University College of the Cayman Islands
FIN301 Financial Management
Tutorial 8  Bond Valuation – Chapter 7
(
Note
– With respect to the textbook questions, the solutions for the ones
that require the yield to maturity are presented in
financial calculator
format and/or straight
trial and error
format. Additionally, the nontext
book solutions for the YTM questions are presented using
linear
interpolation
. However, you may use the
Rodriques
formula to do all of them,
even in the exams!
)
1. M = $1,000;
I = $1,000 x 8% = $80;
P
b
=
I(PVIFA
k%,n
)+
M(PVIF
k%,n
)
=
$80(PVIFA
12%,12
) +
$1,000(PVIF
12%,12
)
=
$80(6.1944)
+
$1,000(0.2567)
=
$495.55
+
$256.70
=
$752.25
2.
81
With your financial calculator, enter the following:
N = 10; I = YTM = 9%; PMT = 0.08
×
1,000 = 80; FV = 1000; PV = V
B
= ?
PV = $935.82.
Alternatively,
V
B
= $80(PVIFA
9%, 10
) + $1,000(PVIF
9%, 10
)
= $80(6.4177) + $1,000(0.4224)
= $513.42 + $422.40 =
$935.82.
3.
85
The problem asks you to find the price of a bond, given the
following facts:
N = 16; I = 8.5/2 = 4.25; PMT = 45; FV = 1000.
With a financial calculator, solve for PV =
$1,028.60.
Or
V
B
= $45(PVIFA
4.25%, 16
) + $1,000(PVIF
4.25%, 16
)
= $45(11.4403) + $1,000(0.5138) –
Note that you have to use the
algebraic format of the PVIFA and PVIF, respectively.
= $514.81 + $513.80 =
$1,028.61
1
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M = $1,000; I=
P
b
=
I / m
(PVIFA
k%/m,nn
)+
M(PVIF
k%/m,nm
)
=
$90 / 2
(PVIFA
8%/2, 8 x 2
) +
$1,000(PVIF
8%/2, 8 x 2
)
=
$45(PVIFA
4%,16
) +
$1,000(PVIF
4%,16
)
=
$45(11.6523)
+
$1,000(0.5339)
=
$524.35
+
$533.90
=
$1,058.25
P
b
=
I(PVIFA
k%,n
)+
M(PVIF
k%,n
)
=
$90(PVIFA
8%,8
) +
$1,000(PVIF
8%, 8
)
=
$90(PVIFA
8%,8)
+
$1,000(PVIF
8%,8
)
=
$90(5.7466)
+
$1,000(0.5403)
=
$517.19
+
$540.30
=
$1,057.49
5.
(a)
P
b
=
$130(PVIFA
14%,15
) +
$1,000(PVIF
14%,15
)
=
$130(6.1422)
+
$1,000(0.1401)
=
$798.49
+
$140.10
=
$938.59
(b)
No.
The market value is greater than the bond’s intrinsic value.
(c)
P
b
=
$130(PVIFA
12%,15
) +
$1,000(PVIF
12%,15
)
=
$130(6.8109)
+
$1,000(0.1827)
=
$885.42
+
$182.70
=
$1,068.12
The answer is still
no
!
6.
86
a. V
B
= I(PVIFA
i,n
) + M(PVIF
i,n
)
1. 5%:
Bond L:
V
B
= $100(10.3797) + $1,000(0.4810) = $
1,518.97.
Bond S:
V
B
= ($100 + $1,000)(0.9524) = $
1,047.64
.
2. 8%:
Bond L:
V
B
= $100(8.5595) + $1,000(0.3152) = $
1,171.15
.
Bond S:
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 Spring '10
 na
 Finance, Interest Rate, Net Present Value, YTM

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