Chapter Twelve
Principles of Bond Valuations and Investments
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McGraw-Hill/Irwin
© 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.
Bond: Players and Factors



Indebted entity
Investors
Certificate (or bond)
• Interest rate (coupon rate)
• Coupon payment dates (semi-annually)
• Maturity date
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Fundaments of the Bond Valuation
Process
Rates of Return
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Current Yield
Yield to Maturity
Yield to Call
Anticipated Realized Yield
Reinvestment Assumption
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Yield



Principal (amount invested)
Dollar amount of return on investment
Percentage return (at an annual rate)
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Current Yield
Current bond price
 Annual coupon rate
 Ignores capital gains or losses.

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Current Yield Calculation
Current Yield =
Annual_Dol lar_Intere st_Paid  X100%
Market_Pri ce
Current Yield Calculation Example
An example might be a 10% coupon rate
$1000 par value bond selling for $950.
The current yield would be:
$100 / $950 = 10.53%
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Yield to maturity (YTM)

Return (coupon payments received)

Maturity value

Market price

YTM equates the sum of the present
value of the cash flows of the bond with
its market price (IRR)
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Risk vs. Expected Return
Rate of return (high/Low)
 Degree of risk
• Default risk
• Bond ratings

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Calculating Bond Prices and YTM
Method 1 - using Tables
t n
Ct
Pn
V 

t
n
(1  i )
t 1 (1  i )




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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
Calculating Bond Prices –
Method 2 – Using Equation
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

Based on the principle of:
Time value of money
Present Value
Future Value
Interest rate
---------
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Fundamentals of the Bond
Valuation Process –
The Value of a Bond
n
V

t 1
Ct
(1+i)
t
+
Pn
n
(1+i)
V = Market value or price of the bond
n = Number of periods
t = Each period
C t = Coupon or interest payment for each period, t
Pn= Par or maturity value
i = interest rate in the market
Yield to Maturity (YTM)




Current market price
Par value
Coupon interest rate
Time to maturity
Assumption: all coupons are reinvested at
the same (YTM) rate.
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The Formula for Approximate
Yield to Maturity
Y 
Y 
Pn-V
Ct 
n
+ V+ (0.4) P
++(0.6)
n
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
Yield to Call


Call date
Yield to call value is determined by:
• the coupon rate,
• the length of time to the call date,
and
• the market price.
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Yield to Call Example
Assume a 20-year bond was initially
issued at 11.5% interest rate, and after
two years, rates have dropped. Let us
assume the bond is currently selling for
$1,180, and the yield to maturity on the
bond is 9.48%. However, the investor
who purchases the bond for $1,180 may
not be able to hold the bond for the
remaining 18 years because the issue can
be called. Under theses circumstances,
yield to maturity may not be the
appropriate measure of return over the
expected holding period.
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Yield to Call Calculation – Example cont.
In the present case, we assume the bond
can be called at $1,090 five years after
issue. Thus, the 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, we
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.
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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
Y i

1
100 
i 1 




100
Y  M

1
100 







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
Figure 12-1 Term Structure of Interest
Rates
Yield
Yield
Normal
a
b
Maturity
Maturity
Yield
Yield
Inverted
c
Maturity
d Maturity
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Investment Strategy: InterestRate Considerations
Bond-Pricing Rules
 Example of Interest-Rate Change
 Deep Discount verses Par Bonds
 Yield Spread Considerations
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Investment Strategy: Interest-Rate
Considerations (7 rules)

Bond Pricing Rules
• 1. Bond prices and interest rates are
inversely related.
• 2. Prices of long-term bonds are more
sensitive to a change in yields to
maturity than short-term bonds.
• 3. Bond price sensitivity increases at a
decreasing rate as maturity increases.
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Investment Strategy: Interest-Rate
Considerations (cont.)
• 4. Bond prices are more sensitive to a
decline in market YTM than to a rise in
YTM.
• 5. Prices of low-coupon bonds are more
sensitive to a change in YTM than high
coupon bonds.
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Investment Strategy: Interest-Rate
Considerations (cont.)
• 6. Bond prices are more sensitive when
YTM is low than when YTM is high.
• 7. Margin trading magnifies profits and
losses of bond investments by a factor
of 1/(margin requirement).
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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
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Bond Swaps
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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.
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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.
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A sample of the numerous useful
bond websites – click on the links

New York Stock Exchange

U.S. Securities and Exchange
Commission

Terms Used in Bond Calculators
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Click on the following hyperlinks
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1. Treasury Direct
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2. Public debt
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3. Online Financial Tutorial
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