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Chapter 03  Interest Rates and Security Valuation
Answers to Chapter 3 Questions
1.
935 = 75(PVIFA
rr, 5
) + 980(PVIF
rr, 5
)
Ψ
rr = 8.83%
2.
980 = 75(PVIFA
Err, 3
) + 990(PVIF
, 3
)
Ψ
Err = 7.97%
3.
V
b
= 1,000(.08) (PVIFA 9%, 10) + 1,000(PVIF 9%, 10) = $935.82
4.
EXCEL Problem: Bond Value = $1,268.27
Bond Value = $1,169.36
Bond Value = $1,000.00
Bond Value = $862.01
5.
$1,100 = 1,000(.12)
(PVIFA ytm/2, 10(2) ) + 1,000(PVIF ytm/2, 10(2) ) => ytm = 10.37%
2
6.
EXCEL Problem: Yield to Maturity = 9.87%
Yield to Maturity = 9.19%
Yield to Maturity = 7.69%
Yield to Maturity = 5.97%
7.
V
b
= 1,000(.07)
(PVIFA 14%/4, 4(4) ) + 1,000(PVIF 14%/4, 4(4) ) = $788.35
4
8.
$863.73
= 1,000(.08) (PVIFA 10%, n) + 1,000(PVIF 10%, n) => n = 12 years
9.
a. V
b
= 1,000(.1)
(PVIFA
6%/2, 10(2)
) + 1,000(PVIF
6%/2, 10(4)
) = $1,297.55
2
b.
V
b
= 1,000(.1)
(PVIFA
8%/2, 10(2)
) + 1,000(PVIF
8%/2, 10(4)
) = $1,135.90
2
c.
From parts a. and b. of this problem, there is a negative relation between required rates and
fair values of bonds.
10.
a.
Premium bond
b.
Par bond
c.
Discount bond
d.
Discount bond
e.
Premium bond
f.
Discount bond
11.
a.
985 = 1,000(.09)
(PVIFA
ytm/2, 15(2)
) + 1,000(PVIF
ytm/2, 15(2)
)
Ψ
ytm = 9.186%
2
b.
915 = 1,000(.08)
(PVIFA
ytm/4, 10(4)
) + 1,000(PVIF
ytm/4, 10(4)
)
Ψ
ytm = 9.316%
4
c.
1,065 = 1,000(.11) (PVIFA
ytm, 6
) + 1,000(PVIF
ytm, 6
)
Ψ
ytm = 9.528%
31
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View Full Document Chapter 03  Interest Rates and Security Valuation
12.
a.
V
b
= 1,000(.06)
(PVIFA
10%/2, 12(2)
) + 1,000(PVIF
10%/2, 12(2)
)
= $724.03
2
b.
V
b
= 1,000(.08)
(PVIFA
10%/2, 12(2)
) + 1,000(PVIF
10%/2, 12(2)
)
= $862.01
2
c.
V
b
= 1,000(.10)
(PVIFA
10%/2, 12(2)
) + 1,000(PVIF
10%/2, 12(2)
)
= $1,000.00
2
d.
From parts a. through c. in this problem, there is a positive relation between coupon rates
and present values of
bonds.
13. a. V
b
= 1,000(.06)
(PVIFA
8%/2, 12(2)
) + 1,000(PVIF
8%/2, 12(2)
)
= $847.53
2
b.
V
b
= 1,000(.08)
(PVIFA
8%/2, 12(2)
) + 1,000(PVIF
8%/2, 12(2)
)
= $1,000.00
2
% change in bond value versus part (a) = ($1,000  $847.53)/$847.53 = 17.99%
c.
V
b
= 1,000(.10)
(PVIFA
8%/2, 12(2)
) + 1,000(PVIF
8%/2, 12(2)
)
= $1,152.47
2
% change in bond value versue part (b) = ($1,152.47  $1,000)/$1,000 = 15.25%
d.
From these results we see that as coupon rates increase, price volatility decreases.
14.
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This note was uploaded on 03/22/2012 for the course FINA 210 taught by Professor Dakroub during the Spring '12 term at American University in Cairo.
 Spring '12
 Dakroub
 Finance, Interest, Interest Rate, Valuation

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