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 semi-annual 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 semi-annual 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
Semi-annual 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%:
Semi-annual 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 semi-annual 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 End-of-Chapter Problems
B-41