ActSc 371: Assignment #2 Solutions
Question 1
As calculated in class, the present value of the rental payments is
75
1
.
04
+
. . .
+
75
(1
.
04)
20
=
75
.
04
1

(1
.
04)

20
= 1019
.
27
Today’s actions provide us with a cash inflow of this amount and a cash
outflow of $1000 (the amount spent on the machine).
Therefore the net
cash flow to us today is $19.27.
The deposit is equal to the difference between the rental payment of $75
and the interest payment.
The interest payment is 4% of the principal,
which is equal to (using the middle expression above) 75 1

(1
.
04)

20
.
Therefore the amount of each deposit is 75(1
.
04)

20
. It is also acceptable
to say that the deposit is equal to 75(.04)(1019.27)=7540.77=34.23
The first deposit sits in the account for 19 years, the second for 18 years
. . .
the nineteenth for one year. Therefore the account balance with Bank B in
twenty years will be
B
=
75(1
.
04)

20
(1
.
04)
19
+ 75(1
.
04)

20
(1
.
04)
18
+
. . .
+ 75(1
.
04)

20
(1
.
04)
=
75
1
1
.
04
+
1
(1
.
04)
2
+
. . .
+
1
(1
.
04)
19
Alternatively, the balance will be
B
=
34
.
23(1
.
04)
19
+ 34
.
23(1
.
04)
18
+
. . .
+ 34
.
23(1
.
04)
=
34
.
23(1
.
04)
19
"
1 +
1
1
.
04
+
. . .
+
1
1
.
04
18
#
=
34
.
23(1
.
04)
19
1

(1
.
04)

19
1

(1
.
04)

1
=
985
.
07
The cash inflow in twenty years will be
B
+ 75
=
75
1 +
1
1
.
04
+
1
(1
.
04)
2
+
. . .
+
1
(1
.
04)
19
=
75
1

(1
.
04)

20
[1

(1
.
04)

1
]
=
75(1
.
04)
.
04
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Wood
 Net Present Value

Click to edit the document details