Chapter 13 investments equity valuation

Valuation MethodsBook value - Value of common equity on the balance sheet - Based on historical values of assets and liabilities, which may not reflect current values - Some assets such

Chapter 13

Equity Valuation

13.1 Valuation by Comparables

Fundamental Stock Analysis:

Models of Equity Valuation

Basic Types of Models

- Balance Sheet Models

- Dividend Discount Models

- Price/Earnings Ratios

Models of Equity Valuation

Valuation models using comparables

- Look at the relationship between price and various determinants of value for similar firms

The internet provides a convenient way to access firm data Some examples are:

- EDGAR

- Finance.yahoo.com

Table 13.1 Microsoft Corporation Financial Highlig

hts 2009

Valuation Methods

Book value

- Value of common equity on the balance sheet

- Based on historical values of assets and liabilities, which may not reflect current values

- Some assets such as brand name or specialized skills are not on a balance sheet

Valuation Methods

Market value of the shareholders’ equity

- Current market value of assets minus current market value of liabilities

: Market value of assets may be difficult to ascertain

- Market value based on stock price

- Better measure than book value of the worth of the stock to the investor

- Stock prices reflect the value of the firm as a going concern

Valuation Methods

Is book value a floor value for market value of equity?

(The market price never fall below the book value?)

- While it is not common, there are always some firms selling at a market price below book value

EX) Firm in distress Citigroup in 2009 was selling at only 20% of book value

Valuation Methods (Other Measures)

Liquidation value

- A better measure of a floor for the stock price

- Net amount realized from sale of assets and paying off all debt

- Firm becomes a takeover target if market value stock falls below this amount, so liquidation value may serve as floor to value

13.2 Intrinsic Value Versus Market Price

Expected Holding Period Return

The most popular model for assessing the value of a firm as a going concern

The return on a stock investment comprises cash dividends and capital gains or losses

- Assuming a one-year holding period

0

( ) ( ) Expected HPR= ( )E r E D E P P

P

+ −

=

Expected Holding Period Return

EX) Expected dividend per share = $4 The current price of share = $48 The expected price at the end of a year = $52

Expected HPR = E(r) = = = 0.167=16.7%

P

+ −

=

Required Return

CAPM gave us required return, call it k

(market capitalization rate):

K: The market-consensus estimate of th

e appropriate discount rate for a firm’s c

ash flows

 Provide the rate of return an investor

can expect to earn on a security give

n its risk as measured by beta.

If the stock is priced correctly, required

return should equal expected return

Expected Holding Period Return

EX) rf = 6%, E(rM) – rf = 5%, β = 1.2

k = 6% + 1.2 X 5% = 12%

From prior example, expected HPR = 16.7%

The rate of return the investor expects exceeds the required rate based on its risk by a margin of 4.7%  Undervalued

 The investor will want to include more of this stock in the portfolio than a passive strategy would dictate

( )

k r = + β   E r − r  

Intrinsic Value

The present value of all cash payments to the investor in the stock discounted

at the appropriate risk-adjusted interest rate, k.

All cash payments include dividends as well as the proceeds from the sale of th

) P ( E )

D (

E

0

+ +

=

Intrinsic Value and Market Price

Market Price

- Consensus value of all traders

- In equilibrium, the current market price will equal intrinsic value

Intrinsic Value

From example, V0 = = $50

Equivalently, at a price of $50, the investor would derive a 12% rate of return o

n an investment in the stock

However, at the current price of $48, the stock is underpriced compared to intr insic value, providing better than a fair rate of return relative to its risk

Investors will want buy more of it

13.3 Dividend Discount Models

For now assume price = intrinsic value

Basic Dividend Discount Model

Already established that

Basic Dividend Discount Model

Given that firms are “going concern”, the stock price should equal the PV of all expected future dividends into perpetuity

Intrinsic value of a stock can be found from the following:

) k 1

( D V

Basic Dividend Discount Model

Intrinsic value of a stock can be found from the following:

This equation is not useable because it requires dividend forecasts for every year into the indefinite future

Therefore we have to make assumptions about the dividends to make the model tractable.

