Levelized costs are calculated correctly

The Utility Dive recently published an opinion article that claimed that the conventional method of calculating the levelized cost of energy (LCOE) is incorrect. The UD article was derived from an article published in 2019 in the Electricity Journal by the same author, James Loewen. The article claimed that conventional method gave biased results against more capital intensive generation resources such as renewables compared to fossil fueled ones. I wrote a comment to the Electricity Journal showing the errors in Loewen’s reasoning and further reinforcing the rationale for the conventional LCOE calculation. (You have until August 9 to download my article for free.)

I was the managing consultant that assisted the California Energy Commission (CEC) in preparing one of the studies (CEC 2015) referenced in Loewen. I also led the preparation of three earlier studies that updated cost estimates. (CEC 2003, CEC 2007, CEC 2010) In developing these models, the consultants and staff discussed extensively this issue and came to the conclusion that the LCOE must be calculated by discounting both future cashflows and future energy production. Only in this way can a true comparison of discounted energy values be made.

The error in Loewen’s article arises from a misconception that money is somehow different and unique from all other goods and services. Money serves three roles in the economy: as a medium of exchange, as a unit of account, and as a store of value. At its core, money is a commodity used predominantly as an intermediary in the barter economy and as a store of value until needed later. (We can see this particularly when currency was generally backed by a specific commodity–gold.) Discounting derives from the opportunity cost of holding, and not using, that value until a future date. So discounting applies to all resources and services, not just to money.

Blanchard and Fischer (1989) at pp. 70-71, describe how “utility” (which is NOT measured in money) is discounted in economic analysis. Utility is gained by consumption of goods and services. Blanchard and Fischer has an extensive discussion of the marginal rate of substitution between two periods. Again, note there is no discussion of money in this economic analysis–only the consumption of goods and services in two different time periods. That means that goods and services are being discounted directly. The LCOE must be calculated in the same manner to be consistent with economic theory.

We should be able to recover the net present value of project cost by multiplying the LCOE by the generation over the economic life of the project. We only get the correct answer if we use the conventional LCOE.  I walk through the calculation demonstrating this result in the article.

26 thoughts on “Levelized costs are calculated correctly

    1. Richard McCann Post author

      We’ve already had an extended discussion about this via email. This is not about a fundamental mathematical question–it is about a fundamental conceptual question that needs to be answered before delving into the mathematical formula. Dr. Szymanski makes a fundamental error in overlooking that the discount rate applies to all resources, not just to money. Therefore both the numerator and the denominator in the levelized cost calculation must be discounted. His comment erroneously discounts only the numerator.

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      1. Adam Szymański

        In my article, I presented a method of introducing the LCOE definition from the costs-revenues equilibrium equation. It is a consistent method from an economic and mathematical point of view. I propose that Dr. MCann introduce a similar model. Then a constructive discussion will be possible.

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      2. Richard McCann Post author

        I already showed that the current conventional LCOE method is correctly established. The correct formulation calculates the net present value of both the monetary streams and the physical production streams and divides the monetary NPV by the physical units NPV. The mathematically equivalent calculation is to calculate the annualized payment and production amounts and divide the payment by the production. All of this has nothing to do with the principles of calculus. The method you propose is not economically consistent because it discounts the monetary stream but does not discount the physical production stream. Money is not a separate entity–it is a unit of barter between two types of physical units. Therefore the physical units also need to be discounted. I explained all of this in my comment on Loewen’s initial article.

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      3. Adam Szymański

        Dr. MCCann’s definition of the LCOE constant; LCOE = NPV (costs) / NPV (production) does not satisfy the cost-revenues equilibrium equation. The definition of LCOE should follow from fundamental economic principles, in this case from the equilibrium equation. NPV (production) has no rational economic justification. Discounting physical quantities is a pure nonsense. In my article, I showed a mathematically and economically consistent technique for defining LCOE. Production is technically degraded due to the depreciation of the quality of the equipment used for production, and this has nothing to do with the cash flow discounting function. This is clearly highlighted in my article. The degradation function is an equivalent of the discounting function for physical quantities. In the article, I showed where the formal assumption leads; discount function = degradation function. This is exactly what J. Loewen described. NPV (production) does not follow the economic definition of the discounting function.

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      4. Richard McCann Post author

        I showed in my initial comment that the method that you’re proposing leads to an underestimate of the total NPV for the entire project. life. Please read that section again where I demonstrate that mathematical fact.

