Bond Valuation

Bond Valuation and Yield to Maturity
Examples:
Company Settlement Maturity Coupon Yield to
Date Redemption Date Rate Maturity
IBM
Bond Valuation and Yield to Maturity:

The PRICE function is used to value a bond and the YIELD function is used to determine the yield to
maturity of a bond. With both of these functions it is necessary to specify the "day count basis"; how
the number of days per month and the number of days in a year calculated. Excel provides five
alternatives to specifying this basis. The actual number of days per month and per year has been used in
these example.

Basic conventions with bonds: Bond prices are quoted as a percentage of a bond's final maturity value
(usually $1,000 for a corporate bond) and in the U.S. corporate bonds normally pay interest
semiannually.
Bond Valuation Example:

IBM 8 1/4% Coupon Bond
Semiannual Coupon Interest Payments
Maturity Date of 1 September 2012
Bond Investor's Required Yield to Maturity of 7.821%
Purchased and Settled on 26 February 2003
Actual Number of Days per Month and Year
Bond Yield to Maturity Example:

AT & T 8 3/8% Coupon Bond
Semiannual Coupon Interest Payments
Maturity Date of 1 July 2019
Quoted Bond Price of 110.875 on 26 February 2003
Purchased and Settled on 26 February 2003
Actual Number of Days per Month and Year
Bond Valuation and Yield to Maturity
Company Settlement Maturity Coupon Quoted
Date Redemption Date Rate Price
AT&T
Company Settlement Maturity Discount Date
Date Redemption Date Rate Basis
Citicorp
Valuation and Yield to Maturity of Pure Discount Instruments:

The PRICEDISC function may be used to value a pure discount instrument such as commercial paper
and the YIELDDISC function is used to determine the yield to maturity of pure discount instruments.
As with the PRICE and YIELD functions it is necessary to specify the "day count basis"; how the
number of days per month and the number of days in a year calculated. Excel provides five alternatives
to specifying this basis. The actual number of days per month and per year has been used in these
example.

As with bonds, prices on pure discount instruments are quoted as a percentage of the final maturity
value.
Commercial Paper Valuation Example:

Citicorp Commercial Paper Issue of $10,000,000
Maturity Date of 3 June 2003
Investor's Required Discount Rate of 2.144%
Purchased and Settled on 26 February 2003
Actual Number of Days per Month and Year
Commercial Paper Yield Example:

SBC Communications, Inc. Commercial Paper Issue of $100,000,000
Maturity Date of 14 July 2003
Bond Valuation and Yield to Maturity
Company Settlement Maturity Quoted Date
Date Redemption Date Price Basis
SBC Comm. Inc.
Settlement Maturity Discount Computed
Date Redemption Date Rate Price
T Bill
Maturity Date of 14 July 2003
Reported Market Price of the Paper of 98.283
Purchased and Settled on 26 February 2003
Actual Number of Days per Month and Year
Valuation and Yield to Maturity of U.S. Government Treasury Bills

U.S. Government Treasury Bills are also pure discount instruments. Treasury Bills might be valued
using the PRICEDISC function presented above or with the TBILLPRICE function. In a similar
manner the YIELDDISC function maybe used to determine the yield to maturity of Treasury Bills or
the TBILLYIELD function might be used. Both the TBILLPRICE and the TBILLYIELD functions
assume a day count basis of 360 days per year.

As with bonds, Treasury Bills prices are quoted as a percentage of the final maturity value.
U.S. Government Treasury Bill Valuation Example:

Treasury Bill Issue of $1,000,000
Maturity Date of 12 June 2003
Investor's Required Discount Rate of 1.194%
Purchased and Settled on 26 February 2003

Bond Valuation and Yield to Maturity
Settlement Maturity Quoted Computed
Date Redemption Date Price Yield
T Bill
U.S. Government Treasury Bill Yield Example:

Treasury Bill Issue of $1,000,000
Maturity Date of 24 Jul4 2003
Market Price of the Treasury Bill of 99.533
Purchased and Settled on 26 February 2003

Bond Valuation and Yield to Maturity
Solutions:
Compounding Date Computed Company Settlement
Per/Year Basis Bond Price Date
IBM 26-Feb-2003
The PRICE function is used to value a bond and the YIELD function is used to determine the yield to
maturity of a bond. With both of these functions it is necessary to specify the "day count basis"; how
the number of days per month and the number of days in a year calculated. Excel provides five
alternatives to specifying this basis. The actual number of days per month and per year has been used in
Basic conventions with bonds: Bond prices are quoted as a percentage of a bond's final maturity value
(usually $1,000 for a corporate bond) and in the U.S. corporate bonds normally pay interest
Bond Valuation Example:

