1. Contemporary Engineering Economics
Incremental Analysis
Lecture No. 26
Chapter 7
Contemporary Engineering Economics
Copyright © 2016
In this section, we present the decision procedures that should be used in comparing two or more mutually exclusive projects on the basis of the rate-of-return measure. We will
consider two situations: (1) alternatives that have the same economic service life, and (2) alternatives that have unequal service lives.

2. Flaws in Project Ranking by IRR
AtIssue: Can we rank the mutually exclusive projects by the magnitude of its IRR?
Assuming that you have enough money to select either alternative, would you prefer A1 simply because it has a higher ROR?
Comparing Mutually Exclusive Alternatives Based on IRR
Under NPW or AE analysis, the mutually exclusive project with the highest worth was preferred. (This is known as the “total investment approach.”) Unfortunately, the analogy
does not carry over to IRR (or MIRR) analysis: The project with the highest IRR (or MIRR) may not be the preferred alternative.
To illustrate the flaws inherent in comparing IRRs in order to choose from mutually exclusive projects, suppose you have two mutually exclusive alternatives, each with a one year
service life: One requires an investment of $1,000 with a return of $2,000, and the other requires $5,000 with a return of $7,000. You already obtained the IRRs and NPWs
at MARR = 10% as given in Table.
Sonra:
We can see that A2 is preferred over A1 by the NPW measure. On the other hand, the IRR measure gives a numerically higher rating for A1. This inconsistency in ranking
occurs because the NPW, NFW, and AE are absolute (dollar) measures of investment worth, whereas the IRR is a relative (percentage) measure and cannot be applied in the
same way. That is, the IRR measure ignores the scale of the investment. Therefore, the answer to our question in the previous paragraph is no; instead, you would prefer the
second project with the lower rate of return but higher NPW. Either the NPW or the AE measure would lead to that choice, but a comparison of IRRs would rank the smaller
project higher. How do we resolve this inconsistency in ranking the projects? Another approach, referred to as incremental analysis, is needed.

3. Who Got a Bigger Pay Raise?
At Issue: Can you say that Bill got a bigger raise than Nancy?
10%
Bill 5%
Nancy

4. Cannot Compare Without Knowing Their Base Salaries
For the same reason, we can’t compare mutually exclusive projects based on the magnitude of their IRR. We need to know the size of the investment and its timing of cash flows over the life of the project.
Bill
Nancy
Base Salary
$50,000
$200,000
Pay Raise (%)
10% 5%
Pay Raise ($)
$5,000
$10,000

5. Incremental Analysis Incremental cash flows
At Issue: Can we justify the higher cost investment, say A2? Suppose you have exactly $5,000 to invest and MARR = 10%.
Option 1: If you go with A1, the $4,000 of unspent funds will remain in your investment pool to earn 10%, so you will have $4,400 at the end of one year.
Option 2: By investing the additional $4,000 in A2, you would make an additional $5,000, which is equivalent to earning at the rate of 25%. Therefore, the higher cost investment (A2) is justified.

6. Incremental Analysis (Procedure)
Step 1: Compute the cash flow series 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).
Step 2: Compute the IRR on this incremental investment (IRRB-A ).
Step 3: Accept the investment B if, and only if, IRR B-A>MARR.
Now we can generalize the decision rule for comparing mutually exclusive projects. For a pair of mutually exclusive projects (A and B, with B defined as the more costly option),
we may rewrite B as
A = A
incremental investment
B = A + (B - A)
En Sonda:
If a “do-nothing” alternative is allowed, the smaller cost option must be profitable (its IRR must be greater than the MARR) at first. This means that you compute the rate of return for each alternative in the mutually exclusive group and then eliminate the alternatives whose IRRs are less than the MARR before applying the incremental analysis. It may seem odd to you how this simple rule always allows us to select the right project. Example 7.11 illustrates the incremental investment decision rule.
NOTE: Make sure that both IRRA and IRRBare greater than MARR.

7. Example 7.11: IRR on Incremental Investment: Two Alternatives
Given: Project Cash Flows
Find: Which project is a better choice at MARR = 10%?

8. Solution Project Cash Flows
Conclusion
Since IRRB2-B1=15% > 10%, and also IRRB2 > 10%, select B2.

9. Example 7.12: IRR on Incremental Investment: Three Alternatives
Given: MARR = 15%
Find: Which project to choose?
When you have more than two mutually exclusive alternatives, they can be compared in pairs by successive examination. Example 7.13 illustrates how to compare three mutually exclusive alternatives.

10. Solution
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.

11. Example 7.14: Incremental Analysis for Service Projects
At Issue: Can we compare mutually exclusive service projects based on IRR criterion?
Falk Corporation is considering two types of manufacturing systems to produce its shaft couplings over six years: (1) a cellular manufacturing system (CMS), and (2) a flexible manufacturing system (FMS). The average number of pieces to be produced with either system would be 544,000 per year. The operating cost, initial investment, and salvage value for each alternative are estimated as given in Table.

12. Solution Given: MARR = 15%, incremental cash flows (FMS-CMS)
Find: Select the better alternative on the basis of IRR criterion.
ROR on Incremental Investment
Comments: Note that the CMS option is marginally preferred to the FMS option. However, there are risks in relying solely on the easily quantified savings in input factors—such as labor, energy, and materials—from the FMS and in not considering gains from improved manufacturing performance that are more difficult and subjective to quantify. Factors such as improved product quality, increased manufacturing flexibility (rapid response to customer demand), reduced inventory levels, and increased capacity for product innovation are frequently ignored, because we have inadequate means for quantifying their benefits. If these intangible benefits were considered, the FMS option could come out better than the CMS option.

13. Example 7.15: IRR Analysis for Projects with Different Lives
At Issue: Can we compare projects with different service lives based on the principle of IRR criterion?
Given: MARR = 15%, incremental cash flows on service projects (Model B − Model A)
Find: Which model to select?
In Chapters 5 and 6, we discussed the use of the NPW and AE criteria as bases for comparing projects with unequal lives. The IRR measure also can be used to compare projects with unequal lives, as long as we can establish a common analysis period. The decision procedure is then exactly the same as for projects with equal lives. It is likely, however, that we will have a multiple-root problem, which creates a substantial computational burden. For example, suppose we apply the IRR measure to a case in which one Project has a five-year life and the other project has an eight-year life, resulting in a least common multiple of 40 years. Then when we determine the incremental cash flows over the analysis period, we are bound to observe many sign changes. This leads to the possibility of having many i*s. Example 7.14 uses i* to compare mutually exclusive projects in which the incremental cash flows reveal several sign changes. (Our purpose is not to encourage you to use the IRR approach to compare projects with unequal lives; rather, it is to Show the correct way to compare them if the IRR approach must be used.)

14. Solution
Assumptions: Project repeatability is likely. Use LCM of 12 years.
The incremental cash flows (Model B − Model A) result in a mixed investment. We need to calculate the RIC at 15%.
RICB–A = 50.68% > 15%
Select Model B.

15. 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 methods.

16. 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 the rate of return analysis correctly, we need to classify an investment as either a simple or a nonsimple investment.

17. A simple investment is defined as one in which the initial cash flow is negative and only one sign change occurs in the net cash flow series, 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. A unique positive i* for a project does not imply a simple investment.

18. For a pure investment, the solving rate of return (i
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, otherwise known as the “return on invested capital (RIC).” However, if your objective is simply to make an accept or reject decision, it is recommended that either NPW or AE analysis be used to make an accept/reject decision.
To compare mutually exclusive alternatives by IRR analysis,incremental analysis must be adopted.