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Valuation of Securities

Timothy R. Mayes, Ph.D.

FIN 3300: Chapters 6 and 7

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What is Value?

In general, the value of an asset is the price that awilling and able buyer pays to a willing and ableseller

Note that if either the buyer or seller is not bothwilling and able, then an offer does not establish thevalue of the asset

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Several Kinds of Value

There are several types of value, of which we areconcerned with three: Book Value - The assets 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 futurecash flows discounted at the decision makers required rateof return

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Determinants of Intrinsic Value

There are two primary determinants of the intrinsicvalue of an asset to an individual: The size and timing of the expected future cash flows

The individuals required rate of return (this is determined bya 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 (thats whatmakes markets work)

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Bonds

A bond is a tradeable instrument that represents adebt owed to the owner by the issuer. Mostcommonly, bonds pay interest periodically (usually

semiannually) and then return the principal atmaturity.

Most corporate, and some government, bonds arecallable. That means that at the companys option, it

may force the bondholders to sell them back to thecompany. Ordinarily, there are restrictions on thetiming of the call and the amount that must be paid.

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Calculating the Value of a Bond

There are two types of cash flows that are providedby 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 bonds

cash flows:

0 1 2 3 4 5

100 100 100 100 100

1,000

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Calculating the Value of a Bond (cont.)

We can use the principle of value additivity to findthe value of this stream of cash flows

Note that the interest payments are an annuity, andthat the face value is a lump sum

Therefore, the value of the bond is simply the presentvalue of the annuity-type cash flow and the lumpsum:

V Pmt

k

k

FV

kB

d

N

d d

N

1 11

1

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Bond Terminology

There are several terms with which you must befamiliar 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 theface value determines the annual interest payment amount.

Face Value - This is the principal amount (nominally, theamount that was borrowed). This is the amount that will berepaid at maturity

Maturity Date - This is the date after which the bond nolonger exists. It is also the date on which the loan is repaidand the last interest payment is made.

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Bond Valuation: An Example

Assume that you are interested in purchasing a bondwith 5 years to maturity and a 10% coupon rate. Ifyour 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

VB

100

1 11 012

012

1000

1 0 12927 90

5

5

.

.

,

..

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Some Notes About Bond Valuation

The value of a bond depends on several factors suchas time to maturity, coupon rate, and required return

We can note several facts about the relationshipbetween 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 viceversa

Longer terms to maturity lead to lower bond prices, andvice-versa

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Common Stocks

A share of common stock represents an ownershipposition in the firm. Typically, the owners areentitled to vote on important matters regarding the

firm, to vote on the membership of the board ofdirectors, and (often) to receive dividends.

In the event of liquidation of the firm, the commonshareholders will receive a pro-rata share of the

assets remaining after the creditors and preferredstockholders have been paid off.

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Common Stock Valuation

Just like with bonds, the first step in valuing commonstocks 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 flowsand adding them together will give us the value

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Common Stock Valuation: An Example

Assume that you are considering the purchase of astock 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 yourrequired return is 15%?

VCS

2 00

1 15

2 16 33 33

1 152857

1 2

.

.

. .

..

2.00 2.1633.33

?

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Some Notes About Common Stock

In valuing the common stock, we have made twoassumptions: We know the dividends that will be paid in the future

We know how much you will be able to sell the stock for inthe future

Both of these assumptions are unrealistic, especiallyknowledge of the future selling price

Furthermore, suppose that you intend on holding onto the stock for twenty years, the calculations wouldbe very tedious!

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Common Stock: Some Assumptions

We cannot value common stock without makingsome simplifying assumptions

If we make the following assumptions, we can derivea 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 predictevery future dividend, as long as we know the mostrecent dividend

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The Dividend Discount Model (DDM)

With these assumptions, we can derive a modelwhich is known as the Dividend Discount Model, orthe Gordon Model

This model gives us the present value of an infinitestream of dividends that are growing at a constantrate:

V D gk g

Dk g

CS

CS CS

0 11

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The DDM: An Example

Recall our previous example in which the dividendswere growing at 8% per year, and your requiredreturn was 15%

The value of the stock must be:

VCS

185 1 08

15 08

2 00

0 15 08

2857. .

. .

.

. .

.

Note that this is exactly the same value that we gotearlier

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The DDM Extended

There is no reason that we cant use the DDM at anypoint in time

For example, we might want to calculate the pricethat a stock should sell for in two years

To do this, we can simply generalize the DDM:

V D gk g

Dk g

NN

CS

N

CS

1 1

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The DDM Example (cont.)

In the earlier example, how did we know that thestock would be selling for $33.33 in two years?

Note that the period 3 dividend must be 8% largerthan the period 2 dividend, so:

V2

2 16 1 08

15 08

2 33

0 15 08

3333

. .

. .

.

. .

.

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Preferred Stock

Preferred stock represents an ownership claim on thefirm that is superior to common stock in the event ofliquidation. Typically, preferred stock pays a fixed

dividend periodically and the preferred stockholdersare usually not entitled to vote as are the commonshareholders.

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Preferred Stock Valuation

Preferred stock is very much like common stock,except that the dividends are constant (i.e., thegrowth rate is 0%)

Therefore, we can use the DDM with a 0% growthrate to find the value:

V

D

k

D

kP

CS CS

0 1 0

0

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Preferred Stock: An Example

Suppose that you are interested in purchasing sharesof a preferred stock which pays a $5 dividend everyyear. If your required return is 7%, what is the

intrinsic value of this stock?

VP 5

0 077143

..