Asset Valuation: Stock and Market Efficiency

Chapter 9

Computing the Price of
Stock:

Done the same way as any
other asset

Compute the PV of the cash
flows

Preferred Stock:

Pays a constant dividend
forever (a perpetuity)

The PV of a perpetuity is
the cash flow divided by the interest rate.

Example

What is the price of a share of preferred stock that pays a constant $3.00 dividend if the appropriate discount equals 10%?

P_{preferred} = PV / K_{P}

Solution

P =
$3.00 / .10 = $30.00

Common Stock:

The
cash flows from common stock will be the dividends and the final sales price.

One
Period Dividend Model:

Assume
you will receive one dividend payment and a final sales price

P_{0} = __Div___{1}__ P___{1}

1+i 1+i

Example

What
should you pay for stock that will pay a $1.00 dividend and can be sold for
$20.00 in one year assuming a 10% required return?

Solution

P_{O}
= $1 / 1.10 + $20 / 1.10

= $21 / 1.10 = $19.09

The Generalized Dividend
Valuation Model

Shows
the value of stock to equal the present value of the dividends it will
generate.

The
Final Sales Price:

Using
the one period model, the final sales price can be replaced with a stream of
dividends.

This
substitution can continue until the final sales price is pushed so far into the
future as to be insignificant.

Generalized
Dividend Model:

The
Gordon Growth Model:

If
we assume dividends will grow at a constant rate, We can reduce the generalized
dividend model to a simpler equation called the Gordon Growth Model.

The Gordon Growth Model:

PO = __ D1 __

i g

Example

What
is the price of a share of stock expected to pay a $2.00 dividend next year if
it will grow

at 5% per year and the required return is 10%?

Solution

PO = __ 2 __ =
__$2.00__ = $40.00

.10 .05 .05

The Discount Rate used by
the Gordon Growth Model

Is
the required return

It
can be computed using the CAPM

Non-Constant Growth

It
may be possible to estimate the next few dividends.

After
which, the best that can be done is to estimate an average constant growth
rate.

Example

What
is the price of stock if the next dividend is $2.00, the one after that is
$3.00, and then the dividends grow at a constant 5%, assuming a 10% required
return?

Solution

Draw
a timeline:

2 3 3.15

|---||||

5%

P_{O} = __ $2 __ + __ $3
__ +_{( } __ $3.15 __ _{)} χ
(1.10)^{2 }

1.10 (1.10)^{2}
.10 .05

P_{O} = 1.82 + 2.48 + 52.07 = 56.37

Valuation using PE method:

Estimate expected earnings

Determine an industry
average PE

P_{O} = PE E

Example

Next
years earnings are expected to be $3.00 per share. If the industry average PE ratio is 16, what should the price of
the stock be?

Solution

16
$3.00 = $48.00

Why are stock prices so
volatile?

Because the inputs to
valuation models are so uncertain.

nvestors dont know what
future dividends, growth or earnings will be.

It is even difficult to
determine required return.

If a change in the markets estimate of any input changes:

The value of the stock will
change.

Economic data is released to
the public daily, and stock prices must adjust to this information.

How accurately and quickly
the market adjusts to new information

All prices accurately
reflect all that is known about a security

If markets are efficient, an
investment in Apple computer stock is as good as an investment in Microsoft
stock.

Consider the following graph
. . .

If the stock provides a
return higher than other stocks with similar risk, investors will buy it.

This will cause the price to
rise, thus lowering its return.

This will continue until the
return matches other similar investments.

What
does market efficiency say about predicting future stock prices?

Answer

In
an efficient market, historical trends do not predict future prices.

The Degrees of Efficiency:

1. Weak form of market efficiency: All historical information is reflected in the stock price.

2. Semi-Strong form of market efficiency: All public information is reflected in the
stock price.

3. Strong form of market
efficiency: All information is
reflected in the stock price.

The evidence is mixed . . .

Test of Market Efficiency:

Recent evidence suggests CAPM may not fully explain required returns.