in market YTM than to a rise in
market YTM
5. Prices of low-coupon bonds are more
sensitive to a change in YTM than highcoupon bonds.
6. Bond prices are more sensitive when YTM
IS low than when YTM is high.
12-40
Deep Discount versus Par Bonds

Significant discount from par value

Coupon rate significantly less than
the prevailing rates of fixed-income
securities with similar risk profiles

Generally trade at lower YTM than
bonds selling at close to par
12-41
Yield Spread Considerations


Yield spread between different
grades of bonds
At certain phases of business cycle,
yield spread changes
• Higher during recession
• Lower during recovery
12-42
Yield Spread Differentials on LongTerm Bonds
12-43
Bond Swaps


Investor sells one bond and uses the
proceeds to purchase another bond, often
at the same price.
Investors engage in bond swaps
• to take a tax loss by selling one bond at a
loss but then preserve their investment by
simultaneously buying a similar bond.
• to obtain a higher yield and return on their
bond investments.
Click on the bonds icon for :
An Investor's Guide to Bond Swapping
12-44
A detailed tutorial of the more
complex concepts and calculations
for trading bonds. Additional/advanced
• Bond Pricing
• Yield
 Current Yield
 Yield to Maturity
• Term Structure of Interest Rates
• Duration and much more
Click on the investopedia
12-45
Yield to Maturity – HYPERLINK
Additional/advanced

What is my yield to maturity?
Click on the Bonds icon
12-46
A sample of the numerous useful
bond websites – click on the icons

New York Stock
Exchange ------
Terms Used in bond Calculators ----------->
12-47
Click on the following hyperlinks

1. Treasury Direct

2. Public debt

3. Online Financial
Tutorial
12-48