Bond valuation (lecture 3)

Содержание

Слайд 2

Lecture 3. Bond Valuation

Lecture 3. Bond Valuation

Слайд 3

Definition of Bond
Terminology & Characteristics of Bonds
Bond Valuation
Premium Bonds vs Discount Bonds
Yield

Definition of Bond Terminology & Characteristics of Bonds Bond Valuation Premium Bonds
to Maturity (YTM)
Important factors in bond relationship
Exercise

Contents :

Слайд 4

A type of debt (long-term promissory note) issued by the borrower,

A type of debt (long-term promissory note) issued by the borrower, promising
promising to pay fixed coupon (interest) payments at fixed intervals (6 months, 1 year etc ) and pay the par value at maturity.

Definition of Bonds…

Слайд 5

Par value = $1,000
Coupon = 6.5% on par value per year,
or $65

Par value = $1,000 Coupon = 6.5% on par value per year,
per year ($32.50 every six months).
Maturity = 28 years (matures in 2048).
Issued by AT&T.

Example:

Слайд 7

Different Types of Bonds

Debentures: Unsecured long-term debt.
Subordinated debentures: Bonds that have a

Different Types of Bonds Debentures: Unsecured long-term debt. Subordinated debentures: Bonds that
lower claim on assets in the event of liquidation than do other senior debt holders.
Mortgage bonds: Bonds secured by a lien on specific assets of the firm, such as real estate.
Eurobonds: Bonds issued in a country different from the one in whose currency the bond is denominated; for instance, a bond issued in Europe or Asia that pays interest and principal in U.S. dollars.
Zero and low coupon bonds: Allow the issuing firm to issue bonds at a substantial discount from their $1,000 face value with a zero or very low coupon.

Слайд 8

Different Types of Bonds

Junk Bonds: bonds rated BB or below
Treasury Bonds: Bonds

Different Types of Bonds Junk Bonds: bonds rated BB or below Treasury
issued by the federal government, sometimes referred to as government bonds.
Corporate Bonds: Bonds issued by corporations.
Call Provision: A provision in a bond contract that gives the issuer the right to redeem the bonds under specified terms prior to the normal maturity date.
Convertible Bond: A bond that is exchangeable, at the option of the holder, for common stock of the issuing firm

Слайд 9

Terminologies of bond

Terminologies of bond

Слайд 10

The Fundamental Valuation Model

This model can express the price of any asset

The Fundamental Valuation Model This model can express the price of any
at t = 0 mathematically.

Слайд 11

Valuing Coupon Bonds

A non-zero coupon-paying bond is a coupon paying bond with

Valuing Coupon Bonds A non-zero coupon-paying bond is a coupon paying bond
a finite life.

(1 + kd)1

(1 + kd)2

(1 + kd)n

V =

+

+ ... +

C

C + MV

C

= Σ

n

t=1

(1 + kd)t

C

V = C (PVIFA kd, n) + MV (PVIF kd, n)

(1 + kd)n

+

MV

Слайд 12

Valuing Zero Coupon Bonds

A zero coupon bond is a bond that pays

Valuing Zero Coupon Bonds A zero coupon bond is a bond that
no interest but sells at a deep discount from its face value; it provides compensation to investors in the form of price appreciation.

(1 + kd)n

V =

MV

= MV (PVIFkd, n)

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? 1000* 0.0573

Слайд 13

Valuing Perpetual Bonds

A perpetual bond is a bond that never matures. It

Valuing Perpetual Bonds A perpetual bond is a bond that never matures.
has an infinite life.

(1 + kd)1

(1 + kd)2

(1 + kd)∞

V =

+

+ ... +

C

C

C

= Σ


t=1

(1 + kd)t

C

or C (PVIFA kd, ∞ )

V = C / kd [Reduced Form]

Example. Bond P has a $1,000 face value and provides an 8% annual coupon. The appropriate discount rate is 10%. What is the value of the perpetual bond?

Слайд 14

Non-annual Compounding

Semiannually m=2
Quarterly m=4
Monthly m=12
Weekly m=52
Daily m=365

Non-annual Compounding Semiannually m=2 Quarterly m=4 Monthly m=12 Weekly m=52 Daily m=365

Слайд 15

Semiannual Compounding

A non-zero coupon bond adjusted for semiannual compounding.

An example....
Value a T-Bond

Semiannual Compounding A non-zero coupon bond adjusted for semiannual compounding. An example....

Par value = $1,000
Maturity = 2 years
Coupon rate = 4%
k = 4.4% per year

Слайд 16

Bond Premiums and Discounts

What happens to bond values if the required return

Bond Premiums and Discounts What happens to bond values if the required
is not equal to the coupon rate?

The bond's price will differ from its par value.

