1. Valuation of SecuritiesValuation of Securities
Adapted from Timothy R. Mayes, Ph.D.
FIN 3300: Chapters 6 and 7

2. What is Value?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

3. Several Kinds of “Value”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

4. Determinants of Intrinsic ValueDeterminants 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)

5. BondsBonds
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.

6. Calculating the Value of a BondCalculating 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

7. Calculating the Value of a Bond (cont.)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:

8. Bond TerminologyBond 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.

9. Bond Valuation: An ExampleBond 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

10. 1
Class work 1:Bond ValuationClass work 1:Bond Valuation
Assume that you are interested in purchasing a bond
with 5 years to maturity and a 12% coupon rate. If
your required return is 14%, what is the highest price
that you would be willing to pay?
0 1 2 3 4 5
? ? ? ? ?
1,000

11. 1
Class work 2:Bond ValuationClass work 2:Bond Valuation
Assume that you are interested in purchasing a bond
with 5 years to maturity and a 14% coupon rate. If
your required return is 16%, what is the highest price
that you would be willing to pay?
0 1 2 3 4 5
? ? ? ? ?
1,000

12. 1
Class work 3:Bond ValuationClass work 3:Bond Valuation
Assume that you are interested in purchasing a bond
with 5 years to maturity and a 16% coupon rate. If
your required return is 9%, what is the highest price
that you would be willing to pay?
0 1 2 3 4 5
? ? ? ? ?
1,000

13. 1
Class work 4:Bond ValuationClass work 4:Bond Valuation
Assume that you are interested in purchasing a bond
with 5 years to maturity and a 15% coupon rate. If
your required return is 5%, what is the highest price
that you would be willing to pay?
0 1 2 3 4 5
? ? ? ? ?
1,000

14. 1
Class work 5:Bond ValuationClass work 5:Bond Valuation
Assume that you are interested in purchasing a bond
with 5 years to maturity and a 18% coupon rate. If
your required return is 8%, what is the highest price
that you would be willing to pay?
0 1 2 3 4 5
? ? ? ? ?
1,000

15. 1
Some Notes About Bond ValuationSome 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

16. 1
Common StocksCommon 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.

17. 1
Common Stock ValuationCommon 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

18. 1
Common Stock Valuation: An ExampleCommon 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%?
2.00 2.16
33.33
?

19. 1
Class work 6: Common Stock ValuationClass work 6: Common Stock Valuation
Assume that you are considering the purchase of a
stock which will pay dividends of $1.5 next year, and
$1.75 the following year. After receiving the second
dividend, you plan on selling the stock for $25.75.
What is the intrinsic value of this stock if your
required return is 20%?
? ?
?
?

20. 2
Class work 7: Common Stock ValuationClass work 7: Common Stock Valuation
Assume that you are considering the purchase of a
stock which will pay dividends of $1.75 next year,
and $1.95 the following year. After receiving the
second dividend, you plan on selling the stock for
$35.75. What is the intrinsic value of this stock if
your required return is 18%?
? ?
?
?

21. 2
Class work 8: Common Stock ValuationClass work 8: Common Stock Valuation
Assume that you are considering the purchase of a
stock which will pay dividends of $2.75 next year,
and $2.95 the following year. After receiving the
second dividend, you plan on selling the stock for
$55.75. What is the intrinsic value of this stock if
your required return is 16%?
? ?
?
?

22. 2
Class work 9: Common Stock ValuationClass work 9: Common Stock Valuation
Assume that you are considering the purchase of a
stock which will pay dividends of $3.75 next year,
and $4.95 the following year. After receiving the
second dividend, you plan on selling the stock for
$75.75. What is the intrinsic value of this stock if
your required return is 15%?
? ?
?
?

23. 2
Class work 10: Common Stock ValuationClass work 10: Common Stock Valuation
Assume that you are considering the purchase of a
stock which will pay dividends of $4.75 next year,
and $5.95 the following year. After receiving the
second dividend, you plan on selling the stock for
$95.75. What is the intrinsic value of this stock if
your required return is 12%?
? ?
?
?

24. 2
Some Notes About Common StockSome 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!

25. 2
Common Stock: Some AssumptionsCommon 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

26. 2
The Dividend Discount Model (DDM)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:

27. 2
The DDM: An ExampleThe 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:
Note that this is exactly the same value that we got
earlier

28. 2
Class work 11: DDMClass work 11: DDM
The dividends (of 1.00) were growing at 8% per year,
and your required return was 15%
The value of the stock must be:

29. 2
Class work 12: DDMClass work 12: DDM
The dividends (of 1.50) were growing at 7% per year,
and your required return was 12%
The value of the stock must be:

30. 3
Class work 13: DDMClass work 13: DDM
The dividends (of 1.75) were growing at 9% per year,
and your required return was 14%
The value of the stock must be:

31. 3
Class work 14: DDMClass work 14: DDM
The dividends (of 2.00) were growing at 11% per
year, and your required return was 15%
The value of the stock must be:

32. 3
Class work 15: DDMClass work 15: DDM
The dividends (of 2.50) were growing at 5% per year,
and your required return was 13%
The value of the stock must be:

33. 3
The DDM ExtendedThe 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:

34. 3
The DDM Example (cont.)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:

35. 3
Preferred StockPreferred 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.

36. 3
Preferred Stock ValuationPreferred 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:

37. 3
Preferred Stock: An ExamplePreferred 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?

38. 3
Class work 15: Preferred StockClass work 15: Preferred Stock
Suppose that you are interested in purchasing shares
of a preferred stock which pays a $4 dividend every
year. If your required return is 11%, what is the
intrinsic value of this stock?

39. 3
Class work 16: Preferred StockClass work 16: Preferred Stock
Suppose that you are interested in purchasing shares
of a preferred stock which pays a $4.5 dividend every
year. If your required return is 12%, what is the
intrinsic value of this stock?

40. 4
Class work 17: Preferred StockClass work 17: Preferred Stock
Suppose that you are interested in purchasing shares
of a preferred stock which pays a $4.75 dividend
every year. If your required return is 11%, what is
the intrinsic value of this stock?

41. 4
Class work 18: Preferred StockClass work 18: Preferred Stock
Suppose that you are interested in purchasing shares
of a preferred stock which pays a $5.75 dividend
every year. If your required return is 10%, what is
the intrinsic value of this stock?

42. 4
Class work 19: Preferred StockClass work 19: Preferred Stock
Suppose that you are interested in purchasing shares
of a preferred stock which pays a $1.75 dividend
every year. If your required return is 18%, what is
the intrinsic value of this stock?

43. 4
Class work 20: Preferred StockClass work 20: Preferred Stock
Suppose that you are interested in purchasing shares
of a preferred stock which pays a $1.05 dividend
every year. If your required return is 5%, what is the
intrinsic value of this stock?