Financial Management
FIN6934.030
May 6, 2006
Assignment 4
Beth Clark
Theresa Lynn P. Collins
John C. Harris
Barry Manz
George Stein
Professor Chris Pantzalis, Ph. D.
Financial Management I
Assignment 4 – Mini Case 10
Lisa’s Soups, Salads, & Stuff versus Sam’s Wonderful Fried Chicken
a. What is capital budgeting?
“Simply put, capital budgeting is the whole process of analyzing projects and deciding
which ones to include in the capital budget” (Page 344). The five key methods used to
evaluate projects for capital budgeting include: (1) payback period, (2) discounted
payback period, (3) net present value, (4) internal rate of return, and (5) modified internal
rate of return. Using these criteria, financial 'analysts seek to identify those projects that
will lead to the maximization of the firm's stock price (FM 11_Ch_10_Mini Case).
b. What is the difference between independent and mutually exclusive projects?
“Independent projects are projects whose cash flows don’t affect one another” and
mutually exclusive projects are projects that if one project is taken on, the other must be
rejected” (Page 348).
c.
(1) What is the payback period?
The payback period is “the expected number of years to recover the original investment
and was the first normal method used to evaluate capital budgeting projects” (347).
Discounted payback period uses the project's cost of capital to discount the expected cash
flows. The calculation of discounted payback period is identical to the calculation of
regular payback period, except you must base the calculation on a new row of discounted
cash flows. Note that both projects have a cost of capital of 10% (FM 11_Ch_10_Mini
Case).
Find the paybacks for Franchises L and S.
The payback period for Franchise L is 2.38 and the payback period for Franchise S is
1.60, see the table that follows.
L
Time period:
Cash flow:
Cumulative cash flow:
Payback:
0
(100,000)
(100,000)
1
10,000
(90,000)
2
60,000
(30,000)
3
80,000
50,000
1
70,000
(30,000)
2
50,000
20,000
3
20,000
40,000
2.38
S
Time period:
Cash flow:
Cumulative cash flow:
Payback:
Page 2 of 16
0
(100,000)
(100,000)
1.60
Financial Management I
Assignment 4 – Mini Case 10
(2) What is the rationale for the payback method?
“The NPV method of capital budgeting dictates that all independent projects that have
positive NPV should accepted. The rationale behind that assertion arises from the idea is
that all such projects add wealth, and that should be the overall goal of the manager in all
respects. If strictly using the NPV method to evaluate two mutually exclusive projects,
you would want to accept the project that adds the most value (i.e. the project with the
higher NPV).
According to the payback criterion, which franchises should be accepted if the
firm’s maximum acceptable payback is 2 years?
If the maximum acceptable payback is two years then firm S with a payback of 1.60
should be accepted versus firm L, which has a payback of 2.38.
If Franchises L and S are independent?
If considering the above two projects, you would accept both franchises L and S if they
are independent.
If they are mutually exclusive?
You would only accept Project S as it has the higher NPV of $19,984.97 versus L which
has a lower NPV of $18,782.87 if the franchises are mutually exclusive.
(3) What is the difference between the regular and discounted payback periods?
The calculation of discounted payback period is identical to the calculation of regular
payback period, except the calculation of the discounted payback period is based on a
new row of discounted cash flows (FM 11_Ch_10_Mini Case).
(4) What is the main disadvantage of discounted payback?
The main disadvantage of the discounted payback is that it still falls short of fully
analyzing projects, but does account for timing issues (to some extent). However, all else
equal, these two methods do provide some information about projects' liquidity and risk.
Is the payback method of any real usefulness in the capital budgeting decisions?
The payback method does provide real usefulness in that they “do provide information on
how long funds will be tied up in the project (349).
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Financial Management I
Assignment 4 – Mini Case 10
d.
(1) Define the term net present value (NPV).
“Net present value is defined as a way to improve the effectiveness of project evaluations
through the use of discounted cash flow techniques. To find the present value of a
project, you must first find the present value of each cash flow discounted at the cost of
capital. Then, sum the discounted cash flows. If the NPV is positive, accept the project.
