-
Chapter 6: Some Alternative Investment
Rules
Concept Questions -
Chapter 6
6.2
?
List the
problems of the payback period rule
.
1.
It does not
take into account the time value of money.
2.
It ignores
payments after the payback period.
3.
The cutoff
period is arbitrary.
?
What are some
advantages?
1.
It
is simple to implement.
2.
It may help in controlling and
evaluating managers.
6.4
?
What are the
three steps in calculating AAR?
1.
Determine
average net income.
2.
Determine average investment
3.
Divide average
net income by average investment.
?
What are some
flaws with the AAR approach?
1.
It uses
accounting figures.
2.
It takes no account of timing.
3.
The cutoff
period is arbitrary.
6.5
?
How does one
calculate the IRR of a project?
Using
either trial-and-error or a financial calculator,
one finds the discount rate
that
produces an NPV of zero.
6.6
?
What is the
difference between independent projects and
mutually exclusive
projects?
An
independent project is one whose acceptance does
not affect the acceptance of
another.
A mutually exclusive project, on the other hand is
one whose acceptance
precludes the
acceptance of another.
?
What are two
problems with the IRR approach that apply to both
independent and mutually exclusive
projects?
1.
The
decision rule depends on whether one is investing
of financing.
2.
Multiple rates of return are possible.
?
What are two additional problems
applying only to mutually exclusive
projects?
1.
The IRR
approach ignores issues of scale.
2.
The IRR
approach does not accommodate the timing of the
cash flows
properly.
6.7
?
How does one
calculate a project's profitability index?
Divide the present value of the cash
flows subsequent to the initial investment by
the initial investment.
?
How is the
profitability index applied to independent
projects, mutually
exclusive projects,
and situations of capital rationing?
1.
With
independent projects, accept the project if the PI
is greater than 1.0 and
reject if less
than 1.0.
2.
With
mutually exclusive projects, use incremental
analysis, subtracting the
cash flows of
project 2 from project 1. Find the PI. If the PI
is greater than
1.0, accept project 1.
If less than 1.0, accept project 2.
Answers to End-of-Chapter Problems
B-65
3.
In capital
rationing, the firm should simply rank the
projects according to their
respective
PIs and accept the projects with the highest PIs,
subject to the
budget constrain.
Answers to End-of-Chapter
Problems
QUESTIONS AND PROBLEMS
The Payback Period Rule
6.1
Fuji Software, Inc., has the following projects.
Year Project A Project B
0
_$$7,500 _$$5,000
1 4,000 2,500
2 3,500 1,200
3 1,500 3,000
a. Suppose Fuji
’
s
cutoff payback period is two years. Which of these
two projects should be chosen?
b.
Suppose Fuji uses the NPV rule to rank these two
projects. If the appropriate discount rate is 15
percent,
which project should be
chosen?
6.1
a.
b.
Payback period of Project A = 1 +
($$7,500 - $$4,000) / $$3,500 = 2 years
Payback period of Project B = 2 +
($$5,000 - $$2,500 -$$1,200) / $$3,000 = 2.43 years
Project A should be chosen.
NPV
A
= -$$7,500 +
$$4,000 / 1.15 + $$3,500 /
1.15
2
+ $$1,500 /
1.15
3
= -$$388.96
NPV
B
= -$$5,000 +
$$2,500 / 1.15 + $$1,200 /
1.15
2
+ $$3,000 /
1.15
3
= $$53.83
Project B should be chosen.
6.2 Suppose Peach Paving Company
invests $$1 million today on a new construction
project. The project
will generate
annual cash flows of $$150,000 in perpetuity. The
appropriate annual discount rate for the
project is 10 percent.
a.
What is the payback period for the project? If the
Peach Paving Company desires to have a 10-year
payback period, should the project be
adopted?
b. What is the discounted
payback period for the project?
c. What
is the NPV of the project?
6.2
a.
b.
c.
Payback period = 6 +
{$$1,000,000 - ($$150,000
?
6)} / $$150,000 = 6.67 years
Yes, the
project should be adopted.
$$150,000
?
11
0
.
10
= $$974,259
The discounted payback period = 11 +
($$1,000,000 - $$974,259) / ($$150,000 /
1.1
12
)
= 11.54
years
NPV = -$$1,000,000 + $$150,000 /
0.10 = $$500,000
The Average Accounting
Return
6.3 The annual, end-of-year,
book-investment accounts for the machine whose
purchase your firm is
considering are
shown below.
Purchase Year Year Year
Year
Date 1 2 3 4
Gross
investment $$16,000 $$16,000 $$16,000 $$16,000 $$16,000
Less: accumulated
depreciation ______0_ ___4_,0_0_0_
___8_,0_0_0_ __1_2_,0_0_0_ _1_6_,_0_0_0
Net investment $$16,000 $$12,000 $$ 8,000
$$ 4,000 $$ 0
If your firm purchases this
machine, you can expect it to generate, on
average, $$4,500 per
year in additional
net income.
a. What is the average
accounting return for this machine?
b.
