Chapter 7: Some Alternative Investment Rules
7.1
a.
The payback period is the time that it takes for the cumulative undiscounted cash
inflows to equal the initial investment.
Project A
:
Cumulative Undiscounted Cash Flows Year 1
= $4,000
Cumulative Undiscounted Cash Flows Year 2
= $4,000 +$3,500 = $7,500
Payback period = 2
Project
A
has a payback period of two years.
Project B
:
Cumulative Undiscounted Cash Flows Year 1
= $2,500
Cumulative Undiscounted Cash Flows Year 2
= $2,500+$1,200 = $3,700
Cumulative Undiscounted Cash Flows Year 3
= $2,500+$1,200+$3,000
= $6,700
Project
B
’s cumulative undiscounted cash flows exceed the initial investment of
$5,000 by the end of year 3.
Many companies analyze the payback period in
whole years.
The payback period for project
B
is 3 years.
Project
B
has a payback period of three years.
Companies can calculate a more precise value using fractional years.
To
calculate the fractional payback period, find the fraction of year 3’s cash flows
that is needed for the company to have cumulative undiscounted cash flows of
$5,000.
Divide the difference between the initial investment and the cumulative
undiscounted cash flows as of year 2 by the undiscounted cash flow of year 3.
Payback period = 2 + ($5,000  $3,700) / $3,000
= 2.43
Since project
A
has a shorter payback period than project
B
has, the company
should choose project
A
.
b.
Discount each project’s cash flows at 15 percent.
Choose the project with the
highest NPV.
Project A
= $7,500 + $4,000 / (1.15) + $3,500 / (1.15)
2
+ $1,500 / (1.15)
3
= $388.96
Project B
= $5,000 + $2,500 / (1.15) + $1,200 / (1.15)
2
+ $3,000 / (1.15)
3
= $53.83
The firm should choose Project
B
since it has a higher NPV than Project
A
has.
Answers to EndofChapter Problems
B57
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View Full Document7.2
a.
Find the payback period for the project.
Since the cash inflows are constant,
divide the initial investment by the annual cash inflow to determine the payback
period.
Payback Period = Initial Investment / Annual Cash Inflow
= $1,000,000 / $150,000
= 6.67
The payback period is 6.67 years.
Since the payback period is shorter than the
cutoff period of ten years, the project should be accepted.
b.
Find the number of years needed for the discounted cash inflows to equal the
initial investment of $1 million.
Apply the annuity formula, discounted at 10
percent, to find the approximate discounted payback period.
The approximate
discounted payback period is the year
in which
the PV of the initial investment is
surpassed.
Since the discounted payback period will always be greater than the undiscounted
payback period when there are positive cash inflows, start the approximation at
year 7.
Cumulative Discounted Cash Flows Year 7
= $150,000 A
7
0.1
=
$730,262.82
Cumulative Discounted Cash Flows Year 8
= $150,000 A
8
0.1
=
$800,238.93
Cumulative Discounted Cash Flows Year 9
= $150,000 A
9
0.1
=
$863,853.57
Cumulative Discounted Cash Flows Year 10
= $150,000 A
10
0.1
= $921,685.07
Cumulative Discounted Cash Flows Year 11
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 Fall '08
 Wood
 Net Present Value, PAYBACK PERIOD

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