This PPT especially for Bond Valuation,

1. 1
1
Bonds and Their Valuation

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.

4. 4
Key Features of a Bond
• Par value = face amount of the bond, which is paid at maturity
(assume $1,000).
=

5. 5
Key Features of a Bond
• Coupon rate – stated interest rate (generally fixed) paid by the
issuer. Multiply by par to get dollar payment of interest.

6. 6
Key Features of a Bond
• Maturity date – when the bond must be repaid.
• Yield to maturity - rate of return earned on a bond held until
maturity.

7. 7
Bond Value
•Bond Value = PV(coupons) + PV(par)
•Bond Value = PV(annuity) + PV(lump sum)
•Remember:
• As interest rates increase present values decrease
• ( r → PV  )
• As interest rates increase, bond prices decrease
and vice versa

8. 8
The Bond-Pricing Equation
n
n
i)
(1
FV/MV
i
i)
(1
1
-
1
I
Value
Bond

















9. 9
9
Bond Valuation
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 where the Face Value of the bond
is $1,000.
What are the annual interest payments ($)?

10. 10
10
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:

11. 11
11
$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:

12. 12
12
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?

13. 13
13
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

14. 14
14
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

15. 15
Semiannual Bonds
• 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

16. 16
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


















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)

17. 17
 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

18. 18
Valuing a Discount Bond
with Annual Coupons
• Coupon rate = 10%
• Annual coupons
• Par = $1,000
• Maturity = 5 years
• YTM = 11%
• Price= ?

19. 19
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)

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

21. 21
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)

22. 22
Bond Yields
• Current Yield - Annual coupon payments divided by bond price.
• Yield To Maturity - Interest rate for which the present value of the
bond’s payments equal the price. Also known as the market’s
required rate of return.
• Yield To Maturity = total expected return = current yield + expected
capital gains yield (change in price)
22

23. 23
Yield Definitions





















CGY
Expected
CY
Expected
YTM
return
total
Expected
price
Beginning
price
in
Change
(CGY)
yield
gains
Capital
price
Current
payment
coupon
Annual
(CY)
eld
Current yi
23

24. 24
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

25. 25
Bond values over time
• At maturity, the value of any bond must equal its par value.
• If rd remains constant:
• The value of a premium bond would decrease over time, until it reached
$1,000.
• The value of a discount bond would increase over time, until it reached
$1,000.
• A value of a par bond stays at $1,000.
25

26. 26
Changes in Bond Value over Time
• What would happen to the value of these three bonds
is bond if its required rate of return remained at 10%:
26
Years
to Maturity
1,184
1,000
816
10 5 0
13% coupon rate
7% coupon rate
10% coupon rate.
VB

27. 27
Types of Bonds
• Vanilla – fixed coupons, repaid at maturity
• Zero Coupon – pay no explicit interest but instead, sell at a deep
discount
• Convertible – can be converted into to stock

28. 28
Zero Coupon Bonds
• A zero coupon bond has a specific maturity date when it returns the
bond principal
• A zero coupon bond pays no periodic income
• The only cash inflow is the par value at maturity
28

29. 29
Zero Coupon Bonds
• For a zero-coupon bond (annual and semiannual compounding):
29
0
0 2
(1 )
(1 / 2)
t
t
Par
P
R
Par
P
R





30. 30
Zero Coupon Bonds (cont’d)
Example
A zero coupon bond has a par value of $1,000 and currently
sells for $400. The term to maturity is twenty years.
What is the yield to maturity (assume semiannual
compounding)?
30

31. 31
Zero Coupon Bonds (cont’d)
Example (cont’d)
Solution:
31
0 2
40
(1 / 2)
$1,000
$400
(1 / 2)
4.63%
t
Par
P
R
R
R






32. 32
Types of Bonds
• Junk Bonds – below investment grade

33. 33
Government Bonds
•Treasury Securities = Federal government debt
• Treasury Bills (T-bills)
• Pure discount bonds
• Original maturity of one year or less
• Treasury notes (T-notes)
• Coupon debt
• Original maturity between one and ten years
• Treasury bonds (T-bonds)
• Coupon debt
• Original maturity greater than ten years