Unit 5: Stock Valuation

If you own a share of stock, you can receive cash in two ways

– The company pays dividends

– You sell your shares, either to another investor in the market or back to the company

As with bonds, the price of the stock is the present value of these

expected cash flows

– Dividends → cash income

– Selling → capital gains

Common Stock Valuation

– Cash flows for stocks (the dividends) are not promised like cash flows

for bonds (coupons)

– There is no maturity. Must decide when to sell but can’t reliably

predict what the “future value” will be

– No easy way to determine the rate of return for discounting

Developing The Model

• You could continue to push back when you would sell the stock

• You would find that the price of the stock is really just the present value of all expected future dividends

This is because if the stock price is pushed back far enough, the discounting would

make the stock price sale worth approx. zero today

Stock Value =

PV of Dividends

Estimating Dividends

Zero Growth

Constant dividend growth

Non-constant then constant growth (two stage model)

Zero Growth

– Firm will pay a constant dividend forever

– Price is computed using the perpetuity formula

Constant dividend growth

– Firm will increase the dividend by a constant percent every period

– Price is computed using the growing perpetuity formula

Non-constant then constant growth (two stage model)

– Dividend growth is not consistent initially (or has an abnormal growth

rate), but settles down to constant growth eventually

How to Solve for Zero Growth

Dividends expected at regular intervals forever = perpetuity

2. Constant Growth Stock

When a firm’s dividends are expected to grow forever at a

constant rate, g.

Constant Growth Model Conditions

1. Dividend expected to grow at g forever

2. Stock price expected to grow at g forever

3. Expected dividend yield is constant

4. Expected capital gains yield is constant and equal to g

5. Expected total return, R, must be > g

6. Expected total return (R):

= expected dividend yield (DY) + expected growth rate (g)

= dividend yield + g

Dividend Growth Model (DGM)

The value of the stock depends on the expected dividend level, the discount rate (R), and the growth rate (g).

Rearranging DGM

- Required (total) return on a stock has two parts: dividend yield and capital gains yield.

-I is the dividend yield

- Capital gains yield = expected growth rate of the stock price, which matches the dividend growth rate.

3. Non-constant + Constant Growth (Two Stage Model)

There’s a lot more going on here than prior examples. Remember

that all we have to do is find the PV of all expected future

dividends.

Growth and Payout

Two conditions must exist if a company is to grow:

– It must not pay out all of its earnings as dividends all the time, and

– It must invest in good projects

Why don’t firms with no dividends have a stock price of $0?

– Such firms believe their earnings are better used to pursue growth opportunities;

High growth firms tend to have zero or low payout.

• Firms later in their life cycle are typically those that pay dividends

– Investors of a zero-dividend firm pay the stock price based on the expected

growth rate.

Ratio Analysis – interpretive questions we want to ask

ourselves:

• How is it computed?

– Note: Not all ratios are created from same data.

• What is it intended to measure, and why might we be interested?

• What is the unit of measurement?

• What might a high or low value tell us?

• How might such values be misleading?

• How could this measure be improved?

Market Value Ratios

Price to Earnings (PE) Ratio =

PEG Ratio =

Price to Sales (PS) Ratio

Market to Book (MB) Ratio

Price to Earnings (PE) Ratio

Price per share

Price to Earnings (PE) Ratio = Earning per share

PEG Ratio

PE Ratio

PEG Ratio = Earnings Growth Rate (%)

Price to Sales (PS) Ratio

Price per share

Price to Sales (PS) Ratio = Sales per share

Market to Book (MB) Ratio

Price per share

Market to Book (MB) Ratio = Book value per share

PE Ratio Description

PE: Because the PE ratio measures how much investors are willing to pay

per dollar of current earnings, higher PEs are often taken to mean the firm

has significant prospects for future growth

PEG Description

is taking PE one step further and adjusting for future growth in earnings

• Example: If Apple has a P/E of 24.16 and expected earnings growth in next five years of of

10.61%, its PEG is 24.16/10.61 = 2.3

PS Description

PS: In some cases, companies will have negative earnings for extended

periods, so their PE ratios are not meaningful. PS is our next best

alternative

MTB Description

compares the market value of the firm’s investments to their cost.

A value less than 1 could mean that the firm has not been successful overall in

creating value for its stockholders. Also means the stock may be cheap if you are

looking to invest.

Benchmarking

Ratios need to be compared to something

Time-Trend Analysis

Peer Group Analysis

Time-Trend Analysis

– How the firm’s performance is changing through time

– Internal and external uses

Peer Group Analysis

– Compare to similar companies or within industries

– SIC or NAICS code.

• But these SIC and NAICS groupings are not perfect.

– Academics have also proposed industry peers

Other Factors for Choosing to Invest in Ford or Tesla

What does your current portfolio look like?

– Diversification will come up in later units

– Lifecycle of firm is an important consideration of diversification

What macroeconomic factors affect each firm?