If NPV is negative, reject the project. It is important to remember that if two projects are
mutually exclusive, the project that has the higher NPV should be selected” (349).
What is each franchise’s NPV?
The net present value for Franchise L is $18,782.87 and the net present value for
Franchise S is $19,948.97, see the table that follows.
L
Time period:
Cash flow:
Disc. cash flow:
NPV(L) =
0
(100,000)
(100,000)
1
10,000
9,091
2
60,000
49,587
$18,782.87
3
80,000
60,105
$18,782.87
S
Time period:
Cash flow:
Disc. cash flow:
NPV(S) =
0
(100,000)
(100,000)
1
70,000
63,636
2
50,000
41,322
$19,984.97
3
20,000
15,026
$ 19,984.97
(2) What is the rationale behind the NPV method??
“The NPV method is based on a logical approach. An NPV of zero signifies that the
project’s cash flows are exactly sufficient to repay the invested capital and to provide the
required rate of return on that capital.” If NPV > 0, then the project is generating a larger
amount of cash that required to service debt and to allow a return to shareholders. So if
the firm takes on projects that have positive net present values (NPV) then the wealth of
shareholders will increase, enticing them to increase their investment in the firm” (350).
The NPV method of capital budgeting dictates that all independent projects that have
positive NPV should accepted. The rationale that is behind that assertion arises from the
idea that all such projects add wealth, and that should be the overall goal of the manager
in all respects. If strictly using the NPV method to evaluate two mutually exclusive
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Financial Management I
Assignment 4 – Mini Case 10
projects, you would want to accept the project that adds the most value (i.e. the project
with the higher NPV).
According to NPV, which franchise or franchises should be accepted if they are
independent?
If considering the above two projects, accept both projects if they are independent.
Mutually exclusive?
Only Project S would be accepted if they are mutually exclusive.
WACC
0%
5%
8.68%
10%
23.56%
18.13%
15.0%
20%
25%
Project NPVs
L
$18,782.87
$50,000.00
$33,052.59
$22,322.04
$18,782.87
-$10,204.71
$0.00
$6,665.57
-$3,703.70
-$12,640.00
S
$19,984.97
$40,000.00
$29,294.89
$22,322.04
$19,984.97
$0.00
$7,225.43
$11,827.07
$4,629.63
-$1,760.00
(3) Would the NPV’s change if the cost of capital changed?
Yes, “a project might have a positive NPV if it is part of a ‘normal size’ capital budget,
but the same project might have a negative NPV if it is part of an unusually large capital
budget.” “The cost of capital may depend on the size of the capital budget.” “This
means that the cost of capital jumps upward after a company invests all of its internally
generated cash and must sell new common stock. In addition, investors often perceive
extremely large capital investments to be riskier, which may also drive up the cost of
capital as the size of the capital budget increases.”
e.
(1) Define the term internal rate of return (IRR). What is each franchise’s IRR?
“The internal rate of return (IRR) is defined as the discount rate that equates the present
value of a project’s expected cash inflows to the present value of the projects cost or
equivalently, the IRR is the rate that forces the NPV to equal zero” (351).
What is each franchise’s IRR?
The IRR of L is 18.13% and the IRR of S is 23.56%, see the table that follows.
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Financial Management I
Assignment 4 – Mini Case 10
Expected after-tax
net cash flows (CFt)
Year (t)
0
L
($100,000)
S
($100,000)
1
10,000
70,000
IRR L =
18.13%
2
3
60,000
80,000
50,000
20,000
IRR S =
23.56%
(2) How is the IRR on a project related to the YTM on a bond?
“If you invest in a bond, hold it to maturity, and receive all of the promised cash flows,
you will earn the YTM. Exactly the same concepts are employed in capital budgeting
when the IRR method is used. The IRR is defined as the discount rate that equates the
present values of a project’s expected cash inflows to the present value of the project’s
costs” (Page 351). Additionally, “when dealing with independent projects, the NPV and
IRR methods will always yield the same accept/reject result. 'However, in the case of
mutually exclusive projects, NPV and IRR can give conflicting results. One shortcoming
of the internal rate of return is that it assumes that cash flows received are reinvested at
the project's internal rate of return, which is not usually true. The nature of the
congruence of the NPV and IRR methods is further detailed in a latter section of this
model” (FM 11_Ch_10_Mini Case).
