61
HW 1 Solutions
Chapter 8
Net Present Value and Other Investment Criteria
1.
NPV
A
= –$200 + [$80
annuity factor(11%, 4 periods)] =
–
20
.
48
$
(1.11)
0.11
1
0.11
1
$80
$200
4
NPV
B
= –$200 + [$100
annuity factor(11%, 3 periods)] =
–
37
.
44
$
(1.11)
0.11
1
0.11
1
$100
$200
3
Both projects are worth pursuing.
2.
Choose Project A, the project with the higher NPV.
3.
NPV
A
= –$200 + [$80
annuity factor(16%, 4 periods)] =
–
85
.
23
$
(1.16)
0.16
1
0.16
1
$80
$200
4
NPV
B
= –$200 + [$100
annuity factor(16%, 3 periods)] =
–
59
.
24
$
(1.16)
0.16
1
0.16
1
$100
$200
3
Therefore, you should now choose project B.
4.
IRR
A
= Discount rate (r) which is the solution to the following equation:
200
$
r)
(1
r
1
r
1
$80
4
r = IRR
A
= 21.86%
IRR
B
= Discount rate (r) which is the solution to the following equation:
200
$
r)
(1
r
1
r
1
$100
3
r = IRR
B
= 23.38%
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5.
No.
Even though project B has the higher IRR, its NPV is lower than that of project A when
the discount rate is lower (as in Problem 1) and higher when the discount rate is higher (as in
Problem 3).
This example shows that the project with the higher IRR is not necessarily better.
The IRR of each project is fixed, but as the discount rate increases, project B becomes
relatively
more attractive compared to project A.
This is because B’s cash flows come earlier,
so the present value of these cash flows decreases less rapidly when the discount rate increases.
6.
The profitability indexes are as follows:
Project A: $48.20/$200 + 1 = 1.2410
Project B: $44.37/$200 + 1 = 1.2219
In this case,
with equal initial investments
, both the profitability index and NPV give
projects the same ranking.
This is an unusual case, however, since it is rare for the initial
investments to be equal.
7.
Project A has a payback period of: $200/$80 = 2.5 years
Project B has a payback period of 2 years.
13.
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 Spring '09
 LI
 Annuity, Net Present Value

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