стр. 91 
$2 $32.26
=$2
13.2% 7% 0.062
rg
72
.1 Stock Valuation. Investors require a 20 percent per year return on the stock of M Company.
Yesterday M Company paid a $2 dividend (dividends are paid annually). The dividend is
expected to grow 30 percent per year for the next 2 years and at 8 percent per year thereafter.
At what price should the stock sell?
SOLUTION
Do = $2
D1 = $2(1+ 0.3) = $2.60
0 2 = $2(1+ 0.3)2= $2(1.69) = $3.38
0 3 = $3.38(1 + 0.08) = $3.65
Present value of dividends for the first 2 years are:
$2.60 $3.38
+
+
= $2.6O(PVIF26%,1) $3.38(PVIFm,,,)
(1 + 0.2)2
(1 + 0.2)
= $2.60(0.8333) + $3.38(0.6944) = $2.17 + $2.35 = $4.52
Find P2:
p 2 =  0=3 $3*65 = $30.42
0.2  0.08
rg
194 RISK, RETURN, AND VALUATION [CHAP 7
Present value of $30.42 is:
$30.42
= $30.42(PVIF,O%,,) = $30.42(0.6944) = $21.12
(1 + 0.2)2
Add these two PV figures to obtain PO:
P = $4.52 + $21.12 = $25.64
O
Stock Valuation. Investors require a 10 percent per year return on the stock of the TakeвЂ™Iko
7.22
Corporation, which anticipates a nonconstant growth pattern for dividends. The company paid
a $2 per share dividend. The dividend is expected to grow by 15 percent per year until the end
of year 4 (i.e., for the next 3 years) and 7 percent thereafter.
( a ) Project dividends for years 1through 4. (b) Compute the present value of the dividends
in part (a). (c) Project the dividend for the fifth year ( O S )(.d ) Find the present value of all future
dividends beginning with the fifth yearвЂ™s dividend. The present value you find will be at the end
of the fourth year. Use the formula P4= Ds/(r g ) . ( e ) Discount back the value found in part
( d ) for 4 years at 10 percent. cf)Determine the value of the stock PO.
SOLUTION
&(given) = $2
D = $2(1 + 0.15) = $2.30
1
D2 = $2.30(1 + 0.15) = $2.65
0 3 = $2.65(1 + 0.15) = $3.05
D4 = $3.05(1 + 0.15) = $3.51
+ $3.51
$2.30 $2.65 $3.05
 + +
(b) PV of dividends =
(1 +o.i) (1 +o.i)2 (1 +0.1)3 (1 +0.1)4
+ +
= $2.30(PVIFlo%,l) t$2.65(PVIFloya,2) $3.05(PVIFi0%3) $3.51(PVIFi0%,4)

= $2.30(0.9091) + $2.65(0.8264) + $3.05(0.7513) + $3.51(0.6830)
= $2.09 + $2.19 + $2.29 + $2.40 = $8.97
Ds = $3.51(1 + 0.15) = $4.04
(c)
p4==s
D $4.04  $4.04
= $134.67
r g 0.1  0.07 0.03
$134.67
$134.67(PVIFlo%,,) = $134.67(0.6830) = $91.98
( e ) Therefore, =
(1 +0.1)4
The value of the stock, PO,is:
(f)
PO = $8.97 + $91.98 = $100.95
72
.3 Stock Valuation. On December 31,19X2, the shares of Amacom, Inc., closed at $20.The company
subsequently paid a yearend dividend in each of the years 19x3 through 19x7 as follows:
19x3: $1.00 19x6: $1.25
19x4: $1.00 19x7: $1.25
19x5: $1.10
Suppose you had purchased a share of Amacom stock on December 31,19X2. Find the price at
which you must sell your share at 19x7yearend in order to realize an annual compounded total
rate of return of 10 percent on your initial investment (before commissions and taxes). (CFA,
adapted.)
195
RISK, RETURN, AND VALUATION
CHAR 71
SOLUTION
Dt ps
+
(l+,>r (1 + r ) 5
=
Substituting the value given yields:
2 (1 +Df + (1 +
5
PS
$20 =
0.1)вЂ˜
r=l 0.95
First compute the present value of dividends for the years 19x3 through 19x7.
$1.00 $1.00 $1.10 $1.25 $1.25
+ + + +
(1 + o . i ) 2 (1 + 0.1)3 (1 + 0.114
(1 + o.iy (1 + 0.1)s
+ $1.00(0.8264) + $1.10(0.7513) + $1.25(0.6830) + $1.25(0.6209)
= $1.00(0.9091)
= $0.91 + $0.83 + $0.83 + $0.85 + $0.78 = $4.20
Therefore,
p5
$20 = $4.20 +
(1 + 0.1)5
$20 = $4.20 + P5(PV1F10yo,S)
$20 = $4.20 + Ps(0.6209)
Ps(O.6209) = $20  $4.20
Ps(O.6209) = $15.80
$15.80
pp= $25.45
стр. 91 