Chapter 7 - Valuation and
Characteristics of Bonds
Chapter 8 - Stock Valuation
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Tujuan Pembelajaran 1
Mahasiswa mampu untuk:
Membedakan berbagai jenis obligasi dan menjelaskan
beberapa karakteristik obligasi yang populer
Menjelaskan definisi nilai untuk berbagai penggunaan
Menjelaskan faktor-faktor yang menentukan nilai
Menjelaskan proses dasar penilaian aset
Menghitung nilai obligasi dan yield to maturity
Menjelaskan lima hubungan penting pada penilaian
obligasi
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Pokok Bahasan 1
Jenis-jenis obligasi
Terminologi dan karakterisitik obligasi
Definisi nilai
Penentu nilai
Proses dasar penilaian
Penilaian obligasi
Yield to maturity
Lima hubungan penting pada penilaian obligasi
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Tujuan Pembelajaran 2
Mahasiswa mampu untuk:
Menguraikan karakterisitik dan ciri saham
preferen
Menghitung nilai saham preferen
Menjelaskan karakteristik dan ciri saham biasa
Menghitung nilai saham biasa
Menghitung tingkat imbal hasil yang
diharapkan dari saham
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Pokok Bahasan 2
Jenis dan ciri saham preferen
Me nilai saham preferen
Karakteristik saham biasa
Menilai saham biasa
Menghitung tingkat imbal hasil yang
diharapkan pemegang saham
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Characteristics of Bonds
 Bonds pay fixed coupon (interest)
payments at fixed intervals (usually
every six months) and pay the par
value at maturity.
$I
0
IIS
$I
1
$I
$I
$I
$I+$M
2
...
n
6
Example: AT&T 6 ½ 32
Par value = $1,000
Coupon = 6.5% or par value per year,
or $65 per year ($32.50 every six months).
Maturity = 28 years (matures in 2032).
Issued by AT&T.
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Example: AT&T 6 ½ 32
Par value = $1,000
Coupon = 6.5% or par value per year,
or $65 per year ($32.50 every six months).
Maturity = 28 years (matures in 2032).
Issued by AT&T.
$32.50
0
IIS
$32.50 $32.50 $32.50 $32.50 $32.50+$1000
1
2
…
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8
Types of Bonds
Debentures - unsecured bonds.
Subordinated debentures - unsecured
“junior” debt.
Mortgage bonds - secured bonds.
Zeros - bonds that pay only par value at
maturity; no coupons.
Junk bonds - speculative or belowinvestment grade bonds; rated BB and
below. High-yield bonds.
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Types of Bonds
Eurobonds - bonds denominated in
one currency and sold in another
country. (Borrowing overseas.)
example - suppose Disney decides to sell
$1,000 bonds in France. These are U.S.
denominated bonds trading in a foreign
country. Why do this?
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Types of Bonds
Eurobonds - bonds denominated in
one currency and sold in another
country. (Borrowing overseas).
example - suppose Disney decides to sell
$1,000 bonds in France. These are U.S.
denominated bonds trading in a foreign
country. Why do this?
If borrowing rates are lower in France.
To avoid SEC regulations.
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The Bond Indenture
The bond contract between the firm
and the trustee representing the
bondholders.
Lists all of the bond’s features:
coupon, par value, maturity, etc.
Lists restrictive provisions which are
designed to protect bondholders.
Describes repayment provisions.
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Value
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Book value: value of an asset as shown on
a firm’s balance sheet; historical cost.
Liquidation value: amount that could be
received if an asset were sold individually.
Market value: observed value of an asset
in the marketplace; determined by supply
and demand.
Intrinsic value: economic or fair value of
an asset; the present value of the asset’s
expected future cash flows.
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Security Valuation
In general, the intrinsic value of an
asset = the present value of the stream
of expected cash flows discounted at
an appropriate required rate of
return.
Can the intrinsic value of an asset
differ from its market value?
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Valuation
n
V =
S
t=1
$Ct
(1 + k)t
Ct = cash flow to be received at time t.
k = the investor’s required rate of return.
V = the intrinsic value of the asset.
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Bond Valuation
Discount the bond’s cash flows at
the investor’s required rate of
return.
The coupon payment stream (an
annuity).
The par value payment (a single
sum).
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Bond Valuation
S
n
Vb =
t=1
$It
(1 + kb)t
+
$M
(1 + kb)n
Vb = $It (PVIFA kb, n) + $M (PVIF kb, n)
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Bond Example
Suppose our firm decides to issue 20-year
bonds with a par value of $1,000 and
annual coupon payments. The return on
other corporate bonds of similar risk is
currently 12%, so we decide to offer a 12%
coupon interest rate.
What would be a fair price for these
bonds?
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0
120
120
120
...
1000
120
1
2
3
...
