Chapter 9

An Introduction to Security Valuation

2

The Investment Decision Process

Determine the required rate of returnEvaluate the investment to determine if its market price is consistent with your required rate of return

Estimate the value of the security based on its expected cash flows and your required rate of returnCompare this intrinsic value to the market price to decide if you want to buy it

3

Valuation ProcessTwo approaches

1. Top-down, three-step approach2. Bottom-up, stock valuation, stock picking approach

4

Overview of the Investment Process

Exhibit 9.1

5

Top-Down, Three-Step Approach1. General economic influences

Decide how to allocate investment funds among countries, and within countries to bonds, stocks, and cash

2. Industry influencesDetermine which industries will prosper and which industries will suffer on a global basis and within countries

3. Company analysisDetermine which companies in the selected industries will prosper and which stocks are undervalued

6

Theory of Valuation

The value of an asset is the present value of its expected returnsYou expect an asset to provide a stream of returns while you own it

7

Theory of ValuationTo convert this stream of returns to a value for the security, you must discount this stream at your required rate of returnThis requires estimates of:

The stream of expected returns, andThe required rate of return on the investment

8

Stream of Expected Returns

Form of returnsEarningsCash flowsDividendsInterest paymentsCapital gains (increases in value)

9

Required Rate of Return

Determined by1. Risk-free rate of return2. Expected rate of inflation during the holding period3. Risk premium determined by the uncertainty of returns

10

Investment Decision Process: A Comparison of Estimated Values and Market Prices

If Estimated Value > Market Price, Buy

If Estimated Value < Market Price, Don’t Buy

11

Valuation of Bonds

Example: in 2002, a $10,000 bond due in 2017 with 10% couponDiscount these payments at the investor’s required rate of return (if the risk-free rate is 9% and the investor requires a risk premium of 1%, then the required rate of return would be 10%)

12

Valuation of BondsPresent value of the interest payments is

an annuity for thirty periods at one-half the required rate of return:

$500 x 15.3725 = $7,686The present value of the principal is

similarly discounted:$10,000 x 0.2314 = $2,314

Total value of bond at 10 percent = $10,000

13

Valuation of Bonds

Alternatively, assuming an investor requires a 12 percent return on this bond, its value would be:

$500 x 13.7648 = $6,882$10,000 x .1741 = 1,741

Total value of bond at 12 percent = $8,623

Higher rates of return lower the value

14

Valuation of Preferred Stock

Owner of preferred stock receives a promise to pay a stated dividend, usually quarterly, for perpetuitySince payments are only made after the firm meets its bond interest payments, there is more uncertainty of returnsTax treatment of dividends paid to corporations (80% tax-exempt) offsets the risk premium

15

Valuation of Preferred Stock

pk

DividendV

The value is simply the stated annual dividend divided by the required rate of return on preferred stock (kp)

Assume a preferred stock has a $100 par value and a dividend of $8 a year and a required rate of return of 9 percent

89.88$0.09

$8V

16

Valuation of Preferred Stock

Given a market price, you can derive its promised yield

At a market price of $85, this preferred stock yield would be

Price

Dividendk p

0941.$85.00

$8k p

17

Approaches to the Valuation of Common

Stock

Two approaches have developed1. Discounted cash-flow valuation2. Relative valuation technique

18

Use the Discounted Cash Flow Valuation Approach

The measure of cash flow usedDividends

Cost of equity as the discount rate

Operating cash flowWeighted Average Cost of Capital (WACC)

Free cash flow to equityCost of equity

19

Discounted Cash-Flow Valuation Techniques

nt

tt

tj k

CFV

1 )1(

Where:

Vj = value of stock j

n = life of the assetCFt = cash flow in period t

k = the discount rate

20

Valuation Approaches and Specific Techniques

Approaches to Equity Valuation

Discounted Cash Flow Techniques

Relative Valuation Techniques

•Present Value of Dividends (DDM)•Present Value of Operating Cash Flow•Present Value of Free Cash Flow

•Price/Earnings Ratio (PE)•Price/Cash flow ratio (P/CF)•Price/Book Value Ratio (P/BV)•Price/Sales Ratio (P/S)

Exhibit 9.2

21

The Dividend Discount Model (DDM)

n

tt

t

j

k

D

k

D

k

D

k

D

k

DV

1

33

221

)1(

)1(...

)1()1()1(

Where:Vj = value of common stock jDt = dividend during time period tk = required rate of return on stock j

22

The Dividend Discount Model (DDM)

If the stock is not held for an infinite period, a sale at the end of year 2 would imply:

2

2

221

)1()1()1( k

SP

k

D

k

DV jj

23

The Dividend Discount Model (DDM)If there is constant growth rate for

estimating future dividends

This can be reduced to:

n

n

j k

gD

k

gD

k

gDV

)1(

)1(...

