When comparing 2 options using ROR, use the IRR of the difference between
cash flows.
Do not rank option by individual IRR.
Example: MARR=6% $15,000 to
spend
Cash Flow
Year
Option
A
Option
B
B-A
0
-10,000 -15,000
-5000
1
3000
5000
2000
2 5000
5000
0
3
2000
5000
3000
4
4000
5000
1000
IRR (Found
by
14.96%
12.59%
7.71%>MARR
any correct
method)
Choose B.
Option A and B > MARR .Hence acceptable.
Cash flow B-A > MARR. So
expenditure of added $5000 is justified. Why?
Option A -- Extra $5000 not used is invested @ the MARR.
Weighted
IRR(A) = 10(14.96)+5(6) =
11.97%
15
IRR(B) = 12.59%
Choose B.
IRR is not always consistent with PW or AW results.
Another extreme incremental Rate of return example:
MARR=5%
Option
0 1
2 3
IRR
PW(5)
A
-$1 $10 $10 $10
999% $23.87
B
-$100
$100
$100 $100
84%
$148.69
B-A
-$99
$90 $90
$90 73.5% $124.82
WTD ROR(A) = 1(999)+99(5) =
14.94%
100
WTD ROR(B) = 84%
Even
though option A yields 999%, it is with very little
return.
Option B yields a greater monetary gain with a
lesser, yet acceptable IRR.
Why use IRR analysis?
Types of Alternatives
To this point we have not discussed the types of alternatives, that we are analyzing. They are:
Mutually Exclusive
If in choosing one option, it precludes the choice of any other
option.
Usually are ranked against one another through many means, including
incrementally.
Only one, that with the best incremental IRR over any that have
IRR>MARR.
Example: Buy new generator from vendor A or
B?
Hire 4,5 or 6 new staff
members?
Route pipeline on alignment A, B or
C?
Contingent Proposals
Alternatives are contingent upon other alternatives.
A - Do
nothing and continue as before
B - Purchase new
bulldozer.
C - Purchase maintenance contract for new
bulldozer.
C is contingent upon B.
Can be converted to 3 mutually
exclusive alternatives.
A - Do nothing
B'
- Purchase new bulldozer w/o maintenance contract.
C'
- Purchase new bulldozer with maintenance contract.
Now choose A,B' or
C' = Mutually exclusive.
Independent Alternatives
The choice of one has no effect on whether another can be chosen.
All
alternatives w/ IRR>MARR can be accepted.
Example: Considering following
upgrades to a service
truck
Alternative
Cost
A - Hydraulic
hoist
$3000
B - Paint spray
unit
$4000
C - Power wash
unit $7000
Any can be chosen that
provides benefits that yields IRR>MARR.
What if you only have $7000 to spend ?
The problem is then financially
constrained and can be converted to mutually exclusive alternatives that are
feasible.
Package Alternative Cost
1 Do
nothing
0
2
A
$3000
3
B
$4000
4
C
$7000
5
A+B $7000
Mutually
exhaustive alternatives are the fundamental unit of interest, in most every
economic analysis.
Analysis of Multiple Mutually Exclusive Alternatives (MEA's)
When you have multiple MEA (3 or more) a standard procedure helps, to be able to determine which alternative to choose.
Multiple MEA Method
1. Order the alternatives from lowest to highest initial
investment (I.I.).
2a. If the alternatives are "Cash
producing"
Defender--->
Do nothing -- Go to
step 3
Challenger--->
Lowest I.I. -- Go to step 3
b. If alternatives are all
negative
Defender---> Lowest I.I. -- Go to step
4
Challenger--->Next higher I.I. -- Go to step 4
3. Compute i*
for Challenger
If i* > MARR ----> Challenger is now
defender
If i* < MARR ----> Continue to next highest I.I.
until i* > MARR
4. Find incremental IRR between
Challenger and
defender.
Incremental cash flow = Challenger cash flow - Defender cash
flow.
5. Find i* for
ICF
6. If i*(ICF)>MARR Challenger = >
Defender. Remove defender.
If i*(ICF)<MARR keep defender, go to next
I.I.
7. Repeat steps 4-6 until one alternative remains.
Example : Four different buildings can be constructed at
different sites, with each one presenting its own savings,
cash flows due to various factors. Only one site will be used. Which should
be
constructed?
MARR=10%
N=30yrs
Location
A
B C
D
Building
cost $200,000 $275,000 $190,000 $350,000
Annual cash
flow
$22,000 $35,000
$19,500 $42,000
Step
(1) (2) (3)
(4)
Location C A
B
D
1st cost,
$ 190,000 200,000 275,000 350,000
Cash flow,
$ 19,500 22,000
35,000
42,000
Comparison C to
do-no A to do-no B to
A D to
B
Inc.1st cost,
$ 190,000 200,000 75,000 75,000
Inc.Cash
flow,$ 19,500 22,000
13,000 7,000
(P/A,
i*,30) 9.7436
9.0909
5.7692
10.7143
i*,
%
* 9.63 10.49
17.28
8.55
Increment justified No,
i*<MARR Yes
Yes No
Project selected Do
nothing
A
B
B
Choose
B.
*
By Excel or chart interpolation
or dispense with finding
i* until the final alternative is found, instead using
(P/A,
i*,30) compared to (P/A,10,30) =
9.4269
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