McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.

Stock Valuation

Chapter 9 (8)

9-2

Key Concepts and Skills Understand how stock prices depend on future

dividends and dividend growth Be able to compute stock prices using the

dividend growth model Understand how growth opportunities affect

stock values Understand valuation comparables Understand how stock markets work

9-3

Chapter Outline9.1 The Present Value of Common Stocks9.2 Estimates of Parameters in the Dividend

Discount Model9.3 Growth Opportunities9.4 Comparables9.5 Valuing the Entire Firm9.6 The Stock Markets

9-4

9.1 The PV of Common Stocks The value of any asset is the present value of its

expected future cash flows. Stock ownership produces cash flows from:

Dividends Capital Gains

Valuation of Different Types of Stocks Zero Growth Constant Growth Differential Growth

9-5

Case 1: Zero Growth Assume that dividends will remain at the same level forever

RP

RRRP

Div

)1(

Div

)1(

Div

)1(

Div

0

33

22

11

0

321 D ivD ivD iv Since future cash flows are constant, the value of a zero

growth stock is the present value of a perpetuity:

9-6

Case 2: Constant Growth

)1(DivDiv 01 g

Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity:

gRP

1

0

Div

Assume that dividends will grow at a constant rate, g, forever, i.e.,

2012 )1(D iv)1(D ivD iv gg

3023 )1(D iv)1(D ivD iv gg

...

9-7

Constant Growth Example Suppose Big D, Inc., just paid a dividend of

$.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk level, how much should the stock be selling for?

P0 = .50(1+.02) / (.15 - .02) = $3.92

9-8

Case 3: Differential Growth Assume that dividends will grow at different rates

in the foreseeable future and then will grow at a constant rate thereafter.

To value a Differential Growth Stock, we need to: Estimate future dividends in the foreseeable future. Estimate the future stock price when the stock

becomes a Constant Growth Stock (case 2). Compute the total present value of the estimated

future dividends and future stock price at the appropriate discount rate.

9-9

Case 3: Differential Growth

)(1DivDiv 101 g

Assume that dividends will grow at rate g1 for N years and grow at rate g2 thereafter.

210112 )(1D iv)(1D ivD iv gg

NNN gg )(1D iv)(1D ivD iv 1011

)(1)(1D iv)(1D ivD iv 21021 ggg NNN

...

...

9-10

Case 3: Differential Growth

)(1Div 10 g

Dividends will grow at rate g1 for N years and grow at rate g2 thereafter

210 )(1Div g

Ng )(1Div 10 )(1)(1Div

)(1Div

210

2

gg

gN

N

…0 1 2

…N N+1

…

9-11

Case 3: Differential GrowthWe can value this as the sum of: a T-year annuity growing at rate g1

T

T

A R

g

gR

CP

)1(

)1(1 1

1

plus the discounted value of a perpetuity growing at rate g2 that starts in year T+1

TB R

gRP

)1(

Div

2

1T

9-12

Case 3: Differential GrowthConsolidating gives:

TT

T

R

gR

R

g

gR

CP

)1(

Div

)1(

)1(1 2

1T

1

1

Or, we can “cash flow” it out.

9-13

A Differential Growth ExampleA common stock just paid a dividend of $2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity.

What is the stock worth? The discount rate is 12%.

TT

T

R

gR

R

g

gR

CP

)1(

Div

)1(

)1(1 2

1T

1

1

9-14

With the Formula

3

3

3

3

)12.1(

04.12.)04.1()08.1(2$

)12.1(

)08.1(1

08.12.

)08.1(2$

P

3)12.1(

75.32$8966.154$ P

3 1.2 3$5 8.5$ P 8 9.2 8$P

9-15

Equity Valuation

The present value of a stock (Pt) assuming zero growth in dividends can be written as:

D = dividend paid at end of every year

Pt = the stock’s price at the end of year t

R = the interest rate used to discount future cash flows

The present value of a stock (Pt) assuming zero growth in dividends can be written as:

D = dividend paid at end of every year

Pt = the stock’s price at the end of year t

R = the interest rate used to discount future cash flows

RDPt /

9-16

Equity Valuation

The present value of a stock (Pt) assuming constant growth in dividends can be written as:

D0 = current value of dividendsDt = value of dividends at time t = 1, 2, …, ∞g = the constant dividend growth rate

The present value of a stock (Pt) assuming constant growth in dividends can be written as:

D0 = current value of dividendsDt = value of dividends at time t = 1, 2, …, ∞g = the constant dividend growth rate

gR

D

gR

gDP

t

t

101

)1(

9-17

Equity Valuation

The return on a stock with zero dividend growth, if purchased at current price P0, can be written as:

The return on a stock with constant dividend growth, if purchased at price P0, can be written as:

The return on a stock with zero dividend growth, if purchased at current price P0, can be written as:

The return on a stock with constant dividend growth, if purchased at price P0, can be written as:

g

P

Dg

P

gDR

0

1

0

0 )1(

0/ PDR

9-18

9.2 Estimates of Parameters

The value of a firm depends upon its growth rate, g, and its discount rate, R. Where does g come from?

g = Retention ratio × Return on retained earnings

9-19

Where Does R Come From? The discount rate can be broken into two parts.

The dividend yield The growth rate (in dividends)

In practice, there is a great deal of estimation error involved in estimating R.

9-20

Using the DGM to Find R Start with the DGM:

gP

D g

P

g)1(D R

g-R

D

g - R

g)1(DP

0

1

0

0

100

Rearrange and solve for R:

9-21

9.4 Comparables Comparables are used to value companies based

primarily on multiples. Common multiples include:

Price-to-Earnings Enterprise Value Ratios

9-22

Price-Earnings Ratio The price-earnings ratio is calculated as the current stock price divided by

annual EPS. The Wall Street Journal uses last 4 quarter’s earnings

EPS = Earning per share. EPS

shareper Priceratio P/E

9-23

Enterprise Value Ratios The PE ratio focuses on equity, but what if we want the value of

the firm? Use Enterprise Value:

EV = market value of equity + market value of debt - cash

Like PE, we compare the value to a measure of earnings. From a firm level, this is EBITDA, or earnings before interest, taxes, depreciation, and amortization. EBITDA represents a measure of total firm cash flow

The Enterprise Value Ratio = EV / EBITDA

9-24

9.5 The Stock Markets Dealers vs. Brokers New York Stock Exchange (NYSE)

Largest stock market in the world License Holders (formerly “Members”)

Entitled to buy or sell on the exchange floor Operations Floor activity

9-25

NASDAQ Not a physical exchange – computer-based

quotation system Multiple market makers Electronic Communications Networks Three levels of information

Level 1 – median quotes, registered representatives Level 2 – view quotes, brokers & dealers Level 3 – view and update quotes, dealers only

Large portion of technology stocks

9-26

Stock Market Reporting52WEEKS YLD VOL NET

HI LO STOCKSYMDIV % PE 100s CLOSE CHG21.89 9.41 Gap Inc GPS 0.34 3.1 8 88298 11.06 0.45

Gap has been as high as $21.89 in the last year.

Gap has been as low as $9.41 in the last year.

Gap pays a dividend of 34 cents/share.

Given the current price, the dividend yield is 3.1%.

Given the current price, the PE ratio is 8 times earnings.

8,829,800 shares traded hands in the last day’s trading.

Gap ended trading at $11.06, which is up 45 cents from yesterday.

9-27

Quick Quiz What determines the price of a share of stock? What determines g and R in the DGM? Discuss the importance of valuation ratios. What are some of the major characteristics of

NYSE and Nasdaq?