IBM 8 1/4% Coupon Bond
Semiannual Coupon Interest Payments
Maturity Date of 1 September 2012
Bond Investor's Required Yield to Maturity of 7.821%
Purchased and Settled on 26 February 2003
Actual Number of Days per Month and Year
Bond Yield to Maturity Example:

AT & T 8 3/8% Coupon Bond
Semiannual Coupon Interest Payments
Maturity Date of 1 July 2019
Quoted Bond Price of 110.875 on 26 February 2003
Purchased and Settled on 26 February 2003
Actual Number of Days per Month and Year
This bond would trade at 102.839% of its maturity value ($1,000) or
$1,028.39 for investors with a required yield to maturity of 7.821%
Bond Valuation and Yield to Maturity
Compounding Date Yield to Company Settlement
Per/Year Basis Maturity Date
AT&T 26-Feb-2003
Computed Company Settlement
Price Date
Citicorp 26-Feb-2003
The PRICEDISC function may be used to value a pure discount instrument such as commercial paper
and the YIELDDISC function is used to determine the yield to maturity of pure discount instruments.
As with the PRICE and YIELD functions it is necessary to specify the "day count basis"; how the
number of days per month and the number of days in a year calculated. Excel provides five alternatives
to specifying this basis. The actual number of days per month and per year has been used in these
As with bonds, prices on pure discount instruments are quoted as a percentage of the final maturity
Valuation and Yield to Maturity of Pure Discount Instruments:

The PRICEDISC function may be used to value a pure discount instrument such as commercial paper
and the YIELDDISC function is used to determine the yield to maturity of pure discount instruments.
As with the PRICE and YIELD functions it is necessary to specify the "day count basis"; how the
number of days per month and the number of days in a year calculated. Excel provides five alternatives
to specifying this basis. The actual number of days per month and per year has been used in these
example.

As with bonds, prices on pure discount instruments are quoted as a percentage of the final maturity
value.
Commercial Paper Valuation Example:

Citicorp Commercial Paper Issue of $10,000,000
Maturity Date of 3 June 2003
Investor's Required Discount Rate of 2.144%
Purchased and Settled on 26 February 2003
Actual Number of Days per Month and Year
Commercial Paper Yield Example:

SBC Communications, Inc. Commercial Paper Issue of $100,000,000
Maturity Date of 14 July 2003
This bond would trade at a yield to maturity of 7.229% at a quoted price of 110.875.
This commercial paper would trade at 99.430% of its maturity value ($10,000,000)
or $9,943,000 for investors with a required yield to maturity (discount rate) of
2.144%
Bond Valuation and Yield to Maturity
Computed Company Settlement
Yield Date
SBC Comm. Inc. 26-Feb-2003
Settlement
Date
T Bill 26-Feb-2003
U.S. Government Treasury Bills are also pure discount instruments. Treasury Bills might be valued
using the PRICEDISC function presented above or with the TBILLPRICE function. In a similar
manner the YIELDDISC function maybe used to determine the yield to maturity of Treasury Bills or
the TBILLYIELD function might be used. Both the TBILLPRICE and the TBILLYIELD functions
As with bonds, Treasury Bills prices are quoted as a percentage of the final maturity value.
Maturity Date of 14 July 2003
Reported Market Price of the Paper of 98.283
Purchased and Settled on 26 February 2003
Actual Number of Days per Month and Year
Valuation and Yield to Maturity of U.S. Government Treasury Bills

U.S. Government Treasury Bills are also pure discount instruments. Treasury Bills might be valued
using the PRICEDISC function presented above or with the TBILLPRICE function. In a similar
manner the YIELDDISC function maybe used to determine the yield to maturity of Treasury Bills or
the TBILLYIELD function might be used. Both the TBILLPRICE and the TBILLYIELD functions
assume a day count basis of 360 days per year.

