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A B C D E F G H I J K L M N O P Q R S
12/10/2012
Situation
Franchise S
Year (t) Franchise S Franchise L 0 1 2 3
0($100) ($100) (100) 70 50 20
170 10
250 60 Franchise L
320 80
0 1 2 3
(100) 10 60 80
Chapter 10. Mini Case
Expected
Net Cash Flows
You have just graduated from the MBA program of a large university, and one of your favorite courses was “Today‘s
Entrepreneurs.” In fact, you enjoyed it so much you have decided you want to “be your own boss.” While you were in
the master’s program, your grandfather died and left you $1 million to do with as you please. You are not an inventor,
and you do not have a trade skill that you can market; however, you have decided that you would like to purchase at
least one established franchise in the fast-foods area, maybe two (if profitable). The problem is that you have never
been one to stay with any project for too long, so you figure that your time frame is three years. After three years you
Depreciation, salvage values, net working capital requirements, and tax effects are all included in these cash flows.
You also have made subjective risk assessments of each franchise and concluded that both franchises have risk
characteristics that require a return of 10%. You must now determine whether one or both of the franchises should
be accepted.
c. (1.) Define the term net present value (NPV). What is each franchise’s NPV?
a. What is capital budgeting? Answer: See Chapter 10 Mini Case Show
b. What is the difference between independent and mutually exclusive projects? Answer: See Chapter 10 Mini Case
Show
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A B C D E F G H I J K L M N O P Q R S
Franchise L
Time period: 0 1 2 3
Cash flow: (100) 10 60 80
Disc. cash flow: (100) 950 60
NPV(L) = $18.78 $18.78 = Uses NPV function.
Internal Rate of Return (IRR)
Year (t) Franchise S Franchise L
0($100) ($100)
170 10
IRR S = 23.56%
250 60
IRR L = 18.13%
320 80
Constant Cash Flows
Year (t) Cash Flow
0($100) 0 123
(2.) What is the rationale behind the NPV method? According to NPV, which franchise or franchises should be
accepted if they
Expected
The IRR function
assumes payments
occur at end of periods,
(3.) Would the NPVs change if the cost of capital changed? Answer: See Chapter 10 Mini Case Show
The internal rate of return is defined as the discount rate that equates the present value of a project’s cash inflows to
for Franchises S and L are shown below, along with the data entry for Franchise S.
d. (1.) Define the term internal rate of return (IRR). What is each franchise’s IRR?
net cash flows
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A B C D E F G H I J K L M N O P Q R S
IRR = 7.08%
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A B C D E F G H I J K L M N O P Q R S
NPV Profiles
e. Draw NPV profiles for Franchises L and S. At what discount rate do the profiles cross?
Franchise S Franchise L
r$19.98 r$18.78
0% 40.00 0% 50.00
2% 35.53 2% 42.86
4% 31.32 4% 36.21
6% 27.33 6% 30.00
(3.) What is the logic behind the IRR method? According to IRR, which franchises should be accepted if they are
independent?
The IRR method of capital budgeting maintains that projects should be accepted if their IRR is greater than the cost
of capital. Strict adherence to the IRR method would further dictate that mutually exclusive projects should be
chosen on the basis of the greatest IRR. In this scenario, both franchises have IRRs that exceed the cost of capital
(10%) and both should be accepted, if they are independent. If, however, the franchises are mutually exclusive, we
would choose Franchise S. Recall, that this was our determination using the NPV method as well. The question that
Previously, we had discussed that in some instances the NPV and IRR methods can give conflicting results. First, we
X-axis.
(4.) Would the franchises‘ IRRs change if the cost of capital changed?
(2.) Look at your NPV profile graph without referring to the actual NPVs and IRRs. Which franchise or franchises
should be accepted if they are independent? Mutually exclusive? Explain. Are your answers correct at any cost of
capital less than 23.6%?
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50
60
NPV ($)
NPV Profile of Franchises S and L
Project L
Crossover Rate =
8.7%
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years, when the discount penalty is largest; hence, they are most severely impacted by high capital costs. (3)
Therefore, Franchise L‘s NPV profile is steeper than that of S. (4) Since the two profiles have different slopes, they
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A B C D E F G H I J K L M N O P Q R S
Cash Flow
Year (t) Franchise S Franchise L Differential
0($100) ($100) 0
170 10 60
250 60 (10)
320 80 (60)
IRR = Crossover rate = 8.68%
Modified Internal Rate of Return (MIRR)
WACC = 10%
MIRRS = 16.89%
f. What is the underlying cause of ranking conflicts between NPV and IRR?
The modified internal rate of return is the discount rate that causes a project‘s cost (or cash outflows) to equal the
present value of the project’s terminal value. The terminal value is defined as the sum of the future values of the
project’s cash inflows, compounded at the project’s cost of capital. To find MIRR, calculate the PV of the outflows
and the FV of the inflows and then find the discount rate that equates the two. Or, you can solve using Excel’s MIRR
function.
g. Define the term modified IRR (MIRR). Find the MIRRs for Franchises L and S.
