Description
In neoclassical economics, the value of an object or service is often seen as nothing but the price it would bring in an open and competitive market. This is determined primarily by the demand for the object relative to supply.
1
Valuation of Securities
2
What is Value?
? In general, the value of an asset is the price that a
willing and able buyer pays to a willing and able
seller
? Note that if either the buyer or seller is not both
willing and able, then an offer does not establish the
value of the asset
Prof.Mahesh Renguntwar
3
Several Kinds of “Value”
? There are several types of value, of which we are
concerned with three:
• Book Value - The asset’s historical cost less its accumulated
depreciation
• Market Value - The price of an asset as determined in a
competitive marketplace
• Intrinsic Value - The present value of the expected future
cash flows discounted at the decision maker’s required rate
of return
Prof.Mahesh Renguntwar
4
Determinants of Intrinsic Value
? There are two primary determinants of the intrinsic
value of an asset to an individual:
• The size and timing of the expected future cash flows
• The individual’s required rate of return (this is determined by
a number of other factors such as risk/return preferences,
returns on competing investments, expected inflation, etc.)
? Note that the intrinsic value of an asset can be, and
often is, different for each individual (that’s what
makes markets work)
Prof.Mahesh Renguntwar
5
Bonds
? A bond is a tradeable instrument that represents a
debt owed to the owner by the issuer. Most
commonly, bonds pay interest periodically (usually
semiannually) and then return the principal at
maturity.
? Most corporate, and some government, bonds are
callable. That means that at the company’s option, it
may force the bondholders to sell them back to the
company. Ordinarily, there are restrictions on the
timing of the call and the amount that must be paid.
Prof.Mahesh Renguntwar
6
Calculating the Value of a Bond
? There are two types of cash flows that are provided
by a bond investments:
• Periodic interest payments (usually every six months, but
any frequency is possible)
• Repayment of the face value (also called the principal
amount, which is usually $1,000) at maturity
? The following timeline illustrates a typical bond’s
cash flows:
0 1 2 3 4 5
100 100 100 100 100
1,000
Prof.Mahesh Renguntwar
7
Calculating the Value of a Bond (cont.)
? We can use the principle of value additivity to find
the value of this stream of cash flows
? Note that the interest payments are an annuity, and
that the face value is a lump sum
? Therefore, the value of the bond is simply the present
value of the annuity-type cash flow and the lump
sum:
( )
( )
V Pmt
k
k
FV
k
B
d
N
d
d
N
=
÷
+
¸
(
¸
(
(
(
(
+
+
1
1
1
1
Prof.Mahesh Renguntwar
8
Bond Terminology
? There are several terms with which you must be
familiar to solve bond valuation problems:
• Coupon Rate - This is the stated rate of interest on the bond.
It is fixed for the life of the bond. Also, this rate time the
face value determines the annual interest payment amount.
• Face Value - This is the principal amount (nominally, the
amount that was borrowed). This is the amount that will be
repaid at maturity
• Maturity Date - This is the date after which the bond no
longer exists. It is also the date on which the loan is repaid
and the last interest payment is made.
Prof.Mahesh Renguntwar
9
Bond Valuation: An Example
? Assume that you are interested in purchasing a bond
with 5 years to maturity and a 10% coupon rate. If
your required return is 12%, what is the highest price
that you would be willing to pay?
0 1 2 3 4 5
100 100 100 100 100
1,000
( )
( )
V
B
=
÷
+
¸
(
¸
(
(
(
+
+
= 100
1
1
1 012
012
1 000
1 012
927 90
5
5
.
.
,
.
.
Prof.Mahesh Renguntwar
10
Some Notes About Bond Valuation
? The value of a bond depends on several factors such
as time to maturity, coupon rate, and required return
? We can note several facts about the relationship
between bond prices and these variables (ceteris
paribus):
• Higher required returns lead to lower bond prices, and vice-
versa
• Higher coupon rates lead to higher bond prices, and vice
versa
• Longer terms to maturity lead to lower bond prices, and
vice-versa
Prof.Mahesh Renguntwar
11
Common Stocks
? A share of common stock represents an ownership
position in the firm. Typically, the owners are
entitled to vote on important matters regarding the
firm, to vote on the membership of the board of
directors, and (often) to receive dividends.
