The document provides an overview of bonds, including their basic features such as par value, maturity date, yield to maturity, and coupon rate. It explains how to compute the value of bonds using present value calculations for both annual and semiannual payments, with examples illustrating bonds sold at a discount or premium. Key concepts discussed include bond valuation, cash flows, and the relationship between yield to maturity and coupon rates.

1. 1
1

2. 2
 Bonds are simply long-term IOUs that represent
claims against a firm’s assets.
 Bonds are a form of debt
 Bonds are often referred to as fixed-income
investments.
Bond Basics

3. 3
Key Features of a Bond
 Debt instrument issued by a corp. or government.
 Par value = face amount of the bond, which is paid
at maturity (assume $1,000).
 Maturity date – when the bond must be repaid.
 Yield to maturity - rate of return earned on a bond
held until maturity.
 Coupon rate – stated interest rate (generally fixed)
paid by the issuer. Multiply by par to get dollar
payment of interest.

4. 4
Bond Value
 Bond Value = PV(coupons) + PV(par)
 Bond Value = PV(annuity) + PV(lump sum)

5. 5
5
Bond Valuation
1. 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.

6. 6
6
0 1 2 3 4 5
2009 2010 2011 2012 2013
63.75 63.75 63.75 63.75 63.75
1,000.00
IBM Bond Timeline:

7. 7
7
$63.75 Annuity for 5 years $1000 Lump Sum in 5 years
0 1 2 3 4 5
2009 2010 2011 2012 2013
63.75 63.75 63.75 63.75 63.75
1000.00
IBM Bond Timeline:

8. 8
8
= 63.75 PMT , 1000 FV , 8% I , 5 N
= PV = 935.12
$63.75 Annuity for 5 years $1000 Lump Sum in 5 years
0 1 2 3 4 5
2009 2010 2011 2012 2013
63.75 63.75 63.75 63.75 63.75
1000.00
IBM Bond Timeline:

9. 9
9
Semi -Annual Bonds:
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?

10. 10
10
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.
0 1 2 3 4 5
2013 2014 2015 2016 2017
45 45.00
1000.00
45 45 45 45 45 45 45 45

11. 11
11
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
10 - N
Most Bonds Pay Interest Semi-Annually:
0 1 2 3 4 5
2013 2014 2015 2016 2017
45 45.00
1000.00
45 45 45 45 45 45 45 45

12. 12
12
Most Bonds Pay Interest Semi-Annually:
= PV = 961.39
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
0 1 2 3 4 5
2013 2014 2015 2016 2017
45 45
1,000
45 45 45 45 45 45 45 45

13. 13
Semiannual Bonds
Ex 2
 Coupon rate = 14% - Semiannual
 YTM = 16% (APR)
 Maturity = 7 years
 Value of bond?
 Number of coupon payments? (2t or N)
 14 = 2 x 7 years
 Semiannual coupon payment? (C/2 or PMT)
 $70 = (14% x Face Value)/2
 Semiannual yield? (YTM/2 or I/Y)
 8% = 16%/2

14. 14
Semiannual Bonds
 Semiannual coupon = $70
 Semiannual yield = 8%
 Periods to maturity = 14
 Bond value =
 70[1 – 1/(1.08)14] / .08 + 1000
/ (1.08)14 = 917.56
 
 2t
2t
2
YTM
1
F
2
YTM
2
YTM
1
1
-
1
2
C
Value
Bond
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
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

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
14
14
)
08
.
1
(
1000
08
.
0
)
08
.
1
(
1
1
70
B 














Using the calculator:
14 N
8 I/Y
70 PMT
1000 FV
CPT PV = -917.56
Using Excel: =PV(0.08, 14, 70, 1000, 0)

15. 15
 If bond Sells at a DISCOUNT (less than
$1,000) then YTM > Coupon Rate
 If bond Sells at a PREMIUM (more than
$1,000) then YTM < Coupon Rate
Yield to Maturity
-1,000
0 1 2 3 4 5
2013 2014 2015 2016 2017
80 80 80 80 80
1,000

16. 16
Valuing a Discount Bond
with Annual Coupons
 Coupon rate = 10%
 Annual coupons
 Par = $1,000
 Maturity = 5 years
 YTM = 11%
 Price= ?

17. 17
Valuing a Discount Bond
with Annual Coupons
 Coupon rate = 10%
 Annual coupons
 Par = $1,000
 Maturity = 5 years
 YTM = 11%
5
5
)
11
.
1
(
1000
11
.
0
)
11
.
1
(
1
1
100
B 














Using the formula:
B = PV(annuity) + PV(lump sum)
B = 369.59 + 593.45 = 963.04
Using the calculator:
5 N
11 I/Y
100 PMT
1000 FV
CPT PV = -963.04
Note: When YTM > Coupon rate  Price < Par = “Discount Bond”
Using Excel: =PV(0.11, 5, 100, 1000, 0)

18. 18
Valuing a Premium Bond
with Annual Coupons
 Coupon rate = 10%
 Annual coupons
 Par = $1,000
 Maturity = 20 years
 YTM = 8%
 Price = ?

19. 19
Valuing a Premium Bond
with Annual Coupons
 Coupon rate = 10%
 Annual coupons
 Par = $1,000
 Maturity = 20 years
 YTM = 8%
20
20
)
08
.
1
(
1000
08
.
0
)
08
.
1
(
1
1
100 














B
Using the formula:
B = PV(annuity) + PV(lump sum)
B = 981.81 + 214.55 = 1196.36
Note: When YTM < Coupon rate  Price > Par = “Premium Bond”
Using the calculator:
20 N
8 I/Y
100 PMT
1000 FV
CPT PV = -1196.36
Using Excel: =PV(0.08, 20, 100, 1000, 0)

20. 20
Yield to Maturity
 If an investor purchases a 6.375% annual
coupon bond today for $900 and holds it until
maturity (5 years), what is the expected annual
rate of return (YTM)?
-900
??
0 1 2 3 4 5
2013 2014 2015 2016 2017
63.75 63.75 63.75 63.75 63.75
1000.00
+ ??
900

21. 21
Yield to Maturity
63.75 =PMT 1000= FV 5= N -900 =PV
I = ? YTM??
• If an investor purchases a 6.375% annual coupon bond today for $900
and holds it until maturity (5 years), what is the expected annual rate of
return ? Will it be >< than 6.375%?
0 1 2 3 4 5
2013 2014 2015 2016 2017
63.75 63.75 63.75 63.75 63.75
1000.00

22. 22
What’s the YTM on a 10-year, 9% annual
coupon, $1,000 par value bond that sells for
$887?
90 90
90
0 1 9 10
rd=?
1,000
PV1
.
.
.
PV10
PVM
887 Find rd that “works”!
...

23. 23
10 -887 90 1000
N I/YR PV PMT FV
10.91
INPUTS
OUTPUT