        As for discounting physical quantities, I’ll pose the classic introductory economics example: Would you rather have a piece of cake today or one year from now? Would it take two pieces of cake a year from now to be equal to a piece of cake today? Of course you would prefer your cake now. That is by definition discounting of a physical product–there is no money involved. We know that five year olds show different levels of patience, which is the definition of discounting: https://www.vox.com/science-and-health/2018/6/6/17413000/marshmallow-test-replication-mischel-psychology.

        Discounting is NOT about a physical immutable process like gravity–it is entirely based in the human experience and how we perceive time and how that affects our preferences. It has nothing to do with degradation (that’s picked up in the depreciation rate, which is NOT the discount rate.) If you have an economic citation that shows how money is discounted while all other physical products and services have exactly the same experiential value in the future as today, then provide those citations. You need to provide much more than just your assertions that are based on a misunderstanding about discounting. I provided citations showing that products and services are discounted.

        We have nothing further to discuss if you can’t accept the principle that discounting extends beyond just money. Your method might be mathematically consistent only IF you separately treat money as a completely separate good with a unique set of properties. I discussed this issue in my comment and don’t yet have anything further to add on this. Loewen saw that his approach was incorrect based on this discussion which is why he withdrew his original article and submitted a different one that relied on the conventional method.

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      5. Adam Szymański

        Yes, my method is economically consistent because I treat money as a completely separate good with a unique set of properties. This results from the costs-revenues equilibrium equation, and this in turn is a mathematical description of what I wrote above. Unfortunately, your method relies on a verbal description of the problem and lacks a consistent mathematical approach, making it wrong. Of course, technical degradation has nothing to do with the discounting procedure. One could ask completely formally; what happens when the discount function equals the function of technical degradation? Then we get, once again, that your method does not make sense. This is also a mathematical proof. If you want to question it, you have to use purely mathematical methods, not verbal deliberations.

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      6. Richard McCann Post author

        First, money is not a stand alone “good”. Money is a means of transference of value amongst different goods and services. You cannot consume or directly use money to satisfy a human need or want–it is only a means of acquiring those goods and services. If you continue to assert this position, you need to provide a peer-reviewed citations that support this.

        Second, your method is not economically consistent. Let’s start with the definition of “levelized cost”. Levelized cost is the annual cashflow that arrives at the total net present value when summing the discounted stream of those cashflows. Mathematically, the equation is:

        NPV = sum(t)[CF(t)/(1+r)], with CF = levelized cost, where CF(t) = cost C(t) * output O(t) and sum(t) is the sum of the equation over time (t)

        That means that the annual CF is discounted over time and the CF is a function of the price or cost per unit times the physical output of the resource. So the equation can be expanded to

        NPV = sum(t)[(C(t) * O(t))/(1+r)] = sum(t)[C(t)/(1+r) * O(t)/(1+r)]

        Thus the physical output is also discounted in this equation as shown by the term O(t)/(1+r)

        We can see how this works in our every day life when examining load payments on a house or a car. The output of a house or car from this perspective is a period (month or year) of service Y, e.g., the year that we reside in a house. The loan payment can be calculated using this equation:

        Payment = Loan amount / sum(t)[Y(t) / (1+r)] where Y

        We can show an example with a loan of $500,000 over 30 years at a 3% mortgage rate. Using the Excel PMT function and adjusting to monthly, we arrive at a payment of $2,108 per month. Alternatively, we can calculate this by taking the present value of the months of housing service: sum(t)[1 month(t) / (1.0025)] That present value is 237.19 months (vs. a nominal total of 360 months):

        $500,000 / 237.19 months = $2,108 per month

        This is the levelized cost of homeownership.

        Given that the entire finance industry is premised on this equation, you are asserting that the entire structure of financial transactions are wrong.

        Before I approve another comment from you, you will need to provide the answers to these three questions. If you don’t answer these questions, I will assume that you have conceded the validity of my points and I will not publish your attempts to distract from those points or try to obscure it by using a mathematical method that is beyond what is required to demonstrate these points:

        (1) If given a choice when offered a piece of cake for dessert, most of the time would you prefer to eat that cake now or a week from today? If offered time off from work for a vacation, would you prefer that time off now or a year from now (generally)? If offered an additional benefit at work such as a new office or a new computer, would you prefer to receive the benefit today or a year from now?