)1(

)1(

)1(

)1( 02

200

gk

DV j

1

24

Infinite Period DDM and Growth CompaniesAssumptions of DDM:1. Dividends grow at a constant rate2. The constant growth rate will

continue for an infinite period3. The required rate of return (k) is

greater than the infinite growth rate (g)

25

Present Value of Operating Free Cash Flows

nt

tt

j

tj WACC

OCFV

1 )1(Where:Vj = value of firm jn = number of periods assumed to be infiniteOCFt = the firms operating free cash flow in

period tWACC = firm j’s weighted average cost of

capital

26

For infinite periods:

OCFjj gWACC

OCFV

1

Where:OCF1=operating free cash flow in period 1gOCF = long-term constant growth of operating free cash flow

27

Present Value of Free Cash Flows to Equity

“ Free” cash flows to equity are derived after operating cash flows have been adjusted for debt payments (interest and principle)The discount rate used is the firm’s cost of equity (k) rather than WACC

28

Present Value of Free Cash Flows to Equity

Where:Vj = Value of the stock of firm jn = number of periods assumed to be infiniteFCFt = the firm’s free cash flow in period tK j = the cost of equity

n

tt

j

tj k

FCFV

1 )1(

29

Relative Valuation Techniques

Value can be determined by comparing to similar stocks based on relative ratiosRelevant variables include earnings, cash flow, book value, and salesThe most popular relative valuation technique is based on price to earnings

30

Earnings Multiplier ModelThis values the stock based on expected annual earningsThe price earnings (P/E) ratio, or

Earnings Multiplier

Earnings Expected

PriceMarket Current

31

Earnings Multiplier Model

The infinite-period dividend discount model indicates the variables that should determine the value of the P/E ratio

Dividing both sides by expected earnings during the next 12 months (E1)

gk

DPi

1

gk

ED

E

Pi

11

1

/

32

Earnings Multiplier ModelThus, the P/E ratio is determined by

1. Expected dividend payout ratio2. Required rate of return on the stock

(k)3. Expected growth rate of dividends

(g)

gk

ED

E

Pi

11

1

/

33

Earnings Multiplier ModelAs an example, assume:

Dividend payout = 50%Required return = 12%Expected growth = 8%D/E = .50; k = .12; g=.08

12.5

.50/.04

.08-.12

.50P/E

34

Earnings Multiplier ModelA small change in either or both k or

g will have a large impact on the multiplier

D/E = .50; k=.13; g=.08 P/E = .50/(.13-.08) = .50/.05 = 10

gk

ED

E

Pi

11

1

/

35

Earnings Multiplier ModelA small change in either or both k or g will

have a large impact on the multiplierD/E = .50; k=.13; g=.08 P/E = 10D/E = .50; k=.12; g=.09P/E = .50/(.12-.09) = .50/.03 = 16.7

gk

ED

E

Pi

11

1

/

36

Earnings Multiplier ModelA small change in either or both k or g will

have a large impact on the multiplierD/E = .50; k=.13; g=.08 P/E = 10D/E = .50; k=.12; g=.09 P/E = 16.7D/E = .50; k=.11; g=.09P/E = .50/(.11-/.09) = .50/.02 = 25

gk

ED

E

Pi

11

1

/

37

Earnings Multiplier Model

Given current earnings of $2.00 and growth of 9%

You would expect E1 to be $2.18

D/E = .50; k=.12; g=.09 P/E = 16.7V = 16.7 x $2.18 = $36.41

38

The Price-Cash Flow Ratio

1

/

t

ti CF

PCFP

Where:P/CFj = the price/cash flow ratio for firm jPt = the price of the stock in period tCFt+1 = expected cash low per share for firm j

39

The Price-Book Value RatioWidely used to measure bank values

(most bank assets are liquid (bonds and commercial loans)

40

The Price-Book Value Ratio

Where:P/BVj = the price/book value for firm j

Pt = the end of year stock price for firm j

BVt+1 = the estimated end of year book value per share for firm j

1

/

t

tj BV

PBVP

41

The Price-Sales Ratio

1

t

t

S

P

S

P

tjS

jP

jS

P

t

t

j

j

Year during firmfor shareper sales annual

firmfor pricestock year of end

firmfor ratio sales toprice

1

42

Required Rate of Return (k)

Three factors influence an investor’s required rate of return:The economy’s real risk-free rate (RRFR)The expected rate of inflation (I)A risk premium (RP)

43

Risk ComponentsBusiness riskFinancial riskLiquidity riskExchange rate riskCountry risk

44

Expected Growth Rate of Dividends

Determined bythe growth of earningsthe proportion of earnings paid in dividends

Earnings growth is also affected by compounding of earnings retention

g = (Retention Rate) x (Return on Equity)

= RR x ROE

45

Breakdown of ROE

EquityCommon

Assets Total

Assets Total

Sales

Sales

IncomeNet

ROE

Profit Total Asset Financial

Margin Turnover Leverage= xx