Слайд 17

Yield to Maturity (YTM)/Expected Rate of Return

Also called Expected Rate of Return

Estimate

Yield to Maturity (YTM)/Expected Rate of Return Also called Expected Rate of
of return investors earn if they buy
the bond at P0 and hold it until maturity

The YTM on a bond selling at par will always equal
the coupon rate.

YTM is the discount rate that equates the
PV of a bond’s cash flows with its price.

Слайд 18

Determining the YTM: Interpolation

Julie Miller want to determine the YTM for an

Determining the YTM: Interpolation Julie Miller want to determine the YTM for
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 (face value = $1000).
What is the YTM?

Слайд 19

Interpolation formula

V=$1,250 shows bond sells on premium (higher than par value 1,000)
Therefore,

Interpolation formula V=$1,250 shows bond sells on premium (higher than par value
Coupon rate is higher than rate of return (YTMSo we try next highest rate after 10%
Try 9%
$1,250 = $100(PVIFA9%,15) + $1,000(PVIF9%, 15)
$1,250 = $806.07 + $274.50
= $1,080.57 [Rate is too high!]
Try 8%
$1,250 = $100(PVIFA8%,15) + $1,000(PVIF8%, 15)
$1,250 = $855.95 + $315.2
= $1,171.15 [Rate is still higher]
Value $1,171.15(k=8%) is closer to $1,250 than the value $1,080.57(k=9%), so we drop value $1,080.57(k=9%)

Слайд 20

Solution

Try 7%
$1,250 = $100(PVIFA7%,15) + $1,000(PVIF7%, 15)
$1,250 = $910.79 + $362.4
=

Solution Try 7% $1,250 = $100(PVIFA7%,15) + $1,000(PVIF7%, 15) $1,250 = $910.79
$1,273.19 [Rate is low!]
YTM = 7.22%
What is the meaning of V=$1250 at YTM=7.22%?

Слайд 21

Decision making

With the given rate of return (7.22%), If the bond is

Decision making With the given rate of return (7.22%), If the bond
sold at a price above the bond value ( $1250) it is known as overvalued and investor should not buy the bond, or can sell existing bonds if any.
With the given rate of return (7.22%), If the bond is sold at a price below the bond value($1250) it is known as undervalued and a wise decision is to invest in those bonds, or should not sell existing bonds if any.

Слайд 22

Determining the YTM: Approximation Method
C = dollar amount of interest
MV = face

Determining the YTM: Approximation Method C = dollar amount of interest MV
value of bond
P = price of bond
n = number of years to maturity
In the previous example,

Слайд 23

FIRST RELATIONSHIP
The value of the bond is inversely related to changes in

FIRST RELATIONSHIP The value of the bond is inversely related to changes
the investor’s required rate of return (current interest rate) kb
If kd decrease , the value of the bond will increase
If kd increase , the value of the bond will decrease

FIVE IMPORTANT RELATIONSHIPS

Слайд 24

FIVE IMPORTANT RELATIONSHIPS

SECOND RELATIONSHIP
The market value (Po) will be less than the

FIVE IMPORTANT RELATIONSHIPS SECOND RELATIONSHIP The market value (Po) will be less
par value (M) if the investor’s required rate of return (kb) is above the coupon rate (I), but it will be valued above the par value if the investor’s required rate of return (kb) is below the coupon rate (I),
If kd = C , then MV = Po (sold at par)
If kd > C , then MV > Po (discount bond)
If kd < C , then MV < Po (premium bond)

Слайд 25

FIVE IMPORTANT RELATIONSHIPS

THIRD RELATIONSHIP
As the maturity approaches, the market value of the

FIVE IMPORTANT RELATIONSHIPS THIRD RELATIONSHIP As the maturity approaches, the market value
bond approaches its par value
FOURTH RELATIONSHIP
Change in price due to changes in interest rates
Long term bond have greater interest rate risk than do short –term bonds
Low coupon rate bonds have more price risk than high coupon rate bonds

Слайд 26

Relationship between bond value & interest rate

Relationship between bond value & interest rate

Слайд 27

FIVE IMPORTANT RELATIONSHIPS
FIFTH RELATIONSHIP
The sensitivity of a bond’s value to changing -

FIVE IMPORTANT RELATIONSHIPS FIFTH RELATIONSHIP The sensitivity of a bond’s value to
depends on:
Length of time to maturity
The pattern of the cash flows provided by the bond

Слайд 28

Exercise: YTM with semiannual coupon

Suppose a bond with a 10% coupon rate

Exercise: YTM with semiannual coupon Suppose a bond with a 10% coupon
and semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $1197.93.
Is the YTM more or less than 10%?
What is the semiannual coupon payment?
How many periods are there?
Calculate the YTM.

Слайд 29

Solution

 

Solution
Имя файла: Bond-valuation-(lecture-3).pptx
Количество просмотров: 36
Количество скачиваний: 0