Re: An Empirical Nonlinear Filter



Fred Marshall wrote:

"jim" <"sjedgingN0sp"@m@xxxxxxx> wrote in message
news:1193580730_14343@xxxxxxxxxxxxxxxxxxxxxxxx


There are fixed costs.

Yes. As I mentioned.

Extra use by one party means paying a larger
share of those fixed costs.

Yes. As I acknowledged.

Debt service might be a fixed cost.

It's a fixed cash outlay but not a "cost" in this context. It's tied to the
investment. You might well call the time value of money a cost, and I
normally would, but in this case it complicates things beyond what's
reasonable so it's lumped into the value of the asset if at all - when the
time comes, if it does, for transfer of assets from one participant to the
other. More about this below.

Reading between the lines you seem to be saying that the plant isn't in
danger of being pushed to the limit so it won't need to be replaced
prematurely and that usage patterns don't really affect the life span of
the plant. So the life expectancy and capital costs are known and don't
really change much with time.

I thought it was stated more directly than that ... but yes.
So, the focus is, has always been, on the investment and how to make
adjustments for that alone.

I think I see the source of confusion:
If you imagine lumping the amortized cost of investment in capacity say into
monthly figures and include it in the monthly fixed costs then the
apportionment of these expanded costs would be the question. It creates a
somewhat different framework for consideration. In our model the costs are
Operating & Maintenance (O&M) which could be split into fixed and variable
parts if one wished - and then there is the investment as a separate
consideration and loan payments are made according to share of initial
investment/ownership.

There is both "capacity that I own" and "capacity that I use".
One invests in order to have immediate capacity and capacity for the future.
In fact, many covet their future capacity and worry about losing it to
others. Future planning rather forces people to think this way. It means
that people *want* to invest to a point and *want* to protect their
investment thereafter. And, since the investments are large, they want to
make sure that the financial treatment is sound.

Our model simply says this:
- Each participant invests up front according to agreement. This buys a
fraction of the total capacity. Financing methods have almost nothing to do
with it. If there are loans then the loan payments are apportioned
according to the investment split.
then
- Each participant pays the operational costs for using (usually their own)
capacity such that 100% of all operating costs are covered. The formula for
doing this could be based on ownership/fixed costs and loading/variable
costs or could be based on loading alone - with whatever distortions come
along with the latter.
then
- If one participant encroaches into the other's capacity,while they are
covering the operating costs of doing so, they are also taking advantage of
the other's investment and there's an investment-related cost to pay.


Ok that part is still not very clear. What exactly are you saying. If
someone's usage increased they are obligated to buy more capacity?
That's weird because obviously that means someone else is obligated to
sell.
I don't know if a judge is going to buy the theory that increased use
by itself is "encroaching on the other's capacity". The Judge may point
out that one of the purpose of a cooperative venture is to benefit from
the economies of scale and the increased flexibility it provides.





If, as you suggest, the investment cost were lumped into fixed costs then I
envision a more complicated model:
- There could still be up-front cash investments that would have to be
recognized and treated when necessary.
- Variable costs could be apportioned according to loading same as above.
- Fixed costs would now include O&M plus amortized value of the investment.

The question is how to apportion the fixed costs?
- If it's based on loading then it could be highly distorted if one
participant decided to invest heavily into having ample future capacity that
remains unused today.
- If it's based on ownership of capacity then we're right back to the model
I've described above.
- If one participant encroaches into the other's capacity they are taking
advantage of the other's investment and there's an investment-related cost
to pay. No different than above.

Maybe a step-response model will help:

We start out buying 50% each.
We operate for 5 years sharing operating costs and covering loan payments
50/50.
I get a new development in town and rather suddenly "need", according to the
regulating agency, to have 60% of the capacity apportioned to my city. You
have no capacity demand to stop this.
Purely from an investment financial point of view, you will rightly say
this:
- I want you to take over 20% of my loan payments
- I want you to pay me for 20% of my original investment, plus interest.
- I want you to refund me for 20% of the past loan payments I've made, plus
interest.
- I want you to refund me for 20% of the fixed costs I've paid(that
preserved the capacity for your use), plus interest.
- In return, we will change the overuse thresholds from 50% of capacity each
to 60% / 40% respectively.

That isn't necessarily going to be my response to a step :) For one
thing aren't I losing some control by selling 1/5 of my share? What
happens when I no longer have a 50% share of the decision making
process?
But as a result of the step input the value of my investment hasn't
decreased. My load charge is now cheaper. It seems that the contract
provides that if I ever need my entire 50% capacity that I own I am
guaranteed to get it, and at that point if the other party needs more
capacity they will have to pay for building the new capacity or have to
send it somewhere else.
If I understand correctly, neither party is close to using the full 50%
of the total that the plant is capable of handling. So I don't see how
it is encroaching on the others share just because you use a little more
of your own share.

I'm not convinced that more use doesn't shorten the life of the plant
and that would be something that would be reason for compensation, but
you say it doesn't shorten the life.

At any rate if what you are saying should happen is how it is supposed
to work it seems it should be spelled out clearly in the contractual
agreement.

-jim


I hope that's clear enough. It's a move that's done totally independent of
today's loading and completely about investment.

It seems pretty easy to see from this step model what the issue would be
when one participant occasionally or perhaps on an ever-increasing basis
exceeds their own capacity. Then there needs to be a method for doing two
things:
- decide when a trigger point demanding compensation occurs.
- decide how to use loading information combined with financial information
to calculate the price.

Oh yeah, superposition applies and some of these elements really can be
treated as orthogonal! And one set of elements is high bandwidth (hourly
flow and daily rate of invoices) and one element is very low bandwidth
(creeping capacity needs over months to years). So, there's a rather large
temporal difference. :-)

I once expanded a waveform using a Taylor Series to study distortion in an
analog multiplier design. One of the issues was how many terms to carry in
a meaningful analysis. First or second order cross terms were necessary to
do the intended work AND were plenty. Higher order terms would have been
less than helpful. Thus my comment about "orthogonality"...... Mixing use
with ownership/investment seems to add unecessary higher order terms.
Perhaps as we study this more I'll see the necessity.

I value the opportunity to hammer on this as it always helps clarify my
thinking. Thanks for the responses!

Fred

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