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d. 1. Define the term internal rate of return (IRR). What is each franchise’s IRR?
0 = SUM OF PVs = NPV.
website, in whole or in part.
A financial calculator is extremely helpful when calculating IRRs. The cash flows
23.6%. Note that with many calculators, you can enter the cash flows into the cash
flow register, also enter r = I/YR, and then calculate both NPV and IRR by pressing
the appropriate buttons.
d. 2. How is the IRR on a project related to the YTM on a bond?
d. 3. What is the logic behind the IRR method? According to IRR, which franchises
should be accepted if they are independent? Mutually exclusive?
economic loss, or a project that will not earn enough to cover its cost of capital.
d. 4. Would the franchises’ IRRs change if the cost of capital changed?
website, in whole or in part.
e. 1. Draw NPV profiles for Franchises L and S. At what discount rate do the profiles
cross?
Answer: The NPV profiles are plotted in the figure below.
Mini Case: 10 - 34
website, in whole or in part.
4. From the figure below, it appears that the crossover rate is between 8% and 9%.
The precise value is approximately 8.7%. One can calculate the crossover rate by
(1) going back to the data on the problem, finding the cash flow differences for
each year, (2) entering those differences into the cash flow register, and (3)
pressing the IRR button to get the crossover rate, 8.68% ≈ 8.7%.
r
NPVL
NPVS
0%
$50
$40
5
33
29
10
19
20
15
7
12
20
(4)
5
e. 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%?
Answer: The NPV profiles show that the IRR and NPV criteria lead to the same accept/reject
decision for any independent project. Consider Franchise L. It intersects the X-axis
at its IRR, 18.1%. According to the IRR rule, L is acceptable if r is less than 18.1%.
Also, at any r less than 18.1%, L’s NPV profile will be above the X-axis, so its NPV
will be greater than $0. Thus, for any independent project, NPV and IRR lead to the
rule says choose S. Thus, if r is less than the crossover rate, a ranking conflict occurs.
f. What is the underlying cause of ranking conflicts between NPV and IRR?
Answer: For normal projects’ NPV profiles to cross, one project must have both a higher
conclude that NPV profiles can cross in two situations: (1) when mutually exclusive
projects differ in scale (or size) and (2) when the projects’ cash flows differ in terms
of the timing pattern of their cash flows (as for Franchises L and S).
g. Define the term modified IRR (MIRR). Find the MIRRs for Franchises L and S.
0 1 2 3
| | | |
$100 =
3
)MIRR1(
10.158$
.
PV costs =
N
)MIRR1(
TV
=
N
0t t
t
)r1(
COF
=
N
N
1t
tN
t
)MIRR1(
)r1(CIF
.
After you calculate the TV, enter N = 3, PV = -100, PMT = 0, FV = 158.1, and then
press I/YR to get the answer, MIRRL = 16.5%. We could calculate MIRRS similarly:
MIRRS = 16.9%. Thus, Franchise S is ranked higher than L. This result is consistent
with the NPV decision.
h. What does the profitability index (PI) measure? What are the PI’s for
Franchises S and L?
PIS = $119.98 / $100 = 1.1998.
r = 10%
Mini Case: 10 - 37
i. 1. What is the payback period? Find the paybacks for Franchises L and S.
0 ($100) ($100)
1 10 (90)
2 60 (30)
3 80 50
i. 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 Franchises L and S are
independent? If they are mutually exclusive?
Payback is
between t = 2
and t = 3
i. 3. What is the difference between the regular and discounted payback periods?
0 ($100) ($100.00) ($100.00)
1 10 9.09 (90.91)
2 60 49.59 (41.32)
3 80 60.11 18.79
i. 4. What is the main disadvantage of discounted payback? Is the payback method
of any real usefulness in capital budgeting decisions?
