Transcript Chapter 6

Chapter 6
Bonds
and Bond
Valuation
Copyright © 2010 Pearson Prentice Hall. All rights reserved.
Learning Objectives
1. Understand basic bond terminology and apply the time value
of money equation in pricing bonds.
2. Understand the difference between annual and semiannual
bonds and note the key features of zero-coupon bonds.
3. Explain the relationship between the coupon rate and the
yield to maturity.
4. Delineate bond ratings and why ratings affect bond prices.
5. Appreciate bond history and understand the rights and
obligations of buyers and sellers of bonds.
6. Price government bonds, notes, and bills.
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6-2
6.1 Application of the Time Value of
Money Tool: Bond Pricing
•
•
•
•
Bonds – Long-term debt instruments
Provide periodic interest income – annuity series
Return of the principal amount at maturity – future lump sum
Prices can be calculated by using present value techniques, i.e.,
discounting of future cash flows
• Combination of present value of an annuity and of a lump sum
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6-3
Table 6.1 Bond Information August 1,
2008
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6-4
6.1 (A) Key Components of a Bond
• Par value: Principal or face
value; typically $1000
• Coupon rate: Annual rate of
interest paid.
• Coupon: Regular interest
payment received by holder
per year.
• Maturity date: Expiration date
of bond when par value is
paid back.
• Yield to maturity: Expected
rate of return, based on price
of bond.
FIGURE 6.1 Merrill Lynch corporate bond.
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6-5
6.1 (A) Key Components of a Bond
Example 1: Key Components of a
Corporate Bond
Let’s say you see the following price quote
for a corporate bond:
Issue
Price
Hertz Corp. 91.50
Coupon(%) Maturity
YTM% Current Yld. Rating
6.35
15-Jun-2010 15.438
6.94
B
Price = 91.5% of $1000$915; Annual coupon = 6.35% *1000  $63.50
Maturity date = June 15, 2010; If bought and held to maturityYield =
15.438%
Current Yield = $ Coupon/Price = $63.5/$915  6.94%
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6-6
6.1 (B)
Pricing a Bond in Steps
Since a bond involves a combination of an annuity
(coupons) and a lump sum (par value), its price is best
calculated by using the following steps:
FIGURE 6.2 How to price a bond.
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6-7
6.1 (B) Pricing a Bond in Steps
(continued)
Example 2: Calculating the Price of a Corporate Bond
Calculate the price of an AA-rated, 20-year, 8% coupon (paid annually)
corporate bond (par value = $1,000), which is expected to earn a yield to
maturity of 10%.
Year 0
1
2
3
$80
$80
$80
18
…
$80
19
$80
20
$80
$1,000
Annual coupon = Coupon rate * Par value = .08 * $1,000 = $80 = PMT
YTM = r = 10%
Maturity = n = 20
Price of bond = Present value of coupons + Present value of par value
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6-8
6.1 (B) Pricing a Bond in Steps
(continued)
Example 2: Calculating the price of
a corporate bond
1 

