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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 End-of-Chapter Problems
B-57

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*Sign up* 7.3
a.
The
average accounting return
is the average project earnings after taxes,
divided by the average book value, or average net investment, of the machine
during its life.
The book value of the machine is the gross investment minus the
accumulated depreciation.
Average Book Value
= (Book Value
0
+ Book Value
1
+ Book Value
2
+ Book
Value
3
+ Book Value
4
+ Book Value
5
) / (Economic Life)
= ($16,000 + $12,000 + $8,000 + $4,000 + $0) / (5
years)
= $8,000
Average Project Earnings
= $4,500
Divide the average project earnings by the average book value of the machine to
calculate the average accounting return.
Average Accounting Return
= Average Project Earnings / Average Book
Value
= $4,500 / $8,000
= 0.5625
= 56.25%
The average accounting return is 56.25%.
b.
1.
The average accounting return uses accounting data rather than net cash
flows.
2.
The average accounting return uses an arbitrary firm standard as the
decision rule.
The firm standard is arbitrary because it does not
necessarily relate to a market rate of return.
3.

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