Annualised Value Investment Ratio - AVIR

 The purpose of this post is solely to protect my Intellectual Property Rights (IPR) if ever there arises a situation where I need to prove the novelty of my work.

The post will not be structured. It is going to be a copy-paste operation. The only purpose is to document and date my idea.

I first developed this idea in early 2020. I then developed it further in August 2023. Vinay helped me throughout this process. 

Very briefly, AVIR or Annualised Value Investment Ratio (AVIR) is a capital budgeting metric that will help rank projects of different sizes and durations. Every common metric that exists now, like NPV, IRR, PI, EAB, etc.. suffers from one or more major flaws and my contention is that AVIR addresses these flaws and is the most superior metric available.

The copy paste starts now.

1. What is Annualised Value Investment Ratio (AVIR)? How is it different from VIR?

Ans: VIR is the discounted value generated per dollar (discounted) invested. AVIR takes this a step further and is the discounted value generated per dollar (discounted) invested per year (discounted). This ensures that, unlike VIR, AVIR is directly comparable for projects of different durations.

2. Okay. But what exactly does AVIR represent? 

Ans: The AVIR of the project is the excess annual return over and above the cost of capital.

3. I am beginning to get a sense of what AVIR represents. But can you explain it more mathematically? For example, what does an AVIR of 7% mean?

Ans: The AVIR of a project is the excess rate of annual return over and above the cost of the capital that will result in the same NPV as the reference project.

4. Can you please share an example?

Ans: Sure! As can be seen from Illustration 1, adding AVIR cashflows to the cost of capital cashflows each year results in the same NPV as the original cashflows of the reference project.

5. But does excess return over cost of capital not simply mean IRR less cost of capital, since IRR is essentially the annual rate of return?

Ans. That is not true. IRR is merely the discount rate which would result in the net present value of all cash flows to be exactly zero.

6. Are you sure? Can you prove that IRR is not annual rate of return?

Ans: Of course! In Illustration 2, you can see that annual return at the rate of IRR does not result in the same NPV as the reference project. In fact, this is one of the reasons why IRR is not a perfect metric for ranking projects. 

In fact, for a positive NPV project, the NPV when annual returns at IRR are discounted will always be greater than or equal to the NPV of the original project. This is because IRR assumes reinvestment at IRR itself. AVIR  addresses this limitation of IRR.

7. Does AVIR also work for projects with multiple years of cash outflows? Can you provide an example?

Ans: It certainly does. In fact, AVIR will work for any pattern of cash flows as long as there is at least one cash outflow. This robustness of AVIR renders it to be an excellent ranking metric for projects of different sizes, shapes, and duration. 

As can be seen in Illustration 3, which has multiple years of cash outflows, the sum of AVIR and cost of capital cashflows results in exactly the same NPV as that of the reference project.

8. If IRR assumes reinvestment at IRR itself, what rate of reinvestment does AVIR assume? How does it compare to the rate of reinvestment assumed by IRR?

Ans: VIR assumes reinvestment at the rate of cost of capital, hence resulting in zero incremental value being generated. This is too conservative an assumption and is also unreasonable since Shell requires a return above cost of capital which is the reason why the VIR threshold and the ranking mechanisms exist in the first place.

IRR assumes reinvestment at the rate of IRR itself. Often, this is too aggressive and unrealistic an assumption.

AVIR takes the middle path and assumes that the project of the same size can be replicated at the same IRR and the excess cash flow generated can be reinvested at cost of capital. This means that the overall reinvestment rate assumed by AVIR always falls between the two extremes of aggressive IRR and conservative VIR.