PS3_Solution
Chapter 5
(1)
Coupon rate = 8% => coupon payment = 80. r
d
= 9% = yield to maturity.
With your financial calculator, enter the following: N = 10; I = YTM = 9%; PMT = 0.08
×
1,000 = 80; FV = 1000; PV = ? PV = $935.82.
Alternatively,
P=80/(1+9%)+80/((1+9%))+...+80/((1+9%)^10)+1000/((1+9%)^10)
= $80((1 1/1.09
10
)/0.09) + $1,000(1/1.09
10
)
= $513.42 + $422.40 = $935.82.
(2) a
. V
B
=
)
r
+
(1
M
+
)
r
+
(1
INT
N
d
t
d
N
1
=
t
∑
=
PMT((1 1/(1+r
d
n
))/r
d
) + FV(1/(1+r
d
)
n
).
M = $1,000.
INT = 0.09($1,000) = $90.
i. $829= $90((1
1/(1+r
d
4
))/rd) + $1,000(1/(1+r
d
)
4
).
The YTM can be found by trialanderror. If the YTM was 9 percent, the bond value
would be its maturity value (face value, 1000). Since the bond sells at a discount, the
YTM must be greater than 9 percent. Let's try 10 percent.
At YTM=10%, V
B
= $968.29.
$968.29 > $829.00; therefore, the bond's YTM is greater than 10 percent.
Try 15 percent. At 15%, V
B
= $828.75.
Therefore, the bond's YTM is approximately 15 percent. (You could have used financial
calculator to find YTM=15%: Input N = 4, PV = 829, PMT = 90, FV = 1000, I = ? I =
14.99%)
ii. $1,104 = $90((1 1/(1+r
d
4
))/rd) + $1,000(1/(1+r
d
)
4
).
Input N = 4, PV = 1104, PMT = 90, FV = 1000, I = ? I = 6.00%.
b
. Yes. At a price of $829, the yield to maturity, 15 percent, is greater than your required
rate of return of 12 percent. If your required rate of return were 12 percent, you should be
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 Spring '08
 DASILVA

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