Expected
Net Cash Flows
Looking further at the NPV profiles, we see that the two franchises profiles intersect at a point we shall call the
crossover rate. We observe that at costs of capital greater than the crossover rate, the franchise with the greater IRR
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Discounted Payback Period
calculation on a new row of discounted cash flows. Note that both projects have a cost of capital of 10%.
A B C D E F G H I J K L M N O P Q R S
PROFITABILITY INDEX
h. What does the profitability index (PI) measure? What are the PI’s for Franchises S and L?
i. (1.) What is the payback period? Find the paybacks for Franchises L and S.
Payback Period
The profitability index is the present value of all future cash flows divided by the intial cost. It measures the PV per
dollar of investment.
(3.) What is the difference between the regular and discounted payback periods?
The payback period is defined as the expected number of years required to recover the investment, and it was the
first formal method used to evaluate capital budgeting projects. First, we identify the year in which the cumulative
cash inflows exceed the initial cash outflows. That is the payback year. Then we take the previous year and add to it
the fraction calculated as the unrecovered balance at the end of that year divided by the following year’s cash flow.
Generally speaking, the shorter the payback period, the better the investment.
(2.) What is the rationale for the payback method? According to the payback criterion, which franchise or
franchises should be accepted if the firm’s maximum acceptable payback is 2 years, and if Franchise L and S are
independent? If they are mutually exclusive?
Answer: See Chapter 12 Mini Case Show
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A B C D E F G H I J K L M N O P Q R S
Discounted Payback: 1.9
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operation. However, it would then take another year, and $5 million of costs, to demolish the site and return it to its
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IRR M 2 = 400%
The two solutions to this problem tell us that this project will have a positive NPV for all costs of capital between 25%
and 400%. We illustrate this point by creating a data table and a graph of the project NPVs.
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A B C D E F G H I J K L M N O P Q R S
Franchise L
Time period: 0 1 2 3 4
Cash flow: (100) 10 60 80 0
Disc. cash flow: (100) 950 60 0
Disc. cum. cash flow: (100) (91) (41) 19 19
Discounted Payback: 2.7
Multiple IRRs
NPVM = ($386.78)
IRR M 1 = 25.0% MIRR = 5.6%
(4.) What is the main disadvantage of discounted payback? Is the payback method of any real usefulness in capital
We will solve this IRR twice, the first time using the default guess of 10%, and the second time we will enter a guess
of 200%. Notice, that the first IRR calculation is exactly as it was above.
j. As a separate project (Project P), you are considering sponsoring 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
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extent), it still falls short of fully analyzing projects. However, all else equal, these two methods do provide some
information about projects’ liquidity and risk.
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A B C D E F G H I J K L M N O P Q R S
r = 25.0%
NPV = 0.00
NPV
r$0.0
0% (800.00)
25% 0.00
50% 311.11
75% 424.49
100% 450.00 Max.
125% 434.57
475% (81.66)
500% (105.56)
525% (128.00)
550% (149.11)
PROJECTS WITH UNEQUAL LIVES
Year Project T Project R
0($100,000) ($100,000)
Project T r: 10.0%
k. In an unrelated analysis, you have the opportunity to choose between the following two mutually exclusive
projects, Project T (which lasts for two years) and Project F (which lasts for four years):
(1.) What is each project’s initial NPV without replication?
The projects provide a necessary service, so whichever one is selected is expected to be repeated into the
foreseeable future. Both projects have a 10% cost of capital.
(3.) Draw Project P’s NPV profile. Does Project P have normal or nonnormal cash flows? Should this project be accepted?
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600
NPV ($)
Multiple Rates of Return
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150% 400.00
175% 357.02
200% 311.11
225% 265.09
250% 220.41
275% 177.78
300% 137.50
425% (29.02)
450% (56.20)
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End of Period:
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Operating
Cash Flow
Salvage
Value
(2.) Would the NPV change if the company planned to terminate the project at the end of Year 2?
A B C D E F G H I J K L M N O P Q R S
Equivalent Annual Annuity (EAA) Approach
Here are the steps in the EAA approach.
2. Convert the NPV into an annuity payment with a life equal to the life of the project.
EAAT = $1.95 Note: we used Excel’s PMT function by using the function wizard.
EAAF = $2.38
Project T
Project T
ECONOMIC LIFE VS. PHYSICAL LIFE
Year
Operating
Cash Flow
Salvage
Value
0($5,000) $5,000
1$2,100 $3,100
2$2,000 $2,000
3$1,750 $0
(3.) Now apply the replacement chain approach to determine the projects’ extended NPVs. Which project should
be chosen?
l. 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:
(1.) Using the 10% cost of capital, what is the project’s NPV If it is operated for the full 3 years?
End of Period:
(2.) What is each project’s equivalent annual annuity?
(4.) Now assume that the cost to replicate Project T in 2 years will increase to $105,000 because of inflationary
pressures.
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A B C D E F G H I J K L M N O P Q R S
2-Year NPV =
Initial Cost +
PV of
Operating
Cash Flow
+
PV of
Salvage
Value
=($5,000.00) +$3,561.98 +$1,652.89
2-Year NPV = $214.88
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Operating
1-Year NPV = ($272.73)