Citibank: basic of corporate finance
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9-20 FIXED INCOME SECURITIES
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To solve this problem, enter the appropriate dates for a seven year
maturity, enter 7.8% as the coupon rate and 6.4% as the yield to
maturity. You should get $107.7054 when you push the price key.
Since this is the percentage price, divide it by 100 and then multiply
this by the face value of $10,000 to get the actual sale price of
$10,770.54.
Comparing
U.S. bonds to
Eurobonds
U.S. Treasury securities make semi-annual interest payments and
Eurobonds make annual interest payments. Now the question becomes:
Which bond offers the investor the higher return on investment?
Clearly, we need a way to compare the two investments.
Suppose that we are considering a U.S. Treasury bond with a 6.5%
yield to maturity and a Eurobond with a 6.75% yield to maturity.
There is a simple formula that relates the two quoted yields. It is:
(1 + Y
E
) = [1 + (Y
T
/ 2) ]
2
Where:
Y
E
= Annual Eurobond yield to maturity
Y
T
= Annual Treasury bond yield to maturity
Example
Using this formula, the Eurobond annual yield that is equivalent to
the Treasury yield of 6.5% is:
(1 + Y
E
) = [1 + (Y
T
/ 2)]
2
(1 + Y
E
) = [1 + (0.065 / 2)]
(1 + Y
E
) = [1 + 0.0325]
2
(1 + Y
E
) = 1.0661
Y
E
= 0.0661 or 6.61%
The annual 6.5% yield to maturity on the Treasury security is
equivalent to a 6.61% annual yield to maturity for a Eurobond.
Therefore, the 6.75% Eurobond appears to be the better investment,
all other things being constant.
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Other Bonds
Make certain
comparisons
are valid
Like the U.S. Treasury, many other governments issue bonds.
Corporations also issue bonds for investors to purchase. The
calculations for the price and yield of these bonds are based on the
same principles as for Treasury securities. Make certain that
comparisons between securities are valid. For example, an adjustment
to computations is needed to allow direct and valid comparison of a
corporate bond that pays semi-annual coupons, on a 360-day year, to a
Treasury bond which is priced on a 365-day year.
Accrued Interest
Additional
adjustment for
true selling
price
To find the true selling price of a security that makes periodic
interest payments, one other adjustment is required. Because it is
common for a bond or note to sell on a date other than the date
interest is paid, the buyer will pay the seller the interest accrued
from the date the last coupon payment was made until the security is
sold. Otherwise, the buyer will receive the entire interest payment
even though s/he owned the bond for only part of the coupon period.
Semi-annual
coupon
payments
The convention is to adjust the coupon payment by the number of
days in the coupon period that the security is actually held by the
seller. We use this formula:
AI = (C / 2) x (D
H
/ D
C
)
Where:
AI = Accumulated interest on the security
C = Annual coupon payment
D
H
= Number of days that the security was
held
D
C
= Number of days in the coupon period
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Number of days
in coupon
period
The number of days in the coupon period can vary from 181 to 184,
depending on the dates the coupon is paid. For example, if the coupon
payments are made on May 15 and November 15 of each year, there
are 184 days from May 15 to November 15 and 181 days from
November 15 to May 15.
Annual coupon
payments
However, if the security pays one annual coupon (such as a
Eurobond), then two adjustments to this formula are needed. These
adjustments are: (1) the annual coupon is not divided by 2 and (2) the
number of days in the coupon period will be 360 or 365, depending
on the type of bond and its conventions.
Examples
Two examples will help demonstrate the use of these formulas.
1. What is the accumulated interest on a $10,000 face value
9.8% coupon Treasury bond that has 130 days until the next
coupon payment, and the coupon payment period has 182
days? Use the formula with $980 as the annual coupon
payment, and 52 (182 day coupon period minus 130 days
remaining in the period) as the number of days that the
security has been held.