Present value of coupons

PMT


=


1
1 r n 
r


=
1


1
20

1 0.10  

$80  

0.10




=
$80 x 8.51359 = $681.09
Present Value of par value =
Present Value of par value =
FV 
1
1 r n
$1,000 
1
1 0.1020
Present Value of par value = $1,000 x 0.14864 = $148.64
Price of bond
= $681.09 + $148.64
= $829.73
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6-9
6.1 (B) Pricing a Bond in Steps
(continued)
Method 2. Using a financial calculator
Mode:
P/Y=1; C/Y = 1
Input:
Key:
Output
N
20
I/Y
10
PV
PMT
?
80
-829.73
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FV
1000
6-10
6.2 Semiannual Bonds and ZeroCoupon Bonds
• Most corporate and government bonds pay coupons on
a semiannual basis.
• Some companies issue zero-coupon bonds by selling
them at a deep discount.
• For computing the price of these bonds, the values of
the inputs have to be adjusted according to the
frequency of the coupons (or absence thereof).
– For example, for semiannual bonds, the annual coupon is
divided by 2, the number of years is multiplied by 2, and
the YTM is divided by 2.
– The price of the bond can then be calculated by using the
TVM equation, a financial calculator, or a spreadsheet.
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6-11
6.2 Semiannual Bonds and ZeroCoupon Bonds (continued)
FIGURE 6.4 Coca-Cola semiannual corporate bond.
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6-12
6.2 Semiannual Bonds and ZeroCoupon Bonds (continued)
FIGURE 6.5 Future cash flow of the Coca-Cola bond.
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6-13
6.2 Semiannual Bonds and ZeroCoupon Bonds (continued)
Method 1:
Using the TVM Equation
Method 2:
Using a Financial
Calculator
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6-14
6.2 Semiannual Bonds and ZeroCoupon Bonds (continued)
Method 3: Using a spreadsheet We note again that the
spreadsheet wants the periodic rate of 4.4%, not the annual yield
to maturity rate of 8.8%.
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6-15
6.2 (A) Pricing Bonds after Original
Issue
The price of a bond is a function of the remaining
cash flows (i.e., coupons and par value) that would
be paid on it until expiration.
As of August 2008, the 8.5%, 2022 Coca-Cola bond
has only 27 coupons left to be paid on it until it
matures on Feb. 1, 2022.
FIGURE 6.6 Remaining cash flow of the Coca-Cola
bond.
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6-16
6.2 (A) Pricing Bonds after Original
Issue (continued)
Example 3: Pricing a Semiannual Coupon Bond
after Original Issue
Four years ago, the XYZ Corporation issued an 8%
coupon (paid semiannually), 20-year, AA-rated bond
at its par value of $1000. Currently, the yield to
maturity on these bonds is 10%. Calculate the
price of the bond today.
Remaining number of semiannual coupons
= (20-4)*2 = 32 coupons = n
Semiannual coupon = (.08*1000)/2 = $40
Par value = $1000
Annual YTM = 10% YTM/25% = r
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6-17
6.2 (A) Pricing Bonds after Original
Issue (continued)
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6-18
6.2 (A) Pricing Bonds after Original
Issue (continued)
Method 2: Using a financial calculator
Mode:
P/Y=2; C/Y = 2
Input: N
Key:
32
Output
I/Y PV
PMT
10
?
40
-841.97
Copyright © 2010 Pearson Prentice Hall. All rights reserved.
FV
1000
6-19
6.2 (B) Zero-Coupon Bonds
• Known as “pure” discount bonds and sold at a
discount from face value
• Do not pay any interest over the life of the bond.
• At maturity, the investor receives the par value,
usually $1000.
• Price of a zero-coupon bond is calculated by
merely discounting its par value at the prevailing
discount rate or yield to maturity.
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6-20
Table 6.2 Amortized interest on a ZeroCoupon Bond
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6-21
6.2 (C) Amortization of a ZeroCoupon Bond
• The discount on a zero-coupon bond is amortized
over its life.
• Interest earned is calculated for each 6-month
period.
• For example, .04*790.31=$31.62
• Interest is added to price to compute ending
price.
• Zero-coupon bond investors have to pay tax on
annual price appreciation, even though no cash is
received.
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6-22
6.2 (C) Amortization of a ZeroCoupon Bond (continued)
Example 4: Price of and Taxes Due on a
Zero-Coupon Bond:
John wants to buy a 20-year, AAA-rated, $1000 par value,
zero-coupon bond being sold by Diversified Industries, Inc.
The yield to maturity on similar bonds is estimated to be
9%.
A)
How much will he have to pay for it?
B)
How much will he be taxed on the investment after 1
year, if his marginal tax rate is 30%?
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6-23