20
Note: If the coupon rate = discount rate,
the bond will sell for par value.
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n ) + FV (PVIF k, n )
PV = 120 (PVIFA .12, 20 ) + 1000 (PVIF .12, 20 )
PV = PMT
1
1 - (1 + i)n
i
PV = 120 1 IIS
+ FV / (1 + i)n
1
(1.12 )20 + 1000/ (1.12) 20 = $1000
.12
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Suppose interest rates fall
immediately after we issue the
bonds. The required return on
bonds of similar risk drops to 10%.
What would happen to the bond’s
intrinsic value?
Note: If the coupon rate > discount rate,
the bond will sell for a premium.
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n ) + FV (PVIF k, n )
PV = 120 (PVIFA .10, 20 ) + 1000 (PVIF .10, 20 )
PV = PMT
PV =
IIS
1
1 - (1 + i)n
i
120 1 -
+ FV / (1 + i)n
1
(1.10 )20 + 1000/ (1.10) 20 = $1,170.27
.10
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Suppose interest rates rise
immediately after we issue the
bonds. The required return on
bonds of similar risk rises to 14%.
What would happen to the bond’s
intrinsic value?
Note: If the coupon rate < discount rate,
the bond will sell for a discount.
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n ) + FV (PVIF k, n )
PV = 120 (PVIFA .14, 20 ) + 1000 (PVIF .14, 20 )
PV = PMT
PV =
IIS
1
1 - (1 + i)n
i
120 1 -
+ FV / (1 + i)n
1
(1.14 )20 + 1000/ (1.14) 20 = $867.54
.14
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Suppose coupons are semi-annual
Mathematical Solution:
PV = PMT (PVIFA k, n ) + FV (PVIF k, n )
PV = 60 (PVIFA .14, 20 ) + 1000 (PVIF .14, 20 )
PV = PMT
PV =
IIS
1
1 - (1 + i)n
i
60 1 -
+ FV / (1 + i)n
1
(1.07 )40 + 1000 / (1.07) 40 = $866.68
.07
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Yield To Maturity
The expected rate of return on a
bond.
The rate of return investors earn on
a bond if they hold it to maturity.
S
n
P0 =
t=1
IIS
$It
(1 + kb)t
+
$M
(1 + kb)n
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YTM Example
Suppose we paid $898.90 for a
$1,000 par 10% coupon bond
with 8 years to maturity and
semi-annual coupon payments.
What is our yield to maturity?
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n ) + FV (PVIF k, n )
898.90 = 50 (PVIFA k, 16 ) + 1000 (PVIF k, 16 )
PV = PMT
1
1 - (1 + i)n
i
1
898.90 = 50 1 - (1 + i )16
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i
+ FV / (1 + i)n
+ 1000 / (1 + i) 16
solve using trial and error
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Zero Coupon Bonds
No coupon interest payments.
The bond holder’s return is
determined entirely by the
price discount.
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Zero Example
Suppose you pay $508 for a zero
coupon bond that has 10 years
left to maturity.
What is your yield to maturity?
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Zero Example
Suppose you pay $508 for a zero
coupon bond that has 10 years
left to maturity.
What is your yield to maturity?
-$508
0
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$1000
10
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PV = -508
0
Zero Example
FV = 1000
Mathematical Solution:
PV = FV (PVIF i, n )
508 = 1000 (PVIF i, 10 )
.508 = (PVIF i, 10 ) [use PVIF table]
10
PV = FV /(1 + i) 10
508 = 1000 /(1 + i)10
1.9685 = (1 + i)10
i = 7%
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The Financial Pages: Corporate Bonds
Polaroid 11 1/2 06
Cur
Yld
Vol
19.3
395 59 3/4
Close
Net
Chg
...
What is the yield to maturity for this bond?
P/YR = 2, N = 10, FV = 1000,
PV = $-597.50,
PMT = 57.50
Solve: I/YR = 26.48%
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The Financial Pages: Corporate Bonds
HewlPkd zr 17
Cur
Yld
Vol
...
20
Close
51 1/2
Net
Chg
+1
What is the yield to maturity for this bond?
P/YR = 1, N = 16,
PV = $-515,
PMT = 0
FV = 1000,
Solve: I/YR = 4.24%
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The Financial Pages: Treasury Bonds
Maturity
Rate Mo/Yr
9
Nov 18
Bid
Asked
139:14 139:20
Chg
-34
Ask
Yld
5.46
What is the yield to maturity for this
Treasury bond? (assume 35 half years)
P/YR = 2, N = 35, FV = 1000,
PMT = 45,
PV = - 1,396.25 (139.625% of par)
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Solve: I/YR = 5.457%
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Preferred Stock
A hybrid security:
It’s like common stock - no fixed maturity.
Technically, it’s part of equity capital.
It’s like debt - preferred dividends are
fixed.