V0 = Intrinsic Value of Stock

) k 1

( D V

No Growth Model

Use: Stocks that have earnings and dividends that are expected to remain constan

t over time (zero growth)

V0 =

Constant Growth Model

Use: Stocks that have earnings and dividends that are expected to grow at a constant rate forever

A common stock share just paid a $2.00 per share dividend and the stock has a required return of 10% Dividends are expected to grow at 6% per year forever Wh

at is the most you should be willing to pay for the stock?V 0 ( 1 ) 1 ; perpetual growth rate in dividends

D g

k

g D

Constant Growth Model (Implication)

The constant-growth DDM is valid only when g is less than k

The constant growth rate DDM implies that a stock’s value will be greater:

- The larger its expected dividend per share

- The lower the market capitalization rate, k

- The higher the expected growth rate of dividends

dividends

in rate growth

perpetual

;

) 1

D g

k

g D

Constant Growth Model (Implication)

Implies that the stock price is expected to grow at the same rate as dividends

The expected holding period return will be E(r) = Dividend yield + Capital gains yield = + = + g

) 1

( )

1 (

) 1

(

0

1 1

2

g k

D g

k

g

D g

Constant Growth Model (Implication)

Estimating the growth rate of dividends, we can compute stock’s market capitalization(k)

If the stock is selling at its intrinsic value, then E(r) = k, k = D1/P0 + g

 This equation is known also as the discounted cash flow (DCF) formula

Stock Prices and Investment Opportunities

g = growth rate in dividends is a function of two variables:

- ROE = Return on Equity for the firm

- b = plowback or retention percentage rate

= (1- dividend payout percentage rate)

g increases if a firm increases its retention ratio and/or its ROE

b ROE

g = ×

Value of Growth Opportunities

Cash Cow, Inc (CC)

Value of Growth Opportunities

Cash Cow, Inc (CC)

b = 60%; therefore g = 9%

D1 = 0.40 x $5 = $2.00

k = 12.5%; Find VGP

ROE = 15%

GP Value has increased, why?

Value with 40% dividend payout

Value of Growth Opportunities

Value of assets in place for GP = $40.00 (value with all dividends paid out, with R

OE = 12.5%)

Value of growth opportunities with ROE = 15% may be inferred from the differen

ce between the new VGP = $57.14 and the no growth value of $40.00

 The increase in the stock price reflects that planned investments provid

e an expected rate of return greater than the required rate

Thus, the present value of growth opportunities (PVGO)

= $57.14 - $40.00 = $17.14

Figure 13.1 Dividend Growth for

Two Earnings Reinvestment Policies

Click to edit Master text styles

Second level

Third level

Fourth level

Fifth level

Value of Growth Opportunities

In reality, dividends cuts almost always are accompanied by steep drops in sto

ck prices

Dividend cuts are usually taken as bad news about the future prospects of the f irm

Case: Florida Power & Light

- Announced a cut in dividend, not because of financial distress, but

because it wanted to better position itself for a period of deregulation

- At first, the stock price dropped 14% on the day of the announcement.

Multistage Growth Models

As firms progress through their industry life cycle, earnings and dividend growth rates ar

e likely to change

A two stage growth model:

g1 = first growth rate

g2 = second growth rate

T = number of periods of growth at g1

T 2

2 T

T

1

t 1 0

0

k) )(1

g (k

) g (1

D k)

(1

) g

(1 D

V

+

−

+ +

Multistage Growth Rate Model: Example

2 0

) 15 1 )(

05 0 15

0 (

63 3

$ 15

1

46 3

$ 15

1

88 2

$ 15

1

40 2

$

−

+ +

+

=

V

Table 13.2 Financial Ratios

Attractive investment opportunities

More representative

of mature firms

Figure 13.2 Honda Motor

A

B

C D E

Two Stage DDM for Honda

Two Stage DDM for Honda

The required rate of return:

βHonda = 1.05

Rf in 2008 = 3.5%

Market risk premium = historical average of 8%

from Value Line

Honda f

M f

Honda R ( R R )

Two Stage DDM for Honda

k = 11.90%

g = 7.70%

Find the intrinsic value

Value Line reported the actual price = $21.37,

so Honda was undervalued by $0.51 or about 2.4%

3 2

0

) 119

1 )(

077

0 119

0 (

077

1 15 1

$ 119

1

15 1

$ 119

1

06 1

$ 119

1

98 0

$ 119

.

