Steps of the Incr. Analysis 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.
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Steps of the Incr. Analysis 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.
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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
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IRR Incr. Analysis Example
Life = 9 years Project A Project B Project C Project D Project E
1st Cost
75
25
15
45
65
Annual Revenue
25
5
2
20
20
Salvage
40
----10
50
IRR 20.6%
12.7%
8.0%
23.8%
15.3%
Find the single, best option if:
1.) MARR = 11%/year
a.) What is the comparison order?
b.) For the 1st Comparison:
Increment
IRR Increment
A-B
27.6%
A-C
26.8%
A-D
16.7%
A-E
50.0%
Find the incremental 1st Cost:
Find the incremental Ann. Revenue:
Increment
IRR Increment
B-A
27.6%
B-C
24.0%
B-D
55.7%
B-E
19.1%
Find the incremental Salvage:
Give the IRR Equation:
Increment
IRR Increment
C-A
26.8%
C-B
24.0%
C-D
41.2%
C-E
20.6%
Increment
IRR Increment
D-A
16.7%
D-B
55.7%
D-C
41.2%
D-E
0.0%
2.) MARR = 18%/year
3.) MARR =15
22%/year
Increment
IRR Increment
E-A
50.0%
E-B
19.1%
E-C
20.6%
E-D
0.0%
4.) MARR = 7%/year
5.) MARR = 25%/year
Perform the incremental comparison:
c.) Perform (b.) for the 2nd Comparison:
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