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Chapter 5: Stock Valuation. Professor Thomson Finance 3013. Debt vs. Equity: Debt. Debt securities represent a legally enforceable claim. Debt securities offer fixed or floating cash flows. Bondholders don’t have any control over how the company is run.

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chapter 5 stock valuation

Chapter 5: Stock Valuation

Professor Thomson

Finance 3013

debt vs equity debt
Debt vs. Equity: Debt
  • Debt securities represent a legally enforceable claim.
  • Debt securities offer fixed or floating cash flows.
  • Bondholders don’t have any control over how the company is run.
debt vs equity equity

Common stockholders are residual claimants.

  • No claim to earnings or assets until all senior claims are paid in full
  • High risk, but historically also high return
Debt vs. Equity: Equity
  • Stockholders have voting rights on important company decisions.

Debt and equity have substantially different marginal benefits and marginal costs.

preferred stock
Preferred Stock

Preferred stock is a hybrid having some features similar to debt and other features similar to equity.

  • Claim on assets and cash flow senior to common stock
  • As equity security, dividend payments are not tax deductible for the corporation.
  • For tax reasons, straight preferred stock held mostly by corporations.

Promises a fixed annual dividend payment, but not legally enforceable. Firms cannot pay common stock dividends if preferred stock is in arrears (i.e. preferred stock is typically “cumulative”)

- Preferred stockholders usually do not have voting rights.

- May be convertible to common stock

valuing preferred stock
Valuing Preferred Stock
  • Because preferred stock pay a constant dividend, they are easy to value because the dividends are a perpetuity.
  • Recall the present value of a perpetuity is:

Where : D1 is the constant dividend whose first payment is one period from today

example 5 1 valuing preferred
Example 5.1: Valuing preferred
  • You purchase a preferred stock with a $12 per year dividend. For a 10% market rate, what is its value?
rights of common stockholders
Rights of Common Stockholders
  • Common stockholders’ voting rights can be exercised in person or by proxy.
  • Most US corporations have majority voting, with one vote attached to each common share.
  • Cumulative voting gives minority shareholders greater chance of electing one or more directors.

Shareholders have no legal rights to receive dividends. They are declared by the board of directors, and typically paid quarterly if it is a dividend paying stock. Dividends typically increase over time

common stock

Par value

Little economic relevance today

Shares authorized by stockholders to be sold by the board of directors without further stockholders approval

Shares authorized

Shares issued and outstanding

Number of shares owned by stockholders

Additional paid-in capital

Amount received in excess of par value when corporation initially sold stock

Common Stock
common stock9

Market capitalization

  • Market price per share x number of shares outstanding

Stock repurchased by corporation; Usually purchased for stock options

Treasury stock

Two-for-one split issues one new share for each already held; reduces per share price. e.g. A stock selling for $50 per share will sell for $25 per share after a 2 for 1 stock split

