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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.
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
11/20/2018
Situation
Franchise S
Year (t) Franchise S Franchise L Year 0 1 2 3
0-$100 -$100 CF -100 70 50 20
170 10
250 60 Franchise L
320 80
Year 0 1 2 3
CF -100 10 60 80
Franchise S
Time period: 0 1 2 3
Cash flow: -100 70 50 20
Disc. cash flow: -100 64 41 15
NPV(S) = $19.98 = Sum disc. CF’s. or $19.98
= Uses NPV function.
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.
a. What is capital budgeting? Answer: See Chapter 10 Mini Case Show
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
Notice that the NPV function isn‘t really a net present value.
Instead, it is the present value of future cash flows. Thus,
you specify only the future cash flows in the 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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NPV(L) = $18.78 $18.78
= Uses NPV function.
rationale 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 projects, you would want to
they
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Note: You can use the Rate function if
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 9 50 60
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%
Constant Cash Flows
(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 its
outflows. It is the discount rate that forces the PV of the inflows to equal the initial cost. In other words, the internal rate of
return is the interest rate that forces NPV to zero. The calculation for IRR can be tedious, but Excel provides an IRR function
that merely requires you to access the function and enter the array of cash flows. The IRR’s 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?
(2.) How is the IRR on a project related to the YTM on a bond?
net cash flows
Expected
The IRR function
assumes payments
The IRR is the discount rate that forces the PV of a project’s expected future cash flows to equal the initial cash flow. This is
analogous to a bond’s yield because a bond’s yield is the discount rate that forces the present value of a bonds coupons
and maturity value to equal the price of the bond.
Suppose the initial cost of a project is $100 and it has cash flows of $40 at Years 1, 2, and 3. What is its IRR? Use the Excel
RATE function as though the project were a bond.
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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
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%
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 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 naturally arises is whether or not
the NPV and IRR methods will always arrive at the same conclusion.
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-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 project will have an NPV of zero.
Looking at our graph, it is a logical conclusion that the project IRR is defined as the point at which its profile intersects the
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%?
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 flows are
heavily penalized by high discount rates–the denominator is (1 + r)t, and it increases geometrically; hence, it gets very large
at high values of t. (2) Long-term projects like L have most of their cash flows coming in the later 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 cross one another.
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. To find MIRR, use Excel’s MIRR function. Alternatively, calculate the PV of the outflows
and the FV of the inflows and then find the discount rate that equates the two.
(20)
(10)
0
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30
40
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60
0% 5% 10% 15% 20% 25%
NPV ($)
Cost of Capital
NPV Profile of Franchises S and L
Project L
Project S IRRS= 23.56%
IRRL= 18.13%
Crossover
Rate = 8.7%
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Year 0 1 2 3
CF (100) 70 50 20
MIRRS = 16.89%
A B C D E F G H I J K L M N O P Q R S
Year 0 1 2 3
CF (100) 10 60 80
66
12.1
PV = (100) TV = 158.1
MIRRL =16.50%
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For Franchise S:
For Franchise L:
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Payback: 1.600
Franchise L
Time period: 0 1 2 3
Cash flow: -100 10 60 80
Cumulative cash flow: -100 -90 -30 50
Payback: 2.375
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Franchise S
Time period: 0 1 2 3
Cash flow: -100 70 50 20
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
Franchise S
Time period: 0 1 2 3
Cash flow: -100 70 50 20
Cumulative cash flow: -100 -30 20 40
—1.60 —
Payback: 1.600
Discounted Payback Period
r = 10%
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 cash flows discounted at r back to t = 0. 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? If they
Intermediate calculation to
identify payback: