978-1259277160 Chapter 10 Lecture Note

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Valuation and Rates of Return

Author’s Overview

The student can clearly see that the material covered in the previous chapter on time value of

money is now being applied. The recurring theme throughout the chapter is that valuation is

based on the present value of benefits to be received in the future. The instructor should

establish this point at the outset and then repeatedly demonstrate it in the evaluation of bonds,

preferred stock, and common stock. The instructor should also emphasize the relationship of

the discount rate in present value analysis to the required rate of return demanded by security

holders. The authors suggest that the instructor go through the process of defining the

investor’s required return in terms of a real rate of return, an inflation premium, and a risk

premium. The instructor can then vary one of these components and show the impact on overall

required return and valuation.

Not all professors wish to use an example of supernormal growth, so we have included

Appendix 10A to cover this topic. This model is good at demonstrating that Ke (the required

rate of return on equity) has to be greater than g (the expected growth rate) in order to use the

constant divided growth model. When growth is greater than the required rate of return, the

supernormal growth model is appropriate. This appendix will help solidify the concepts of

uneven cash flow before getting into the capital budgeting section.

Appendix 10B is an optional discussion on using calculators in financial analysis. Both a Texas

Instruments algebraic calculator and the Hewlett Packard HP12C are used to demonstrate how

to use the calculators to calculate the present value, the future value, the bond values, present

value of an annuity, the present value of an uneven cash flow and the internal rate of return.

We suggest that you refer your students to this appendix. It will help reinforce the concepts in

Chapter 9 and Chapter 10 as well as being useful for the chapters that follow.

Chapter Concepts

LO1. The valuation of a financial asset is based on the present value of future cash flows.

LO2. The required rate of return in valuing an asset is based on the risk involved.

LO3. Bond valuation is based on the process of determining the present value of interest

payments plus the present value of the principal payment at maturity.

LO4. Preferred stock valuation is based on the dividend paid and the market required return.

LO5. Stock valuation is based on determining the present value of the future benefits of equity

ownership.

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Annotated Outline and Strategy

PPT Relationship between Time Value of Money, Required Return, Cost of

Financing, and Investment Decisions (Figure 10-1)

I. Valuation Concepts

A. The value of an asset is the present value of the expected cash flows associated

with the asset. In order to compute the present value of an asset, an investor must

know or estimate the amount of expected cash flows, the timing of expected

cash flows and the risk characteristics of the expected flows.

B. The price (present value) of an asset will be based on the collective assessment

of the asset’s cash flow characteristics by the many capital market participants.

II. Valuation of Bonds

A. The value of a bond is derived from cash flows composed of periodic interest

payments and a principal payment at maturity.

B. The present value (price) of a bond is equal to the present value of the interest

payments plus the present value of the principal (Face Value or Par Value)

payment. It is given in Formula 10-1 as follows:

where:

Pb= the market price of the bond

It= the periodic interest payments

Pn= the principal payment at maturity

t= the period from 1 to n

n= the total number of periods

Y= the yield to maturity (required rate of return)

1. The present value of interest payments can be calculated using Formula

9-6 from the previous chapter.

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(1 ) (1 )

t n

bt n

I P

PY Y

= +

+ +

2. The present value of the principal payment (par value) at maturity may be

computed by applying Formula 9-2 from the previous chapter.

3. The present value (price) of the bond will be the sum of the present value

of the interest payments plus the present value of the principal.

Perspective 10-1: Sometimes it is instructive to have the students calculate the present value

of the interest payments and principal independently rather than just the final bond price. This

can be valuable in showing how a change in required return or maturity can cause the two cash

flows to change. This is most easily demonstrated using a calculator or an Excel spreadsheet.

C. Bond valuation using a financial calculator or an Excel spreadsheet is presented

on page 299 of the text. The Excel spreadsheet is a very instructive way to do

sensitivity testing by varying the years to maturity and the required rate of

return.

D. Concept of Yield to Maturity

1. Three factors influence an investor’s required rate of return on a bond.

a. The required real rate of return: the rate of return demanded for

giving up current use of funds on a no-risk, non-inflation adjusted

basis.

b. An inflation premium: a premium to compensate the investor for

the effect of inflation on the value of the dollar.

c. Risk premium: all financial decisions are made within a risk-return

framework. An astute investor will require compensation for risk

exposure. There are two types of risk associated with the required

rate of return (yield to maturity) on a bond:

(1) Business risk is the possibility of a firm not being able to

sustain its competitive position and growth in earnings.

(2) Financial risk is the possibility that a firm will be unable

to meet its debt obligations as they come due.

E. Changing the Yield to Maturity and the Impact on Bond Valuation

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1(1 )

–+

= ´

PV FV (1 )n

= ´ +

1. Bond prices are inversely related to required rates of return. A change in

the required rate of return will cause a change in the bond price in the

opposite direction.

PPT Bond Price Table (Table 10-1)

Perspective 10-2: Table 10-1 illustrates the impact of differences between yield to maturity

and coupon rates on bond prices and reinforces the inverse relationship between bond prices

and required yield to maturity.

2. The impact of the change in required rate of return on the bond price is

dependent upon the remaining time to maturity. The impact will be

greater as the time to maturity increases.

PPT Impact of Time to Maturity on Bond Prices (Table 10-2)

Perspective 10-3: Table 10-2 shows the critical effect of time to maturity on bond price

sensitivity. The longer the time to maturity the bigger the change in bond price with a change in

yield to maturity.

PPT Relationship between Time to Maturity and Bond Price (Figure 10-2)

Perspective 10-4: The critical effect of time to maturity on bond price sensitivity is further

supported by this figure.