Stock split

Common Stock
stock valuation
Stock Valuation
  • Like other assets in finance, the value of a stock is the PV of its CF’s
  • Stocks are typically valued as perpetual securities as corporations potentially have an infinite life, and thus can pay dividends forever.
how to make money in the stock market
How to make money in the stock market
  • The standard answer – “Buy Low, Sell High” i.e. Earn capital gains
  • From dividends – Over the long run, historically speaking almost ½ of the total return to stock market investors was from dividends.
example 5 2 stock valuation with a one year holding period
Example 5.2. Stock valuation with a one year holding period
  • You expect that JK Corp stock will sell for $25 one year from today. You expect to receive $1.20 in dividends over the year you hold this stock. For a 15% required rate of return for this stock, how much should you pay for it? What is your projected capital gain?
example 5 3 stock valuation with a two year holding period
Example 5.3. Stock valuation with a two year holding period
  • You expect to sell MyCo for $28 two years from today. You expect to receive $1 dividend the first year, and a $1.10 dividend the second year. For a 16% discount rate, what is the maximum you should pay for this stock?
example 5 4 stock valuation with a three year holding period
Example 5.4. Stock valuation with a three year holding period
  • What you be willing to pay for a stock which pays a $2 dividend the first year, a $2.10 dividend the second year, and $2.21 in the third year if you will sell the stock for $40 after three years? Discount rate is 13%
model assumption
Model assumption
  • Probably the biggest weakness in the previous three examples was that we had to predict a selling price.
  • The buyer of the stock, when we sell it, will presumably go through a similar procedure to value the stock – in other words the buyer will be using future dividends to value the stock.
  • The selling price of the stock should thus be the value of all future dividends.
valuation of common stock assume 1 year holding
Valuation of Common StockAssume 1 year holding
  • P0 = Present value or price of stock today
  • P1 = Price of stock next period
  • D1 = Dividends received in first period
  • i = discount rate
valuation fundamentals common stock
Valuation Fundamentals:Common Stock
  • How was P1 determined?
    • PV of expected stock price P2, plus dividends
    • P2 is the PV of P3 plus dividends, etc...
  • Repeating this logic over and over, you find that today’s price equals PV of the entire dividend stream the stock will pay in the future:

Must be able to predict future dividends to use this model

zero growth valuation model

Zero growth model assumes a constant,

non-growing dividend stream. (Think preferred stock)

  • D1 = D2= ... = D
Zero Growth Valuation Model
  • To value common stock, you must make assumptions about future dividend growth.
  • Plugging constant value D into the common stock valuation formula reduces to simple equation for the present value of a perpetuity:
constant growth valuation model
Constant Growth Valuation Model
  • Assumes dividends will grow at a constant rate (g) that is less than the required return (r)
  • If dividends grow at a constant rate forever, you can value stock as a growing perpetuity, denoting next year’s dividend as D1:

Note: D1 = D0(1+g)

Commonly called the Gordon growth model

Also called a DDM : Dividend Discount Model

dividends over time
Dividends over time
  • In the Gordon growth model:
review notation
Review Notation
  • D0 = Current Dividend (time period 0)
  • D1 = Dividend one period from now
  • r = appropriate discount rate or rate of return for the particular stock (adjusts for time value of money and risk)
  • g = constant growth rate in dividends
  • P0 = the present value of the infinite series of dividends, which is the estimate stock price
use the gordon model when
Use the Gordon model when . . .
  • A dividend is paid on a regular basis
  • Growth rate in the dividends is constant
  • r>g

Dynasty Corp. will pay a $3 dividend in one year.  If investors expect that dividend to remain constant forever, and they require a 10% return on Dynasty stock, what is the stock worth?

What is the stock worth if investors expect Dynasty’s dividends to grow at 3% per year?

example 5 5 applying the ddm
Example 5.5: Applying the DDM
  • Sombria industries recently paid a $2 dividend, and its dividends have been growing at 5% per year. The appropriate discount rate for this stock is 12%.
  • What should its current price be?
  • What do you projects its price to be 5 years from now?
example 5 6 rate of return
Example 5.6: Rate of Return
  • Ootsa Corp. is trading for $50 per share. Next year you expect it to pay a $2 dividend, and dividends have been growing at a 6% rate. What rate of return do investors require from this stock? What is the dividend yield? What is the capital gain yield?
example 5 7 delayed dividends
Example 5.7: Delayed Dividends
  • Joogle is high tech start up that is not expected to pay a dividend for 10 years. At that time you expect it will pay an $8 dividend, with a growth rate of 7%. For a 12% required return, what should you be willing to pay for Joogle today? What will its stock price be 5 years from today?
example 5 8 variable growth model example
Example 5.8: Variable Growth Model Example
  • Estimate the current value of Morris Industries' common stock, P0
  • Assume:
    • The most recent annual dividend payment of Morris Industries was $4 per share.
    • Investors expect that these dividends will increase at an 8% annual rate over the next 3 years.
    • After three years, dividend growth will level out at 5%.
    • The firm's required return, r, is 12%.
review smart animation
Review Smart Animation

