Transcript No Slide Title

The value of any asset can be found as the
present value of its expected future cash flows,
CFt, discounted at the rate K:
CF   CF
V  CF 
(1 K) (1 K)
(1 K)
The discount rate depends on:
1
n
2
1
2
n
1. The riskiness of the cash flows, which reflect
default risk,maturity (interest rate) risk, and
liquidity.
2. The general level of interest rates, which reflects
inflation,supply of and demand for money,
production opportunities, and time preferences 1
for consumption.
A. Bond
B. Par, or Face, Value;
Maturity Value, M
C. Coupon Interest Rate;
Coupon Payment, INT
D. Maturity; Maturity Date
E. Call Provision; Call
Protection; Call Premium
F. Issue Date
G. Default Risk
H. Kd
2
W h a t is th e va lu e o f a 1 0 - y e a r , $ 1 , 0 0 0 p a r
va lu e b o n d w ith a 1 0 p e r c e n t a n n u a l c o u p o n
if th e r e q u ir e d r a te o f r e tu r n i s 1 0 p e r c e n t?
Th e c a sh f lo w s tr e a m
0
1
10% |
|
100
N
VB  
INT
lo o k s li ke th is :
2
9
|
|
100
100
M

(1K d) (1 K d)
 INT ( PVIFA )  M ( PVIF
)
 $100( PVIFA )  $1,000( PVIF
t
10
|
100
1,000
N
t 1
Kd ,N
10%,10
Kd, N
10%,10
)
 $614.46  $385.54
 $1,000
Financ ial Calc ulator Solution:
Input N=10, I=10, PMT=100, FV=1,000, PV=?
PV=1,000.
3
0
|
1
|
INT
2
2N
V B  t1
|
INT
2
|
INT
2
INT / 2
2
N-1
|
|
INT
2
INT
2

N
|
INT
2
|
INT
2
M
(1 K d / 2) (1 K d / 2)
 INT / 2( PVIFAKd / 2, 2 N )  M ( PVIF Kd / 2,2 N )
t
2N
4
P ar Value = $ 1 ,0 00
Current price = $ 8 87
Annual c oupo n = $ 90
Te rm to maturity = 1 0 ye ar s
0
|
-$8 8 7
1
|
$ 90
2
|
$ 90
9
|
$9 0
10
|
$9 0
$1 ,0 0 0
$887  $90( PVIFAYTM ,10 )  $1,000( PVI F YTM ,10 )
YTM  10 .91 %
We can solve for YTM using:
1. Interest factor tables and trial and error.
2. Financial calculator with bond valuation capability.
5
Current Yield, Capital Gains Yield, and
Total Return
C urrent yield 
C ap ital gains yield 
An nual coupon payment
C urrent price
Expected change in bond' s price
p rice
 Y TM - Current yi eld
Fo r the 10 .91 percent YTM bo nd selling for $ 887,
Current yield = $90 /$88 7 = 1 0.15%
Capital gains yield = 10 .91% - 10 .15% = 0.76 %
Fo r the 7.0 8 percent YTM bond selling fo r $1 ,134.20
Current yield = $90 /$1,1 34.20 = 7.94 %
Capital gains yield = 7.0 8%-7.94 % = -0.86 %
6
P ar Val ue
C urre nt pri c e
C o upo n inte re s t ra te
S e m ian nual p aym e nt bo nd
Te r m to m atur ity
YTM
C all p ro vis i o n
$ 1 ,0 0 0
$ 1 , 1 3 5 .9 0
10%
ye s
1 0 ye ars
8%
C al lable afte r 5
ye a rs at a pric e
o f $ 1 ,0 5 0
YTC = ?
V
B
 $1,135 .90 
2N

t 1
$1,135.90 
t 1
K
d
INT / 2

M

$1, 050
(1 K d / 2) (1 K d / 2)
t
10

=
=
=
=
=
=
=
$50
2N
(1 K d / 2) (1 K d / 2)
t
10
/ 2  3 .765%; K d  7. 5301%  7. 5%
Financial Calculator Solution :
Input N  10, PV  -1,135.90, PMT  50,
FV  1,050, I 
K / 2  ? I  K / 2  3.765 %
EAR  (1.03765)  1  7 .67%
d
d
2
7
General Stock Valuation Model
ˆP  D  D
(1 K s) (1 K s)
1
2
1
0
2

D
(1 K s)
n
n
Time Patterns of D1
$
g=Nonconstant
g=Constant
Dg
g=Zero
g=Negative Constant
t
For a constant growth stock, D1=Do(1+g)
(1  g )
D
D
and Pˆ   g 
K
K g
0
1
0
s
ˆ
K
s

s
D
P
1
g
0
Note (1) that g must be constant forever, and
(2) that Ks must be >g
Value of perpetuity
PMT
K
$2
V 
 $12.50
0.16
V 
Bon Temps: Supernormal Growth
0
|
$2.000
g=30%
1
|
$2.600
g=30%
Normal Growth
2
|
$3.380
g=30%
3
|
$4.394
4
|
$4.658
g=6%
g=6%
Bon Temps Example, supernormal Growth
PV of Supernormal Dividends
PV D1= $2.600/(1.16)1 = $2.241
PV D2= $3.380/(1.16)2 = $2.512
PV D3= $4.394/(1.16)3 = $2.815
$7.568
St ock P rice at t  3
D  $4.658  $4.658  $46.58
K  g 0.16  0.06 0.10
P V of P
ˆ
Pˆ
3

4
s
3
$46.58
3
(1.16)
 $29.84
Value of St ock
Pˆ
0
 $7.57  $29.84  $37.41
HOW STOCK ARE VALUED
EXP ECT EDRET URN EXP ECT EDDIVIDENDYIELD
 EXP ECT EDCAP IT ALGAIN
DIV
r
1
 ( P1  P0)
P
0
P rice 
BUT
P0 
P1 
DIV  P
1 r
DIV
T HUSP0 
1
1
2
 P2
1 r
DIV
(1 r)
1

,
P2 
DIV
(1 r)
2
2
DIV  P
3
1 r

3
, Et c
P
(1 r)
H
H
FOR INFINIT EHORIZON,
P RICE  P V (EXP ECT EDDIVIDENDSP ERSHARE)
ESTIMATED THE CAPITALIZATION RATE
IF DIVIDENDS ARE EXPECTED TO GROW AT A
CONSTANT RATE, g
P
0
r

DIV
rg
DIV
P
1
1
g
0
IF A FIRM EARNS A CONSTANT RETURN ON
BOOK EQUITY AND PLOWS BACK A CONSTANT
PROPORTION OF EARNINGS, THEN
DIVIDEND
= g = PLOWBACK X RETURN
GROWTH RATE
RATION
ON EQUITY
WHAT’S PVGO FOR FLEDGING ELECTRONICS?
SUPPOSE EPS = 8.33
(RETURN ON EQUITY=.25
EQUITY INVESTMENT=33.33)
EPS
 PVGO
r
8.33
100 
 PVGO
0.15
PVGO  44.44
P
NOTE: *PVGO IS LARGE BECAUSE FLEDGLING EARNS
MORE THAN COST OF CAPITAL(.25>.15)
*FLEDGLING’S EARNINGS-PRICE RATIO
UNDERSTATES ITS COST OF CAPITAL
8.33/100 = .083 <.15