1

90 0

$

V

−

× +

+ +

+

=

88 21

$

V0 =

Two Stage DDM for Honda

Should we trust the valuation result?

What if the beta is slightly incorrect, suppose it is 1.10 (< 5% error) rather than 1.05?

Now k = 12.3% and the intrinsic value estimate V0= $19.98, reversing our

13.4 Price-Earnings (P/E) Ratios

P/E Ratio and Growth Opportunities

P/E Ratios are a function of two factors

Price = No-Growth value per share + PVGOP0 = + PVGO  =

- Required Rates of Return (k) (inverse relationship)

- Expected Growth in Dividends (direct relationship)

Uses

P/E Ratio and Growth Opportunities

Price = No-Growth value per share + PVGO

P0 = + PVGO  =

When PVGO = 0, P0 = E1/K

As PVGO becomes an increasingly dominant contributor to price, the P/E ratio can rise dramatically

The ratio of PVGO to E/K

: the ratio of the component of firm value reflecting growth opportunities to the value reflecting asse

ts already in place

P/E, ROE and Growth

P O = D 1/( k-g ) from DDM formula

D 1 = E 1(1- b ), g = ROE X b

) (

) 1

(

0

b ROE k

b E

) 1

(

1 0

b ROE k

b

E P

×

−

−

=

P/E, ROE and Growth

With positive growth:

With zero growth:

If g = 0 then b should = 0 and the ratio simplifies to:

b ROE

g k

) b 1

( E

Numerical Example: No Growth

E1 = $2.50 g = 0 k = 12.5%; Find P/E and V0

P/E = 1/k = 1/.125 = 8

V0 = P/E x E1 = 8 x $2.50 = $20.00

Numerical Example with Growth

P/E, ROE and Growth

P O = D 1/( k-g ) from DDM formula

D 1 = E 1(1- b ), g = ROE X b

• The P/E ratio increases with ROE.

• The P/E ratio increases for higher plowback, b , as long as ROE exceed k

) (

) 1

(

0

b ROE k

b E

) 1

(

1 0

b ROE k

b

E P

×

−

−

=

ROE and b and growth and P/E

Always Increase

Not necessary to increase

P/E Ratios and Stock Risk

Riskier firms will have higher required rates of return (higher values of k)

Riskier stocks will have lower P/E multiples

Observe many small, risky, start-up companies with very high P/E multiples

 Does not contradict our claim Instead, it is evidence of the

market’s expectations of high growth rates for those companies

g k

) b 1

( E

Pitfalls in Using P/E Ratios

Earnings management is a serious problem

- Earnings management which is the practice of using

flexibility in accounting in accounting rules to improve the

apparent profitability of the firm

P/E should be calculated using pro forma earnings

- Ignore certain expenses such as restructuring charges and

stock option expenses

Pitfalls in Using P/E Ratios

The use of P/E ratios is related to the business cycle

- Reported earnings can fluctuate dramatically around a trend

line over the business cycle

The P/E ratio reported in the newspaper is the ratio of price to the most recent past accounting earnings

- Current accounting earnings can differ significantly from

future economic earnings because it can vary substantially

over the business cycle

Figure 13.4 & 13.5

In 2003 and 2005, Con Ed’s earnings

temporarily dipped below their trend line

and McDonald’s earnings rose faster than

The market seems to have recognized that these were both temporary conditions: prices did not respond dramatically to these fluctuations in

Figure 13.6 P/E Ratios

Other Comparative Valuation Ratios

Figure 13.7 Valuation Ratios for the S&P 500

Valued Honda using several approaches