I still don't "get" what you're doing or trying to do.
May I suggest you switch from "COKE" to "PEPSI" :shock:
The million dollar question is
What is an IRR?
Simply stated it is the profitability rate
It should in theory tell an investor how much money she made or lost from an investment in terms of a percentage rate.
The way IRR is currently defined, in terms of a interest rate that brings net present value of the investment to a naught, makes it very difficult to determine or find the IRR.
Asking the NPV=0 model to give us the IRR is akin to asking a crack cocaine addict to detemine the rate. The NPV=0 model like the junkie on freebase crack cocaine gives us conflicting replies of which one or none may be correct. In my opinion the NPV=0 model has to go through a drug rehab so to remove the toxics that have piled up on its brain.
The key problem with NPV or any other equaiton such as NFV, NIV, NHV, B/C ratio, EAA to find IRR has to do with the discount factor \(\displaystyle 1/(1+i)^n\)
Here a rate of -100% would cause division by zero something not allowed in mathematics.
Using any of the models based on NPV, NFV, NIV, NHV, B/C ratio OR EAA, requires solving these equations with numerical methods (iterative methods)
I have personally researched and developed over 300 iterative or numerical methods to find the IRR
Such methods give one or more real valued IRR, however a number of such methods would give all real and complex valued IRR solutions to a given equation.
Yet just as the case with NPV=0, all these models report IRR values that conflict with each other.
Theorem 1.1
In my theory, there is either 1 or no IRR solution
The no IRR solution only occurs when all cash flows are positive and there is no negative cash flow. Otherwise there is always a single IRR solution.
To find this actual single IRR solution, we must look in other directions to define the IRR and simple payback period is the right candidate.
The very fact that for any investment, at the time period equal to payback period the IRR is 0% offer us a venue to find the IRR of the total investment.
After time period equal to payback period the cash flows will be all positive or zero. Thus the task remaining is to determine how much money was made from the investment.
Same idea holds if the investment didn't reach its payback period thus cash flows to the left are short of any profits and task remaining is to determine the amount of loss incurred from the investment.
Theorem 2.1
Nothing is impossible, the modeller who designed this universe didn't use numerical methods to design and create the model or else the Universe would still be in womb of its mother.
Theorem 2.1a
There is a formula for everything
The Challenge
Is to find the IRR formula
Let us revisit Dexter's Lab in South Essia
https://www.dropbox.com/s/aie86f04l7kycgc/older_and_modern_mathematicians.jpg?dl=0
The top row shows those mathematicians who invented Calculus and extended its reach
The middle row shows those mathematicians from the last 70 years who invented "Theory of finance" and extended its reach.
Harry M. Markowitz, Merton H. Miller, William F. Sharpe, Myron Scholes, Robert C. Merton, Eugene F. Fama, Lars Peter Hansen, and Robert J. Shiller
The models these mathematicians have built help determine term structure of interest rates, a forward looking task.
The last row shows notes of major currencies
Followed at the end by someone who thinks he will join the ranks of Theorists of finance by presenting his own "New Theory of Finance" to determine the term structure of interest rates by looking back at the future that has passed
See this
Code:
(You are here) 2015 2020 2025 2030 2035 2040 2045 (I am here looking back at 2015 so I know the yields on Treasury bills, notes and bonds for the last 30 years)
Sir Wilmer
It's hard to quit Coke and switch to Pepsi, as the company says in it's TV commercial "Coke! You can't beat the feeling"