? In the event of liquidation of the firm, the common
shareholders will receive a pro-rata share of the
assets remaining after the creditors and preferred
stockholders have been paid off.
Prof.Mahesh Renguntwar
12
Common Stock Valuation
? Just like with bonds, the first step in valuing common
stocks is to determine the cash flows
? For a stock, there are two:
• Dividend payments
• The future selling price
? Again, finding the present values of these cash flows
and adding them together will give us the value
Prof.Mahesh Renguntwar
13
Common Stock Valuation: An Example
? Assume that you are considering the purchase of a
stock which will pay dividends of $2 next year, and
$2.16 the following year. After receiving the second
dividend, you plan on selling the stock for $33.33.
What is the intrinsic value of this stock if your
required return is 15%?
( ) ( )
V
CS
=
+
+
+
+
=
2 00
1 15
216 3333
1 15
2857
1 2
.
.
. .
.
.
2.00
2.16
33.33
?
Prof.Mahesh Renguntwar
14
Some Notes About Common Stock
? In valuing the common stock, we have made two
assumptions:
• We know the dividends that will be paid in the future
• We know how much you will be able to sell the stock for in
the future
? Both of these assumptions are unrealistic, especially
knowledge of the future selling price
? Furthermore, suppose that you intend on holding on
to the stock for twenty years, the calculations would
be very tedious!
Prof.Mahesh Renguntwar
15
Common Stock: Some Assumptions
? We cannot value common stock without making
some simplifying assumptions
? If we make the following assumptions, we can derive
a simple model for common stock valuation:
? Assume:
• Your holding period is infinite (i.e., you will never sell the
stock)
• The dividends will grow at a constant rate forever
? Note that the second assumption allows us to predict
every future dividend, as long as we know the most
recent dividend
Prof.Mahesh Renguntwar
16
The Dividend Discount Model (DDM)
? With these assumptions, we can derive a model
which is known as the Dividend Discount Model, or
the Gordon Model
? This model gives us the present value of an infinite
stream of dividends that are growing at a constant
rate:
( )
V
D g
k g
D
k g
CS
CS CS
=
+
÷
=
÷
0
1
1
Prof.Mahesh Renguntwar
17
The DDM: An Example
? Recall our previous example in which the dividends
were growing at 8% per year, and your required
return was 15%
? The value of the stock must be:
( )
V
CS
=
+
÷
=
÷
=
185 1 08
15 08
2 00
015 08
2857
. .
. .
.
. .
.
? Note that this is exactly the same value that we got
earlier
Prof.Mahesh Renguntwar
18
The DDM Extended
? There is no reason that we can’t use the DDM at any
point in time
? For example, we might want to calculate the price
that a stock should sell for in two years
? To do this, we can simply generalize the DDM:
( )
V
D g
k g
D
k g
N
N
CS
N
CS
=
+
÷
=
÷
+
1
1
Prof.Mahesh Renguntwar
19
The DDM Example (cont.)
? In the earlier example, how did we know that the
stock would be selling for $33.33 in two years?
? Note that the period 3 dividend must be 8% larger
than the period 2 dividend, so:
( )
V
2
216 1 08
15 08
2 33
015 08
3333 =
+
÷
=
÷
=
. .
. .
.
. .
.
Prof.Mahesh Renguntwar
20
Preferred Stock
? Preferred stock represents an ownership claim on the
firm that is superior to common stock in the event of
liquidation. Typically, preferred stock pays a fixed
dividend periodically and the preferred stockholders
are usually not entitled to vote as are the common
shareholders.
Prof.Mahesh Renguntwar
21
Preferred Stock Valuation
? Preferred stock is very much like common stock,
except that the dividends are constant (i.e., the
growth rate is 0%)
? Therefore, we can use the DDM with a 0% growth
rate to find the value:
( )
V
D
k
D
k
P
CS CS
=
+
÷
=
0
1 0
0
Prof.Mahesh Renguntwar
22
Preferred Stock: An Example
? Suppose that you are interested in purchasing shares
of a preferred stock which pays a $5 dividend every
year. If your required return is 7%, what is the
intrinsic value of this stock?
V
P
= =
5
0 07
7143
.
.