As with bonds, Treasury Bills prices are quoted as a percentage of the final maturity value.
U.S. Government Treasury Bill Valuation Example:

Treasury Bill Issue of $1,000,000
Maturity Date of 12 June 2003
Investor's Required Discount Rate of 1.194%
Purchased and Settled on 26 February 2003

This commercial paper would trade at a yield to maturity of 4.621% at a quoted price of
98.283.
This U.S. T-Bill would trade at 99.648% of its maturity value ($1,000,000) or $996,480 for investors
with a required yield to maturity (discount rate) of 1.194%
Bond Valuation and Yield to Maturity
Settlement
Date
T Bill 26-Feb-2003
U.S. Government Treasury Bill Yield Example:

Treasury Bill Issue of $1,000,000
Maturity Date of 24 Jul4 2003
Market Price of the Treasury Bill of 99.533
Purchased and Settled on 26 February 2003

This U.S. T-Bill would trade at a yield to maturity of 1.224% at a quoted price of 99.533.
Bond Valuation and Yield to Maturity
Maturity Coupon Yield to Compounding Date Computed
Redemption Date Rate Maturity Per/Year Basis Bond Price
1-Sep-2012 8.250% 7.821% 2 1 102.839
Semiannual Coupon Interest Payments
Maturity Date of 1 September 2012
Bond Investor's Required Yield to Maturity of 7.821%
Purchased and Settled on 26 February 2003
Actual Number of Days per Month and Year
Bond Yield to Maturity Example:
Semiannual Coupon Interest Payments
Quoted Bond Price of 110.875 on 26 February 2003
Purchased and Settled on 26 February 2003
Actual Number of Days per Month and Year
This bond would trade at 102.839% of its maturity value ($1,000) or
$1,028.39 for investors with a required yield to maturity of 7.821%
Bond Valuation and Yield to Maturity
Maturity Coupon Quoted Compounding Date Yield to
Redemption Date Rate Price Per/Year Basis Maturity
1-Jul-2019 8.375% 110.875 2 1 7.229%
Maturity Discount Date Computed
Redemption Date Rate Basis Price
3-Jun-2003 2.144% 1.00 99.430
Valuation and Yield to Maturity of Pure Discount Instruments:
The PRICEDISC function may be used to value a pure discount instrument such as commercial paper
and the YIELDDISC function is used to determine the yield to maturity of pure discount instruments.
As with the PRICE and YIELD functions it is necessary to specify the "day count basis"; how the
number of days per month and the number of days in a year calculated. Excel provides five alternatives
to specifying this basis. The actual number of days per month and per year has been used in these
As with bonds, prices on pure discount instruments are quoted as a percentage of the final maturity
Commercial Paper Valuation Example:
Citicorp Commercial Paper Issue of $10,000,000
Maturity Date of 3 June 2003
Investor's Required Discount Rate of 2.144%
Purchased and Settled on 26 February 2003
Actual Number of Days per Month and Year
Commercial Paper Yield Example:
SBC Communications, Inc. Commercial Paper Issue of $100,000,000
Maturity Date of 14 July 2003
This bond would trade at a yield to maturity of 7.229% at a quoted price of 110.875.
This commercial paper would trade at 99.430% of its maturity value ($10,000,000)
or $9,943,000 for investors with a required yield to maturity (discount rate) of
Bond Valuation and Yield to Maturity
Maturity Quoted Date Computed
Redemption Date Price Basis Yield
14-Jul-2003 98.283 1.00 4.621%
Maturity Discount Computed
Redemption Date Rate Price
12-Jun-2003 1.194% 99.648
Maturity Date of 14 July 2003
Reported Market Price of the Paper of 98.283
Purchased and Settled on 26 February 2003
Actual Number of Days per Month and Year
Valuation and Yield to Maturity of U.S. Government Treasury Bills
U.S. Government Treasury Bills are also pure discount instruments. Treasury Bills might be valued
using the PRICEDISC function presented above or with the TBILLPRICE function. In a similar
manner the YIELDDISC function maybe used to determine the yield to maturity of Treasury Bills or
the TBILLYIELD function might be used. Both the TBILLPRICE and the TBILLYIELD functions
assume a day count basis of 360 days per year.
As with bonds, Treasury Bills prices are quoted as a percentage of the final maturity value.
U.S. Government Treasury Bill Valuation Example:
Treasury Bill Issue of $1,000,000
Maturity Date of 12 June 2003
Investor's Required Discount Rate of 1.194%
Purchased and Settled on 26 February 2003
This commercial paper would trade at a yield to maturity of 4.621% at a quoted price of
Bill would trade at 99.648% of its maturity value ($1,000,000) or $996,480 for investors
with a required yield to maturity (discount rate) of 1.194%
Bond Valuation and Yield to Maturity
Maturity Quoted Computed
Redemption Date Price Yield
14-Jul-2003 99.533 1.224%
U.S. Government Treasury Bill Yield Example:
Treasury Bill Issue of $1,000,000
Maturity Date of 24 Jul4 2003
Market Price of the Treasury Bill of 99.533
Purchased and Settled on 26 February 2003
Bill would trade at a yield to maturity of 1.224% at a quoted price of 99.533.
Examples: Zero Positive
AT & T Bonds Coupon Coupon
Coupon Rates 0.000% 8.000%
Semiannual Compounding Yes Yes
Maturity Date 15-Jan-2013 15-Jan-2013
Quoted Bond Prices 50.257 107.106
Yield to Matuity 7.000% 7.000%
Settlement Date 15-Jan-2003 15-Jan-2003
Basis Actual/Actual Actual/Actual
Examples Settlement Maturity Coupon Price Redemption
Date Date
Zero Coupon
Positive Coupon
Bond Duration:

