Chapter 9 Stocks and Their Valuation 301APPENDIX 9A
Stock Market Equilibrium
Recall that rX, the required return on Stock X, can be found using the Security
Market Line (SML) equation from the Capital Asset Pricing Model (CAPM) as
discussed in Chapter 8:
rX! rRF " (rM $ rRF)bX! rRF " (RPM)bX
If the risk-free rate is 6%, the market risk premium is 5%, and Stock X has a beta of
2, the marginal investor will require a return of 16% on the stock:
rX! 6% " (5%)2.0
! 16%
This 16% required return is shown as the point on the SML in Figure 9A-1 associ-
ated with beta " 2.0.
A marginal investor will purchase Stock X if its expected return is more than
16%, will sell it if the expected return is less than 16%, and will be indifferent (will
hold but not buy or sell) if the expected return is exactly 16%. Now suppose the
investor’s portfolio contains Stock X; he or she analyzes its prospects and con-
cludes that its earnings, dividends, and price can be expected to grow at a constant
rate of 5% per year. The last dividend was D 0 " $2.8571, so the next expected divi-
dend is as follows:
D 1! $2.8571(1.05)! $3
The investor observes that the present price of the stock, P 0 , is $30. Should he or
she buy more of Stock X, sell the stock, or maintain the present position?
The investor can calculate Stock X’s expected rate of return as follows:
rˆX!
D 1
__P
0" g! (^) $30____$3 " 5%! 15%
Expected and Required Returns on Stock X
F I G U R E 9 A! 1
Rate of Return
(%)
rX = 16
rX = 15
rM = 11
rRF = 6
0 1.0 Risk, bi
SML: ri = rRF + (rM – rRF) bi
X
2.0
ˆ