Incremental Analysis
Ismu Kusumanto
Pengertian
Incremental analysis is used to find the impact
of changes in costs or revenues, given a
specific potential scenario. Decisions involving
incremental analysis include the following:

Sell or process further: Sell or process further issues
often arise in industries which refine raw materials. The
key question is whether the incremental revenues from a
more highly refined product will at least offset the
increased costs associated with additional processing
Pengertian

Make or buy: Should we make a component ourselves
or farm out the work to someone else? Qualitative
considerations may or may not override quantitative
issues. For example, we may be able to subcontract
work more economically than we can do it ourselves, but
if the contractor is unable to maintain the necessary level
of quality or meet delivery schedules, subcontracting
may not be worthwhile. The impact of quality and/or
delivery problems may not be quantifiable, thus making
the whole business a judgment call.
Pengertian

Changes in production and/or technology:
Modifications in production processes or
acquisition of new machinery typically entail
adjustments in costs. New machinery or a
revised process may enhance efficiency in the
use of labor and/or material. It is clearly
important to know whether the improvements
offset whatever incremental costs may be
associated with the changes.
Types of Incremental Analysis
A number of different types of decisions involve
incremental analysis. The more common types of
decisions are whether to:
1) Accept an order at a special price.
2) Make or buy.
3) Sell or process further.
4) Retain or replace equipment.
5) Eliminate an unprofitable business segment.
6) Allocate limited resources.
MANAGEMENT’S
DECISION MAKING PROCESS

Considers both financial and
nonfinancial information

Financial information
 Revenues and costs
 Overall profitability

Nonfinancial information
 Effect of decision on
employee turnover
 Environment
 Overall image of company
Comparing Mutually Exclusive
Alternatives Based on IRR
• Issue: Can we rank the mutually exclusive
projects by the magnitude of its IRR?
n
A1
A2
0
-$1,000
-$5,000
1
$2,000
$7,000
IRR
100%
>
40%
$818
<
$1,364
PW (10%)
Who Got More Pay Raise?
Bill
Hillary
10%
Contemporary
Engineering Economics,
5%
Can’t Compare without Knowing Their
Base Salaries
Bill
Hillary
Base Salary
$50,000
$200,000
Pay Raise (%)
10%
5%
Pay Raise ($)
$5,000
$10,000
For the same reason, we can’t compare mutually exclusive projects based on
the magnitude of its IRR. We need to know the size of investment and its timing
of when to occur.
Incremental Investment
n
0
1
ROR
PW(10%)
Project A1
-$1,000
$2,000
100%
$818
Project A2
-$5,000
$7,000
40%
$1,364
Incremental
Investment
(A2 – A1)
-$4,000
$5,000
25%
$546
• Assuming a MARR of 10%, you can always earn that rate from other
investment source, i.e., $4,400 at the end of one year for $4,000
investment.
• By investing the additional $4,000 in A2, you would make additional
$5,000, which is equivalent to earning at the rate of 25%. Therefore,
the incremental investment in A2 is justified.
Incremental Analysis (Procedure)
Step 1:
Step 2:
Step 3:
Compute the cash flow for the difference
between the projects (A,B) by subtracting
the cash flow of the lower investment
cost project (A) from that of the higher
investment cost project (B).
Compute the IRR on this incremental
investment (IRRB-A ).
Accept the investment B if and only if
IRR B-A > MARR
NOTE: Make sure that both IRRA and IRRB are greater than MARR.
Example 7.10 - Incremental Rate of Return
n
0
1
2
3
IRR
B1
B2
-$3,000 -$12,000
1,350
4,200
1,800
6,225
1,500
6,330
25%
17.43%
B2 - B1
-$9,000
2,850
4,425
4,830
15%
Given MARR = 10%, which project is a better choice?
Since IRRB2-B1=15% > 10%, and also IRRB2 > 10%, select B2.
IRR on Increment Investment:
Three Alternatives
n
0
D1
D2
D3
-$2,000 -$1,000 -$3,000
1
1,500
800
1,500
2
1,000
500
2,000
3
800
500
1,000
IRR
34.37% 40.76% 24.81%
Step 1: Examine the IRR for each
project to eliminate any project
that fails to meet the MARR.
Step 2: Compare D1 and D2 in pairs.
IRRD1-D2=27.61% > 15%,
so select D1. D1 becomes the
current best.
Step 3: Compare D1 and D3.
IRRD3-D1= 8.8% < 15%,
so select D1 again.
Here, we conclude that D1 is the best
alternative.
For example, assume the ABC Company is
planning to expand its productive capacity. The plan
consists of purchasing a new machine for $50,000
and disposing of the old machine without receiving
anything for it. The new machine has a five-year
life. The old machine has a five-year remaining life
and a book value of $12,500. The new machine will
reduce variable operating costs from $35,000 per
year to $20,000 per year. Annual sales and other
operating costs are shown below:
At first glance, it appears that the new machine
provides an increase in net income of $7500 per
year. The book value of the present machine,
however, is a sunk cost and is irrelevant in this
decision. Furthermore, sales and fixed costs such
as insurance and taxes are also irrelevant since
they do not differ between the two alternatives
being considered. Eliminating all the irrelevant
costs leaves us with only the incremental costs, as
follows:
Savings in variable costs $15,000
Less: Increase in fixed costs 7,500
Net annual cash savings arising from the new
machine $ 7,500
Practice Problem
You are considering
four types of
engineering designs.
The project lasts 10
years with the following
estimated cash flows.
The interest rate
(MARR) is 15%. Which
of the four is more
attractive?
Project
A
B
C
D
Initial cost
$150
$220
$300
$340
Revenues/
Year
$115
$125
$160
$185
Expenses/
Year
$70
$65
$60
$80
27.32
24.13
31.11
28.33
IRR (%)
Example 7.13 Incremental Analysis for Cost-Only
Projects
Items
CMS Option
FMS Option
Annual O&M costs:
Annual labor cost
$1,169,600
$707,200
832,320
598,400
3,150,000
1,950,000
Annual tooling cost
470,000
300,000
Annual inventory cost
141,000
31,500
Annual income taxes
1,650,000
1,917,000
Total annual costs
$7,412,920
$5,504,100
Investment
$4,500,000
$12,500,000
$500,000
$1,000,000
Annual material cost
Annual overhead
cost
Net salvage value
Incremental Cash Flow (FMS – CMS)
n
CMS Option
FMS Option
Incremental
(FMS-CMS)
0
-$4,500,000
-$12,500,000
-$8,000,000
1
-7,412,920
-5,504,100
1,908,820
2
-7,412,920
-5,504,100
1,908,820
3
-7,412,920
-5,504,100
1,908,820
4
-7,412,920
-5,504,100
1,908,820
5
-7,412,920
-5,504,100
1,908,820
6
-7,412,920
-5,504,100
Salvage
+ $500,000
+ $1,000,000
$2,408,820
Solution:
PW (i) FMS CMS  $8,000,000
$1,908,820( P / A, i,5)
$2,408,820( P / F, i,6)
0
IRRFMS CMS  12.43%  15%,
select CMS.
Example 7.14 IRR Analysis for Projects
with Different Lives
MARR = 15%
 The incremental cash flows
(Model B – Model A) result
in a nonsimple and mixed
investment.
RICB–A = 50.68% > 15%
Select Model B
Summary



