# IENG 302 Lecture 10: Incremental Analysis & IRR

```Internal Rate of Return
Internal Rate of Return (IRR):
The interest rate i* at which NPW = 0
Note: This is the same as finding the roots of a
polynomial equation. If there is more than one
sign change in the net annual cash flows over the
life of the project, then there is more than one
internal rate of return (root)!
We may find the IRR by either the manual method we
used for the bond yield, or we may use the
computer to find the roots by either plots or
numerical methods
1
IRR Example
Project A costs \$10,000 and will last for 10
years. Annual, end of year revenues will
be \$3000, and expenses will be \$1000.
There is no salvage value.
Project B costs \$20,000 and will also last for
10 years. Annual revenues will be \$4000
with annual expenses of \$1500. Salvage
value is \$14,500.
What is each project’s IRR?
2
Table Example
i*
(P/A, i*, 10)
(P/F, i*, 10)
6%
7.3601
.5584
8%
6.7101
.4632
10%
6.1446
.3855
12%
5.6502
.3220
18%
4.4941
.1911
Numerical Method Example: IENG 302 IRR.xls
3
25000
Project A
Net Present Worth (\$)
20000
Project B
15000
10000
5000
0
0
5
10
15
20
-5000
-10000
Interest Rate (% )
4
Decisions with IRR
When applied to project selection
among independent projects –
i.e. there are enough funds such
that any or all of the projects
may be selected – then investing
based on IRR is easy:
Select all projects with IRR > MARR!
Note: Make sure that there is only one IRR (root)!
5
Decisions with IRR
When applied to project selection
among mutually exclusive projects –
i.e. there is not enough money to do
them all – IRR can produce the
same result as NPW and EAW.
However, incremental analysis MUST
be used!
REASON: IRR is a relative measure of
project merit
6
Why Must Incremental
Analysis be Used for
Competing Projects?
Assume that an MARR of 16% per year is
required, and \$85 000 is available to invest:
• Project A requires \$50 000 upfront to obtain
an IRR of 35% per year.
• Project B requires an \$85 000 first cost and
returns an IRR of 29% per year.
• What could we do with the un-invested
money from Project A? (\$35 000)
7
Why Must Incremental
Analysis be Used for
Competing Projects?
It would be reasonable to invest the remaining
\$35 000 at the MARR:
• Overall IRRA = 50 000(.35) + 35 000(.16)
85 000
= 27.2% per year
• Project B returns an IRR of 29% per year on
ALL the money available to invest.
8
Incremental Analysis
A technique or approach that can
be used with NPW, EAW, and
later with IRR and Cost/Benefit
to determine if an incremental
Note: If using NPW or IRR, lifetimes must be equal –
so use Least Common Multiple or Study Period!
9
Incremental Analysis
Incremental Analysis can used by putting
the options in the order of increasing initial
investment.
Check the feasibility of the first investment.
• If it is feasible, then you consider the
increment to the next level of investment.
• If it is not feasible, then you check the
second investment alternative for
feasibility, and so on until all options are
considered.
10
Incremental Analysis
Incremental Analysis can also be
incurring an expense
(e.g., DSL internet service)
and you are trying to determine if
it is a good decision to spend
(e.g., satellite or cable?).
11
Steps of the Process
1. Order alternatives from lowest to highest
initial investment.
2. Let Alternative A0 (do nothing) be considered
the current best.
3. Consider next Alternative ( j = j+ 1)
4. Determine cash flows for “current best” and
Alternative j.
5. Determine incremental cash flows between
“current best” and Alternative j.
6. Calculate PW, AW, FW, IRR (or Benefit/Cost)
of only the incremental cash flows.
12
Steps of the Process
7. If incremental investment yields NPW,
EAW, or a NFW > 0*, then the new
“current best” becomes Alternative j.
* (B/C ratio > 1, or IRR > MARR)
8. If there are remaining alternatives, go to
Step 3.
9. If all alternatives have been considered,
select the “current best” alternative as
the preferred alternative.
13
i = 18%
Net Cash Flows for Alternatives A0 - A3
End of
Year, t
0
A0
A1
A2
A3
\$0
\$0
-\$50,000
-\$75,000
1
0
4,500
20,000
20,000
2
0
4,500
20,000
25,000
3
0
4,500
20,000
30,000
4
0
4,500
20,000
35,000
5
0
4,500
20,000
40,000
14
IRR Incremental Analysis
Rank projects from lowest to highest initial cost
Eliminate any projects with IRR < MARR
Starting from the least expensive project to the
next most expensive, justify each incremental
investment
• IRR HC-LC < MARR Accept LC Project
& Reject HC Project
• IRR HC-LC = MARR Indifferent
• IRR HC-LC > MARR Reject LC Project
& Accept HC Project
15
```

– Cards

– Cards

– Cards

– Cards

– Cards