– E.g., price of oil vs price of battery technologies

Are you comfortable with each firm’s management styles?

There are many other factors that we will discuss throughout the semester.

Stock Valuation Using Multiples

The point of looking at all these ratios is to allow us to do valuation by comparing firms to their competitors

The price-earnings (PE) ratio: the current stock price divided by annual EP,S:

In addition to DGM, a common valuation froach is to multiply a benchmark PE ratio

by earnings per share (EPS) to come up with a stock price:

P. = Benchmark PE ratio * EPS

The benchmark PE ratio is often an industry average or based on a company's own historical values.

The idea is to identify how under (or over) valued the stock is due to investors paying too little (or too much) for the stock relative to the firms earnings.

If we get a value of Pt higher (lower) than the current market price of the stock, we say it is under (over) valued

Common Stock

Equity without priority for dividends or bankruptcy.

Comes with voting rights: generally “one share = one vote”

Director elections are typically staggered, and firms can appoint directors temporarily

until next voting term.

Also vote on matters of great importance (e.g., merger)

Proxy voting: grant of authority by a shareholder allowing another individual to vote

his or her shares

Classes of stock

Some firms have multiple classes of stock.

– Typically different share classes have different voting rights

– Ex: Berkshire Hathaway A and B

Preferred Stock

Stock with dividend and bankruptcy priority over common stock

Usually sold in large chunks to institutional investors

Dividends

– Must be paid before dividends can be paid to common stockholders

– Most preferred dividends are cumulative

• Missed preferred dividends have to be paid before common dividends can be paid

• Makes the Dividend growth model well suited to price Preferred Stock

– Preferred shares can also receive a higher dividend yield than common

shares

Preferred stock generally does not carry voting rights

Financial Markets

Primary markets

Secondary markets

Primary markets

Firm raises money directly from investors

– Private Equity offering: Uber Funding Rou

nds

– Public Equity offering: Snapchat IPO

Secondary markets

Provides the means of transferring

ownership between investors

– Stocks are traded on organized markets:

NYSE, NASDAQ, etc

Stock Markets: Who executes the trades?

Dealer

Broker

Dealer

: An agent who buys and sells securities from an inventory.

– Ex: Citadel Securities, Goldman Sachs

– Sells to you at the ask price, buys from you at the bid price. The ask is

higher than the bid — the dealer profits on the bid-ask spread

Broker:

An agent who arranges transactions between buyers and

sellers and does not hold an inventory.

– Ex: Fidelity, Robinhood

– Earns a commission (from you or a market maker) for matching the

two sides, takes no price risk

If companies don’t earn/raise money off of

secondary market trades, why do they care

about the stock price?

1. They ultimately answer to the shareholders

2. Management’s compensation is often tied to share price

3. If the company issues new shares, it will be close to the

current trading price

a) Debt is also generally cheaper to issue

4. A higher share price decreases the likelihood of takeover

NYSE

Founded in 1817

• Historically: Designated Market Makers (dealers) hold

certain stocks and remain at their post auctioning off

shares to brokers and maintaining order.

– Today: 95% of trading is electronic, human intervention

typically occurs at open and close or times of crisis

• Historically: Floor Brokers get a call from the brokerage

company (say Merrill-Lynch) to buy a certain number

of shares of a company on behalf of a client.

– Today: floor brokers only handle large, complex orders,

everything else is routed algorithmically

NASDAQ

Founded 1971

National Association of Securities Dealers

Automated Quotations System.

Purely electronic market with no physical

location.

Market makers post bid and ask prices for

stocks; institutions submit orders that are

algorithmically matched to a central limit

order book

How do firms choose where to list?

Firms consider market structure, listing costs, liquidity, peer firms, governance

signaling, and IPO execution

NYSE vs NASDAQ

– NASDAQ is fully electronic, while the NYSE uses a hybrid model with designated market makers overseeing opening and closing auctions. These differences matter most for IPO price discovery and volatility management.

– Historically, the NYSE was associated with blue-chip firms and NASDAQ with technology companies, but today both exchanges list firms across all sectors and sizes.

– NASDAQ generally has lower listing and compliance costs, making it attractive to smaller and growth-oriented firms.

– NYSE-listed firms tend to be fewer but larger on average, while NASDAQ lists many more firms with a wider size distribution.

– Stocks can now be traded on exchanges outside of the one they are hosted on, but still predominately trade at their host exchange.

Stock Market Indices

Dow Jones Industrial Average and the S&P 500

When the stock market is “up” or “down,” it usually means that the DJIA or the

S&P 500 has gone “up” or “down.”

Different indices can move differently because they include different firms

and use different weighting methods

– DJIA: 30 firms, price-weighted (tracks return on stock price)

– S&P 500: 500 firms, market-cap-weighted (tracks return on overall firm value,

which is seen as a better measure)

Investors and Indices

Investors cannot buy an index directly, but they can invest in low cost index fu

nds or ETFs that are designed to track the performance of a specific index.