Transcript Principles of Finance

Valuation Concepts
Chapter 10
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
Basic Valuation
Asset
value  V 
^
CF
1
1  k 
1
N

t 1

^
CF
2
1  k 
2

^
CF
N
N
1  k 
^
CF
t
1  k 
t
^t = the cash flow expected to be generated by
CF
the asset in period t
Basic Valuation
 k = the return investors consider
appropriate for holding such an asset usually referred to as the required
return, based on riskiness and economic
conditions
Valuation of Financial
Assets - Bonds
 Bond is a long term debt instrument
 Value is based on present value of:
 stream of interest payments
 principal repayment at maturity
Valuation of Financial
Assets - Bonds
 kd = 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  Par value)
 M = par or face, value of the bond to be
paid off at maturity
Valuation of Financial
Assets - Bonds
Bond
value
 Vd 
N
INT
INT
1  k d 1 1  k d 2
INT
  1  k
t 1

d
t

M
1  k d N

INT

M
1  k d N 1  k d N
Valuation of Financial
Assets - Bonds
 Genesco 15%, 15year, $1,000 bonds
valued at 15% required rated of return
Valuation of Financial
Assets - Bonds
 Numerical solution:
1

15
1 


1
.
15
Bond  $150
0.15

value




 1 
  $1,000
15 

 1.15 


Vd = $150 (5.8474) + $1,000 (0.1229)
= $877.11 + $122.89 = $1,000
Valuation of Financial
Assets - Bonds
 Financial Calculator Solution:
Inputs: N = 15; I = k = 15; PMT = INT =
150
M = FV = 1000; PV = ?
Output: PV = -1,000
Changes in Bond Values
over Time
 If the market rate associated with a bond
(kd) equals the coupon rate of interest,
the bond will sell at its par value
Changes in Bond Values
over Time
 If interest rates in the economy fall after
the bonds are issued, kd is below the
coupon rate. The interest payments and
maturity payoff stay the same, causing
the bond’s value to increase (investors
demand lower returns, so they are willing
to pay higher prices for bonds).
Changes in Bond Values
over Time
 Current yield is the annual interest
payment on a bond divided by
its current market value
Current  INT
yield
Vd
 Ending    Beginning 
 bond value   bond value  V
Capital
d, End  Vd, Begin





gains 
Vd,Begin
 Beginning 
 bond value 
yield


Changes in Bond Values
over Time
Discount bond
 A bond that sells below its par value,
which occurs whenever the going rate of
interest rises above the coupon rate
Premium bond
A bond that sells above its par value,
which occurs whenever the going rate of
interest falls below the coupon rate
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
Time path of value of a 15% Coupon,
$1000
par
value
bond
when
interest
Year
k d = 10% k d = 15% k d = 20%
rates
are
10%,$1,000.00
15%, and
20%
0
$1,380.30
$766.23
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
$1,368.33
$1,355.17
$1,340.68
$1,324.75
$1,307.23
$1,287.95
$1,266.75
$1,243.42
$1,217.76
$1,189.54
$1,158.49
$1,124.34
$1,086.78
$1,045.45
$1,000.00
$1,000.00
$1,000.00
$1,000.00
$1,000.00
$1,000.00
$1,000.00
$1,000.00
$1,000.00
$1,000.00
$1,000.00
$1,000.00
$1,000.00
$1,000.00
$1,000.00
$1,000.00
$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
$1,000.00
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
Kd < Coupon Rate
Kd = Coupon Rate
$1,000
$750
$500
Kd > Coupon Rate
$250
$0
1
3
5
7
9
11
13
15
Years
Yield to Maturity
 YTM is the average rate of return earned
on a bond if it is held to maturity
Approximate yield
to maturity
Annual
Accrue d
interest  capital gains

