controlling interests in the stock of other companies.
h.
The value of operations is the present value of all the future free cash flows that are
expected from current assetsinplace and the expected growth of assetsinplace
when discounted at the weighted average cost of capital:
.
WACC
1
FCF
V
1
t
t
t
0)
time
op(at
The terminal, or horizon value, is the value of operations at the end of the explicit
forecast period.
It is equal to the present value of all free cash flows beyond the
forecast period, discounted back to the end of the forecast period at the weighted
average cost of capital:
.
g
WACC
)
g
1
(
FCF
g
WACC
FCF
V
N
1
N
N)
time
op(at
The free cash flow model defines the total value of a company as the value of operations plus the
value of nonoperating assets plus the value of growth options.
73
A perpetual bond is similar to a nogrowth stock and to a share of preferred stock in the following
ways:
1.
All three derive their values from a series of cash inflowscoupon payments from the
perpetual bond, and dividends from both types of stock.
2
All three are assumed to have indefinite lives with no maturity value (M) for the perpetual
bond and no capital gains yield for the stocks.
74
The first step is to find the value of operations by discounting all expected future free cash flows
at the weighted average cost of capital. The second step is to find the total corporate value by
summing the value of operations, the value of nonoperating assets, and the value of growth
options.
The third step is to find the value of equity by subtracting the value of debt and preferred
stock from the total value of the corporation. The last step is to divide the value of equity by the
number of shares of common stock.
35
SOLUTIONS TO ENDOFCHAPTER PROBLEMS
71
D
0
= $1.50; g
13
= 5%; g
n
= 10%; D
1
through D
5
= ?
D
1
= D
0
(1 + g
1
) = $1.50(1.05) = $1.5750.
D
2
= D
0
(1 + g
1
)(1 + g
2
) = $1.50(1.05)
2
= $1.6538.
D
3
= D
0
(1 + g
1
)(1 + g
2
)(1 + g
3
) = $1.50(1.05)
3
= $1.7364.
D
4
= D
0
(1 + g
1
)(1 + g
2
)(1 + g
3
)(1 + g
n
) = $1.50(1.05)
3
(1.10) = $1.9101.
D
5
= D
0
(1 + g
1
)(1 + g
2
)(1 + g
3
)(1 + g
n
)
2
= $1.50(1.05)
3
(1.10)
2
= $2.1011.
72
D
1
= $1.50; g = 6%; r
s
= 13%;
0
P
ˆ
= ?
0
P
ˆ
=
g
r
D
s
1
=
06
.
0
13
.
0
50
.
1
$
=
$21.43.
73
P
0
= $22; D
0
= $1.20; g = 10%;
1
P
ˆ
= ?;
r
s
= ?
1
P
ˆ
= P
0
(1 + g) = $22(1.10) = $24.20.
r
s
=
0
1
P
D
+ g =
22
$
)
10
.
1
(
20
.
1
$
+ 0.10
36
=
22
$
32
.
1
$
+ 0.10 = 16.00%.
r
s
= 16.00%.
74
D
ps
= $5.00; V
ps
= $50; r
ps
= ?
r
ps
=
ps
ps
v
D
=
00
.
50
$
00
.
5
$
= 10%.
37
75
0
1
2
3




D
0
= 2.00
D
1
D
2
D
3
2
P
ˆ
Step 1:
Calculate the required rate of return on the stock:
Step 3:
Calculate the PV of the expected dividends:
38
Step 5:
Calculate the PV of
2
P
ˆ
:
PV = $58.11/(1.123)
2
= $46.08.
Step 6:
Sum the PVs to obtain the stock’s price:
0
P
ˆ
= $4.42 + $46.08 = $50.50.
Alternatively, using a financial calculator, input the following:
CF
0
= 0, CF
1
= 2.40, and CF
2
= 60.99 (2.88 + 58.11) and then enter I/YR = 12.3 to solve for NPV
= $50.50.