        (2) Provide citations to peer reviewed journal articles that demonstrate that money is a separate good with unique properties whereas money is the only good or service that declines in value over time, and provide citations to peer reviewed articles that demonstrate that the value of physical goods and services hold the same intrinsic value to people regardless of how far into the future those goods and services will be consumed.

        (3) Provide a numerical example where the NPV of the stream of annual cashflows represented by your version of the LCOE provides sufficient amount to cover the entire initial capital cost of the resource. (You will find that it underrecovers.)

        By the way if technical degradation has nothing to do with discounting, why did you reference that relationship in your previous comment?

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      7. Richard McCann Post author

        An additional point on the home mortgage example: If we use your proposed LCOE method which implies dividing the house loan of $500,000 by the undiscounted total months (360), the monthly loan payment would be $1,389. The NPV of that stream of payments is only $329,430, far short of the loan amount.

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      8. Adam Szymański

        NPV = sum(t)[CF(t)/(1+r)], with CF = levelized cost, where CF(t) = cost C(t) * output O(t) and sum(t) is the sum of the equation over time (t).

        The correct definion is as follows,
        NPV = sum(t)[CF(t) x D(t)]
        where D(t) – non- dimensional discount function
        CF(t) – cash flow [USD]
        Hence,

        NPV [USD].

        Now,
        NPV = sum(t)[CFdis(t)],
        where CFdis(t) = CF(t) x D(t),
        NPV = sum(t)[(CFdis(t)/O(t)) x O(t)],
        where O(t) – pyhsical output [ appropriate unit].
        In this case NPV [USD]. The unit must be consistent !

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      9. Richard McCann Post author

        This discussion reminds me of the economist’s joke “Sure it works in practice, but does it work in theory???” You still haven’t answered my three questions, but I approved this comment so that I can show that your theoretical method does not work in practice.

        Let’s start with a fundamental of electricity power contracts which is directly tied to the LCOE. All power purchase agreements (PPA) in the U.S. are priced in $/MWH (as I know from working in the industry for more than 35 years.) The annual cashflow to the plant developer/owner equals $/MWH * annual MWH output. The developer/owner is planning on receiving over the term of the PPA at least the net present value of the revenues or cashflow equal initial capital cost of the plant. This is the identical principle of repaying a loan as I discussed in my previous response.

        So let’s compare the outcomes of the two LCOE methods based on this fundamental of PPA pricing. Assume the following parameters for a renewable power plant’s costs, annual output, cost of capital (=discount rate), and PPA term:

        Renewable plant size 100 MW
        Capital cost per MW $1,000,000 per MW
        Plant Cost (PV) $100,000,000

        Cost of capital/discount rate 7%
        Book life 30 years

        Renewable plant output 200 GWh

        The annual cashflow target is $8,058,060 over the 30 year term of the PPA. The total nominal undiscounted output over the 30 year term is 6,000 GWH.

        The conventional LCOE can be calculated in two ways from this information. The first, as shown in equation (1) of your comment, is the NPV of the annual cashflow targets, which equals the initial investment of $100,000,000, divided by the NPV of annual generation output. Over 30 years, that is 2,482 GWH. The LCOE equals $100,000,000 / 2.482 GWH = $40.29/MWH. The second method is to divide the annual revenue requirement by the annual generation. (The annual generation amount = annualized generation amount from the NPV of lifetime generation.) The LCOE equals $8,058,060 / 200 GWH = $40.29/MWH, the same amount as the first method. The annual cashflow is $40.29/MWH * 200 GWH = $8,058,060. The NPV over 30 years equals $100,000,000. The developer/owner will receive a satisfactory return on investment with this price.

        Equation 4 in your comment leads to the equation: Capital investment/Total lifetime output, or $100,000,000 / 6,000 GWH = $16.67 per MWH. The annual cashflow of $16.67/MWH * 200 GWH per year is $3,333,333. The NPV of that cashflow over 30 years is only $41,363,471, well short of the required NPV of $100,000,000. (I showed a similar example in my initial comment.) No plant developer would sign a PPA based on this price where they receive only 41.4% of the NPV of their initial investment.

        The LCOE is based on the methodology for determining price terms in PPAs and it must reflect those PPA terms to be useful for comparing resource costs. Any LCOE method that does not comply with this singular requirement fails this test.

        You will need to answer the other two questions that I posed before I will approve your response. (I’ve provided the real world example that I asked of you.)

