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Chapter 6. Stock Valuation. 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 the PE ratio

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Stock valuation

Chapter 6

Stock Valuation


Key concepts and skills
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 the PE ratio

  • Understand how stock markets work


Chapter outline
Chapter Outline

6.1 The Present Value of Common Stocks

6.2 Estimates of Parameters in the Dividend-Discount Model

6.3 Growth Opportunities

6.4 The Dividend Growth Model and the NPVGO Model

6.5 Price-Earnings Ratio

6.6 Some Features of Common and Preferred Stock

6.7 The Stock Markets


6 1 the pv of common stocks
6.1 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


Case 1 zero growth
Case 1: Zero Growth

  • Assume that dividends will remain at the same level forever

  • Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity:


Case 2 constant growth
Case 2: Constant Growth

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

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:


Constant growth example
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


Case 3 differential growth
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.


Case 3 differential growth1
Case 3: Differential Growth

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

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Case 3 differential growth2
Case 3: Differential Growth

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

0 1 2

N N+1


Case 3 differential growth3
Case 3: Differential Growth

We can value this as the sum of:

  • an N-year annuity growing at rate g1

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


Case 3 differential growth4
Case 3: Differential Growth

Consolidating gives:

Or, we can “cash flow” it out.


A differential growth example
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.

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



With cash flows
With Cash Flows

0 1 2 3 4

The constant growth phase beginning in year 4 can be valued as a growing perpetuity at time 3.

0 1 2 3


6 2 estimates of parameters
6.2 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


Where does r come from
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.


Using the dgm to find r
Using the DGM to Find R

  • Start with the DGM:

Rearrange and solve for R:


6 3 growth opportunities
6.3 Growth Opportunities

  • Growth opportunities are opportunities to invest in positive NPV projects.

  • The value of a firm can be conceptualized as the sum of the value of a firm that pays out 100-percent of its earnings as dividends and the net present value of the growth opportunities.


6 4 the npvgo model
6.4 The NPVGO Model

  • We have two ways to value a stock:

    • The dividend discount model

    • The sum of its price as a “cash cow” plus the per share value of its growth opportunities


The npvgo model example
The NPVGO Model: Example

Consider a firm that has EPS of $5 at the end of the first year, a dividend-payout ratio of 30%, a discount rate of 16%, and a return on retained earnings of 20%.

  • The dividend at year one will be $5 × .30 = $1.50 per share.

  • The retention ratio is .70 ( = 1 -.30), implying a growth rate in dividends of 14% = .70× 20%.

    From the dividend growth model, the price of a share is:


The npvgo model example1
The NPVGO Model: Example

First, we must calculate the value of the firm as a cash cow.

Second, we must calculate the value of the growth opportunities.

Finally,


6 5 price earnings ratio
6.5 Price-Earnings Ratio

  • Many analysts frequently relate earnings per share to price.

  • 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


6 6 features of common stock
6.6 Features of Common Stock

  • Voting rights (Cumulative vs. Straight)

  • Proxy voting

  • Classes of stock

  • Other rights

    • Share proportionally in declared dividends

    • Share proportionally in remaining assets during liquidation

    • Preemptive right – first shot at new stock issue to maintain proportional ownership if desired


Features of preferred stock
Features of Preferred Stock

  • Dividends

    • Stated dividend must be paid before dividends can be paid to common stockholders.

    • Dividends are not a liability of the firm, and preferred dividends can be deferred indefinitely.

    • Most preferred dividends are cumulative – any missed preferred dividends have to be paid before common dividends can be paid.

  • Preferred stock generally does not carry voting rights.


6 7 the stock markets
6.7 The Stock Markets

  • Dealers vs. Brokers

  • New York Stock Exchange (NYSE)

    • Largest stock market in the world

    • Members

      • Own seats on the exchange

      • Commission brokers

      • Specialists

      • Floor brokers

      • Floor traders

    • Operations

    • Floor activity


Nasdaq
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


Stock market reporting

Gap pays a dividend of 18 cents/share.

Gap has been as high as $25.72 in the last year.

Gap ended trading at $21.35, which is unchanged from yesterday.

Given the current price, the dividend yield is .8%.

Given the current price, the PE ratio is 18 times earnings.

Gap has been as low as $18.12 in the last year.

3,996,100 shares traded hands in the last day’s trading.

Stock Market Reporting


Quick quiz
Quick Quiz

  • What determines the price of a share of stock?

  • What determines g and R in the DGM?

  • Decompose a stock’s price into constant growth and NPVGO values.

  • Discuss the importance of the PE ratio.

  • What are some of the major characteristics of common and preferred stock?


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