NPVE, change TIME STEP and FIND ZERO

[oOLauraOo]

Hi,
The model I'm working on (see attachment) aims at exploring different building renovation scenarios, in order to choose the best ones according to their return on investment time (the shorter ROI time, the best).
I designed the renovation scenarios prices and I managed to compare them thanks to the NPVE variable. But of course the NPVE evolution is calculated at every TIME STEP (every year), whereas I need the calculation to be made in one TIME STEP to make a decision the next year. Moreover the analysis of the NPVE is not sufficient to make a decision, I would need to know the TIME at which the NPVE=0 for each scenario.
I was thinking to use a TIME BASE function to calculate the equivalent of 30 years NPVE in 1 year, and then a FIND ZERO function to find the assimilated ROI time. Conclusion: I can't manage to make it work.

Could you please help me find an appropriate solution ?

Thank you a lot in advance !

Laura

[Administrator]

I was thinking to use a TIME BASE function to calculate the equivalent of 30 years NPVE in 1 year

TIME BASE is usually used to give you an alternative x axis for graphs.

I don't really understand the rest of what you are asking. What parameter in your model has the call to FIND ZERO?

[oOLauraOo]

Hi,
Thanks for your help.
There is no more variable to FIND ZERO, I deleted my previous trials not to mislead you. I just wish to have a new variable "ROI", coming from "NPVE scenarios" and giving : ROI = Time when (NPVE scenarios = 0)
And still I need to calculate NPVE scenarios at a different TIME STEP to obtain the analysis results "faster". I understand why I can't use the TIME BASE, so what can I use instead ?

Are my questions clearer ?

Laura

[Administrator]

Are my questions clearer ?

No.

Can you upload the model with the find zero and I'll take a look to see why it's not running?

[tomfid]

It sounds like what you're after is a way to make a decision at a point in time based on the NPV of the expected future stream of benefits. There's no way to do that, because it would be an explicit use of information from the future, which is impossible in reality (but not in a lot of economic models).

There are two options:
- use optimization
- create a decision rule that computes expectations of the future in the present

[oOLauraOo]

It sounds like what you're after is a way to make a decision at a point in time based on the NPV of the expected future stream of benefits.
[...]
- create a decision rule that computes expectations of the future in the present

Exactly !! Do you know how I can create this kind of rule and compute the future values in the present ?

Concerning FIND ZERO, I put the model in attachment with the ROI variable. But I guess I don't really understand how to use the function correctly. I keep having the error message : FIND_ZERO did not sufficiently zero

Thank you a lot for your time and help,

Laura

[tomfid]

Typically, what you need is something like a levelized cost calculation in electric power:
https://www.nrel.gov/analysis/tech-lcoe ... ation.html

As long as the payment streams are constant, or growing/shrinking at a constant inflation rate, the NPV calculation is analytically tractable.

I'd have to know more about the specific situation to say more.

[oOLauraOo]

Levelized Cost of Energy [...] is an economic assessment of the cost of the energy-generating system including all the costs over its lifetime: initial investment, operations and maintenance, cost of fuel, cost of capital. A net present value calculation is performed and solved in such a way that for the value of the LCOE chosen, the project's net present value becomes zero (Source: 2, 3).

I am making EXACTLY the same, except that instead of exploring the energy-generating system including all the costs over its lifetime, I wish to make the economic assessment of the costs-benefits of renovation scenarios over a building lifetime.

> STREAM is the amount of potential savings made each year after a building renovation (current expenses - new expenses = STREAM = savings). For now, STREAM is constant over time.

> I want to know when the amount of savings will cover the renovation investment such as SUM(STREAM(t1+t2+t3+...+tx))-investment cost scenario = 0

> To make it more realistic, I introduced the variable NPVE which is the actualisation of STREAM over time (discount rate = 4%). And I'm looking for SUM(NPVE(t1+t2+t3+...+tx))-investment cost scenario = 0

> When SUM(NPVE(t1+t2+t3+...+tx))-investment cost scenario = 0 , it means that I have reached the "critical" time of return on investment, which is what I want to solve.

> Here tx would be the "date" of equilibrium that I want to find, in order to compare the rentability of different renovation projects. I was thinking it could work with FIND ZERO applyed to NPVE.

I hope those explanations are enough, I'm not sure about what I don't make clear... Do you think it is possible to use FIND ZERO, and if yes can you please help me deal with it ? Or perhaps will you have better ideas ? Because I don't understand very well the documentation provided on Vensim Help about FIND ZERO and now I am totally stuck.


Thank you again for your time,

Laura

[oOLauraOo]

In attachment:

In this model I put a variable ROI 2. Here is the kind of results I would like to obtain (for instance, the first line ==> Building1;Scenario1 : ROI = 5 years)
But I would like to have these results at the begining of the simulation in order to be able to make a decision on which scenario is the most profitable.

I hope this will help !

Laura

[tomfid]

I think you'll find that the math works out such that minimizing levelized cost is exactly the same as maximizing ROI or NPV. The only difference is whether you aggregate the discounted future flow of avoided energy costs to a present value for comparison with the capital invested, or you convert the capital to a stream of amortized payments for comparison with the future cost flow.

There are lots of resources for various versions of the formulas out there, like https://web.iit.edu/sites/web/files/dep ... lation.pdf.

However, if you assume continuous time and an infinite horizon, it's pretty simple. The NPV of a stream of payments is just the payment over the discount rate, i.e. $100/year forever, discounted at 10%/year, is worth $1000 today. This is just a consequence of the fact that the integral of e^-rx = 1/r.

So, a building renovation will be worth it when the capital cost is less than the stream of savings divided by the discount rate. If you expect future inflation of energy prices at a constant rate, the discount rate could be adjusted to reflect that.

Obviously if you need to consider discrete payment timing or finite horizon effects or time-varying savings, it's a little more complex.

[LAUJJL]

Hi

This type of problem may possibly be solved by dynamic programming.

See the book 'dynamic programming and optimal control' by Bertsekas an MIT professor. Two volumes.

It mainly tries to reduce the dimensionnal complexity of dynamic programming by approximation.

But if you can try some easier methods, it is better because the methods proposed in this book are really tricky.

Regards.

JJ

[LAUJJL]

you should too definitely put units in your équations, it will make your models easier to understand.

Regards.

JJ

[LAUJJL]

I have tried to understand your problem, but i find it already to complex for me.

If you could just start again with a much simpler model with no subscripts at all, with visible levels preferably only one, with very few equations, not using the NPLVE and transforming it into a set of readable équations, puting units, this would be a good start and would certainly interest more people.

Regards.

JJ