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Trying to protect IP Rights

 I have been sharing this various finance professors and professionals. So trying to protect IP rights.

Executive summary: Annual Rate of Value (ARV), the proposed metric, allows for projects of all shapes and sizes to be compared and ranked because it accounts for both “project size” and “project duration” but most importantly does not account for these two factors independently but instead as inseparably linked factors by way of a composite metric*.

ARV is value per dollar-year (for the lack of a better term) with NPV as the numerator.

ARV = NPV ÷ [(PV0 × 0) + (PV1 × 1) + (PV2 × 2) + … + (PVn × n)]

NPV is the ultimate measure of value, but it is an absolute measure not suitable for ranking. PI and EAB only consider one of “project size” and “project duration” and hence are inadequate. IRR is indeed suitable for ranking and factors in both size and duration of projects but suffers from well-known inherent flaws; more fundamentally, it is not a rate of return (or value) but merely a “goal-seeked” discount rate. ARV addresses these issues and gaps logically while remaining simple and wed to NPV.

*Composite Metric: Just like how we should not factor for number of workers and number of working hours independently but instead must rely on a composite factor of man-hours, we also should not factor size of investment and duration of investment independently but instead must construct a composite metric (dollar-year?) – this is the unique break-through insight.  
 
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Genesis of the problem – Project duration being ignored: At Shell, we used VIR – Value Investment Ratio to evaluate and rank investment opportunities. VIR refers to what is called Profitability Index (PI) in the outside world and is essentially “Value per Dollar”. This frustrated me because it completely ignored project duration and hence ended up unduly favoring longer term projects at the cost of shorter projects where capital could be recycled.
 
 
Alternate Solutions were inadequate:
• NPV does not help with ranking.
• IRR suffers from well-known flaws/limitations.
• MIRR partially fixes IRR but adds subjectivity and loses link to NPV.
• Profitability Index (PI), effectively value per (discounted) dollar, factors project size but ignores project duration.
• Equivalent Annual Benefit (EAB), effectively value per (discounted) year, factors project duration but ignores project size.
 
 
Initial solution proposed – combine two existing metrics: It seemed obvious. Combine PI and EAB so that both project size and duration are factored. I called this metric Annualized Value Investment Ratio (AVIR) which is value per dollar per year. It appeared that the problem had been solved.
 
 
Problem with AVIR: When I was stress testing this metric, I realized that the metric failed where projects had a long tail or a big bump. For example, if a project had steady cashflows for 5 years but then had minimal (but non-zero) cashflows for another 10 years, then the AVIR collapsed since the project duration got stretched. It failed the common sense test.
 
I was initially extremely puzzled since my metric was nothing but a combination of two existing accepted metrics. So, if those metrics worked in solving one problem each, then my new combined metric should work in solving both the problems. But it did not; at least not perfectly.
 
 
The breakthrough insight - Not sufficient to just factor in both project size and duration independently: Yes, both project size and duration need to be factored. Yes, AVIR was a massive improvement over PI and EAB which only accounted for one of the two factors. But no, it was not sufficient to just factor project size and project duration independently. What was needed was for them to be treated as inseparably linked factors.
 
The analogy that made me see light was man-hours. It was not sufficient to just know how many workers were there and how many hours it took to complete the task; what was needed was to know specifically how many hours each worker worked; what was needed was a composite metric, man-hours.
And so, similarly, it was not sufficient to know how many dollars were invested or how long the project lasted; what was needed was to know specifically how long each individual dollar remained locked in the project.

Please see the illustration below:

 image.png
 

The solution – Value per dollar-year:
The “Value per dollar per year” (AVIR) metric improves upon both the “Value per dollar” (PI) and “Value per year” (EAB) metrics.

But ARV improves further by creating a composite metric. ARV is “Value per dollar-year”.

ARV = NPV ÷ [(PV0 × 0) + (PV1 × 1) + (PV2 × 2) + … + (PVn × n)]

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