Transcript CHAPTER 8 Bonds and Their Valuation

7-1
Bond Basics
 A bond is simply a negotiable IOU, or a loan.
 Investors who buy bonds are lending a specific
sum of money to a corporation, government, or
some other borrowing institution.
 Bonds are often referred to as fixed-income
investments.
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Key Features of a Bond
 Debt instrument issued by a corp. or government.
7-3
Key Features of a Bond
 Par value = face amount of the bond, which is paid at
maturity (assume $1,000).
=
7-4
Key Features of a Bond
 Coupon rate – stated interest rate (generally fixed)
paid by the issuer. Multiply by par to get dollar
payment of interest.
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Key Features of a Bond
 Maturity date – when the bond must be repaid.
 Yield to maturity - rate of return earned on a bond
held until maturity.
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What is reinvestment rate risk?
 Reinvestment rate risk is the concern that
interest rates will fall, and future money will
have to be reinvested at lower rates, hence
reducing income.
7-7
What is interest rate risk?
 Interest rate risk is the concern that interest rates will
rise, and therefore, a reduction in the value of a
security.
7-8
Reinvestment rate risk example
Suppose you just inherited $500,000. You intend to
invest the money and live off the interest.
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Reinvestment rate risk example
 You may invest in either a 10-year bond or a series of
ten 1-year bonds.
 Both bonds currently yield 5%.
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 If you choose the 1-year bond strategy:
 After Year 1, you receive $25,000 in
income and have $500,000 to reinvest.
But, if 1-year rates fall to 3%, your
annual income would fall to $15,000.
 If you choose the 10-year bond strategy:
 You can lock in a 5% interest rate, and
$25,000 annual income.
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Long-term bonds: High interest rate
risk, low reinvestment rate risk.
Short-term bonds: Low interest rate risk,
high reinvestment rate risk.
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Bond Valuation
Compute the value for an IBM Bond with a
6.375% coupon that will mature in 5 years
given that you require an 8% return on your
investment.
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IBM Bond Timeline:
2009
0
2010
2011
1
2
63.75
63.75
2012
3
63.75
2013
4
63.75
5
63.75
1,000.00
7-14
IBM Bond Timeline:
2009
0
2010
2011
1
2
63.75
63.75
$63.75 Annuity for 5 years
2012
3
2013
4
63.75
63.75
5
63.75
1000.00
$1000 Lump Sum in 5 years
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IBM Bond Timeline:
2009
0
2010
2011
1
2
63.75
63.75
$63.75 Annuity for 5 years
2012
3
2013
4
63.75
5
63.75
63.75
1000.00
$1000 Lump Sum in 5 years
= 63.75 PMT 1000 FV 8% I
5N
= PV = 935.12
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Most Bonds Pay Interest Semi-Annually:
What is the value of a bond with a semi-annual
coupon with 5 years to maturity, 9% (nominal)
coupon rate if an investor desires a 10% (nominal)
return?
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Most Bonds Pay Interest Semi-Annually:
e.g. semiannual coupon bond with 5 years
to maturity, 9% annual coupon rate.
Instead of 5 annual payments of $90, the bondholder
receives 10 semiannual payments of $45.
2009
0
2010
1
45
45
2011
2
45
45
2012
3
45
45
2013
4
45
45
5
45
45.00
1000.00
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Most Bonds Pay Interest Semi-Annually:
2009
0
2010
1
45
45
2011
2
45
45
2012
3
45
45
2013
4
45
45
5
45
45.00
1000.00
Compute the value of the bond given that you
require a 10% s-a. return on your investment.
Since interest is received every 6 months, we need to use
semiannual compounding
VB =
45 PMT
1000 FV
5% I
?N
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Most Bonds Pay Interest Semi-Annually:
2009
0
2010
1
45
45
2011
2
45
45
2012
3
45
45
2013
4
45
45
5
45
45
1,000
Compute the value of the bond given that you
require a 10% s-a. return on your investment.
Since interest is received every 6 months, we need to use
semiannual compounding
= PV = 961.39
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Yield to Maturity
2009
0
-1,000
2010
1
80
2011
2
80
2012
2013
3
4
80
80
5
80
1,000
 If YTM > Coupon Rate bond Sells at a
DISCOUNT
 If YTM < Coupon Rate bond Sells at a
PREMIUM
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Yield to Maturity
 If an investor purchases a 6.375% annual
coupon bond today for $966.25 and holds it
until maturity (5 years), what is the expected
annual rate of return ?
2009
0
-966.25
??
+ ??
2010
2011
1
2
63.75
63.75
2012
3
63.75
2013
4
63.75
5
63.75
1000.00
966.25
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Yield to Maturity
• If an investor purchases a 6.375% annual coupon
bond today for $966.25 and holds it until maturity
(5 years), what is the expected annual rate of
return ? Will it be >< than 6.375%?
2009
0
-966.25
??
+ ??
966.25
2010
2011
1
2
63.75
63.75
2012
3
63.75
2013
4
5
63.75
63.75
1000.00
YTMB = 63.75 PMT
1000 FV
5N
-966.25 PV
I=?
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What’s the YTM on a 10-year, 9% annual
coupon, $1,000 par value bond that sells for
$887?
0
rd=?
1
887
10
...
90
PV1
.
.
.
PV10
PVM
9
90
90
1,000
Find rd that “works”!
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INPUTS
OUTPUT
10
N
I/YR
10.91
-887
PV
90
PMT
1000
FV
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Types of Bonds
 Vanilla – fixed coupons, repaid at maturity
 Convertible – can be converted into to stock
 Zero Coupon – pay no explicit interest but instead, sell
at a deep discount
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Types of Bonds
 Junk Bonds – below investment grade
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Bond Ratings
 Moody’s and Standard & Poor’s regularly
monitor issuer’s financial condition and assign a
rating to the debt
Investment
Grade
Below
Investment
Grade
(Junk)
AAA
AA
A
BBB
BB
B
CCC
CC
C
D
Best Quality
High Quality
Upper Medium Grade
Medium Grade
Speculative
Very Speculative
Very Very Speculative
No Interest Being Paid
Currently in Default
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What affects Bond prices?
 Risk
 Interest rates
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What is the “term structure of interest rates”?
What is a “yield curve”?
 Term structure: the relationship between
interest rates (or yields) and maturities.
 A graph of the term structure is called the yield
curve.
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Draw a normal yield curve
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Hypothetical Treasury Yield Curve
Interest
Rate (%)
15
Maturity risk premium
10
Inflation premium
1 yr
10 yr
20 yr
8.0%
11.4%
12.65%
5
Real risk-free rate
Years to Maturity
0
1
10
20
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Current Rates
 Bloomberg
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What factors can explain the shape of this
yield curve?
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What factors can explain the shape of this
yield curve?
 This constructed yield curve is upward
sloping.
 This is due to increasing expected inflation
and an increasing maturity risk premium.
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Default risk
 If an issuer defaults, investors receive less than
the promised return.
 Influenced by the issuer’s financial strength and
the terms of the bond contract.
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