182
14. FI Corporation:
a.
g
= 5%;
D
1
= $8;
k
= 10%
P
0
=
D
1
k

g
=
$8
.10  .05
= $160
b.
The dividend payout ratio is 8/12 = 2/3, so the plowback ratio is
b
= 1/3. The implied
value of ROE on future investments is found by solving:
g
=
b
´
ROE with
g
= 5%
and
b
= 1/3. ROE = 15%.
c.
The price assuming ROE =
k
is just
E
1
/
k
.
P
0
= $12/.10 = $120. Therefore, the market
is paying $40 per share ($160  $120) for growth opportunities.
15. Nogro Corporation:
a.
P
0
= $10,
E
l
= $2, b = .5, ROE = .20
k
=
D
1
/
P
0
+
g
D
1
= .5
´
$2 = $1
g
=
b
´
ROE = .5
´
.2 = .1
Therefore,
k
= $1/$10 + .1 = .1 + .1 = .2 or 20 percent.
b. Since
k
= ROE, the NPV of future investment opportunities is zero:
PVGO =
P
0

E
1
k
= 10  10 = 0
c. Since
k
= ROE, the stock price would be unaffected by cutting the dividend and
investing the additional earnings.
d.
For the same reasoning in part c above, this will not change the stock price.
20. Duo Growth Co.:
0
1
2
3
4
5
...
Dt
1.00 1.25 1.5625
1.953125
g
.25
.25
.25
.05
...
...
a.
The dividend to be paid at the end of year 3 is the first installment of a dividend
stream that will increase indefinitely at the constant growth rate of 5 percent.
Therefore, we may use the constant growth model as of the end of year 2, and can
calculate intrinsic value by adding the present value of the first two dividends plus
the present value of the sales price of the stock at the end of year 2.
The expected price 2 years from now is:
P
2
=
D
3
/(
k

g
) = $1.953125/( .20  .05 ) = $13.02
The PV of this expected price is: