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a. What is capital budgeting? Answer: See Chapter 12 Mini Case Show
b. What is the difference between independent and mutually exclusive projects? Answer: See Chapter 12 Mini Case
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NPV(S) = $19.98 = Sum disc. CF’s. or $19.98 = Uses NPV function.
To find the true NPV, you must add the time zero cash flow to
the result of the NPV function.
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A B C D E F G H I J K L M N O P Q R
1/1/2015
Situation
Franchise S
Year (t)
Franchise S
Franchise L 0 1 2 3
Net Present Value (NPV)
r = 10%
Chapter 12. Mini Case
Expected
Net Cash Flows
You have narrowed your selection down to two choices: (1) Franchise L, Lisa’s Soups, Salads, & Stuff, and (2)
Franchise S, Sam’s Fabulous Fried Chicken. The net cash flows shown below include the price you would receive for
Here are the net cash flows (in thousands of dollars):
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
will go on to something else.
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?
To calculate the NPV, we find the present value of the individual cash flows and find the sum of those discounted
cash flows. This value represents the value the project add to shareholder wealth.
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(2.) How is the IRR on a project related to the YTM on a bond?
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A B C D E F G H I J K L M N O P Q R
Franchise L
Time period: 0 1 2 3
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 NPV method of capital budgeting dictates that all independent projects that have positive NPV should accepted.
(3.) Would the NPVs change if the cost of capital changed? Answer: See Chapter 12 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
its outflows. It is the discount rate that forces the PV of the inflows to equal the initial cost. In other words, the
d. (1.) Define the term internal rate of return (IRR). What is each franchise’s IRR?
net cash flows
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NPV(L) = $18.78 $18.78 = Uses NPV function.
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4% 31.32 4% 36.21
6% 27.33 6% 30.00
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axis at costs of capital of 18.13% and 23.56%, respectively. Not coincidently, those are the IRRs of the franchises. If
we think about the definition of IRR, we remember that the internal rate of return is the cost of capital at which a
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IRR = Crossover rate = 8.68%
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gets very large at high values of t. (2) Long-term projects like L have most of their cash flows coming in the later
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function.
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A B C D E F G H I J K L M N O P Q R
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$18.78
0% 40.00 0% 50.00
2% 35.53 2% 42.86
Cash Flow
Year (t)
Franchise S
Franchise L
Differential
Modified Internal Rate of Return (MIRR)
The modified internal rate of return is the discount rate that causes a project’s cost (or cash outflows) to equal the
present value of the project’s terminal value. The terminal value is defined as the sum of the future values of the
g. Define the term modified IRR (MIRR). Find the MIRRs for Franchises L and S.
(3.) What is the logic behind the IRR method? According to IRR, which franchises should be accepted if they are
independent?
Expected
Net Cash Flows
The intuition behind the relationship between the NPV profile and the crossover rate is as follows: (1) Distant cash
Looking further at the NPV profiles, we see that the two franchises profiles intersect at a point we shall call the
f. What is the underlying cause of ranking conflicts between NPV and IRR?
The IRR method of capital budgeting maintains that projects should be accepted if their IRR is greater than the cost of
capital. Strict adherence to the IRR method would further dictate that mutually exclusive projects should be chosen
on the basis of the greatest IRR. In this scenario, both franchises have IRRs that exceed the cost of capital (10%) and
Previously, we had discussed that in some instances the NPV and IRR methods can give conflicting results. First, we
should attempt to define what we see in this graph. Notice, that the two franchises’ profiles (S and L) intersect the X-
X-axis.
(4.) Would the franchises’ IRRs change if the cost of capital changed?
(2.) Look at your NPV profile graph without referring to the actual NPVs and IRRs. Which franchise or franchises
should be accepted if they are independent? Mutually exclusive? Explain. Are your answers correct at any cost of
capital less than 23.6%?
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NPV ($)
NPV Profile of Franchises S and L
Project L
Crossover Rate =
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A B C D E F G H I J K L M N O P Q R
10%
0 1 2 3
(100) 70 50 20
Franchise L
0 1 2 3
(100) 10 60 80
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Time period: 0 1 2 3
Cash flow: (100) 70 50 20
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r = 10%
Time period: 0 1 2 3
Cash flow: (100) 70 50 20
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A B C D E F G H I J K L M N O P Q R
PROFITABILITY INDEX
h. What does the profitability index (PI) measure? What are the PI’s for Franchises S and L?
For Franchise S:
PI(S) = PV of future cash flows ÷Initial cost
i. (1.) What is the payback period? Find the paybacks for Franchises L and S.
Payback Period
Franchise S
Franchise L
Time period: 0 1 2 3
Cash flow: (100) 10 60 80
Discounted 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.
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%.
(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?
For Franchise L: