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Introduction To Bonds
1. INTRODUCTION TO BONDS
AND THEIR VALUATION
Alan Anderson, Ph.D.
ECI Risk Training
www.ecirisktraining.com
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2. WHAT IS A BOND?
A bond is a debt instrument that provides
a periodic stream of interest payments to
investors while repaying the borrowed
principal on a specified maturity date
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3. BOND TERMINOLOGY
Face (par) value:
the price of a bond when first issued
(often a multiple of $1,000)
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4. Coupon rate:
The periodic interest payments promised
to bondholders are a fixed percentage of
a bond’s face value; this percentage is
known as the coupon rate
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5. Coupon:
the dollar value of the periodic
interest promised to bondholders;
this equals the coupon rate times
the face value of the bond
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6. Maturity
The time until the principal
is scheduled to be repaid
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7. Call Provisions
Some bonds contain a provision that
enables the issuer to buy the bond
back from the bondholder at a pre-
specified price prior to maturity
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8. A bond containing such a
provision is said to be callable
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9. This call option is known as
an embedded option, since
it can’t be bought or sold
separately from the bond
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10. Put Provisions
Some bonds contain a provision that
enables the buyer to sell the bond
back to the issuer at a pre-specified
price prior to maturity
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11. A bond containing such a
provision is said to be putable
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12. Sinking Fund Provisions
Some bonds are issued with a
provision that requires the issuer
to buy back a fixed percentage
of the bonds each year
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13. CONVERTIBLE BONDS
A convertible bond contains an embedded
option; the holder has the right to convert
the bond into a pre-determined number of
shares of stock
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14. BOND ISSUERS
Bonds can be categorized
according to their issuers:
Treasury Bonds
Corporate Bonds
Municipal Bonds
Foreign Bonds
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15. TREASURY BONDS
Treasury bonds are issued by the U.S.
government to finance its deficits
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16. These are free of default risk, which
is the risk that the investor will not
receive all promised payments
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17. They are also not taxed by
state and local governments
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18. CORPORATE BONDS
Corporations can raise funds by issuing
debt in the form of corporate bonds
These bonds offer a higher promised
coupon rate than Treasuries, but expose
investors to default risk
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19. Ratings agencies, such as Standard and
Poor’s and Moody’s, rank corporate issuers
according to their likelihood of default
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20. The riskiest corporations offer the
highest coupon rates to investors
as compensation for default risk
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21. MUNICIPAL BONDS
A municipal bond is issued by a state or
local government; as a result, they carry
little or no default risk
They also offer an extremely favorable
tax treatment to investors
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22. A municipal bond is not
taxed at the Federal level
It is also not taxed by the
issuing municipality
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23. As a result, municipal bonds offer
very low coupon rates to investors
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24. FOREIGN BONDS
Foreign bonds are issued by foreign
governments and corporations
These may be denominated in dollars
or in a foreign currency
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25. ILLUSTRATING A
BOND’S CASH FLOWS
A bond’s cash flows may
be shown with a time line
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26. EXAMPLE
Suppose that a bond is issued with:
a face value of $1,000
a coupon rate of 4%
a maturity of four years
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27. With a face value of $1,000, the
bond will make an annual coupon
payment of:
4%* $1,000 = $40
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28. On the bond’s maturity date, the bond pays:
one final $40 coupon
the face value of $1,000
Therefore, the final cash flow totals $1,040
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29. This is shown as follows:
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31. where:
VB = the bond’s price or value
rd = the interest rate used to compute
the present value of the bond’s cash
flows; this is known as the discount
rate
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32. NOTE
The appropriate discount rate to use for
pricing a bond depends on several factors,
including the bond’s default risk and maturity
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33. PRICING BONDS
A bond’s price equals the present value
of its expected future cash flows
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34. EXAMPLE
Referring to the previous example,
suppose that the appropriate
discount rate for this bond is 4%.
What is the price of this bond?
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35. PRICING BONDS
WITH FORMULAS
A bond may be priced with the
following formula:
N
INT M
VB = +
t =1 (1 + rd ) (1 + rd )
t N
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36. where:
INT = the periodic coupon or
interest payment
rd = the discount rate
M = the bond’s par or face value
N = the number of periods until the
bond’s maturity date
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37. In this example, the price is computed as:
40 40 40 1, 040
1
+ 2
+ 3
+ 4
(1.04) (1.04) (1.04) (1.04)
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38. This equals:
38.4615 + 36.9822 + 35.5599
+ 888.9964 = $1,000.00
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39. At a discount rate of 5%, the price is:
40 40 40 1, 040
1
+ 2
+ 3
+ 4
(1.05) (1.05) (1.05) (1.05)
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40. This equals:
38.0952 + 36.2812 + 34.5535
+ 855.6106 = $964.54
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41. At a discount rate of 3%, the price is:
40 40 40 1, 040
1
+ 2
+ 3
+ 4
(1.03) (1.03) (1.03) (1.03)
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42. This equals:
38.8350 + 37.7038 + 36.6057
+ 924.0265 = $1,037.17
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43. These results show the following
important relationship:
If rd > coupon rate, VB < face value
If rd = coupon rate, VB = face value
If rd < coupon rate, VB > face value
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44. These results also demonstrate that there
is an inverse relationship between interest
rates and bond prices:
when rates rise, bond prices fall
when rates fall, bond prices rise
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45. NOTE
A bond that sells for less than its face
value is known as a discount bond
A bond that sells for more than its face
value is known as a premium bond
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46. ZERO COUPON BONDS
A zero-coupon bond does not make any
coupon payments; instead, it is sold to
investors at a discount from face value
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47. The difference between the
price paid for the bond and the
face value represents the return
to the investor
This is known as a capital gain
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48. The pricing formula for
a zero coupon bond is:
M
VB =
(1 + rd ) N
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49. EXAMPLE
A one-year zero-coupon bond
is issued with a face value of
$1,000. The discount rate for
this bond is 8%. What is the
market price of this bond?
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50. M 1, 000
VB = = = $925.93
(1 + rd ) N
(1 + .08)1
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