F. Determining Yield to Maturity from the Bond Price

1. If the bond price, coupon rate, and number of years to maturity are

known, the yield to maturity (market determined required rate of return)

can be computed.

2. The yield to maturity can most easily be found using a financial

calculator. The keystrokes are as follows:

N Number of years to maturity

PV Present value of the bond (current bond price)

PMT Interest payment (annuity)

FV Future value (par value at maturity)

Function

CPT

I/Y The example in the text gives a yield of 12 percent

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3. The yield to maturity can also be found by using the Goal Seek function

in Excel. The Goal Seek function can be found in the most recent version

of Excel on the Data tab, in the Data Tools group under What-If Analysis.

Examples of this spreadsheet are found on page 306 in the text.

F. Semiannual Interest and Bond Prices: Often interest payments are made

more frequently than once a year. Semiannual interest payments are common.

To compute the price of such a bond, we divide the annual amount of interest

and the yield to maturity by two and multiply the number of years to maturity by

two. For example, 10 years would be 20 semi-annual periods. Annual coupon

payments of $60 would be semi-annual payments of $30, and an annual yield to

maturity of 8% would become a semi-annual yield to maturity of 4%.

Perspective 10-5: Students have the opportunity to use both the annual and semiannual

approaches in working problems at the back of the chapter.

III. Valuation of Preferred Stock

A. Preferred stock is usually valued as a perpetual stream of fixed dividend

payments

where:

Pp= the price of preferred stock

Dp= the annual dividend for preferred stock

Kp= the required rate of return (discount rate) applied to preferred stock

dividends

B. Since the dividend stream is a perpetuity, the preferred stock valuation formula

can be reduced to a more usable form

C. If Kp changes after preferred stock is issued, Pp will change in an inverse fashion.

Since preferred stock theoretically has a perpetual life, it is highly sensitive to

changes in the required rate of return (Kp).

D. If the market price of preferred stock and the annual dividend are known, the

market determined required rate of return can be computed by using the

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1 2 3

….

(1 ) (1 ) (1 ) (1 )

p p p p

p p p

D D D D

K K K

= + + + +

+ + + +

valuation equation and solving for Kp.

IV. Valuation of Common Stock

A. The value of a share of common stock is the present value of an expected stream

of dividends

where:

P0= price of the stock at time zero (today)

D= dividend for each year

Ke= the required rate of return for common stock

B. Unlike dividends on most preferred stock, common stock dividends may vary.

The valuation formula may be applied, with modification, to three different

circumstances: no growth in dividends, constant growth in dividends, and

variable growth in dividends.

1. No Growth in Dividends. Common stock with constant (no growth)

dividends is valued in the same manner as preferred stock.

where:

P0= price of common stock

D0= current annual dividend on common stock = D1

(Expected to remain the same in the future)

Ke= required rate of return for common stock

2. Constant Growth in Dividends. The price of common stock with

constant growth in dividends is the present value of an infinite stream of

growing dividends. Fortunately, in this circumstance the basic valuation

equation can be reduced to the more usable form below if the discount

rate (Ke) is assumed to be greater than the growth rate.

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then

1 2 3

02 3

….

( 1 ) ( 1 ) ( 1 ) ( 1 )

ee e e

D D D D

PKK K K

= + + + +

++ + +

where:

D1= dividend expected at the end of the first year = D0(1 + g)

g= constant growth rate in dividends

P0= price of common stock

Ke= required rate of return for common stock

a. The above formula can also be thought to represent the present

value of dividends for a period of time (such as n = 3) plus the

present value of the stock price after a period of time (such as P3).

Since P3 represents the present value of dividends from D4 through

Dn, P0 will still represent the present value of all future dividends.

b. The value of P0 is quite sensitive to any change in the required rate

of return (Ke) and the growth rate (g).

3. Rearrangement of the constant growth equation allows the calculation of

the required rate of return, Ke, when P0, D1, and g are given.

The first term represents the dividend yield that the stockholder expects

to receive and the second term represents the anticipated growth in

dividends, earnings and stock price.

4. The Price Earnings Ratio Concept and Valuation. Stock valuation may

also be linked to the concept of price-earnings ratios discussed in Chapter

2. Although this is a less theoretical, more pragmatic approach than the

dividend valuation models, the end results may be similar because of the

common emphasis on risk and growth under either approach.

Perspective 10-6: Table 10-4 from Barron’s illustrates how P/E ratios are shown in the

financial press. IBM can be used as an example, and dividend yield and price changes can also

be mentioned to stimulate interest.

5. Variable Growth in Dividends. The most likely variable growth case is

one of supernormal growth followed by constant growth.

a. Value can be found through taking the present value of the

dividends during the supernormal growth period plus the price of

the stock at end of the supernormal growth period. Since growth

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0( )

=–

= +

is then constant, Formula 10-8 can be used for the terminal value.

Finance in Action: An Important Question – What’s a Small Business Really Worth?

This box presents some of the practical issues faced in valuing a small business and serves as a

contrast to the formulas presented in the text.

b. Another type of variable growth is where

the firm is assumed to pay no dividends for a period of time and

then begins paying dividends. In this case, the present value of

deferred dividends can be computed as a representation of value.

c. If no dividends are ever intended, then valuation may rest solely

on the present value of future earnings and the present value of a

future stock price.

Perspective 10-7: Appendix10A Valuation of a Supernormal Growth Firm is optional

found on pages 330-332.

Perspective 10-8: Appendix10B Using Calculators for Financial Analysis is an often

overlooked presentation of comprehensive calculator solutions for both the Texas Instruments

BAII Plus and the Hewlett-Packard 12C. Found on pages 332-340.

Other Chapter Supplements

Cases for Use with Foundations of Financial Management

Case 13, Gilbert Enterprises (Stock Valuation)

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