Prof.Mahesh Renguntwar
doc_189636775.pptx
In neoclassical economics, the value of an object or service is often seen as nothing but the price it would bring in an open and competitive market. This is determined primarily by the demand for the object relative to supply.
1
Valuation of Securities
2
What is Value?
? In general, the value of an asset is the price that a
willing and able buyer pays to a willing and able
seller
? Note that if either the buyer or seller is not both
willing and able, then an offer does not establish the
value of the asset
Prof.Mahesh Renguntwar
3
Several Kinds of “Value”
? There are several types of value, of which we are
concerned with three:
• Book Value - The asset’s historical cost less its accumulated
depreciation
• Market Value - The price of an asset as determined in a
competitive marketplace
• Intrinsic Value - The present value of the expected future
cash flows discounted at the decision maker’s required rate
of return
Prof.Mahesh Renguntwar
4
Determinants of Intrinsic Value
? There are two primary determinants of the intrinsic
value of an asset to an individual:
• The size and timing of the expected future cash flows
• The individual’s required rate of return (this is determined by
a number of other factors such as risk/return preferences,
returns on competing investments, expected inflation, etc.)
? Note that the intrinsic value of an asset can be, and
often is, different for each individual (that’s what
makes markets work)
Prof.Mahesh Renguntwar
5
Bonds
? A bond is a tradeable instrument that represents a
debt owed to the owner by the issuer. Most
commonly, bonds pay interest periodically (usually
semiannually) and then return the principal at
maturity.
? Most corporate, and some government, bonds are
callable. That means that at the company’s option, it
may force the bondholders to sell them back to the
company. Ordinarily, there are restrictions on the
timing of the call and the amount that must be paid.
Prof.Mahesh Renguntwar
6
Calculating the Value of a Bond
? There are two types of cash flows that are provided
by a bond investments:
• Periodic interest payments (usually every six months, but
any frequency is possible)
• Repayment of the face value (also called the principal
amount, which is usually $1,000) at maturity
? The following timeline illustrates a typical bond’s
cash flows:
0 1 2 3 4 5
100 100 100 100 100
1,000
Prof.Mahesh Renguntwar
7
Calculating the Value of a Bond (cont.)
? We can use the principle of value additivity to find
the value of this stream of cash flows
? Note that the interest payments are an annuity, and
that the face value is a lump sum
? Therefore, the value of the bond is simply the present
value of the annuity-type cash flow and the lump
sum:
( )
( )
V Pmt
k
k
FV
k
B
d
N
d
d
N
=
÷
+
¸
(
¸
(
(
(
(
+
+
1
1
1
1
Prof.Mahesh Renguntwar
8
Bond Terminology
? There are several terms with which you must be
familiar to solve bond valuation problems:
• Coupon Rate - This is the stated rate of interest on the bond.
It is fixed for the life of the bond. Also, this rate time the
face value determines the annual interest payment amount.
• Face Value - This is the principal amount (nominally, the
amount that was borrowed). This is the amount that will be
repaid at maturity
• Maturity Date - This is the date after which the bond no
longer exists. It is also the date on which the loan is repaid
and the last interest payment is made.
Prof.Mahesh Renguntwar
9
Bond Valuation: An Example
? Assume that you are interested in purchasing a bond
with 5 years to maturity and a 10% coupon rate. If
your required return is 12%, what is the highest price
that you would be willing to pay?
0 1 2 3 4 5
100 100 100 100 100
1,000
( )
( )
V
B
=
÷
+
¸
(
¸
(
(
(
+
+
= 100
1
1
1 012
012
1 000
1 012
927 90
5
5
.
.
,
.
.
Prof.Mahesh Renguntwar
10
Some Notes About Bond Valuation
? The value of a bond depends on several factors such
as time to maturity, coupon rate, and required return
? We can note several facts about the relationship
between bond prices and these variables (ceteris
paribus):
• Higher required returns lead to lower bond prices, and vice-
versa
• Higher coupon rates lead to higher bond prices, and vice
versa
• Longer terms to maturity lead to lower bond prices, and
vice-versa
Prof.Mahesh Renguntwar
11
Common Stocks
? A share of common stock represents an ownership
position in the firm. Typically, the owners are
entitled to vote on important matters regarding the
firm, to vote on the membership of the board of
directors, and (often) to receive dividends.