What three flaws are inherent in this decision
rule?
6.3
a.
Average Investment:
($$16,000 + $$12,000 + $$8,000 + $$4,000 +
0) / 5 = $$8,000
Average accounting
return:
$$4,500 / $$8,000 = 0.5625 =
56.25%
B-66
Answers to End-of-Chapter Problems
b.
1.
2.
3.
AAR does not consider the timing of the
cash flows, hence it does not
consider
the time value of money.
AAR uses an
arbitrary firm standard as the decision rule.
AAR uses accounting data rather than
net cash flows.
6.4 Western Printing
Co. has an opportunity to purchase a $$2 million
new printing machine. It has an
economic life of five years and will be
worthless after that time. This new investment is
expected to
generate an annual net
income of $$100,000 one year from today and the
income stream will grow at 7
percent
per year subsequently. The company adopts a
straight-line depreciation method (i.e., equal
amounts
of depreciation in each year).
What is the average accounting return of the
investment? Supposing Western
Printing
’
s AAR
cutoff is 20 percent, should the machine be
purchased?
6.4
Average Investment = ($$2,000,000 + 0) /
2 = $$1,000,000
Average net income =
[$$100,000 {(1 + g)
5
- 1} /
g] / 5
=
{$$100,000A (1.07
5
- 1} /
0.07} / 5
= $$115,014.78
AAR = $$115,014.78 / $$1,000,000 = 11.50%
No, since the machine’s AAR is less
than the firm’s cutoff AAR.
6.5 Nokia Group has invested $$8,000 in
a high-tech project. This cost is depreciated on
an accelerated basis
that yields
$$4,000, $$2,500, $$1,500 of depreciation,
respectively, during its three-year economic life.
The
project is expected to produce
income before tax of $$2,000 each year during its
economic life. If the tax
rate is 25%,
what is the project
’
s
average accounting return (AAR)?
a.
44.44%
b. 50.23%
c. 66.67%
d. 70.00%
e. 82.21%
The Internal Rate of Return
6.5
a
6.6 Compute
the internal rate of return on projects with the
following cash flows.
Cash Flows ($$)
Year Project A Project B
0
_3,000 _6,000
1 2,500 5,000
2 1,000 2,000
6.6
PI = $$40,000
?
7
0
.
15
/
$$160,000 = 1.04
Since the PI exceeds
one accept the project.
6.7 CPC, Inc.,
has a project with the following cash flows.
Year Cash Flows ($$)
0 _8,000
1 4,000
2 3,000
3
2,000
a. Compute the internal rate of
return on the project.
b. Suppose the
appropriate discount rate is 8 percent. Should the
project be adopted by CPC?
6.7 The
IRR is the discount rate at which the NPV = 0.
-$$3,000 + $$2,500 / (1 +
IRR
A
) + $$1,000 / (1 +
IRR
A
)
2
= 0
By trial and error,
IRR
A
= 12.87%
Since project B’s cash flows are two
times of those of project A, the
IRR
B
=
IRR
A
=
12.87%
6.8 Compute the internal rate of return
for the cash flows of the following two projects.
Cash Flows ($$)
Time A B
0 _2,000 _1,500
1 2,000 500
Answers to End-of-Chapter Problems
B-67
2 8,000 1,000
3 _8,000 1,500
6.8
a.
b.
Solve x by trial and
error:
-$$4,000 + $$2,000 / (1 + x) +
$$1,500 / (1 + x)
2
+ $$1,000 /
(1 + x)
3
= 0
x =
6.93%
No, since the IRR (6.93%) is less
than the discount rate of 8%.
6.9
Suppose you are offered $$5,000 today and obligated
to make scheduled payments as follows:
Year Cash Flows ($$)
0 5,000
1 _2,500
2 _2,000
3 _1,000
4 _1,000
a. What is the IRRs of this offer?
b. If the appropriate discount rate is
10 percent, should you accept this offer?
c. If the appropriate discount rate is
20 percent, should you accept this offer?
Chapter 6 Some Alternative Investment
Rules 165
d. What is the corresponding
NPV of the project if the appropriate discount
rates are 10 percent and 20
percent,
respectively? Are the choices under the NPV rule
consistent with those of the IRR rule?
6.9
Find the IRRs of project
A analytically. Since the IRR is the discount
rate that makes the NPV
equal to zero,
the following equation must hold.
-$$200 + $$200 / (1 + r) + $$800 / (1 +
r)
2
- $$800 / (1 +
r)
3
= 0
$$200 [-1 + 1 / (1 + r)] -
{$$800 / (1 + r)
2
}[-1 + 1 /
(1 + r)] = 0
[-1 + 1 / (1 + r)] [$$200 - $$800 / (1 +
r)
2
] = 0
For this
equation to hold, either [-1 + 1 / (1 + r)] = 0 or
[$$200 - $$800 / (1 + r)
2
] =
0.
Solve each of these factors for the
r that would cause the factor to equal zero. The
resulting rates are the two IRRs for
project A. They are either r = 0% or r = 100%.
