Asset Valuation: Stock and Market Efficiency
Computing the Price of Stock:
Done the same way as any other asset
Compute the PV of the cash flows
Pays a constant dividend forever (a perpetuity)
The PV of a perpetuity is the cash flow divided by the interest rate.
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
P = $3.00 / .10 = $30.00
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
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?
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
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%?
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
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.
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?
Draw a timeline:
2 3 3.15
PO = $2 + $3 +( $3.15 ) χ (1.10)2
PO = 1.82 + 2.48 + 52.07 = 56.37
Valuation using PE method:
Estimate expected earnings
Determine an industry average PE
PO = PE E
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?
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?
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.