1. Financial
Management Chapter 9
Theory and
Practice
Tenth Edition
Bonds and their Valuation
Eugene F. Brigham
Michael C. Ehrhardt
Instructor: Sanam Taimoor
Institute of Business Management

2. Topics
• Bonds and bond’s characteristics
• Types of bonds
• Bond Valuation
• Yield to Maturity
• Calculating YTM
• Bond Price and Yield relationship

3. BOND
• A long term contract under which a borrower
agrees to make payments of interest and
principal on specific date, to the holders of
the bond
• Bond Indenture
– Is a legal document that specifies both the rights
of the bondholders and duties of the issuing
corporation

4. Types of Bonds
• Treasury Bonds
– Issued by the government
• Corporate Bonds
– Issued by companies
• Municipal Bonds
– Issued by local governments
• Foreign Bonds
– Issued by foreign governments or companies

5. Characteristics of a Bond
• Par Value
– the stated face value of a bond
• Coupon Interest Rate
– the fixed “rate of interest” which remains the
same throughout the life of the bond
• Maturity Date
– Specified maturity date on which par value must
be paid
• Call Option
– It gives the issuer the opportunity to repurchase
the bonds prior to maturity

6. Other Types of Bonds
• Floating Rate Bonds
• Zero Coupon Bonds
• Perpetual Bonds
• Convertible Bonds

7. Bond Valuation
VB INT PVIFA kd , N M PVIF kd , N
INT = Coupon Interest
M = Par value
Kd = Market rate of interest
N = Number of years before the bond matures

8. Example
• Bond C has a $1,000 face value and provides
an 8% annual coupon for 30 years. The
appropriate discount rate is 10%. What is the
value of the coupon bond?
– VB = $80 (PVIFA10%, 30) + $1,000 (PVIF10%, 30)
= $80 (9.427) + $1,000 (.057)
= $754.16 + $57.00
= $811.16.

9. Perpetual Bond Example
• Bond P has a $1,000 face value and provides
an 8% coupon. The appropriate discount rate
is 10%. What is the value of the perpetual
bond?
I
VB
kd
VB = $80 / 10% = $800

10. Zero Coupon Bond Example
• Bond Z has a $1,000 face value and a 30-year
life. The appropriate discount rate is 10%.
What is the value of the zero-coupon bond?
M
VB n
M PVIF kd , N
1 kd
V = $1,000 (PVIF10%, 30)
= $1,000 (.057)
= $57.00

11. Semi Annual Compounding
• Some Bonds pay interest twice a year
• Adjustments needed
– Divide kd by 2
– Multiply N by 2
– Divide INT by 2

12. Semi Annual Compounding Example
• Bond C has a $1,000 face value and provides
an 8% semiannual coupon for 15 years. The
appropriate discount rate is 10% (annual rate).
What is the value of the coupon bond?
– VB = $40 (PVIFA5%, 30) + $1,000 (PVIF5%, 30)
= $40 (15.373) + $1,000 (.231)
= $614.92 + $231.00
= $845.92

13. Yield to Maturity
• The rate of return (Kd) that investors earn if
they buy a bond at a specified price and hold
it until maturity
• In other words it is the rate of interest that
sets the present value of the bond’s expected
future cash-flow stream equal to the bond’s
current market price

14. Calculating YTM
Consider a $1,000 par value bond with the
following characteristics : a current market price
of $ 761; 12 years until maturity and an 8%
coupon rate .
What is the YTM?

15. Calculating YTM
Try 10%:
$761 = $80(PVIFA10%,12) + $1,000(PVIF10%,12)
$761 = $80(6.814) + $1,000(.319)
$761 = $545.12 + $319
= $864.12
[Rate is too low!]

16. Calculating YTM
Try 15%
$761 = $80(PVIFA 15%,12) + $1,000(PVIF 15%, 12)
$761 = $80(5.421) + $1,000(.187)
$761 = $433.68 + $187
= $620.68
[Rate is too high!]

17. Calculating YTM
• YTM Solution (Interpolate)
b a A
YTM a
A B
a = Lower interest rate
b = Higher interest rate
A = Value at lower rate
B = Value at higher rate
• Answer: 12.90%

18. Calculating YTM
• Julie Miller want to determine the YTM for an
issue of outstanding bonds at Basket Wonders
(BW). BW has an issue of 10% annual coupon
bonds with 15 years left to maturity. The
bonds have a current market value of $1,250.
• 7.40%

19. Bond Price- Interest Rate Relationship
• A bond’s price and interest rates are inversely
related;
– When interest rates rise, bond’s price falls
– When interest rates fall, bond’s prices rises

20. Bond Price- Interest Rate Relationship
1600
BOND PRICE ($)
1400
1200
1000
5 Year
600
15 Year
0
0 2 4 6 8 10 12 14 16 18
Coupon Rate
MARKET REQUIRED RATE OF RETURN (%)

21. Bond Price- Interest Rate Relationship
• Assume that the required rate of return on a
15-year, 10% coupon-paying bond rises from
10% to 12%. What happens to the bond
price?
• When interest rates rise, then the market
required rates of return rise and bond prices
will fall

22. Bond Price- Interest Rate Relationship
1600
1400
BOND PRICE ($)
1200
1000
5 Year
600
15 Year
0
0 2 4 6 8 10 12 14 16 18
Coupon Rate
MARKET REQUIRED RATE OF RETURN (%)

23. Bond Price- Interest Rate Relationship
• Assume that the required rate of return on a
15-year, 10% coupon-paying bond falls from
10% to 8%. What happens to the bond price?
• When interest rates fall, then the market
required rates of return fall and bond prices
will rise.

24. Bond Price- Interest Rate Relationship
1600
1400
BOND PRICE ($)
1200
1000
Par 5 Year
600
15 Year
0
0 2 4 6 8 10 12 14 16 18
Coupon Rate
MARKET REQUIRED RATE OF RETURN (%)

25. Bond Price- Interest Rate Relationship
• Discount Bond -- The market required rate of
return exceeds the coupon rate (Par > P0 ).
• Premium Bond -- The coupon rate exceeds the
market required rate of return (P0 > Par).
• Par Bond -- The coupon rate equals the market
required rate of return (P0 = Par).