(3) What is the logic behind the IRR method?
The logic behind the IRR method is:
 The IRR on a project is its expected rate of return.
 If the internal rate of return exceeds the cost of the funds used to finance the
project, a surplus will remain after paying for the capital, and this surplus will
accrue to the firm’s stockholders
 Therefore, taking on a project whose IRR exceeds its cost of capital increases
shareholders’ wealth. On the other had, if the IRR is less than the cost of capital,
then taking on the project will impose a cost on current stockholders. It is this
“breakeven” characteristic that makes the IRR useful in evaluating capital
projects.” (Page 352)
According to IRR, which franchises should be accepted if they are independent?
“The IRR method of capital budgeting maintains that projects should be accepted if their
IRR is greater than the cost of capital. Strict adherence to the IRR method would further
dictate that mutually exclusive projects should be chosen on the basis of the greatest IRR.
Page 6 of 16
Financial Management I
Assignment 4 – Mini Case 10
In this scenario, both projects have IRR's that exceed the cost of capital (10%) and both
should be accepted, if they are independent (FM 11_Ch_10_Mini Case).
Mutually exclusive?
“If the projects are mutually exclusive, we would choose Project S. Recall, that this was
our determination using the NPV method as well. The question that naturally arises is
whether or not the NPV and IRR methods will always agree” (FM 11_Ch_10_Mini
Case).
(4) Would the franchises’ IRR’s change if the cost of capital changed?
Yes, if the cost of capital is changed the franchises’ IRR also changes.
f.
(1) Draw NPV profiles for Franchises L and S.
NPV Profiles (L & S)
$60,000.00
CONFLICT
$50,000.00
$40,000.00
NO CONFLICT
$30,000.00
$20,000.00
$10,000.00
$0.00
0%
5%
8.68%
10%
23.56%
18.13%
-$10,000.00
CROSSOVER
-$20,000.00
Franchise L
Year
Net Cash Flows
L
S
Page 7 of 16
WACC =
Franchise S
10.0%
15.0%
20%
25%
Financial Management I
Assignment 4 – Mini Case 10
0
1
2
3
-$100,000
$10,000
$60,000
$80,000
-$100,000
$70,000
$50,000
$20,000
NPV =
IRR =
Crossover =
L
$18,782.87
18.13%
8.68%
S
$19,984.97
23.56%
At what discount rate do profiles cross?
The NPV profiles for franchises L and S cross at a discount rate of 8.68 % where both
projects have the same NPV. This is the indifference point between the two projects;
refer to the graph of the NPV profiles that follow.
If these are independent projects and cost of capital is 10%, they should both be accepted.
Both return a positive NPV at the designated cost of capital and would therefore be
profitable.. If the two projects are mutually exclusive at a capital cost of 10%, franchise
S should be selected because its NPV is slightly greater than L (The graph of S is above L
at a capital cost of 10%). If capital costs are less than 8%, Franchise L becomes the
better deal. Franchise L is a better deal when capital costs are low because it generates
more total income but that income arrives later than franchise S. When capital costs are
high, the time value of money is greater so a project which provides the bulk of its
income sooner would be more desirable than a project which produces greater income but
produces it later.
(2) Look at your NPV profile graph without referring to the actual NPVs and IRRs.
Which franchise or franchises should be accepted if they are independent?
If these are independent projects and cost of capital is 10%, they should both be accepted.
Both return a positive NPV at the designated cost of capital and would therefore be
profitable.
Mutually exclusive? Explain.
If the two projects are mutually exclusive at a capital cost of 10%, franchise S should be
selected because its NPV is slightly greater than L (The graph of S is above L at a capital
cost of 10%). If capital costs are less than 8%, Franchise L becomes the better deal.
Franchise L is a better deal when capital costs are low because it generates more total
income but that income arrives later than franchise S. When capital costs are high, the
time value of money is greater so a project which provides the bulk of its income sooner
would be more desirable than a project which produces greater income but produces it
later.