AI = (C / 2) x (D
H
/ 182)
AI = ($980 / 2) x (52 / 182)
AI = $140.00
The buyer of the security would have to add $140.00 to the
quoted price of the security to compensate the seller for the
52 days in the coupon period that the seller owned the security.
2. What is the accumulated interest for a $1,000 face value 6.5%
Eurobond that was held for 270 days since the last coupon
payment? In this case, the annual coupon payment is $65 dollars
and D
H
= 270.
AI = C x (D
H
/ 365)
AI = ($65) x (270 / 365)
AI = $48.08
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The seller would receive the transaction price plus $48.08
compensation for interest earned from the last coupon payment
until the security was sold.
BOND PRICE QUOTES
Newspaper
source
Most newspapers contain a financial section that quotes recent stock
and bond prices. The Wall Street Journal is generally considered a
very good source for financial information.
Treasury Bill Quotes
Figure 9.1 contains price information for U.S. Treasury bills as it
may appear in the financial section.
TREASURY BILLS
Maturity
Days to
Mat. Bid Asked Chg.
Ask
Yld.
Jan 13 '94
Jan 20 '94
Jan 27 '94
Feb 03 '94
Feb 10 '94
Feb 17 '94
Feb 24 '94
Mar 03 '94
Mar 10 '94
Mar 17 '94
Mar 24 '94
Mar 31 '94
Apr 07 '94
1
8
15
22
29
36
43
50
57
64
71
78
85
3.06
2.97
2.90
2.90
2.90
2.89
2.89
2.86
2.92
2.93
2.94
2.93
2.99
2.06
2.87
2.80
2.80
2.80
2.85
2.85
2.82
2.88
2.91
2.92
2.91
2.97
+0.07
....
+0.01
+0.01
-0.01
-0.01
-0.01
-0.02
-0.03
-0.03
-0.03
-0.02
-0.02
3.00
2.91
2.84
2.84
2.85
2.90
2.90
2.87
2.93
2.97
2.98
2.97
3.03
Figure 9.1: Price Quotes for U.S. Treasury Bills
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An explanation of each column of information beginning with the
top left column is as follows:
Maturity: The maturity date of the bill
Days to Mat.: Number of days until the security matures
Bid: Discount rate that buyers are asking for when
purchasing the bill
Asked: The discount rate that sellers are requesting when
they sell the bill
The difference between these two rates is often referred to as the
bid/ask spread. The transaction price will occur somewhere between
these two rates.
Chg.: The net change in the asked discount rate from the
previous trading day
Ask Yld.: The yield to maturity of the bill, based on the asked
discount rate
Example
An example will illustrate the relationships between the columns of
information in Figure 9.1. Follow the instructions.
Maturity: Beginning at the top of Column 1, read down the
column to find the bill that matures on Feb 10, '94.
Now read across the row.
Days to Mat.: This bill has 29 days until maturity.
Bid: The bid discount rate is 2.90%.
Asked: The asked rate is 2.80%.
Chg.: This indicates that the asked rate is down 1/100 of 1%
from the last price quote (the day before). The term
basis point refers to 1/100 of 1%. An analyst might
say, "The asked rate is one basis point less than the
previous day."
Ask Yld.: The yield to maturity of the bill, based on the
asked rate, is 2.85%.
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Verify the
yield to
maturity
We can verify the yield to maturity for this bill using the simple
interest formula. To make that calculation, we first need to find the
dollar price of the bill.
P = F [1 - ((R x D
M
) / 360)]
P = $10,000 [1 - ((0.028 x 29) / 360)]
P = $9,977.44
Now, use a face value of $10,000 as the selling price of the bill and
use the simple interest formula.
i = [(P
s
- P
b
) / P
b
] x [365 / D
H
]
i = [($10,000 - $9,977.44) / $9,977.44 ] x [365 / 29]
i = 0.0285 or 2.85%
This is the yield to maturity of the Feb 10, '94 bill, which corresponds
to the Ask Yld. column in the figure.
Treasury Note and Bond Quotes
Newspaper
source
Price quotes for U.S. Treasury notes and bonds are shown in Figure
9.2. Let's see how they may appear in the financial section of the
newspaper.
Rate
Maturity
Mo/Yr Bid Asked Chg.
Ask
Yld.
6 Nov 94n 102:01 102:03 .... 3.45
8 1/4 Nov 94n 103:28 103:30 .... 3.46
10 1/8 Nov 94 105:13 105:15 .... 3.47
11 5/8 Nov 94n 106:23 106:25 + 1 3.38
4 5/8 Nov 94n 100:30 101:00 .... 3.46
4 5/8 Dec 94n 101:00 101:02 + 1 3.50
7 5/8 Dec 94n 103:27 103:29 + 1 3.48
8 5/8 Jan 95n 104:29 104:31 .... 3.56
4 1/4 Jan 95n 100:21 100:23 + 1 3.55
3 Feb 95 100:10 101:10 .... 1.78
5 1/2 Feb 95n 101:31 102:01 + 1 3.59
7 3/4 Feb 95n 104:12 104:14 + 1 3.57
10 1/2 Feb 95 107:11 107:13 + 3 3.53
11 1/4 Feb 95n 108:06 108:08 + 3 3.49
Figure 9.2: Price Quotes for U.S. Treasury Notes and Bonds
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The columns provide the following information:
Rate: Coupon rate being paid by the security
Maturity Maturity month and year. [An (n) next to the year
Mo/Yr: indicates that the security is a note.]
Bid: Bid price quoted in percentage terms
Asked: Asked price quoted in percentage terms
(The numbers following a colon mean "32nds of a
dollar." Therefore, a price quote of 101:22 means that
the price of the security is 101 22/32.)
Chg: Net price change in the asked price from the previous
day, reported in 32nds
Ask Yld.: Yield to maturity of the security, based on the asked price
Some long-term bonds have call features. If the bond is selling at
a premium (above par value), then the yield is calculated using the
earliest call date. If the bond is selling at a discount (below par
value), then the yield is calculated until maturity.
Verifying yield
to maturity
We can calculate the yield to maturity if we know the date (day,
month, year) when the security matures. Treasury notes come due
on the second and fourth Friday of each month. Let's look at an
example to illustrate the relationship.
Example
Use your calculator to verify the yield of a bond in Figure 9.2.
− Locate the Jan 95n security that shows an 8 5/8% coupon rate
(Column 2, Row 8).
− Enter the maturity date, Jan. 13, 1995.
− Enter 8.625% (8 5/8%) for the coupon rate.
− Enter 104.96875 (104:31 or 104 31/32) for the current
percentage price.
− Press the yield to maturity key.
The calculator should display 3.5638% as the yield, which
corresponds to the 3.56% quote.
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Summary
Eurobonds make up another large group of fixed income debt
securities issued in a currency that is different from the currency of
the country in which it is issued. The price is calculated using this
formula:
T
P = å C
+
F
a
i = 1 (1 + Y)
i
(1 + Y)
T
Quotes for Treasury bills, notes, and bonds may be found in the
financial section of some newspapers.
Interest earned by the seller, during the coupon period in which a
bond is sold, is accrued and added to the price paid by the buyer.
You will learn about the significance of bond duration in the final section of this unit. First,
however, please practice what you have learned about Eurobonds and accrued interest in the
exercise which follows.
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FIXED INCOME SECURITIES 9-29
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PRACTICE EXERCISE 9.3
Directions: Use the bond features on your calculator to calculate the correct answer to
each question. Check your solutions with the Answer Key on the next page.
8. A new Eurobond issue is available to investors. The bonds carry a 7.375% coupon rate,
have a maturity of 10 years, and are priced to yield 8.0%.
What price percentage would investors expect to pay for the new bonds? Give your
answer in percentage terms.
______________%
9. A Eurobond with five years to maturity has a percentage price of 97.85%. If the
coupon rate of the security is 6.325%, what is the yield to maturity of the bond?
______________%
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