A-10 Appendix A Solutions to Self-Test Questions and Problems
d. If more randomly selected stocks were added to a portfolio, σp would decline
to somewhere in the vicinity of 20%. (See Figure 8-6.) σp would remain con-
stant only if the correlation coef! cient was $1.0, which is most unlikely. σp
would decline to zero only if the correlation coef! cient, ρ, was equal to zero
and a large number of stocks was added to the portfolio, or if the proper pro-
portions were held in a two-stock portfolio with ρ! "1.0.
a. b! (0.6)(0.70) # (0.25)(0.90) # (0.1) (1.30) # (0.05)(1.50)
! 0.42 # 0.225 # 0.13 # 0.075! 0.85
b. rRF! 6%; RPM! 5%; b! 0.85
rp! 6% # (5%)(0.85)
! 10.25%
c. bN! (0.5)(0.70) # (0.25)(0.90) # (0.1)(1.30) # (0.15)(1.50)
! 0.35 # 0.225 # 0.13 # 0.225
! 0.93
r! 6% # (5%)(0.93)
! 10.65%Chapter 9
a. This is not necessarily true. Because G plows back two-thirds of its earnings, its
growth rate should exceed that of D; but D pays higher dividends ($3 versus $1).
We cannot say which stock should have the higher price.
b. Again, we do not know which price would be higher.
c. This is false. The changes in rd and rs would have a greater effect on G; its price
would decline more.
d. The total expected return for D is rˆD! D 1 /P 0 $ g! 12% $ 0%! 12%. The
total expected return for G will have D 1 /P 0 less than 12% and g greater than
0%, but rˆG should be neither greater nor smaller than D’s total expected
return, 12%, because the two stocks are stated to be equally risky.
e. We have eliminated a, b, c, and d; so e should be correct. On the basis of the
available information, D and G should sell at about the same price, $25; thus,
rˆs! 12% for both D and G. G’s current dividend yield is $1/$25! 4%. There-
fore, g! 12% " 4%! 8%.
The! rst step is to solve for g, the unknown variable, in the constant growth equation.
Since D 1 is unknown but D 0 is known, substitute D 0 (1 $ g) for D 1 as follows:Pˆ 0! P 0!D 1
_____r
s^ " g!
D 0 (1 # g)
________r
s^ " g$36!
$2.40(1 # g)
__________0.12 " gSolving for g, we! nd the growth rate to be 5%:
$4.32 " $36g! $2.40 # $2.40g
$38.4g! $1.92
g! 0.05! 5%
The next step is to use the growth rate to project the stock price 5 years hence:Pˆ 5!D 0 (1 # g)^6
________r
s^ " g
! $2.40(1.05)
6
__________
0.12 " 0.05
! $45.95(Alternatively, Pˆ 5! $36(1.05)^5! $45.95.)
Therefore, the! rm’s expected stock price 5 years from now, Pˆ 5 , is $45.95.