Average value of bond
 M - Vd 
INT  

 N 

 2 Vd   M 


3


Bond Values with
Semiannual Compounding
INT
2N
M
2
Vd  

t
2N
t 1 
kd  
kd 
1 
 1 

2 
2 

Interest Rate Risk
on a Bond
 Interest Rate Price Risk - the risk of
changes in bond prices to which investors
are exposed due to changing interest rates
 Interest Rate Reinvestment Rate Risk - the
risk that income from a bond portfolio will
vary because cash flows have to be
reinvested at current market rates
Value of Long and Short-Term
15% Annual Coupon Rate Bonds
Current Market
Interest Rate, k d
5%
10%
15%
20%
25%
Value of
1-Year
14-Year
Bond
Bond
$ 1,095.24
$ 1,045.45
$ 1,000.00
$
958.33
$
920.00
$
$
$
$
$
1,989.86
1,368.33
1,000.00
769.47
617.59
Value of Long and Short-Term
15% Annual Coupon Rate Bonds
Bond
Value
($) 2,000
14-Year Bond
1,500
1,000
1-Year Bond
500
0
5
10
15
20
25
Interest Rate, k d (%)
Valuation of Financial
Assets - Equity (Stock)
 Common stock
 Preferred stock
 hybrid
 similar to bonds with fixed dividend amounts
 similar to common stock as dividends are not
required and have no fixed maturity date
Stock Valuation Models
 Terms:
Stock Valuation Models
 Terms: Expected Dividends
D̂ t  dividend the stockholde r expects to
recieve at the end of Year t
D 0 is the most recent dividend already paid
D̂1 is the next dividend expected to be paid,
and it will be paid at the end of this year
D̂ 2 is the dividend expected at the end of two years
All future dividends are expected values, so the
estimates may differ among investors
Stock Valuation Models
 Terms: Market Price
P0  the price at which a stock
sells in the market tod ay
Stock Valuation Models
 Terms: Intrinsic Value
P̂0  the value of an asset that, in the
mind of an investor, is justified
by the facts and may be different
from the asset's current market
price, its book value, or both
Stock Valuation Models
 Terms: Expected Price
P̂t  the expected price of the stock
at the end of each Year t
Stock Valuation Models
 Terms: Growth Rate
g  the expected rate of change
in dividends per share
Stock Valuation Models
 Terms: Required Rate of Return
k s  the minimum rate of return on a
common stock that stockholde rs
consider acceptable , given its
riskiness and returns available on
other investment s
Stock Valuation Models
 Terms: Dividend Yield
D̂1
 the expected dividend divided
P0
by the current price of a share
of stock
Stock Valuation Models
 Terms: Capital Gain Yield
P1  P0
 the change in price (capital gain)
P0
during a given year divided by its
price at the beginning of the year
Stock Valuation Models
 Terms: Expected Rate of Return
k̂ s  the rate of return on a common
stock that an individual investor
expects to receive
 expected dividend yield
 expected capital gains yield
Stock Valuation Models
 Terms: Actual Rate of Return
k s  the rate of return on a common
stock that an individual investor
actually receives, after the fact;
equal to the dividend yield plus
the capital gains yield
Stock Valuation Models
 Expected Dividends as the Basis for
Stock Values
 If you hold a stock forever, all you receive
is the dividend payments
 The value of the stock today is the present
value of the future dividend payments
Stock Valuation Models
 Expected Dividends as the Basis for
Stock Values
Value of Stock  Vs  Pˆ 0  PV of expected future dividends
D̂1
D̂ 2
D̂ 



1
2

1  k s  1  k s 
1  k s 

D̂ t

t
t 1 1  k s 
Stock Valuation Models
Stock Values with Zero Growth
A zero growth stock is a common stock
whose future dividends are not expected to
grow at all
D
D
D
P̂0 


1
2

1  k s  1  k s 
1  k s 
D
P̂0 
ks
D
k̂ s 
P0
Stock Valuation Models
 Normal, or Constant, Growth
 Growth that is expected to continue into
the foreseeable future at about the same
rate as that of the economy as a whole
 g = a constant
Stock Valuation Models
 Normal, or Constant, Growth
 (Gordon Model)
D0 1  g  D0 1  g 
D0 1  g 
P̂0 


1
2

1  k s 
1  k s 
1  k s 
1
D 0 1  g 
D̂1


ks  g
ks  g
2

Expected Rate of Return on
a Constant Growth Stock
k̂ s 
D̂ 1
P0

g
 Dividend yield  Capital gain
Nonconstant Growth
 The part of the life cycle of a firm in
which its growth is either much faster or
much slower than that of the economy as
a whole
Nonconstant Growth
 1. Compute the value of the dividends that
experience nonconstant growth, and then find
the PV of these dividends
 2. Find the price of the stock at the end of the
nonconstant growth period, at which time it
becomes a constant growth stock, and discount
this price back to the present
 3. Add these two components to find the
intrinsic value of the stock, P̂.
0
Changes in Stock Prices
 Investors change the rates of return
required to invest in stocks
 Expectations about the cash flows
associated with stocks change
Valuation of Real
(Tangible) Assets
 Valuation is still based on expected cash
flows of the asset
Valuation of Real
(Tangible) Assets
Year
1
2
3
4
5
Expected Cash Flow, CF
$120,000
100,000
150,000
80,000
50,000
To earn a 14% return on investments like this, what
is the value of this machine?
Cash Flow Time Lines
0 14% 1
2
3
4
5
$120,000 $100,000 $150,000 $80,000 $50,000
PV of $120,000
PV of $100,000
PV of $150,000
PV of $80,000
PF of $50,000
Asset Value = V0
$356,790 
$120,000 $100,000 $150,000 $80,000 $50,000




1
2
3
4
1.14
1.14
1.14
1.14
1.145
End of Chapter 10
Valuation
Concepts