Missing a preferred dividend does not
constitute default, but preferred dividends are
cumulative.
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Preferred Stock
Usually sold for $25, $50, or $100 per
share.
Dividends are fixed either as a dollar
amount or as a percentage of par value.
Example: In 1988, Xerox issued $75
million of 8.25% preferred stock at $50
per share.
$4.125 is the fixed, annual dividend per
share.
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Preferred Stock Features
Firms may have multiple classes of
preferreds, each with different features.
Priority: lower than debt, higher than
common stock.
Cumulative feature: all past unpaid
preferred stock dividends must be paid
before any common stock dividends are
declared.
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Preferred Stock Features
Protective provisions are common.
Convertibility: many preferreds are
convertible into common shares.
Adjustable rate preferreds have
dividends tied to interest rates.
Participation: some (very few)
preferreds have dividends tied to the
firm’s earnings.
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Preferred Stock Features
PIK Preferred: Pay-in-kind preferred
stocks pay additional preferred shares
to investors rather than cash dividends.
Retirement: Most preferreds are
callable, and many include a sinking
fund provision to set cash aside for the
purpose of retiring preferred shares.
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Preferred Stock Valuation
A preferred stock can usually be
valued like a perpetuity:
Vps =
IIS
D
k ps
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Example:
Xerox preferred pays an 8.25%
dividend on a $50 par value.
Suppose our required rate of
return on Xerox preferred is 9.5%.
Vps =
IIS
4.125
.095
=
$43.42
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Expected Rate of Return
on Preferred
Just adjust the valuation model:
kps =
IIS
D
Po
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Example
If we know the preferred stock price
is $40, and the preferred dividend is
$4.125, the expected return is:
kps
IIS
D
=
Po
4.125
=
= .1031
40
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The Financial Pages:
Preferred Stocks
52 weeks
Yld
Hi
Lo
Sym
Div %
2788 2506 GenMotor pfG 2.28 8.9
Vol
PE 100s Close
…
86
25 53
Dividend: $2.28 on $25 par value
= 9.12% dividend rate.
Expected return: 2.28 / 25.53 = 8.9%.
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Common Stock
Is a variable-income security.
Dividends may be increased or decreased,
depending on earnings.
Represents equity or ownership.
Includes voting rights.
Limited liability: liability is limited to
amount of owners’ investment.
Priority: lower than debt and preferred.
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Common Stock Characteristics
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Claim on Income - a stockholder has a
claim on the firm’s residual income.
Claim on Assets - a stockholder has a
residual claim on the firm’s assets in case
of liquidation.
Preemptive Rights - stockholders may
share proportionally in any new stock
issues.
Voting Rights - right to vote for the firm’s
board of directors.
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Common Stock Valuation
(Single Holding Period)
You expect XYZ stock to pay a $5.50
dividend at the end of the year. The stock
price is expected to be $120 at that time.
If you require a 15% rate of return, what
would you pay for the stock now?
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5.50 + 120
0
1
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Common Stock Valuation
(Single Holding Period)
Solution:
Vcs = (5.50/1.15) + (120/1.15)
= 4.783
+ 104.348
= $109.13
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The Financial Pages:
Common Stocks
52 weeks
Yld
Vol
Net
Hi Lo Sym Div % PE 100s Hi Lo Close Chg
135 80 IBM .52 .5
21 142349 99 93 9496 -343
82 18 CiscoSys
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…
47 1189057 21
19 2025 -113
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Common Stock Valuation
(Multiple Holding Periods)
Constant Growth Model
Assumes common stock dividends
will grow at a constant rate into
the future.
Vcs =
IIS
D1
kcs - g
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Constant Growth Model
Assumes common stock dividends will grow
at a constant rate into the future.
Vcs =
IIS
D1
kcs - g
D1 = the dividend at the end of period 1.
kcs = the required return on the common
stock.
g = the constant, annual dividend growth
rate.
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Example
XYZ stock recently paid a $5.00
dividend. The dividend is expected to
grow at 10% per year indefinitely.
What would we be willing to pay if our
required return on XYZ stock is 15%?
D0 = $5, so D1 = 5 (1.10) = $5.50
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Example
XYZ stock recently paid a $5.00
dividend. The dividend is expected to
grow at 10% per year indefinitely.
What would we be willing to pay if our
required return on XYZ stock is 15%?
Vcs =
IIS
D1
kcs - g
=
5.50
.15 - .10
= $110
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Expected Return on
Common Stock
Just adjust the valuation model
Vcs =
k =
IIS
(
D
kcs - g
D1
Po
) + g
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Example
We know a stock will pay a $3.00
dividend at time 1, has a price of $27
and an expected growth rate of 5%.
kcs =
kcs = (
IIS
(
3.00
27
D1
Po
) + g
) + .05
= 16.11%
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