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      10. Richard McCann Post author

        That you don’t do calculations illustrates my economist’s joke. Economics is about observing and measuring reality–it isn’t solely theoretical mathematics. One must ALWAYS check the implied results from any economic construct. As I just demonstrated, the algorithm that you are proposing isn’t consistent because when you take a sum, divide it by a value and then multiply it back by a number, you don’t arrive back at the same sum. This violates the fundamental associative property.

        I will look at these files to see if they arrive at the required consistent result that the net present value of annual cashflows must sum to the initial investment amount. I urge others to also review these for consistency.

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      11. Richard McCann Post author

        It’s in Polish (so I can’t read it), but the math appears to make the same mistake that I already responded to. Your problem is that you fail to understand that “money” does not exist on its own, but rather solely as medium for exchanging money and resources amongst individuals. For that reason, it is time and resources, not money, that is being discounted in the future. My previous response was reviewed and accepted by the editors of the Electricity Journal, and that is the final word on this topic.

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      12. Adam Szymański

        Dear Richard,
        ask some mathematician for help, because your comment shows some shortcomings of your teacher in this field.
        greetings
        as

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      13. Richard McCann Post author

        As I’ve pointed out before, this is not about mathematics, its about economic principles. So long as you fail to understand that money is just a medium for the exchange of time and resources, you won’t be able properly construct value discounting economic solutions.

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      14. Adam Szymański

        Dear Richard,
        I suppose you will not contradict the fact that the universal language of engineers, physicists, economists, etc. is the language of mathematics. In its simplest form – algebra. So your comment is inconsistent for many reasons. Money is a measure of the economic value of goods. For example, to calculate the area using integral calculus, you need to enter the appropriate measure to calculate the area of ​​a specific set, etc. In the case of economics, the measure (money) is time dependent, so economists introduced the concept of discounting. It is debatable whether economists’ discounting makes sense, for example, hyperbolic or some other discounting. I am writing about it here: Szymański, Adam, A New Approach for Calculating the LCOE Constant (October 22, 2021). Available at SSRN: https://ssrn.com/abstract=3947777 or http://dx.doi.org/10.2139/ssrn.3947777, and in a more general version here: Szymański, Adam, A new approach for calculating the LCOE constant – An update (December 17, 2021). Available at SSRN: https://ssrn.com/abstract=3987939 or http://dx.doi.org/10.2139/ssrn.3987939. Besides, there is also something like physics, for example, Newtonian physics. It treats time in a very specific way, compared to Einstin’s theory of general relativity. Therefore, when developing a discounting model, it is first of all necessary to decide how we will treat the concept of time. The purpose of this comment is not to detail discounting, but to point out certain purely formal assumptions that you try to forget. Until you try to think comprehensively, I suppose the further discussion will not be of much importance.

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      15. Richard McCann Post author

        First, the papers you’ve published appear to use an approach that we applied in preparing the Cost of Generation Reports for the California Energy Commission starting in 2001. Here’s the more recent versions: https://www.energy.ca.gov/data-reports/energy-almanac/california-electricity-data/cost-generation-report.

        Money is not the only measure of value–the physical use of the resources also has value. Money is just a useful tool for trading resources and time. So the principle of discounting applies to all resources and time, not just money. As I show below, all resources must be discounted in a comparable manner to fundamentally balance the recovery of costs over time.

        Here’s the fundamental mathematics of calculating the LCOE. This presentation focuses first on the calculation for the capital or initial cost of the energy producing plant. This capital cost CC is then distributed over the expected life of the plant T, just as the purchase price of a house is distributed over the life of a loan through a mortgage payment. This equation can be expressed as:

        CC = ∑(t=1)^T▒〖CC/∑(t=1)^T▒〖1/〖(1+r)〗^t 〗〗
        CC = ∑(t=1)^T▒〖(CC/E*E)/∑(t=1)^T▒〖1/〖(1+r)〗^t 〗〗
        CC = ∑(t=1)^T▒〖(CC/E)/∑(t=1)^T▒〖1/〖(1+r)〗^t 〗〗(t=1)^T▒〖E/∑(t=1)^T▒〖1/〖(1+r)〗^t 〗〗
        CC = ∑(t=1)^T▒〖[CC/∑(t=1)^T▒〖1/〖(1+r)〗^t 〗〗/∑(t=1)^T▒〖E/∑(t=1)^T▒1/(1+r)^t ]〗∑(t=1)^T▒〖E/∑(t=1)^T▒〖1/〖(1+r)〗^t 〗〗