Note: By inspection you
should have known that one of the IRRs of project
A is
zero. Notice that the
sum of the un-discounted cash flows for project A
is zero.
Thus, not
discounting the cash flows would yield a zero NPV.
The discount rate
which is
tantamount to not discounting is zero.
Here are some of the interactions used
to find the IRR by trial and error.
Sophisticated calculators can compute
this rate without all of the tedium involved in
the trial-and-error method.
NPV
= -$$150 + $$50 / 1.3 + $$100 /
1.3
2
+ $$150 /
1.3
3
= $$15.91
NPV
= -$$150 +
$$50 / 1.4 + $$100 / 1.4
2
+
$$150 / 1.4
3
= -$$8.60
NPV
= -$$150 + $$50 / 1.37 + $$100 /
1.37
2
+ $$150 /
1.37
3
= -$$1.89
NPV
= -$$150 +
$$50 / 1.36 + $$100 / 1.36
2
+
$$150 / 1.36
3
= $$0.46
NPV
= -$$150 + $$50 / 1.36194 + $$100 /
1.36194
2
+ $$150 /
1.36194
3
= $$0.0010
NPV
= -$$150 + $$50 / 1.36195 + $$100 /
1.36195
2
+ $$150 /
1.36195
3
= -$$0.0013
NPV
= -$$150 + $$50 / 1.361944 + $$100 /
1.361944
2
+ $$150 /
1.361944
3
= $$0.0000906
Thus, the IRR is
approximately 36.1944%.
6.10 As the
Chief Financial Officer of the Orient Express, you
are offered the following two
mutually
exclusive projects.
Year Project A
Project B
0 _$$5,000 _$$100,000
1 3,500 65,000
2 3,500
65,000
a. What are the IRRs of these
two projects?
b. If you are told only
the IRRs of the projects, which would you choose?
B-68
Answers to End-of-Chapter Problems
c. What did you ignore when you made
your choice in part (b)?
d. How can the
problem be remedied?
e. Compute the
incremental IRR for the projects.
f.
Based on your answer to part (e), which project
should you choose?
g. Suppose you have
determined that the appropriate discount rate for
these projects
is 15 percent. According
to the NPV rule, which of these two projects
should be
adopted?
6.10
a.
b.
c.
d.
Solve r in the equation:
$$5,000 - $$2,500 / (1 + r) - $$2,000 / (1
+ r)
2
- $$1,000 / (1 +
r)
3
- $$1,000 /
(1 + r)
4
= 0
By
trial and error,
IRR = r = 13.99%
Since this problem is the case of
financing, accept the project if the IRR is less
than
the required rate of return.
IRR = 13.99% > 10%
Reject
the offer.
IRR = 13.99% < 20%
Accept the offer.
When r =
10%:
NPV = $$5,000 - $$2,500 / 1.1 -
$$2,000 / 1.1
2
- $$1,000 /
1.1
3
- $$1,000 /
1.1
4
= -$$359.95
When r = 20%:
NPV = $$5,000 -
$$2,500 / 1.2 - $$2,000 / 1.2
2
- $$1,000 / 1.2
3
- $$1,000 /
1.2
4
= $$466.82
Yes, they are consistent with the
choices of the IRR rule since the signs of the
cash
flows change only once.
6.11 Consider two streams of cash
flows, A and B. Cash flow A consists of $$5,000
starting three years from
today and
growing at 4 percent in perpetuity. Cash flow B
consists of _$$6,000 starting two years from
today and continuing in perpetuity.
Assume the appropriate discount rate is 12
percent.
a. What is the present value
of each stream?
b. What is the IRR of a
project C, which is a combination of projects A
and B; that is, C _ A _ B?
c. If it is
assumed that the discount rate is always positive,
what is the rule related to IRR for assessing
project C that would correspond to the
NPV rule?
6.11
a.
b.
c.
d.
e.
Project A:
NPV = -$$5,000 + $$3,500 / (1 + r) +
$$3,500 / (1 + r)
2
= 0
IRR = r = 25.69%
Project B:
NPV = -$$100,000 + $$65,000 / (1 + r) +
$$65,000 / (1 + r)
2
= 0
IRR = r = 19.43%
Choose
project A because it has a higher IRR.
The difference in scale is ignored.
Apply the incremental IRR method.
C
0
C
1
C
2
B -
A
-$$95,000
$$61,500
$$61,500
NPV =
-$$95,000 + $$61,500 / (1 + r) + $$61,500 / (1 +
r)
2
= 0
Incremental IRR = r = 19.09%
If the discount rate is less than
19.09%, choose project B.
Otherwise,
choose project A.
NPV
A
= -$$5,000 +
$$3,500 / 1.15 + $$3,500 /
1.15
2
= $$689.98
NPV
B
= -$$100,000
+ $$65,000 / 1.15 + $$65,000 /
1.15
2
= $$5,671.08
Choose project B.
B-69
f.
g.
Answers to End-
of-Chapter Problems