6.2 (C) Amortization of a ZeroCoupon Bond (continued)
Example 4 (Answer)
Method 1: Using the TVM equation
Bond Price = Par Value * [1/(1+r)n]
Bond Price = $1000*(1/(1.045)40
Bond Price = $1000 * .1719287 = $171.93
Method 2: Using a financial calculator
Mode:
P/Y=2; C/Y = 2
Input:
Key:
Output
N
40
I/Y
9
PV
PMT
?
0
-171.93
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FV
1000
6-24
6.2 (C) Amortization of a ZeroCoupon Bond (continued)
Example 4 (Answer—continued): The Tax Piece
Calculate the price of the bond at the end of 1 year.
Mode:P/Y=2; C/Y = 2
Input:
N
I/Y
PV
PMT
FV
Key:
38
9
?
0
1000
Output
-187.75
Taxable income = $187.75 - $171.93 = $15.82
Taxes due = Tax rate * Taxable income =
0.30*$15.82 = $4.75
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6-25
6.2 (C) Amortization of a ZeroCoupon Bond (continued)
Example 4 (Answer—continued)
Alternatively, we can calculate the semiannual
interest earned, for each of the two
semiannual periods during the year.
 $171.93 * .045 = $7.736  Price after 6 months
 $171.93+7.736 = $179.667
 $179.667 * .045=$8.084 Price at end of year
 $179.667+8.084 = $187.75
 Total interest income for 1 year = $7.736+$8.084
 $15.82
 Tax due = 0.30 * $15.82 = $4.75
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6-26
6.3 Yields and Coupon Rates
• A bond’s coupon rate differs from its yield
to maturity (YTM).
• Coupon rate is set by the company at the
time of issue. It is fixed (except for newer
innovations that have variable coupon
rates).
• YTM is dependent on market, economic,
and company-specific factors and is
therefore variable.
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6-27
6.3 (A) The First Interest Rate:
Yield to Maturity
• Expected rate of return on a bond if held to
maturity.
• The price that willing buyers and sellers settle at
determines a bond’s YTM at any given point.
• Changes in economic conditions and risk factors will
cause bond prices and their corresponding YTMs to
change.
• YTM can be calculated by entering the coupon
amount (PMT), price (PV), remaining number of
coupons (n), and par value (FV) into the TVM
equation, financial calculator, or spreadsheet.
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6-28
6.3 (B) The “Other” Interest Rate:
Coupon Rate
• The coupon rate on a bond is set by the
issuing company at the time of issue.
• It represents the annual rate of interest that
the firm is committed to pay over the life of
the bond.
• If the rate is set at 7%, the firm is committing
to pay .07*$1000 = $70 per year on each
bond.
• It is paid either in a single check or two
checks of $35 paid six months apart.
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6-29
6.3 (C) Relationship of Yield to
Maturity and Coupon Rate
• An issuing firm gets the bond rated by a rating agency
such as Standard & Poor’s or Moody’s.
• Then, based on the rating and planned maturity of the
bond, it sets the coupon rate to equal the expected yield,
as indicated in the Yield Book (available in the capital
markets at that time), and sells the bond at par value
($1000).
• Once issued, if investors expect a higher yield on the
bond, its price will go down and the bond will sell below
par or as a discount bond, and vice-versa.
• Thus, a bond’s YTM can be equal to (par bond), higher
than (discount bond) or lower than (premium bond)
its coupon rate.
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6-30
Table 6.3 Premium Bonds, Discount
Bonds, and Par Value Bonds
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6-31
Figure 6.8 Bond prices and interest
rates move in opposite directions
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6-32
6.3 (C) Relationship of Yield to
Maturity and Coupon Rate
(continued)
Example 5: Computing YTM
Last year, The ABC Corporation had issued 8% coupon
(semiannual), 20-year, AA-rated bonds (par value =
$1000) to finance its business growth. If investors are
currently offering $1200 on each of these bonds, what is
their expected yield to maturity on the investment? If
you are willing to pay no more than $980 for this bond,
what is your expected YTM?
Remaining number of coupons = 19*2 = 38
Semiannual coupon amount =( .08*$1000)/2 = $40
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6-33
6.3 (C) Relationship of Yield to
Maturity and Coupon Rate
(continued)
PV = $1200
Mode: P/Y=2; C/Y = 2
Input:
N
I/Y
Key:
38
?
Output
6.19
PV PMT
-1200 40
FV
1000
Note: This is a premium bond, so its YTM <
coupon rate of 8%
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6-34
6.3 (C) Relationship of Yield to
Maturity and Coupon Rate
(continued)
PV = $980
Mode:
P/Y=2; C/Y = 2
Input:
N
I/Y
PV PMT
FV
Key:
38
?
-980 40 1000
Output
8.21%
Note: This would be a discount bond, so its
