Stock V l ti St k Valuation

McGraw-Hill/Irwin

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

Key Concepts and Skills

Understand h stock prices depend on future U d d how k i d d f dividends and dividend growth B able to compute stock prices using the Be bl k i i h dividend growth model U d Understand h growth opportunities affect d how h ii ff stock values U d Understand valuation comparables d l i bl Understand how stock markets work

9-1

Chapter Outline

9.1 91 9.2 9.3 9.4 94 9.5 9.6 The P Th Present Value of C V l f Common S k Stocks Estimates of Parameters in the Dividend Discount Model Growth Opportunities Comparables Valuing the Entire Firm The Stock Markets

9-2

9.1 The PV of Common Stocks

The value of any asset is the present value of its expected future cash flows. Stock S k ownership produces cash fl hi d h flows from: f

Dividends Capital Gains Zero Growth Constant Growth Differential Growth e e t a G owt 9-3

Valuation of Different Types of Stocks

Case 1: Zero Growth

Assume that di id d will remain at the same level A h dividends ill i h l l forever

Div 1 Div 2 Div 3

Since future cash flows are constant, the value of a zero

growth stock is the present value of a perpetuity:

Div 3 Div 1 Div 2 P0 1 2 3 (1 R) (1 R) (1 R) Div P0 R 9-4

Case 2: Constant Growth

Assume that dividends will grow at a constant rate, g, h di id d ill forever, i.e.,

Div 1 Div 0 (1 g )

Div 2 Div 1 (1 g ) Div 0 (1 g ) 2 Div 3 Div 2 (1 g ) Div 0 (1 g ) 3 . . .

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:

Div Di 1 P0 Rg

9-5

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

9-6

Case 3: Differential Growth

Assume that di id d will grow at different A h dividends ill diff rates in the foreseeable future and then will grow at a constant rate thereafter. 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 p p future dividends and future stock price at the appropriate discount rate.

9-7

Case 3: Differential Growth

Assume that dividends will grow at rate g1 for N

years and grow at rate g2 thereafter.

Div 1 Div 0 (1 g1 )

Div 2 Div 1 (1 g1 ) Div 0 (1 g1 ) 2 ( (

Div N Div N 1 (1 g1 ) Div 0 (1 g1 ) N

. . .

Div N 1 Div N (1 g 2 ) Div 0 (1 g1 ) N (1 g 2 ) ( ( ( . . .

9-8

Case 3: Differential Growth

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

Div 0 (1 g1 ) Div 0 (1 g1 ) 2

…

0 1 2

Div 0 (1 g1 ) N

Div Di N (1 g 2 ) Div 0 (1 g1 ) N (1 g 2 )

…

N

…

N+1

9-9

Case 3: Differential Growth

We W can value this as the sum of: l hi h f a T-year annuity growing at rate g1

(1 g1 )T C PA 1 T R g1 (1 R) plus the discounted value of a perpetuity growing at

rate g2 that starts in year T+1 T 1

Div T 1 Rg 2 PB T (1 R)

9-10

Case 3: Differential Growth

Consolidating gives: C lid ti i

Di T 1 Div C (1 g1 )T R g 2 P 1 T T R g1 (1 R ) (1 R ) Or, we can “cash flow” it out.

9-11

A Differential Growth Example

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

9-12...