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Lesson 44

Incremental Analysis for Multiple Alternatives

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Hello! Welcome back to your course on Engineering Economics.

In our last lesson, we established a crucial technique for choosing between two mutually exclusive alternatives: incremental rate of return analysis. We saw that simply picking the project with the highest IRR can be a trap, and that the correct approach is to analyze the return on the additional capital required for the more expensive option.

Today, we will build directly on that foundation. Our goal is to perform incremental analysis for multiple mutually exclusive alternatives. This is a common and practical challenge. For instance, when upgrading your company's server infrastructure, you might face several options: a basic setup, a more robust system, a high-availability cloud deployment, or a top-of-the-line on-premise cluster. Each is a valid, mutually exclusive choice, and this lesson will give you the systematic method to select the best one.

From Two to Many: The Need for a Procedure

When faced with more than two options (say, A, B, C, and D, ordered by cost), you can't simply compare the most expensive option (D) to the cheapest (A). Why not? Because the large incremental investment for D - A might be justified, while the smaller step from A to B (B - A) might have been a poor use of capital.

To handle this correctly, we need a process of sequential, pairwise comparisons. This involves establishing a current "best" option—the defender—and comparing it against the next most expensive option—the challenger.

The procedure ensures that every dollar of additional investment is individually justified against your Minimum Acceptable Rate of Return (MARR).

The Incremental Analysis Algorithm for Multiple Alternatives

The process is methodical and, given your software engineering background, you might appreciate its algorithmic nature. It ensures you arrive at the project that maximizes the economic value.

Vol. II, Essay 4: Financial Assessment

The following essay from MIT's OCW provides a clear, step-by-step procedure for this analysis. Let's focus on the formal steps.

First, please read the bulleted list under the heading 'The procedure illustrated in this example can be used with any set of mutually exclusive investment alternatives'. Then, read the similar list under the heading 'Choosing Among Mutually Exclusive Alternatives'. These sections formalize the process we are about to use.

Here is a summary of that step-by-step procedure:

  1. Order Alternatives: Arrange all mutually exclusive options in order of increasing initial investment cost. If doing nothing is an option, it's your first alternative with zero cost.
  2. Filter by Acceptability: Calculate the overall IRR for each individual alternative. Any alternative with an IRR less than the MARR is unacceptable and should be eliminated from consideration (unless all options are unacceptable, in which case "Do Nothing" wins).
  3. Establish the Defender: The first alternative on your ordered list that is acceptable (IRR ≥ MARR) becomes your initial "defender". This is your current best choice.
  4. Challenge the Defender: Take the next alternative on the cost-ordered list and designate it the "challenger".
  5. Perform Incremental Analysis:
    • Create the incremental cash flow stream by subtracting the defender's cash flows from the challenger's cash flows (Challenger - Defender).
    • Calculate the IRR of this incremental cash flow stream, IRR(Challenger-Defender).
  6. Make the Decision:
    • If IRR(Challenger-Defender) ≥ MARR, the extra investment is justified. The challenger wins and becomes the new defender.
    • If IRR(Challenger-Defender) < MARR, the extra investment is not justified. The challenger is rejected, and the defender remains the same.
  7. Repeat: Continue this process, comparing the current defender against the next challenger on the list, until all alternatives have been evaluated.
  8. Select the Winner: The alternative that survives as the final defender is the economically superior choice.

A Worked Example: Developing a Project Site

Let's apply this algorithm to a classic MIT case study involving four options for developing a plot of land. This will make the abstract steps concrete.

Vol. II, Essay 4: Financial Assessment

This section of the same MIT essay provides a narrative walkthrough of the procedure using a detailed example. It shows exactly how the defender and challenger logic works in practice.

Please read the section from 'Table 2 summarizes the investment...' down to the paragraph ending with '...the incremental investment is in fact justifiable.' As you read, try to identify the 'defender' and 'challenger' at each stage of the analysis.

Let's break down the analysis from the text, assuming a MARR of 10%.

The options, ordered by investment:

  • P: Parking Lot ($200k investment, IRR = 11.0%)
  • B1: One-Story Building ($4M investment, IRR = 15.0%)
  • B2: Two-Story Building ($5.5M investment, IRR = 13.1%)
  • B3: Three-Story Building ($7.5M investment, IRR = 12.8%)

Analysis Steps:

  1. Initial Check: All four projects have an IRR > 10%, so they are all initially acceptable.
  2. Round 1: P vs. B1
    • Defender: Parking Lot (P) - the lowest cost acceptable option.
    • Challenger: One-Story Building (B1).
    • Incremental IRR(B1 - P): 15.2%.
    • Decision: Since 15.2% > 10% (MARR), the incremental investment is justified. B1 wins.
    • New Defender: One-Story Building (B1).
  3. Round 2: B1 vs. B2
    • Defender: One-Story Building (B1).
    • Challenger: Two-Story Building (B2).
    • Incremental IRR(B2 - B1): 8.0%.
    • Decision: Since 8.0% < 10% (MARR), the incremental investment is not justified. B2 is rejected.
    • Defender remains: One-Story Building (B1).
  4. Round 3: B1 vs. B3
    • Defender: One-Story Building (B1).
    • Challenger: Three-Story Building (B3).
    • Incremental IRR(B3 - B1): 10.3%.
    • Decision: Since 10.3% > 10% (MARR), this incremental investment is justified. B3 wins.
    • New Defender: Three-Story Building (B3).

Final Conclusion: We have evaluated all alternatives. The final defender is the Three-Story Building (B3). Even though B1 had the highest overall IRR (15%), B3 represents the best use of capital as every incremental investment required to get there was justified.

Test your understanding!

In the example above, why did we compare B3 against B1 in Round 3, and not against B2?

Show answer

We compared B3 against B1 because B1 was the "current best choice" (the defender) after Round 2. B2 was eliminated in Round 2 because the incremental investment to go from B1 to B2 was not justified (its incremental IRR was below the MARR). You always compare the next challenger against the current winning defender, not against a previously rejected option.

Conclusion

You have now extended your analytical toolkit to handle complex, multi-option investment decisions. By systematically applying the defender-challenger approach, you can confidently navigate choices that go beyond a simple A-vs-B comparison and avoid the common pitfall of being seduced by a high IRR on a small project.

  • Key Takeaways:
    • To compare multiple mutually exclusive alternatives, order them by increasing cost and perform a series of pairwise incremental analyses.
    • The "defender-challenger" method ensures that each additional block of capital provides a return that meets or exceeds your MARR.
    • An alternative is eliminated if its incremental investment over the current defender is not justified.
    • The final defender is the project that should be selected, as it represents the highest justified investment.

Preview of the Next Lesson

Throughout our discussions on IRR, we've occasionally mentioned Present Worth (PW) as a reliable alternative. But how exactly do these two powerful methods relate to one another? Are they just different paths to the same answer? In our next lesson, we will explain the relationship between Present Worth and Rate of Return analysis methods, helping you understand their connections and how to use them together to build an undeniable case for your project recommendations.