As an alternative to measuring the life of a bond by its maturity, the duration of a bond may
also be calculated. Like maturity, a bond's duration is expressed in years.

The duration of a bond may be thought of as the present value weighted life of the coupon
interest payments and the principal repayment at maturity. This is in contrast to maturity
which measures only the life of the principal repayment.

The mathematical formula for duration is as follows:







The conventions for using the DURATION function in Excel are the same as the PRICE and
YIELD functions for bonds.

1
1
* *
(1 ) (1 )
(1 ) (1 )
t N
t
t N
t
t N
t
t N
t
t Coupon N MaturityValue
k k
Duration of Bond
Coupon MaturityValue
k k
=
=
=
=
(
+
(
+ +
¸ ¸
=
(
+
(
+ +
¸ ¸
¿
¿
The zero coupon bond has a duration equal to its maturity. This is consistent with a single
principle repayment being made in exactly ten years. In constrast, the postive coupon bond
has a duration of 7.1776 years. The shorter duration of the postive coupon bond is due
to the coupon payments made at dates earlier than the maturity.
The formula solutions to both of these examples are shown below:
000 . 10
) 07 . 1 (
1000 $
) 07 . 1 (
0 $
) 07 . 1 (
1000 $ * 10
) 07 . 1 (
0 $ *
10
1
10
1
10
=
(
¸
(