Are your answers correct at any cost of capital less than 23.6 percent?
The recommendations given are only good for 10% cost of capital. Franchise L is only
profitable when capital costs are less than 18%, whereas franchise S is viable for capital
costs less than approx 23.5%. Also, at 10% capital costs, project S is better, but if capital
costs are 6% then project L is better. The short answer is no, the answers are not correct
for any cost of capital less than 23.6%
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Financial Management I
Assignment 4 – Mini Case 10
g.
(1) What is the underlying cause of ranking conflicts between NPV and IRR?
A conflict exists if the cost of capital is less than the crossover rate. Two basic conditions
can cause NPV profiles to cross, and thus conflicts to arise between NPV and IRR:
(1) when project size (or scale) differences exist, meaning that the cost of one project
is largest than that of the other, or
(2) when timing differences exist, meaning that the timing of cash flows from the
two projects differs such that most of the cash flows from one project come in the
early years while most of the cash flows from the other project come in the later
years (Page 355)
(2) What is the “reinvestment rate assumption,” and how does it affect the NPV
versus IRR conflict?
The value of early cash flows depends on the return we can earn on those cash flows, that
is the rate at which we can reinvest them. “The NPV method implicitly assumes that the
rate at which cash flows can be reinvested is the cost of capital, whereas the IRR method
assumes that the firm can reinvest at the IRR” (Page 355).
(3) Which methods is the best? Why?
The NPV method is more reliable. The best assumption is that the projects’ cash flows
can be reinvested at the cost of capital (Page 355).
h.
(1) Define the term modified IRR (MIRR). Find the MIRRs for Franchises L and S.
“The modified internal rate of return (MIRR) is the discount rate that causes a project's
cost (or cash outflows) to equal the 'present value of the project's terminal value.
Find the MIRRs for Franchises L and S.
The MIRR for Franchise L is 14.84% and the MIRR for Franchise S is 15.13%, see the
data that follows on the next page.
Page 9 of 16
Financial Management I
Assignment 4 – Mini Case 10
WACC =
10%
Project S
MIRRL
=
14.84%
MIRRS
=
15.13%
10%
0
1
2
3
4
(100,000)
10,000
60,000
80,000
0
Project L
0
1
2
3
4
(100,000)
70,000
50,000
20,000
0
22,000.0
60,500.0
93,170.0
PV:
(100,000)
Terminal
Value:
175,670.0
(3) What are the MIRR’s advantages and disadvantages vis-à-vis the regular IRR?
“The MIRR has an important advantage over regular IRR. MIRR assumes that cash flows
from all the firm’s projects are reinvested at the cost of capital, while regular IRR
assumes that cash flows from each project are reinvested at the project’s own IRR. Since
reinvestment at the cost of capital is generally more correct, the MIRR is a better
indicator of a project’s true profitability” (358). Further, the MIRR solves the multiple
IRR problem, as a set of cash flows can have but one MIRR .
What are the MIRR’s advantages and disadvantages vis-à-vis the NPV?
“If two projects are of equal size and have the same useful life, then NPV and MIRR will
lead to the same decision…If the projects are of equal size, but differ in lives, the MIRR
will always lead to the same decision as the NPV if the MIRR’s are both calculated using
as the terminal year the life of the longer project.” The advantage of the NPV is that it “is
still the best way to choose amount competing projects because it provides the best
indication of how much each project will add to the value of the firm.
i. As a separate project (project P), you are considering a pavilion at the upcoming
World’s Fair. The pavilion would cost $800,000, and it is expected to result in $5
million of incremental cash inflows during its 1 year of operation. However, it would
Page 10 of 16
Financial Management I
Assignment 4 – Mini Case 10
then take another year, and $5 million of costs, to demolish the site and return it to
its original condition. Thus, Project P’s expected net cash flows look like this (in
millions of dollars):
Year
0
1
2
Net Cash Flows
($0.8)
5.0
(5.0)
The project is estimated to be of average risk, so its cost of capital is 10 percent.
(1) What are the normal and non-normal cash flows?
