стр. 93 
$13,500 = $2,000(1+ PVIFA,,g)
$13,500
(1+ PV1FA.g) =  6.75 =
$2,000
PVIFA,,9 = 6.75  1 = 5.75, which is very close to 10 percent as found in Appendix D.
Expected Return on Stock Investment. You are considering the purchase of a share of stock in
7.27
a firm for $40. The company is expected to pay a $2.50 dividend at the end of the year, and its
market price after the payment of the dividend is expected to be $45 a share. What is the
expected return on the investment in this stock?
SOLUTION
r = dividends + (ending price  beginning price)  D1 (PI PO)

+
beginning price PO
Alternatively, we set the current market price equal to the present value of the dividend, plus the
expected market price, as follows:
$250 $45
$40=+
(1 + r) (1 + r )
Solving this equation for r:
$2.50 + $45
$40(1+ r) =
$2.50 + $45
l+r=
$40
$2.50 + $45 I= $47.50
1 = 1.1975  1 = 18.75%
r=
$40 40
198 [CHAP. 7
RISK, RETURN, AND VALUATION
Expected Return on Stock Investment. Tom Laboratory's common stock is currently selling at
7.28
$60 per share. The next annual dividend is expected to be $3 per share, and the earnings,
dividends, and stock prices are expected to grow at a rate of ( a ) 0 percent; (6) 4 percent; and ( c )
6 percent. What is the expected total return in each case from the purchase of the common
stock?
SOLUTION
r = D
1
P +g
O
$3
r =+0 = 5%
$60
r = $34 % 9%
= 5% + 4 % =
+
$60
$3
r = + 6% = 5% + 6% = 11%
$60
Dividend Yield and Capital Gain Yield. N Company's last dividend, Do,was $1.Earnings and
7.29
dividends are expected to grow at a 5 percent rate. The required rate of return on the stock is
13 percent. The current stock price is $25. What is the expected dividend yield and expected
capital gains yield for the coming year?
SOLUTION
$1.00(1 + 0.05)  $1.05
= 4.2%
Dividend yield =
$25
$25
 dividend yield = 13%  4.2%
Capital gain yield = rate of return = 8.8%
The Arbitrage Pricing Model (APM). Suppose a threefactor APM holds and the riskfree rate
7.30
is 6 percent. You are interested in two particular stocks: A and B. The returns on both stocks are
related to factors 1and 2 as follows:
r = 0.06 + bl (0.09)  b2(0.03)+ b3(0.04)
The sensitivity coefficients for the two stocks are given below.
I I
Stock b2
bl b3
I
0.80
0.70
0.50 0.04 1.20
Om20
Calculate the expected returns on both stocks. Which stock requires a higher return?
SOLUTION
r = 0.06+ (0.70)(0.09) (0.80)(0.03) + (0.20)(0.04)
For stock A:
= 10.70%
r = 0.06 + (0.50)(0.09) (0.04)(0.03)+ (1.20)(0.04)
For stock B:
= 14.10%
Stock B requires a higher return, indicating it is the riskier of the two. Part of the reason is that its return
is substantially more sensitive to the third economic force than stock A's is.
199
CHAP. 71 RISK, RETURN, AND VALUATION
73
.1 Duration. You have a 9 percent bond with 4 years to maturity paid interest annually. Its YTM
is 10 percent and its market value is $968.29 per bond. What is the duration of the bond?
SOLUTION
The computation of duration involves the following three steps:
Step 1 Calculate the present value of the bond for each year.
Step 2 Express present values as proportions of the price of the bond.
Step 3 Multiply proportions by years' digits to obtain the weighted average time.
(Step 1) (Step 3)
(Step 2)
(6)
(1) (3) (4)
(2) (5)
PV of PV as proportion Column (1) x
PV factor
Year Cash flow Cashffow of price of bond Column (5)
Q1O0/o
0.0845
$ 81.82
0.9091 0.0845
1 90
$
2 90 0.8264 74.38 0.0768 0.1536
0.2094
3 90 0.7513 67.62 0.0698
0.6830 744.47 3.0756
0.7689
1,090
стр. 93 