CHAPTER 4

Bonds and Their Valuation

    Key features of bonds Bond valuation Measuring yield Assessing risk

6-1

n n

Definition of a Bond

A bond is a security that obligates the issuer to make specified interest and principal payments to the holder on specified dates.

   Coupon rate Face value (or par) Maturity (or term) Bonds are sometimes called fixed income securities.

6-2

Valuation of Financial Assets: Bonds long term debt instruments

Key Terms

  Principal Amount, Face Value, Maturity Value, Par Value: The amount of money the firm borrows and promises to repay at some future date, often at maturity.

Coupon Payment: The specified number of dollars of interest paid each period, generally each six months, on a bond.

6-3

Key Terms

  Coupon Interest Rate: The stated annual rate of interest paid on a bond.

Maturity Date: A specified date on which the par value of a bond must be repaid.

6-4

Types of Bonds

n n n Pure Discount or Zero-Coupon Bonds  Pay no coupons prior to maturity.

 Pay the bond’s face value at maturity.

Coupon Bonds   Pay a stated coupon at periodic intervals prior to maturity.

Pay the bond’s face value at maturity.

Perpetual Bonds (Consols)  No maturity date.

 Pay a stated coupon at periodic intervals.

6-5

Bond Issuers

n n n Federal Government Local Municipalities Corporations

6-6

U.S. Government Bonds

n n Treasury Bills    No coupons (zero coupon security) Face value paid at maturity Maturities up to one year Treasury Notes    Coupons paid semiannually Face value paid at maturity Maturities from 2-10 years

6-7

n n

U.S. Government Bonds

Treasury Bonds     Coupons paid semiannually Face value paid at maturity Maturities over 10 years The 30-year bond is called the long bond.

Treasury Strips   Zero-coupon bond Created by “stripping” the coupons and principal from Treasury bonds and notes.

6-8

Yield Curve

6-9

Municipal Bonds

n n n n Maturities from one month to 40 years.

Exempt from federal, state, and local taxes.

Generally two types:   Revenue bonds General Obligation bonds Riskier than U.S. Government bonds.

6-10

Corporate Bonds

n n Secured Bonds (Asset-Backed)   Secured by real property Ownership of the property reverts to the bondholders upon default.

Debentures   General creditors Have priority over stockholders, but are subordinate to secured debt.

6-11

Basic Valuation

From “The Time Value of Money” we realize that the value of anything is based on the present value of the cash flows the asset is expected to produce in the future.

6-12

Basic Valuation

 value  V    1 

^

k 1  1 N  t  1  1 

^

k t  t   1 

^

k 2  2    1 

^

k N  N

^

CF t = the cash flow expected to be generated by the asset in period t k = the return investors consider appropriate for holding such an asset--usually referred to as the required return- based on riskiness and economic conditions.

6-13

The Basic Bond Valuation Model

    k d = required rate of return on a debt instrument N = number of years before the bond matures INT = dollars of interest paid each year (Coupon rate x Par value) M = par or face, value of the bond to be paid off at maturity

6-14

Bond Value

V d   t  1  INT N   1 k d  1  1   1  INT k d  2 INT k d t   1  M k d     N  1  INT k d   1  M k d  N

6-15

Value of a Bond What is the value of a 10-year, 10% semiannual coupon bond, if k d = 10%?

=PV(0.05,20,100,1000,0) = ?

INPUTS OUTPUT 20 N 5 I/YR PV ?

50 PMT 1000 FV 6-16

Value of a Bond

What is the value of a 10-year, 10% semiannual coupon bond, if k d = 12%?

=PV

INPUTS OUTPUT N I/YR PV ?

PMT FV 6-17

Value of a Bond

What is the value of a 10-year, 10% semiannual coupon bond, if k d = 8%?

=PV

INPUTS OUTPUT N I/YR PV ?

PMT FV 6-18

Changes in Bond Values Over Time

   Par Bond ($1,000):  A bond that sells at par value, which occurs whenever the going rate of interest is equal to the coupon rate.

Discount Bond (< $1,000):  A bond that sells below its par value, which occurs whenever the going rate of interest rises above the coupon rate.

Premium Bond (>$1,000):  A bond that sells above its par value, which occurs whenever the going rate of interest falls below the coupon rate.

6-19

Yield-to-maturity (YTM)

 What is the YTM of a 10-year, 10% semiannual coupon bond, if the current price is $1,000?