? In the event of liquidation of the firm, the common
shareholders will receive a pro-rata share of the
assets remaining after the creditors and preferred
stockholders have been paid off.
Prof.Mahesh Renguntwar
12
Common Stock Valuation
? Just like with bonds, the first step in valuing common
stocks is to determine the cash flows
? For a stock, there are two:
• Dividend payments
• The future selling price
? Again, finding the present values of these cash flows
and adding them together will give us the value
Prof.Mahesh Renguntwar
13
Common Stock Valuation: An Example
? Assume that you are considering the purchase of a
stock which will pay dividends of $2 next year, and
$2.16 the following year. After receiving the second
dividend, you plan on selling the stock for $33.33.
What is the intrinsic value of this stock if your
required return is 15%?
( ) ( )
V
CS
=
+
+
+
+
=
2 00
1 15
216 3333
1 15
2857
1 2
.
.
. .
.
.
2.00
2.16
33.33
?
Prof.Mahesh Renguntwar
14
Some Notes About Common Stock
? In valuing the common stock, we have made two
assumptions:
• We know the dividends that will be paid in the future
• We know how much you will be able to sell the stock for in
the future
? Both of these assumptions are unrealistic, especially
knowledge of the future selling price
? Furthermore, suppose that you intend on holding on
to the stock for twenty years, the calculations would
be very tedious!
Prof.Mahesh Renguntwar
15
Common Stock: Some Assumptions
? We cannot value common stock without making
some simplifying assumptions
? If we make the following assumptions, we can derive
a simple model for common stock valuation:
? Assume:
• Your holding period is infinite (i.e., you will never sell the
stock)
• The dividends will grow at a constant rate forever
? Note that the second assumption allows us to predict
every future dividend, as long as we know the most
recent dividend
Prof.Mahesh Renguntwar
16
The Dividend Discount Model (DDM)
? With these assumptions, we can derive a model
which is known as the Dividend Discount Model, or
the Gordon Model
? This model gives us the present value of an infinite
stream of dividends that are growing at a constant
rate:
( )
V
D g
k g
D
k g
CS
CS CS
=
+
÷
=
÷
0
1
1
Prof.Mahesh Renguntwar
17
The DDM: An Example
? Recall our previous example in which the dividends
were growing at 8% per year, and your required
return was 15%
? The value of the stock must be:
( )
V
CS
=
+
÷
=
÷
=
185 1 08
15 08
2 00
015 08
2857
. .
. .
.
. .
.
? Note that this is exactly the same value that we got
earlier
Prof.Mahesh Renguntwar
18
The DDM Extended
? There is no reason that we can’t use the DDM at any
point in time
? For example, we might want to calculate the price
that a stock should sell for in two years
? To do this, we can simply generalize the DDM:
( )
V
D g
k g
D
k g
N
N
CS
N
CS
=
+
÷
=
÷
+
1
1
Prof.Mahesh Renguntwar
19
The DDM Example (cont.)
? In the earlier example, how did we know that the
stock would be selling for $33.33 in two years?
? Note that the period 3 dividend must be 8% larger
than the period 2 dividend, so:
( )
V
2
216 1 08
15 08
2 33
015 08
3333 =
+
÷
=
÷
=
. .
. .
.
. .
.
Prof.Mahesh Renguntwar
20
Preferred Stock
? Preferred stock represents an ownership claim on the
firm that is superior to common stock in the event of
liquidation. Typically, preferred stock pays a fixed
dividend periodically and the preferred stockholders
are usually not entitled to vote as are the common
shareholders.
Prof.Mahesh Renguntwar
21
Preferred Stock Valuation
? Preferred stock is very much like common stock,
except that the dividends are constant (i.e., the
growth rate is 0%)
? Therefore, we can use the DDM with a 0% growth
rate to find the value:
( )
V
D
k
D
k
P
CS CS
=
+
÷
=
0
1 0
0
Prof.Mahesh Renguntwar
22
Preferred Stock: An Example
? Suppose that you are interested in purchasing shares
of a preferred stock which pays a $5 dividend every
year. If your required return is 7%, what is the
intrinsic value of this stock?
V
P
= =
5
0 07
7143
.
.
Prof.Mahesh Renguntwar
doc_189636775.pptx