Rate of return (ROR) is the interest rate earned on
unrecovered project balances such that an investment’s cash
receipts make the terminal project balance equal to zero.
Rate of return is an intuitively familiar and understandable
measure of project profitability that many managers prefer to
NPW or other equivalence measures.
Mathematically we can determine the rate of return for a
given project cash flow series by locating an interest rate that
equates the net present worth of its cash flows to zero. This
break-even interest rate is denoted by the symbol i*.




Internal rate of return (IRR) is another term for ROR that
stresses the fact that we are concerned with the interest
earned on the portion of the project that is internally invested,
not those portions that are released by (borrowed from) the
project.
To apply rate of return analysis correctly, we need to classify
an investment into either a simple or a nonsimple investment.
A simple investment is defined as one in which the initial
cash flows are negative and only one sign change occurs in
the net cash flow, whereas a nonsimple investment is one for
which more than one sign change occurs in the net cash flow
series.
Multiple i*s occur only in nonsimple investments. However,
not all nonsimple investments will have multiple i*s either.



For a pure investment, the solving rate of return (i*) is the
rate of return internal to the project; so the decision rule is:
If IRR > MARR, accept the project.
If IRR = MARR, remain indifferent.
If IRR < MARR, reject the project.
IRR analysis yields results consistent with NPW and other
equivalence methods.
For a mixed investment, we need to calculate the true IRR, or
known as the “return on invested capital.” However, if your
objective is simply to make an accept or reject decision, it is
recommended that either the NPW or AE analysis be used to
make an accept/reject decision.
To compare mutually exclusive alternatives by the IRR
analysis, the incremental analysis must be adopted.