Chapter 6: How to Value Bonds and Stocks
6.1
a.
$1,000 / 1.05
10
= $613.91
b.
$1,000 / 1.10
10
= $385.54
c.
$1,000 / 1.15
10
= $247.18
6.2
The amount of the semiannual interest payment is $40 (=$1,000
×
0.08 / 2).
There are a
total of 40 periods; i.e., two half years in each of the twenty years in the term to maturity.
The annuity factor tables can be used to price these bonds.
The appropriate discount rate to
use is the semiannual rate.
That rate is simply the annual rate divided by two.
Thus, for
part a the rate to be used is 4.0%, for part b the rate to be used is 5% and for part c it is
3%.
a.
$40
40
04
.
0
Α
+ $1,000 / 1.04
40
= $1,000
Notice that whenever the coupon rate and the market rate are the same, the bond is
priced at par.
b.
$40
40
0.05
Α
+ $1,000 / 1.05
40
= $828.41
Notice that whenever the coupon rate is below the market rate, the bond is priced
below par.
c.$40
40
0.03
Α
+ $1,000 / 1.03
40
= $1,231.15
Notice that whenever the coupon rate is above the market rate, the bond is priced
above par.
6.3
Semiannual discount factor = (1.12)
1/2
 1
=
0.058300
=
5.83%
a.
Price
= $40
40
0.0583
Α
+ $1,000 / 1.0583
40
= $614.98 + $103.67
= $718.65
b.
Price
= $50
30
0.0583
Α
+ $1,000 / 1.0583
30
= $700.94 + $182.70
= $883.64
6.4
Effective annual rate of 10%:
Semiannual discount factor = (1.10)
0.5
 1 = 0.048809 = 4.8809%
Price
= $40
40
0.048809
Α
+ $1,000 / 1.048809
40
= $697.71 + $148.64 =$846.35
6.5
$923.14 = C
30
0.05
Α
+ $1,000 / 1.05
30
= (15.3725) C + $231.38
C = $45.00
The annual coupon rate = $45.00
×
2 / $1,000 = 0.09 = 9%
6.6
a.
The semiannual interest rate is $60 / $1,000 = 0.06.
Thus, the effective annual rate
is 1.06
2
 1 = 0.1236 = 12.36%.
b.
Price = $30
12
0.06
Α
+ $1,000 / 1.06
12
= $251.52 + $496.97 = $748.49
c.
Price = $30
12
0.04
Α
+ $1,000 / 1.04
12
= $281.55+ $624.60= $906.15
Answers to EndofChapter Problems
B41
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Note: In parts b and c we are implicitly assuming that the yield curve is flat.
That is, the
yield in year 5 applies for year 6 as well.
6.7
a.
P
A
= $100
20
0.10
Α
+ $1,000 / 1.1
20
= $1,000.00
P
B
= $100
10
0.1
Α
+ $1,000 / 1.10
10
= $1,000.00
b.
P
A
= $100
20
0.12
Α
+ $1,000 / 1.12
20
= $850.61
P
B
= $100
10
0.12
Α
+ $1,000 / 1.12
10
= $ 887.00
c.
P
A
= $100
20
0.08
Α
+ $1,000 / 1.08
20
= $1,196.36
P
B
= $100
10
0.08
Α
+ $1,000 / 1.08
10
= $1,134.20
6.8
a.
The prices of longterm bonds should fall.
The price of any bond is the PV of the
cash flows associated with the bond.
As the interest rate increases, the PV of
those cash flows falls.
This can be easily seen by looking at a oneyear, pure
discount bond.
P
= $1,000 / (1+i)
As
i
increases, the denominator, (1 +
i
), rises, thus reducing the value of the
numerator ($1,000).
The price of the bond decreases.
b.
The effect on stocks is not as clearcut as the effect on bonds.
The nominal
interest rate is a function of both the real interest rate,
r
, and the inflation rate,
i.e.,
(1+i)
=
(1+r) (1+Inflation)
From this relationship it is easy to conclude that, as inflation rises, the nominal
interest rate,
i
,
rises.
However, stock prices are a function of dividends and
future prices as well as the interest rate.
Those dividends and future prices are
determined by the earning power of the firm.
Inflation may increase or decrease
firm earnings.
Thus, a rise in interest rates has an uncertain effect on the general
level of stock prices.
6.9
a.
$1,200 = $80
20
r
Α
+ $1,000 / (1 + r)
20
r
= 0.0622 = 6.22%
The yield to maturity is 6.22%.
b.
$950 = $80
10
r
Α
+ $1,000 / (1 + r)
10
r
= 0.0877 = 8.77%
The yield to maturity is 8.77%
6.10
The appropriate discount rate is the semiannual interest rate because the bond makes
semiannual payments.
Thus, calculate the appropriate semiannual interest rate for both
bonds
A
and
B
.
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 Fall '08
 Wood
 Time Value Of Money, Net Present Value, Dividend, Dividend yield, NPVGO

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