YTM>coupon rate of 8%.
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6-35
6.4 Bond Ratings
• Ratings are produced by Moody’s, Standard and Poor’s, and Fitch
• Range from AAA (top-rated) to C (lowest-rated) or D (default).
• Help investors gauge likelihood of default by issuer.
• Help issuing companies establish a yield on newly issued bonds.
–
Junk bonds: the label given to bonds that are rated below BBB.
These bonds are considered to be speculative in nature and carry
higher yields than those rated BBB or above (investment grade).
– Fallen angels: the label given to bonds that have had their ratings
lowered from investment to speculative grade.
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6-36
6.4 Bond Ratings (continued)
TABLE 6.4 Bond Ratings
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6-37
6.5 Some Bond History and More
Bond Features
• Corporate bond features have gone through
some major changes over the years.
–
–
–
–
–
–
–
–
Bearer bonds
Indenture or deed of trust
Collateral, or security of a bond
Mortgaged security
Debentures
Senior debt and junior debt
Sinking fund
Protective covenants
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6-38
6.5 Some Bond History and More
Bond Features (continued)
–
–
–
–
–
–
–
–
Callable bond
Yield to call
Putable bond
Convertible bond
Floating-rate bond
Prime rate
Income bonds
Exotic bonds
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6-39
6.5 Some Bond History and More
Bond Features (continued)
Example 6: Calculating Yield to Call.
Two years ago, the Mid-Atlantic Corporation
issued a 10% coupon (paid semiannually),
20-year maturity bond with a 5-year deferred
call feature and a call penalty of one coupon
payment in addition to the par value ($1000),
if exercised.
If the current price on these bonds is $1080,
what is its yield to call?
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6-40
6.5 Some Bond History and More
Bond Features (continued)
Remaining number of coupons until first call date = 6 = n
Semi-annual coupon = $50 = PMT
Call price = $1050 = FV
Bond price = $1080 = PV
Mode:
Input:
Key:
Output
P/Y=2; C/Y = 2
N
I/Y
PV PMT
6
?
-1080 50
8.43
FV
1050
YTC
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6-41
6.6 U.S. Government Bonds
• Include bills, notes, and bonds sold by the
Department of the Treasury.
• Also include state bonds, issued by state
governments
• Also include municipal bonds, issued by county, city,
or local government agencies.
• Treasury bills are zero-coupon, pure discount
securities with maturities ranging from 1-, 3-, and
6-months up to 1 year.
• Treasury notes have between 2- to 10-year
maturities.
• Treasury bonds have greater than 10-year
maturities, when first issued.
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6-42
Table 6.6 Government Notes and
Bonds (Prices as of April 8, 2008)
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6-43
6.6 (A) Pricing a U.S. Government
Note or Bond
•
•
Similar to the method used for pricing corporate bonds and can be done by
using TVM equations, a financial calculator, or a spreadsheet program.
For example, let’s assume you are pricing a 7-year, 6% coupon
(semiannual) $100,000 face value Treasury note, using an expected yield
of 8%:
FIGURE 6.11
U.S. Government
Treasury Note
Cash Flows
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6-44
6.6 (B) Pricing a Treasury bill
Calculated by discounting the bill’s face value for the number
of days until maturity and at the prevailing bank discount
yield.
Bank discount yield: a special discount rate used in
conjunction with Treasury bills under a 360 day- per- year
convention (commonly assumed by bankers).
Bond equivalent yield (BEY): the APR equivalent of the bank
discount yield calculated by adjusting it as follows:
BEY =
_____365 * Bank discount yield________
360 - (days to maturity * discount yield)
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6-45
6.6 (B) Pricing a Treasury bill
(continued)
Example 7: Calculating the Price and BEY of a Treasury Bill
Calculate the price and BEY of a treasury bill that matures in
105 days, has a face value of $10,000, and is currently being quoted
at a bank discount yield of 2.62%.
Price of T-bill = Face value * [1-(discount yield * days until
maturity/360)]
Price of T-bill = $10,000 * [ 1 - (.0262 * 105/360)] =
$10,000*0.9923583
Price of T-bill = $9,923.58
BEY =
_____365 * Bank discount yield_______
360 - (days to maturity * discount yield)
=
__365 * .0262__
360 - (105*.0262)
BEY = .026768 = 2.68% (rounded to 2 decimals)
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6-46
Table 6.7 Selected Historical Treasury
Bill Bank Discount Rates
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6-47
ADDITIONAL PROBLEMS WITH