        Where E= annual energy production, r = discount rate and t is each year up to the expected
        The levelized capital cost of energy is therefore:

        LCCOE = ∑(t=1)^T▒〖[CC/∑(t=1)^T▒〖1/〖(1+r)〗^t 〗〗/∑(t=1)^T▒〖E/∑(t=1)^T▒1/(1+r)^t ]〗

        Similarly, the annual operating costs OC, with parallel treatment of the rate of time preference that undergirds the fundamental principle of discounting:

        OCPV = ∑(t=1)^T▒〖OC/∑(t=1)^T▒〖1/〖(1+r)〗^t 〗〗*∑_(t=1)^T▒〖E/∑_(t=1)^T▒〖1/〖(1+r)〗^t 〗〗

        And the levelized operating cost of energy is therefore:

        LOCOE = ∑(t=1)^T▒〖OC/∑(t=1)^T▒〖1/〖(1+r)〗^t 〗〗

        The LCOE is the sum of the LCCOE and LOCOE:

        LCOE = (∑(t=1)^T▒〖CC/∑(t=1)^T▒1/(1+r)^t 〗)/(∑(t=1)^T▒〖E/∑(t=1)^T▒1/(1+r)^t 〗)+ ∑(t=1)^T▒〖OC/∑(t=1)^T▒〖1/〖(1+r)〗^t 〗〗

        The PDF version of these equations is here: https://mcubedecon.files.wordpress.com/2022/05/fundamentals-of-calculating-the-levelized-cost-of-energy.pdf

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      16. Adam Szymański

        The levelized capital cost of energy is therefore:

        LCCOE = ∑(t=1)^T▒〖[CC/∑(t=1)^T▒〖1/〖(1+r)〗^t 〗〗/∑(t=1)^T▒〖E/∑(t=1)^T▒1/(1+r)^t ]〗

        This equation was not correctly derived. Money is an economic measure, dependent on time, of various goods. What is the value of electricity production? This is the value at which it can be sold to the client (for example) in order to generate income. Now very relevant! We discount the income measured by the cash flow, and not the physical amount of electricity production, eg. in [MWh]. Discounting physical quantities is complete nonsense. One MWh today is the same as one MWh in a hundred years from the point of view of physics, only its economic value changes, so the income really needs to be discounted, because the economic measure (money) depends on time. Hence, your deliberations about discounting everything are pointless and show that you do not understand the mathematical concept of a measure. Ask the mathematicians! Measure theory is a separate branch of mathematics, necessary, for example, in integral calculus.
        “So the principle of discounting applies to all resources and time, not just money”. You can discount whatever you like, but it has to be mathematically and physically consistent. Unfortunately, this is not the case with your approach, as clearly demonstrated by the math you cannot fool. See: Szymański, Adam, Lcoe: An Useless Indicator – Replica to Wilhelm Kuckshinrichs (February 13, 2022). Available at SSRN: https://ssrn.com/abstract=4033669 or http://dx.doi.org/10.2139/ssrn.4033669

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      17. Richard McCann Post author

        The presented equations address the fundamental process of deriving the LCOE. The required first step is allocating the initial capital investment across annual cashflows, as you point out. The next step is then allocating those annual cashflows across the expected energy production within any single year. (A more sophisticated analysis can vary those annual production numbers as we did in the CEC Cost of Generation model.) The math is then very straightforward and the annual energy production is discounted in the same manner as the monetary cashflows. To do otherwise is mathematically inconsistent and is “nonsense”. The net present value of the annual cashflows must sum to the initial capital investment. This is the fundamental principle of the calculation of the LCOE–any other result is not a LCOE; it’s something different.

        Physics has little to do with how humans value a physical commodity or service, and economics is about the human perspective, not the physical world. That the earth will last billions of years is not relevant to economics. A human does not value a MWH produced hundreds of years from now the same as one produced today. The fundamental basis of discounting is described by this simple example: would you value a piece of cake given to you a year from now the same as a piece today? How many pieces of cake a year from now would you accept to give up a piece today? (Or at least ask any 5 year old.) The rate of time preference is about looking at this from a human perspective, not some physical reference point that fails to consider human valuation.