=RATE(20,50,-1000,1000,0) = ?

INPUTS OUTPUT 20 N I/YR ?

- 1,000 PV 50 PMT 1000 FV 6-20



Yield-to-maturity (YTM)

What is the YTM of a 10-year, 10% semiannual coupon bond, if the current price is $1,100?

=RATE

INPUTS OUTPUT N I/YR ?

PV PMT FV 6-21



Yield-to-maturity (YTM)

What is the YTM of a 10-year, 10% semiannual coupon bond, if the current price is $900?

=RATE

INPUTS OUTPUT N I/YR ?

PV PMT FV 6-22

Changes in Bond Values Over Time

   An increase in interest rates will cause the price of an outstanding bond to fall.

A decrease in interest rates will cause the price to rise.

The market value of a bond will always approach its par value as its maturity date approaches, provided the firm does not go bankrupt.

6-23

Time path of value of a 15% Coupon, $1000 par value bond when interest rates are 10%, 15%, and 20% Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 k d = 10% k d = 15% $1,380.30 $1,000.00

$1,368.33 $1,000.00

$1,355.17 $1,000.00

$1,340.68 $1,000.00

$1,324.75 $1,000.00

$1,307.23 $1,000.00

$1,287.95 $1,000.00

$1,266.75 $1,000.00

$1,243.42 $1,000.00

$1,217.76 $1,000.00

$1,189.54 $1,000.00

$1,158.49 $1,000.00

$1,124.34 $1,000.00

$1,086.78 $1,000.00

$1,045.45 $1,000.00

$1,000.00 $1,000.00

k d = 20% $766.23

$769.47

$773.37

$778.04

$783.65

$790.38

$798.45

$808.14

$819.77

$833.72

$850.47

$870.56

$894.68

$923.61

$958.33

Changes in Bond Values Over Time

 Time path of value of a 15% Coupon, $1000 par value bond when interest rates are 10%, 15%, and 20% Bond Value $1,500 $1,250 k d = Coupon Rate $1,000 $750 $500 k d k d < Coupon Rate > Coupon Rate $250 $0 1 3 5 7 9 11 13 15 Years

6-25

YTM = CY + CGY

     YTM = Total return Current Yield (CY) = Return from Interest Capital Gains Yield (CGY) = Return from the difference in purchase price and face value CY = Annual Int ($) / Price ($) CGY = YTM - CY

6-26

An example: Current and capital gains yield  Find the current yield and the capital gains yield for a 10-year, 9% semiannual coupon bond that sells for $887, and has a face value of $1,000.

YTM = 10.88% Current yield = $90 / $887 = 0.1015 = 10.15% CGY= YTM – CY = 10.88% - 10.15% = 0.73%

6-27

Call provision (YTC)

A bond that sells for $950, has five years to maturity, 10 percent semi-annual coupon, and is callable in 2 years at a $50 call premium. What is the yield-to-call?

 YTC = RATE(4,50,-950,1050) = ?

6-28

Call provision (YTC)

A bond that sells for $1075, has 14 years to maturity, 8 percent semi-annual coupon, and is callable in 5 years at a $50 call premium. What is the yield-to-call?

 YTC = ?

6-29

Interest rate risk

6-30

Interest rate risk

6-31

Interest rate risk

6-32

Interest rate risk

6-33

Default risk

  If an issuer defaults, investors receive less than the promised return. Therefore, the expected return on corporate and municipal bonds is less than the promised return.

Influenced by the issuer’s financial strength and the terms of the bond contract.

6-34

Bond Ratings

Moody’s Aaa S&P AAA Quality of Issue Highest quality. Very small risk of default.

Aa A Baa Ba B Caa Ca C D AA A BBB BB B CCC CC C High quality. Small risk of default.

High-Medium quality. Strong attributes, but potentially vulnerable.

Medium quality. Currently adequate, but potentially unreliable.

Some speculative element. Long-run prospects questionable.

Able to pay currently, but at risk of default in the future.

Poor quality. Clear danger of default .

High specullative quality. May be in default.

Lowest rated. Poor prospects of repayment.

In default.

6-35

Factors affecting default risk and bond ratings   Financial performance  Debt ratio   TIE ratio Current ratio Bond contract provisions    Secured vs. Unsecured debt Senior vs. subordinated debt Guarantee and sinking fund provisions  Debt maturity

6-36