ANSWERS
Problem 1
Pricing a Semiannual Bond:
Last year, Harvest Time Corporation sold
$40,000,000 worth of 7.5% coupon, 15-year
maturity, $1000 par value, AA-rated,
noncallable bonds to finance its business
expansion. Currently, investors are
demanding a yield of 8.5% on similar bonds.
If you own one of these bonds and want to
sell it, how much money can you expect to
receive on it?
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6-48
ADDITIONAL PROBLEMS WITH
ANSWERS
Problem 1 (ANSWER)
Using a financial calculator
Mode:
P/Y=2; C/Y = 2
Input:
Key:
Output
N
28
I/Y
8.5
PV
PMT
?
37.5
-919.03
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FV
1000
6-49
ADDITIONAL PROBLEMS WITH
ANSWERS
Problem 2
Yield to Maturity
Joe Carter is looking to invest in a four-year bond
that pays semiannual coupons at a coupon rate of
5.6 percent and has a par value of $1,000. If
these bonds have a market price of $1,035, what
yield to maturity is being implied in the pricing?
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6-50
ADDITIONAL PROBLEMS WITH
ANSWERS
Problem 2 (ANSWER)
Using a financial calculator
Mode:P/Y=2; C/Y = 2
Input:
N
I/Y
PV
Key:
8
?
-1035
Output
4.63
PMT
28
FV
1000
The expected YTM is 4.63%
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6-51
ADDITIONAL PROBLEMS WITH
ANSWERS
Problem 3
Price of a Zero-Coupon Bond
Krypton Inc. wants to raise $3 million by issuing 10year zero-coupon bonds with a face value of
$1,000. Its investment banker informs Krypton that
investors would use a 9.25% percent discount rate
on such bonds. At what price would these bonds sell
in the market place, assuming semiannual
compounding? How many bonds would the firm
have to issue to raise $3 million?
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6-52
ADDITIONAL PROBLEMS WITH
ANSWERS
Problem 3 (ANSWER)
Using a financial calculator : Price of a Zero-Coupon Bond
Mode:
P/Y=2; C/Y = 2
Input:
Key:
Output
N
20
I/Y
9.25
PV
PMT
?
0
-404.85
FV
1000
The zero-coupon bond would sell for $404.85
To raise $3,000,000, the company would have to sell:
$3,000,000/$404.85 = 7,411 bonds
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6-53
ADDITIONAL PROBLEMS WITH
ANSWERS
Problem 4
Tax on Zero-Coupon Bond Income
Let’s say that you buy 100 of the 7411
bonds that were issued by Krypton Inc., as
described in Problem 3 above for $404.85.
At the end of the year, how much money
will the bond be worth, and how much tax
will you be assessed, assuming that you
have a marginal tax rate of 35%?
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6-54
ADDITIONAL PROBLEMS WITH
ANSWERS
Problem 4 (ANSWER)
Calculate the price of the bond at the end of each
semi-annual period during the next year.
The change in price for each semi-annual period
represents the implied interest income on a zero that
is taxed at 35%.
Price of Zero after 6 months, assuming YTM of
9.25%:
Mode:
P/Y=2; C/Y = 2
Input:
N
I/Y
PV
PMT
FV
Key:
19
9.25
?
0
1000
Output
-423.57
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6-55
ADDITIONAL PROBLEMS WITH
ANSWERS
Problem 4 (ANSWER continued)
Price of Zero at the end of 2 semiannual periods
assuming YTM of 9.25%:
Mode:
P/Y=2; C/Y = 2
Input:
Key:
Output
N
18
I/Y
9.25
PV
PMT
FV
?
0
1000
-443.16
Implied interest earned on zero = $443.16 - $404.85 = $38.31
Taxes due =Tax rate*Taxable income = 0.35 * $38.31 =
$13.41
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6-56
ADDITIONAL PROBLEMS WITH
ANSWERS
Problem 5
Price and BEY on a Treasury Bill
Calculate the price and BEY of a treasury
bill that matures in 181 days, has a face
value of $10,000, and is currently being
quoted at a bank discount yield of 2.32%.
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6-57
ADDITIONAL PROBLEMS WITH
ANSWERS
Problem 5 (ANSWER)
Price of T-bill = Face Value * [1-(discount yield * days until
maturity/360)]
Price of T-bill
= $10,000 * [ 1 - (.0232 * 181/360)]
= $10,000 * 0.98833555
Price of T-bill = $9,883.36
_____365 * Bank discount yield_______
__365 * .0232__
=
360 - (days to maturity * discount yield)
360 - (181*.0232)
BEY = .023799 = 2.38% (rounded to 2 decimals)
BEY =
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6-58
Figure 6.3 Future Cash Flow of a Merrill
Lynch Bond
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6-59
Figure 6.7 Goodyear Semiannual
Corporate Bond
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6-60
Table 6.5 Annual Interest Rates on
Corporate Bonds Rated Aaa to Baa, 1980
to 2006
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6-61
Figure 6.9 Pacific Bell Semiannual
Callable Corporate Bond
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6-62
Figure 6.10 Pacific Bell Callable Bond
Cash Flows
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6-63