Chapter 6

Equities

Common Stock

• Represents ownership of a business entity with claims on earnings and dividends

• Can have different classes of stock where one class can be given disproportionate powers

• Right to vote– Proxy

Intrinsic Value

• Present value of expected net cash flows that accrues to the owner of security

Dividend Discount Model

• Process of evaluating stocks on basis of present value of their expected stream of dividends

• Also known as the dividend valuation model

Intrinsic Value of Common Stock

P0 = price of stock today

dt = dividend during period t

r = required rate of return

H = holding period

PH = price of the stock at the end of the holding period

HH

HH

33

221

0r 1

P

r 1

d ....

r 1

d

r 1

d

r 1

d P

Holding Period Model Is Misleading

• Problem with defining price of stock in terms of dividends and selling price is that this is circular argument, as it begs the question of what determines selling price.

• Selling price is present value of dividends to be paid forever thereafter.

Dividend Discount Model

• Because model runs to infinity, it can’t be implemented without making additional assumptions about pattern of future dividends.

r 1

d ....

r 1

d

r 1

d

r 1

d P

33

221

0

1tt

t

r 1

d

Required Rate of Return

• Rate of return on an investment required by market to justify degree of risk incurred

• Risk-free rate plus the risk premium• In equilibrium (quantity supplied equals

quantity demanded), required rate of return equal to expected rate of return.

Value Cannot Be Based on Earnings

• Double counting– Earnings retained (i.e., reinvested) in firm

should lead to higher earnings in future– Higher earnings are NOT additional value to

investor, but simply a return on value of earnings previously invested

Valuation of Stocks That Don’t Pay Dividends

• If they will never, ever pay a dividend:– Truly worthless

• If they will start paying a dividend in the future:– Value today based on when they are expected

to start paying dividends, and amount of payment at that time

Gordon (Constant) Growth Model

• Form of dividend discount model• Used to evaluate the intrinsic value of an

asset based on assumptions of constant growth rate g of cash flow or dividends and a known discount rate r, where r>g.

(continued)

Gordon (Constant) Growth Model (continued)

Vo = d1/(r – g) = d0 x (1 + g)/(r – g)

where V0 = intrinsic value, d1 = next year’s dividend, g = growth rate of dividends, and r = required rate of return.

dn = dn – 1(1+g) or dn = d0(1 + g)n

Implications of Growth Model

• Decrease in required rate of return (that is, discount rate), will cause value of stock to be higher

• Increase in expected growth rate of dividends (g), will cause value of stock to be higher

• Increase in next year’s expected dividend (d1) will

cause value of stock to be higher

Alternative Meaning of “g”

• Can solve constant growth rate model for r:

r = d1/Vo + g = dividend yield plus growth rate

• Return to investor equals dividend yield plus expected percentage price change

• If discount rate = expected return, thendividend growth rate = expected percentage

price change

Zero Growth Model

• Assume dividends will never change (i.e., no growth)

P = d / r

where P = intrinsic value of a stock whose dividends are expected to form

a perpetuity d = the constant, annual dividend r = discount rate

Selection of Discount Rate

• Sufficient to compensate investor for the riskiness of dividend stream

• Frequently use CAPM:

ri = r f + (r m – r f)

Application of CAPM

Risk-free rate

• interest rate on riskless investment, such as Treasury bill

Market portfolio

• portfolio of all assets, but good surrogate is S&P 500

Market-Price Based Ratios

• Used to judge relative appropriateness of current stock price– Price-earnings ratio– Price-cash flow ratio

• Price-free cash flow ratio

– Price-sales ratio– Price-earnings/growth rate ratio

Earnings Per Share (EPS)

• Net income of company, minus any preferred dividend requirements, divided by the number of outstanding common shares

• Provides investor or potential investor with information on stability of dividends and capital gains potential

• Considered one of most important indications of value of common stock

Price-Earnings (P/E) Ratio

• Share price of stock divided by its actual or anticipated earnings per share– For trailing earnings, stock price relative to

most recent 12-month earnings per share• Factual

– For ex ante earnings, stock price relative to expected next 12-month earnings.

• Fantasy

Dividend Payout Ratio

• Dividends on common stock paid out as percentage of net income (after preferred dividends)

Growth Model & P/E Ratio

Where E0 = last year’s earnings m = the payout ratio

(continued)

P0 = E0 x m x (1 + g)/(r – g)

Growth Model & P/E Ratio (continued)

Dividing through by last year’s earnings produces the price-to-past earnings ratio:

 P0 / E0 = m x (1 + g) / (r – g)

or

P0 / [E0 x (1+g)] = m / (r – g)

P0 / E1 = m / (r – g)

Characteristics of Companies with High P/E Ratios

• High expected growth rate of earnings

• Low discount rate (less risky)

• Small spread between the discount rate and growth rate

Growth Stocks vs. Value Stocks

• Growth stocks synonymous with above average PE ratios

• Value stocks synonymous with below average PE ratios

• Recent evidence suggests value stocks perform better than growth stocks the majority of the time

Forecasting with P/E Ratio

• Individual stock:– Forecast earnings per share– Forecast P/E ratio– Multiply the two together

• Market:– Forecast earnings for index– Forecast P/E for that index– Multiply the two together

Other Equity Instruments

• Straight Preferred stock and Participating Preferred stock

• Rights Offering

• Warrants

Rights

• Issued to raise new capital• Exercise Price < Market Price

– Sometimes by a large margin– Hence, Intrinsic Value > 0

• Short lifespan• Transferable

– Trade on exchanges or OTC for larger companies

Mechanics of Dividends

• Declaration date

• Ex-dividend date

• Record date

• Payment date

Dividend Patterns

• Many companies boast of number of years of consecutive dividend payments

• Dividends paid on same date of each quarter

• Dividend increases usually same quarter of each year

Non-Traditional Investments

• Collectables –requires a market for the asset• Noncollectables –items that are unique and expensive• Natural Resources –depletion allowance on some mineral rights• Precious Metals –rare metallic chemical element of high, durable economic value