¸

+
(
¸
(

¸

+
=
¿
¿
=
=
=
=
t
t
N t
t
t
t
t
Bond of Duration
10
10
1
10
1
*$80 10*$1000
(1.07) (1.07)
7.1776
$80 $1000
(1.07) (1.07)
t
t
t
t
t N
t
t
Duration of Bond
=
=
=
=
(
+
(
¸ ¸
= =
(
+
(
¸ ¸
¿
¿
Examples:
AT & T Bonds
Coupon Rates
Semiannual Compounding
Maturity Date
Quoted Bond Prices
Yield to Matuity
Settlement Date
Basis
Frequency Basis Yield to Duration Time to Examples Settlement
Maturity Maturity Date
Zero Coupon 15-Jan-2003
Positive Coupon 15-Jan-2003
As an alternative to measuring the life of a bond by its maturity, the duration of a bond may
The duration of a bond may be thought of as the present value weighted life of the coupon
interest payments and the principal repayment at maturity. This is in contrast to maturity
The conventions for using the DURATION function in Excel are the same as the PRICE and
The zero coupon bond has a duration equal to its maturity. This is consistent with a single
principle repayment being made in exactly ten years. In constrast, the postive coupon bond
Zero Positive
Coupon Coupon
0.000% 8.000%
Yes Yes
15-Jan-2013 15-Jan-2013
50.257 107.106
7.000% 7.000%
15-Jan-2003 15-Jan-2003
Actual/Actual Actual/Actual
Maturity Coupon Price Redemption Frequency Basis Yield to
Date Maturity
15-Jan-2013 0.00% 50.257 100 2 1 7.000%
15-Jan-2013 8.00% 107.106 100 2 1 7.000%
Duration Time to
Maturity
10.0000 10.0007
7.1776 10.0007
Additional Examples:
Bond Valuation
Company Settlement Maturity Interest
Date Redemption Date Payment Dates
AT & T 4-Oct-02 1-Aug-14 F, A 1
Abbot Labs 10-Sep-02 15-Jun-11 J, D 15
Dominion Resources 23-Oct-02 15-Feb-24 F, A 15
Goodyear 1-Nov-02 1-Jan-08 J, J 1
Sears 15-Nov-02 15-Jul-18 J, J 15
Xerox 1-Jan-03 1-Jan-21 J, J 1
Bond Yield to Maturity
Company Settlement Maturity Interest
Date Redemption Date Payment Dates
Bank of America 4-Sep-02 1-Jul-10 J, J 1
Exxon/Mobil 15-Oct-02 15-Jul-18 J, J 15
IBM 7-Nov-02 15-Mar-21 M, S 15
McDonalds 20-Nov-02 1-Apr-20 A, O 1
Safeway 15-Dec-02 1-Feb-09 F, A 1
U S Airways 15-Jan-03 1-Feb-26 F, A 1
Bond Duration Examples
Company Settlement Maturity Interest
Date Redemption Date Payment Dates
ConAgra Foods 5-Oct-2002 15-Jun-2008 J, D 15
CIT Group 12-Dec-2002 1-Jan-2010 J, J 1
Disney 18-Jan-2003 1-Jun-2116 J, D 1
Household Finance 15-Feb-2003 15-Aug-2008 F, A 15
Northfork and Southern 5-Apr-2003 1-Mar-2019 M, S 1
SunTrust 15-Jun-2003 15-Jul-2024 J, J 15
Coupon Yield to Computed
Rate Maturity Bond Prices
6.875% 6.421%
8.125% 8.873%
7.250% 6.825%
8.375% 9.142%
8.925% 8.175%
9.625% 8.885%
Coupon Quoted Yield to
Rate Price Maturity
6.750% 98.250
8.625% 102.375
9.125% 101.750
7.925% 93.875
7.250% 106.750
11.500% 90.250
Coupon Yield to
Rate Maturity Duration
5.850% 5.123%
5.150% 5.898%
8.250% 7.478%
7.875% 8.385%
8.750% 8.210%
7.400% 6.942%
Solutions:
Bond Valuation Examples
Company Settlement Maturity Interest Coupon Yield to
Date Redemption Date Payment Dates Rate Maturity
AT & T 4-Oct-02 1-Aug-14 F, A 1 6.875% 6.421%
Abbot Labs 10-Sep-02 15-Jun-11 J, D 15 8.125% 8.873%
Dominion Resources 23-Oct-02 15-Feb-24 F, A 15 7.250% 6.825%
Goodyear 1-Nov-02 1-Jan-08 J, J 1 8.375% 9.142%
Sears 15-Nov-02 15-Jul-18 J, J 15 8.925% 8.175%
Xerox 1-Jan-03 1-Jan-21 J, J 1 9.625% 8.885%
Bond Yield to Maturity Examples
Company Settlement Maturity Interest Coupon Quoted
Date Redemption Date Payment Dates Rate Price
Bank of America 4-Sep-02 1-Jul-10 J, J 1 6.750% 98.250
Exxon/Mobil 15-Oct-02 15-Jul-18 J, J 15 8.625% 102.375
IBM 7-Nov-02 15-Mar-21 M, S 15 9.125% 101.750
McDonalds 20-Nov-02 1-Apr-20 A, O 1 7.925% 93.875
Safeway 15-Dec-02 1-Feb-09 F, A 1 7.250% 106.750
U S Airways 15-Jan-03 1-Feb-26 F, A 1 11.500% 90.250
Bond Duration Examples
Company Settlement Maturity Interest Coupon Yield to
Date Redemption Date Payment Dates Rate Maturity
ConAgra Foods 5-Oct-2002 15-Jun-2008 J, D 15 5.850% 5.123%
CIT Group 12-Dec-2002 1-Jan-2010 J, J 1 5.150% 5.898%
Disney 18-Jan-2003 1-Jun-2116 J, D 1 8.250% 7.478%
Household Finance 15-Feb-2003 15-Aug-2008 F, A 15 7.875% 8.385%
Northfork and Southern 5-Apr-2003 1-Mar-2019 M, S 1 8.750% 8.210%
SunTrust 15-Jun-2003 15-Jul-2024 J, J 15 7.400% 6.942%
Computed
Bond Prices
103.710
95.488
104.723
96.876
106.540
106.587
Computed
Yield to
Maturity
7.043%
8.349%
8.927%
8.609%
5.919%
12.824%
Duration
4.8580
5.8365
13.7351
4.5558
8.9672
10.9061