Week3 - 5-1 N = 12 I/YR = YTM = 9 PMT = 0.08 1,000 = 80 FV...

5-1
N = 12; I/YR = YTM = 9%; PMT = 0.08 × 1,000 = 80; FV = 1000; PV = V
B
= ?
PV = $928.39.
Alternatively,
V
B
= $80((1- 1/1.09 12 )/0.09) + $1,000(1/1.09 12 )
= $928.39
5-2
N = 12; PV = -850; PMT = 0.10 × 1,000 = 100; FV = 1000; I/YR = YTM = ?
YTM = 12.48%.
5-8 N = 10 × 2 = 20; PV = -1100; PMT = 0.08/2 × 1,000 = 40; FV = 1000; I/YR = YTM = ?
YTM = 3.31% × 2 = 6.62%.
With your financial calculator, enter the following to find YTC:
N = 5 × 2 = 10; PV = -1100; PMT = 0.08/2 × 1,000 = 40; FV = 1050; I/YR = YTC = ?
YTC = 3.24% × 2 = 6.49%
8-1 D
0
= $1.50; g
1-3
= 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.
8-2 D
1
= $1.50; g = 7%; r
s
= 15%; = ? 0Pˆ
0Pˆ = grDs1− = 07.015.050.1$− = $18.75.
Mini Case Chapter 5
a. Describe briefly the legal rights and privileges of common stockholders.
Answer: The common stockholders are the owners of a corporation, and as such, they have certain rights and
privileges as described below.
1. Ownership implies control. Thus, a firm’s common stockholders have the right to elect its firm’s
directors, who in turn elect the officers who manage the business.
2. Common stockholders often have the right, called the preemptive right, to purchase any additional
shares sold by the firm. In some states, the preemptive right is automatically included in every
corporate charter; in others, it is necessary to insert it specifically into the charter.
b. 1. Write out a formula that can be used to value any stock, regardless of its dividend pattern.
Answer: The value of any stock is the present value of its expected dividend stream:
0Pˆ = .)r1(D)r1(D)r1(D)r1(Ds3s3s2ts1∞∞++++++++L
However, some stocks have dividend growth patterns which allow them to be valued using short-cut
formulas.

b. 2. What is a constant growth stock? How are constant growth stocks valued?
Answer: A constant growth stock is one whose dividends are expected to grow at a constant rate forever. “Constant
growth” means that the best estimate of the future growth rate is some constant number, not that we
really expect growth to be the same each and every year. Many companies have dividends which are
expected to grow steadily into the foreseeable future, and such companies are valued as constant
growth stocks.
For a constant growth stock:
D
1
= D
0
(1 + g), D
2
= D
1
(1 + g) = D
0
(1 + g) 2 , and so on.
With this regular dividend pattern, the general stock valuation model can be simplified to the following
very important equation:
0Pˆ = grDs1− = gr)g1(Ds0−+.
This is the well-known “Gordon ,” or “constant-growth” model for valuing stocks. Here D
1
, is the next
expected dividend, which is assumed to be paid 1 year from now, r
s
is the required rate of return on the
stock, and g is the constant growth rate.
b. 3. What happens if a company has a constant g which exceeds its r
s
? Will many stocks have expected g > r
s
in the short run (i.e., for the next few years)? In the long run (i.e., forever)?