Financial Management

Theory and Practice

Tenth Edition

Eugene F. Brigham

Michael C. Ehrhardt

Chapter 9

Bonds and their Valuation

Instructor: Sanam TaimoorInstitute of Business Management

Topics

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

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

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

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

Other Types of Bonds

• Floating Rate Bonds• Zero Coupon Bonds• Perpetual Bonds• Convertible Bonds

Bond Valuation

NkNkB dd PVIFMPVIFAINTV ,,

INT = Coupon Interest M = Par valueKd = Market rate of interestN = Number of years before the bond matures

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.

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?

VB = $80 / 10% = $800

dBk

IV

• 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?

Zero Coupon Bond Example

Nk

nd

B dPVIFMk

MV ,

1

V = $1,000 (PVIF10%, 30)= $1,000 (.057)

= $57.00

Semi Annual Compounding

• Some Bonds pay interest twice a year

• Adjustments needed– Divide kd by 2

–Multiply N by 2–Divide INT by 2

• 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

Semi Annual Compounding Example

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

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?

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!]

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!]

Calculating YTM

• YTM Solution (Interpolate)

• Answer: 12.90%

Calculating YTM

BA

AabaYTM

a = Lower interest rateb = Higher interest rateA = Value at lower rateB = Value at higher rate

• 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%

Calculating YTM

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

Coupon Rate

MARKET REQUIRED RATE OF RETURN (%) Coupon Rate

MARKET REQUIRED RATE OF RETURN (%)

BON

D P

RICE

($)

1000

1600

1400

1200

600

00 2 4 6 8 10 12 14 16 18

5 Year

15 Year

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

Bond Price- Interest Rate Relationship

Coupon Rate

MARKET REQUIRED RATE OF RETURN (%) Coupon Rate

MARKET REQUIRED RATE OF RETURN (%)

BON

D P

RICE

($)

1000

1600

1400

1200

600

00 2 4 6 8 10 12 14 16 18

15 Year

5 Year

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.

Bond Price- Interest Rate Relationship

Coupon Rate

MARKET REQUIRED RATE OF RETURN (%) Coupon Rate

MARKET REQUIRED RATE OF RETURN (%)

BON

D P

RICE

($)

1000 Par

1600

1400

1200

600

00 2 4 6 8 10 12 14 16 18

15 Year

5 Year

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).

Bond Price- Interest Rate Relationship