• Chapter 5. “See a demonstration of the variable growth model.”

other valuation models
Other valuation models
  • Free cash flow analysis
  • Similar to the DDM model, but rather than discounting the dividend, one discounts the free cash flows (see Chapter 2)
  • The discount rate used is the WACC (Weighted Average Cost of Capital) which is the weighted average of the discount rates for the firm’s bonds, stocks and preferred stocks.
common stock valuation other options

Book value

  • The value shown on the balance sheet of the assets of the firm, net of liabilities shown on the balance sheet

Liquidation value

  • Actual net amount per share likely to be realized upon liquidation and payment of liabilities
  • Reflects the amount investors will pay for each dollar of earnings per share
  • P / E multiples differ between and within industries.
  • Especially helpful for privately-held firms.

P / E multiples

Common Stock ValuationOther Options
trading stock
Trading Stock
  • Why does any security trade?
  • Primary Market – a market for newly minted stock – funds go to the company whose name is on the stock
  • Initial Public Offering – the first time a primary market offering is made for a company – it represents the transition from a private firm to a public firm whose stock is freely traded
secondary stock market
Secondary Stock Market
  • Biggest stock market for existing stocks is the NYSE – New York Stock Exchange
    • Trading is at Wall and Broad Street
  • Second biggest market is the Nasdaq
  • Nasdaq was formerly, National Association of Securities Dealers Automatic Quotations
    • Trading is in cyberspace
how to choose stocks
How to choose stocks
  • If you are not a stock analyst, and do not have a lot of money to invest, I suggest choosing broad based mutual funds, especially index funds
  • In general, don’t choose stocks based on hot tips
  • I invest with the Vanguard family of mutual funds

variable growth model valuation steps 1 and 2
Variable Growth ModelValuation Steps 1 and 2
  • Compute the value of dividends in year 1, 2, and 3 as (1+g1)=1.08 times the previous year’s dividend

Div1= Div0 x (1+g1) = $4 x 1.08 = $4.32

Div2= Div1 x (1+g1) = $4.32 x 1.08 = $4.67

Div3= Div2 x (1+g1) = $4.67 x 1.08 = $5.04

  • Find the PV of these three dividend payments:

PV of Div1= Div1 (1+r)1 = $ 4.32  (1.12) = $3.86

PV of Div2= Div2 (1+r)2 = $ 4.67  (1.12)2 = $3.72

PV of Div3= Div3 (1+r)3 = $ 5.04  (1.12)3 = $3.59

Sum of discounted dividends = $3.86 + $3.72 + $3.59 = $11.17

variable growth model valuation step 3
Variable Growth ModelValuation Step 3
  • Find the value of the stock at the end of the initial growth period using the constant growth model.
  • Calculate next period dividend by multiplying D3 by 1+g2, the lower constant growth rate:

D4 = D3 x (1+ g2) = $ 5.04 x (1.05) = $5.292

  • Then use D4=$5.292, g =0.05, r =0.12 in Gordon model:
variable growth model valuation step 342
Variable Growth ModelValuation Step 3
  • Find the present value of this stock price by discounting P3 by (1+r)3
variable growth model valuation step 4
Variable Growth ModelValuation Step 4
  • Add the PV of the initial dividend stream (Step 2) to the PV of stock price at the end of the initial growth period (P3):

P0 = $11.17 + $53.81 = $64.98


stock price

Remember: Because future growth rates might

change, the variable growth model allows for a

changes in the dividend growth rate.

valuing the enterprise free cash flow valuation


Use weighted average cost of capital (WACC) to discount the free cash flows.

Valuing the Enterprise: Free Cash Flow Valuation

Discount estimates of free cash flow that the firm will generate in the future.

WACC: after-tax weighted average required return on all types of securities that firm issues.

We have an estimate of total value of the firm.

How can we use this to value the firm’s shares?

value of firm s shares

An example....

