S
OLUTIONS
– S
TOCK
AND
B
OND
P
RACTICE
SET
1.
A coupon rate of 9% means the total annual payment is $90.
a.
Current price is the present value of all coupon payments plus present value of the
face value.
65
.
431
068
.
)
068
.
1
(
1
1
90
6
=

×
=
coupons
PV
;
86
.
673
)
068
.
1
(
1000
6
=
=
value
face
PV
Price = sum of present values =
$1,105.51
N = 6, I = 6.8, PMT = 90, FV = 1000; Compute PV =
$1,105.51
b.
The timeline should look like this:
N = 6
I =
6.8%
0
1
2
3
4
5
6
CPT PV
90
90
90
90
90
90
Price =
1,105.51
1000
2.
These 20year bonds were issued ten years ago, so they have ten years left to maturity. The
yield to maturity can be found by solving for k
d
in the equation for the price of a bond. The
price is the sum of the present value of the coupon payments plus the present value of the
face value:
(
29
10
10
1
1000
)
1
(
1
1
75
40
.
1110
d
d
d
k
k
k
Price
+
+
+

×
=
=
N = 10, PV = 1110.40, PMT = 75, FV = 1000; Compute I =
6%
3.
All three bonds make annual coupon payments of 60. They have the same YTM but different
maturities.
a.
Compute the prices using the formula above, or your financial calculator:
N
PMT
I
FV
CPT PV
Bond A
1
60
3.8%
1000
1,021.19
Bond B
5
60
3.8%
1000
1,098.49
Bond C
15
60
3.8%
1000
1,248.06
b.
Compute the prices using the formula above, or your financial calculator:
1
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View Full DocumentN
PMT
FV
PV at 5%
PV at 10%
Bond A
1
60
1000
1,009.52
963.63
Bond B
5
60
1000
1,043.29
848.36
Bond C
15
60
1000
1,103.79
695.75
c.
Your graph of the prices of the three bonds at different yields should look something
like this:
$600
$700
$800
$900
$1,000
$1,100
$1,200
$1,300
0%
2%
4%
6%
8%
10%
12%
Bond A
Bond B
Bond C
d.
Ethay elationshipray etweenbay imetay otay aturitymay andway ensitivitysay otay
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 Spring '12
 T
 Ks

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