Consider the project
with the following expected cash flows: Year Cash
flow 0 - $600,000 1 70,000 2 140,000 3 +$600,000
If the discount rate is 0%, what is the project's
net present value? If the discount rate is 5%,
what is the project's net present value? What
is this project's internal rate of return?
The internal rate of return of the project is
10%. Net present value at 0% and 5 % are as follows:
Year Cash Flow Present value factor at 0% Present
Value at 0%
0 -600,000 1 -600,000
1 70,000 1 70,000
2 140,000 1 140,000
3 600,000 1 600,000
Year Cash Flow Present value factor at 5% Present
Value at 5%
0 -600,000 0.9523 -571,380
1 70,000 0.9523 66,661
2 140,000 0.9523 133,322
3 600,000 0.9523 571,380
Consider a project with the expected cash flows:
Year Cash flow 0 - $48,000 1 + 48,000 2 + 93,000
3 - $93,000. What is this project's internal rate
of return? If the discount rate is 5%, what is
this project's net present value?
Year Cash Flow Present value factor at 5% Present
Value at 5%
0 -48,000 0.9523 -45,710
1 48,000 0.9523 45,710
2 93,000 0.9523 88,564
3 -93,000 0.9523 -88,564
The internal rate of return for this project
is un-calculate able.
Part 2. Read the article linked below. Then write
a one to two page paper answering the following
question: Which method do you think is the better
one for making capital budgeting decisions
- IRR or NPV? Defend your answer with references
to the background materials.
- IRR does not keep track of the sign. This is
misdirected. If you borrow money, you will pay
the interest, not receive it. Interest rate tables
use positive amounts and rates. Interest rate
calculation routines use positive principal. We
are accustomed to keeping track of borrower and
lender outside the actual
calculations.
- IRR can supposedly give a different decision
from NPV on mutually exclusive projects.
- More than one IRR is possible with multiple
sign changes. Additional IRRs can occur if the
signs of the cash flows change more than once.
Not uncommonly, this criticism is combined with
Criticism Number One (negative versus positive
flows) and presented as the inverted project K.
This unnecessarily complicates the picture.
- The technique of evaluating differences (also
called incremental flows) bypasses the problem
with different size projects. It is also a practical
way to analyze the difference between alternatives
with cash outflows only—a government Economic
Analysis (EA) for example.
- NPV and IRR can be used together when evaluating
different sized projects. If there is an apparent
conflict, simply understand what is causing it
and present the information differently if necessary.
Of course, more realistically comparable investments,
such as Projects F and H, IRR and NPV give the
same answer regardless. Still, both NPV and IRR
give a clearer picture than either alone gives.
- Under some circumstances IRR is incalculable.
This is perhaps the most serious criticism of
IRR. But IRR critics overlook that this is not
much of a problem in practice and it applies to
NPV as well. The only difference is that it is
not as obvious with NPV as it is with IRR. IRR
is incalculable in at least five circumstances.
First, IRR cannot be calculated if cash flows
are all positive.
- A second circumstance in which IRR is incalculable
is when cash flows are all negative. This, like
the all-positive case, needs no further consideration:
It is a giveaway and follows the same reasoning
as the all-positive case.
- A third circumstance in which a positive IRR
is incalculable is when net cash flows are zero—say
+$1,000 in year 1 and
-$1,000 in year 2.
- The fourth circumstance under which IRR is incalculable
is subtler. It occurs with certain other combinations
of cash flows not described above. See Table 10.
With a positive cash flow of $0.01 (1 cent), IRR
is calculable (IRR is positive but lost in rounding).
With a net negative cash flow of 1 cent, NPV diverges
from zero and IRR is incalculable. If year 0 and
year 1 cash flows are the same, cash flows are
zero and IRR incalculable. If we decrease year
1 revenue by 1 cent (-$0.01) to $999.99, NPV is
negative at any positive discount rate and IRR
is incalculable.
|