A normal cash flow is one which following the normally expected pattern of an initial
investment (cash outflow) followed by one or more returns (cash inflows). A non-normal
cash flow would be a net cash outflow which occurs later in the project after a period of
cash inflows. The costs associated with restoration of land which has been mined out
would be a common example.
(2) What is Project P’s NPV?
NPV is the current value of all cash flows at the relevant cost of capital. NPV for this
project at a 10% cost of capital is -$3,868,000 (work follows) :
NPV = -.8M + 5M / (1 + .1) - 5M / (1 + .1)2 = (-.3868M)
NPV = -$3,868,000
What is IRR?
The IRR is .25 and the IRR is also 4 (work follows).
To compute the IRR, the following equation needs to be solved for IRR
-.8M + 5M / (1+IRR) – 5M / (1+IRR) 2 = 0
-.8*((1+IRR) 2) + 5*(1+IRR) – 5 = 0
This has two solutions, IRR = .25 and IRR = 4.
It’s MIRR?
The MIRR is 5.59% (work follows).
To compute MIRR, compute revenue forward and costs back
Page 11 of 16
Financial Management I
Assignment 4 – Mini Case 10
TV = 5M * (1.1) = 5.5M
PV = - 5M / (1.12) - .8M = -4.9322
To compute MIRR, PV = TV / ((1+MIRR) 2)
4.9322M = 5.5M / (1 + MIRR) 2
MIRR = √(5.5/4.9322)-1 = .0559
MIRR = 5.59%
(3) Draw Project P’s NPV profile. Does Project P have normal or nonnormal cash
flows? Should this project be accepted?
As can be seen from the NPV graph below, this project has a non-normal cash flow. With
a capital cost of 10%, this project should not be accepted because its NPV is negative
3.868 million. Likewise, its MIIR is 5.59%, which is less than the 10% cost of capital.
Project P's
NPV Profile
$600
$500
$400
$300
$200
$100
NPV
$0
-$100
-$200
-$300
-$400
-$500
-$600
-$700
-$800
-$900
0%
100%
200%
300%
WACC
Page 12 of 16
400%
500%
WACC
0%
25%
50%
75%
100%
125%
150%
175%
200%
225%
250%
275%
300%
325%
350%
375%
400%
425%
450%
475%
500%
525%
550%
575%
NPV
-$800.00
$0.00
$311.11
$424.49
$450.00
$434.57
$400.00
$357.02
$311.11
$265.09
$220.41
$177.78
$137.50
$99.65
$64.20
$31.02
$0.00
-$29.02
-$56.20
-$81.66
-$105.56
-$128.00
-$149.11
-$169.00
Financial Management I
Assignment 4 – Mini Case 10
j. In an unrelated analysis, you have the opportunity to choose between the
following two mutually exclusive projects:
EXPECTED NET CASHFLOWS
Year
0
1
2
3
4
Project S
($100,000)
60,000
60,000
-----
Project L
($100,000)
33,500
33,500
33,500
33,500
The projects provide a necessary service, so whichever one is selected is expected to
be repeated into the foreseeable future. Both projects have a 10 percent cost of
capital.
L
WACC:
End of Period:
10.0%
0
($100,000)
1
$33,500
2
$33,500
3
$33,500
NPV
IRR
$6,190
12.8%
2
$60,000
3
$0
4
$33,500
5
$0
S
End of Period:
0
($100,000)
1
$60,000
NPV
IRR
$4,132
13.1%
(1) What is the project’s initial NPV without replication?
The NPV for project L is $6,190 and the NPV for project S is $4,132.
Page 13 of 16
6
$0
Financial Management I
Assignment 4 – Mini Case 10
(2) Now apply the replacement chain approach to determine the projects’ extended
NPV’s. Which project should be chosen?
The NPV for project L is $6,190 for 6 years and NPV for project S with replication is
$79,868, see data below.
L
End of Period:
0
($100,000)
1
$33,500
NPV
IRR
$6,190
12.8%
2
$33,500
3
$33,500
4
$33,500
2
$60,000
$33,500
$93,500
3
4
$33,500
$33,500
$33,500
$33,500
S
0
($100,000)
1
$60,000
($100,000)
$60,000
NPV
IRR
$79,868
48.4%
(3) Now assume that the costs to replicate project S in 2 years will increase to
$105,000 because of inflationary pressures.
How should the analysis be handled now, and which project should be chosen?
k. You are also considering another project which has a physical life of 3 years; that
is, the machinery will be totally worn out after 3 years. However, if the project were
terminated prior to the end of 3 years, the machinery would have a positive salvage
value. Here are the project’s estimated cash flows:
Year
0
1
2
3
Page 14 of 16
Project S
($5,000)
2,100
2,000
1,750
Project L
$5,000
3,100
2,000
0
Financial Management I
Assignment 4 – Mini Case 10
Using 10 percent cost of capital, what is the project’s NPV if it is operated for the
full 3 years?
The projects NPV, assuming it operates for 3 full years, is -$123.22, data follows.
3-Year NPV =
=
3-Year NPV =
Intial
Cost
+
PV
of
Operating
Cash Flow
+
PV
Salvage
Value
($5,000.00)
+
$4,876.78
+
$0.00
of
($123.22)
Would the NPV change if the company planned to terminate the project at the end
of year 2?
If the project is terminated at the end of year 2 the NPV would be $214.88, data follows.
2-Year
NPV =
=
2-Year
NPV =
Intial Cost
+
PV
of
Operating
Cash Flow
+
PV
Salvage
Value
($5,000.00)
+
$3,561.98
+
$1,652.89
of
$214.88
At the end of year 1?
If the project is terminated at the end of year 2 the NPV would be -$272.73, data follows.
1-Year NPV =
=
1-Year NPV =
Intial
Cost
+
PV
of
Operating
Cash Flow
+
PV
Salvage
Value
($5,000.00)
+
$1,909.09
+
$2,818.18
of
($272.73)
What is the project’s optimal (economic) life?
The projects optimal life is 2 years, since at 2 years the project has its highest NPV.
(1) After examining all the potential projects, you discover that there are many
more projects this year with positive NPV’s than in a normal year. What two
problems might this large capital budget cause?
The two problems this extra large capital budget may cause are an increasing cost of
capital and capital rationing. In some cases, the cost of capital may depend on the size of
the budget. The flotation costs associated with issuing new debt or equity may be lofty,
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Financial Management I
Assignment 4 – Mini Case 10
so the cost of the capital can increase exponentially after a firm invests all of it internal
funds and must sell new stock. Depending on the size of the firm, Investors may perceive
large capital expenditures as risky which in turn could drive up the cost of capital as the
size of the project increases; thus the dilemma of an increasing cost of capital.
The problem of Capital rationing, a practice that is common, is a situation where the firm
places a limit on their capital expenditures to an amount that is less what would be
required to fund the optimal capital budget. Some of the reasons for this rationing are
reluctance to issue new stock, constraints on non-monetary resources, and controlling
estimation bias (367-368).
It may not be in the best interests of stockholders to dilute the stock by raising equity
capital, or the increased borrowing could affect bond ratings or other creditworthiness.
The floatation costs of raising new capital may be so high that it would make a reduced
mix of projects more profitable than doing all of them. Also, rapid expansion simply
may not be part of the company strategy.
Limitations on resources and infrastructure also place a limitation on the number of
projects which can be undertaken. If management, engineering or other infrastructure is
stretched too thin, the projects will not be undertaken properly. Profitability could be
reduced or the projects could fail as a result. Building infrastructure to handle an
anomalous increase in workload which may not continue into the future could create the
necessity for layoffs and other unpleasant effects in the future.
It would be nice to be able to do everything, but there is always a practical limitation on
company resources, manufacturing capacity, and capital. Part of being a manager is
choosing alternatives. We are all intimately familiar with the use of linear programming
to solve the problem of creating the optimum mix of production given constrained
resources. These techniques would be applicable here.
Work Cited
Brigham, Eugene F., Michael C. Ehrhardt. Financial Management. 11th ed.
Mason, Ohio: South Western, 2005.
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