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%?

Ppreferred = PV / KP

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

P0     = Div1           P1
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

PO = \$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%

PO  =     \$2    +   \$3         +(    \$3.15    )  χ   (1.10)2

1.10      (1.10)2           .10  .05

PO  = 1.82 + 2.48 + 52.07 = 56.37

Valuation using PE method:

Estimate expected earnings

Determine an industry average PE

PO  = PE  E

Example

Next years 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 dont know what future dividends, growth or earnings will be.

It is even difficult to determine required return.

If a change in the  markets 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.

# Market Efficiency

How accurately and quickly the market adjusts to new information

# In an efficient market

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.

# Question

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.

# Is the market truly efficient?

The evidence is mixed . . .

Test of Market Efficiency:

Recent evidence suggests CAPM may not fully explain required returns.