Morton Restaurant Group (MRG)

First quarter of 2001, traded in the $20 - $25 range

Value of firm’s shares

VS = VF– VD - VP

  • VS = value of firm’s common shares
  • VF = total enterprise value
  • VD = value of firm’s debt
  • VP = value of firm’s preferred stock

We can use the free cash flow approach to estimate the value of MRG shares.

an example mortons restaurant group

At end of 2000, MRG’s debt market value was $66 million.

  • No preferred stock
  • 4,148,002 shares outstanding
  • Free cash flow in 2000 was $4.8 million.
  • Revenues and operating profits grew at 14% between 1998 and 2000.


An Example: Mortons Restaurant Group

Assume that Mortons will experience 14% FCF growth from 2000 to 2004 and 7% annual growth thereafter.

Mortons’ WACC is approximately 11%.

an example mortons restaurant group47
An Example: Mortons Restaurant Group

Use variable growth equation to estimate Mortons enterprise value.

an example mortons restaurant group49

VF = 163,386,865

VD = $66,000,000

VP = $0

VS = $163,386,865 - $66,000,000 - $0 = $97,386,865

An Example: Mortons Restaurant Group

Divide total share value by 4,148,002 shares outstanding to obtain per-share value:

stock valuation50

Stock Valuation

Preferred stock has both debt and equity-like features.

Common stock represents residual claims on firms’ cash flows

Investment bankers play an important role in helping firms issue new securities

The same principles apply to valuation of both preferred and common stock

valuation fundamentals preferred stock

PS0 = Preferred stock’s market price

  • Dp = next period’s dividend payment
  • rp = discount rate

An example: Investors require an 11% return on a preferred stock that pays a $2.30 annual dividend.  What is the price?

Valuation Fundamentals:Preferred Stock

Preferred stock is an equity security that is expected to pay a fixed annual dividend indefinitely.

investment banks role in equity offerings


Investment banking lines of business

Asset management

Corporate finance

Investment banks provide advice with structuringseasoned and unseasoned issues.



Seasoned offering

  • Equity issues by firms that already have common stock outstanding.

Unseasoned offering

  • Initial public offering (IPO): issue of securities that are not traded yet.
Investment Banks’ Role in Equity Offerings
investment banks role in equity offerings53

Firms can choose an investment bank through

Direct negotiated offer

Competitive bidding



  • The bank promises its best efforts to sell the firm’s securities. No guarantees though about the success of the offering.
  • Underwritten offerings, bank guarantees certain proceeds.
  • Vast majority of US security offerings are underwritten.



Investment Banks’ Role in Equity Offerings

Public security issues can be

investment bank services and costs

Services provided by investment banks prior to security offering

  • Primary pre-issue role: provide advice and help plan offer
  • Firm seeking capital selects lead underwriter(s).
  • Top firm is the lead manager, others are co-managers.
  • Offering syndicate organized early in process

Prior to offering, lead investment bank negotiates underwriting agreement

  • Sets offer price and spread; details lock-up agreement
  • Bulge bracket underwriter’s spread usually 7.0% for IPOs
  • Initial offer price set as range; final price set day before offer
Investment Bank Services and Costs
services provided during and after a security offering

Lead underwriter sets each syndicate member’s participation.

How many shares each member must sell and compensation for each sale

Services Provided during and after a Security Offering

Almost all IPOs and SEOs have a green shoe option: over-allotment option to cover excess demand.

Lead underwriter responsible for price stabilization after offering.

After offering, lead underwriter serves as principal market maker.

secondary market

Securities exchanges

  • Centralized locations in which listed securities are bought and sold
  • NYSE: the largest exchange in the world, with almost 360 billionshares listed. Other exchanges: AMEX, regional exchanges

The Over-the-counter market (OTC)

  • OTC has no central, physical location; linked by a mass telecommunication network.
  • A part of the OTC market is made up of stockstraded on NASDAQ.
Secondary Market

On the secondary market, investors deal among themselves.