ECO 362
October 5, 2007
PROBLEM SET 1
FINANCIAL INVESTMENTS (ECO 362)
Professor: Burt Malkiel
Exercise 1
(a) (USING CALCULATOR) For the
f
rst project we have 7 consecutive payments from year 1
to 7 of
330
and a last payment of
1
,
000
at year 8. Let
i
be the interest rate, so that
NPV
=
−
F
0
+
8
X
j
=1
C
i
(1 +
i
)
j
=
−
F
0
+
C
1
1+
i
+
C
1
(1 +
i
)
2
+
···
+
C
1
(1 +
i
)
8
=
−
2
,
000 + 330
×
7
X
j
=1
1
(1 +
i
)
j
+
1
(1 +
i
)
8
×
1
,
000
=
−
2
,
000 +
(1 +
i
)
7
−
1
i
(1 +
i
)
7
×
330 +
1
(1 +
i
)
8
×
1
,
000
since
7
X
j
=1
1
(1 +
i
)
j
=
1
(1+
i
)
−
1
(1+
i
)
8
1
−
1
(1+
i
)
=
(1 +
i
)
7
−
1
i
(1 +
i
)
7
.
Hence, substituting by
i
= 12%
,weget
NPV
=
−
2
,
000 + 330
×
(1
.
12)
7
−
1
0
.
12(1
.
12)
7
+
1
(1
.
12)
8
×
1
,
000
,
=
−
90
.
077
.
(USING TABLES) The best way (in terms of time) is by decomposing the cash
F
ows in two
components —as we did above—: (a) annuity of
330
,and(b
)p
a
y
o
f
of
1
,
000
at the end (of the
project).
Looking at Table B, for seven periods and an interest rate of
12%
,weget
4
.
5638
. Alternatively,
if we look at the Table for annuities (Table C) we obtain that the factor for 7 periods at a
12%
is
10
.
089
. But this is the value of the annuity at
t
=7;
so
,wehavetod
iscountthatpayment
,
10
.
089
(1
.
12)
7
=4
.
5638
.
Next, we have to
f
nd the discount rate for the last payment: (Table A)
0
.
4039
. Therefore,
NPV
=
−
2
,
000 + 330
×
4
.
5638 + 1
,
000
×
0
.
4039
=
−
90