        Your referenced article is not a proof in any way because if fails to show the initial derivation of the LCOE that flows from parsing the initial capital investment into annual cashflows. Until you show how your proposed solution balances from a simple accounting perspective, it must be ignored as erroneous. I’ve already shown that Loewen’s solution was incorrect and the author withdrew his initial article, substituting it with a solution consistent with the formulation that I’ve put forward.

        Until you present a solution that begins with the fundamental principle that the present value of the annual cashflows must equal the initial capital investment, I will reject any further comments from you as failing to address the issue at hand.

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      18. Richard McCann Post author

        Let’s look at an example that demonstrates this point. Another fundamental principle is that two producers in comparable situations should experience comparable economic and financial outcomes. Let’s take two entities that each own a 10 MW generation plant.

        1) The first uses the plant solely to self generate and meet internal loads. This entity does not charge itself a per kWh amount but rather draws an annual amount from its revenue cashflow to repay its capital costs. Let’s assume that the initial investment is $2000 per kW, its cost of capital is 10% and the book life is 30 years. The annual required cashflow is $2.1 million.

        2) The second is a merchant plant owner who sells into market. Let’s assume the plant’s expected capacity factor is 90%, implying expected production is 78,840 MWH per year. Dividing the annual cashflow by annual energy equals $26.90 per MWH By tautology, the net present value of 78,840 * $26.90 = $2.1 million, and the NPV of the annual cashflows equals $20 million. The two entities are on equivalent economic standing on this basis.

        If however is case 2 we instead divide the NPV of the annual cashflows, which equals the initial capital investment, by the total undiscounted energy production over 30 years (which is 2,365,200 MWH), the cashflow per MWH is only $8.46. When we multiply this amount by the annual energy production, the annual cashflow is only $666,666. The NPV over 30 years is only $6.3 million or 31% of the initial capital investment. The second entity is not recovering its full capital investment when compared to the first entity that installed the identical plant at the identical cost with identical financial parameters. This results violates the fundamental principle of the LCOE calculation that calls for comparable results for different investors.

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      19. Adam Szymański

        “Until you present a solution that begins with the fundamental principle that the present value of the annual cashflows must equal the initial capital investment, I will reject any further comments from you as failing to address the issue at hand.”

        1) Look at the basic equation (2) in the article: Szymański, Adam, A brief history of the LCOE definition – An update (July 26, 2021). Available at SSRN: https://ssrn.com/abstract=3893462 or http://dx.doi.org/10.2139/ssrn.3893462.
        This is exactly what you want, and even more!
        2) In the article: Szymański, Adam, Lcoe: An Useless Indicator – Replica to Wilhelm Kuckshinrichs (February 13, 2022). Available at SSRN: https://ssrn.com/abstract=4033669 or http://dx.doi.org/10.2139/ssrn.4033669, I take your LCOE definition and compare it with the correct definition postulated by Loewen. What am I getting? I get it, your definition is wrong because it doesn’t discount cash flows.
        Now, a general note. For you, the problem of defining LCOE has nothing to do with either math or physics. The idea of ​​discounting everything “what you can” is very interesting. Since you like examples, here’s one. You have a piece of iron that is subject to corrosion. Contrary to appearances, this is an example not at all abstract, but from the field of archaeology. Question: What did this piece of iron look like when it was made? One can purely theoretically introduce a mathematical measure of corrosion and try to calculate the NPV, that is, the shape at the time of manufacture. However, no one would come up with the nonsensical idea of ​​using economic discounting for this. On the other hand, you are discounting the physical quantity, in this case, the production of electricity, using the economic discount function, and this leads to such nonsense that you practically discount nothing.

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      20. Richard McCann Post author

        1) In “A brief history…” your error is in your transformation from equation (2) to (3). I can’t see the math that you used, but the correct definition for purposes of the LCOE of C = (c * g)/g and Cd(t) = [(c(t) * g(t))/g(t)] * D(t). (Assuming you intended g(t) to be annual generation.) By simple algebraic rearrangement, this then becomes [c(t)*g(t)] * D(t) * [1/g(t)] * D(t). This shows that energy production also is discounted as well as monetary cashflows. You’ve made an elementary mathematical error.
        (2) Your second paper doesn’t contain the equation as I laid out. Instead you’ve started with your definition of LCOE which is incorrect. Your arguing a tautology there.

        Your right that corrosion has little or nothing to do with discounting. Corrosion occurs whether a human uses it or not. Corrosion is about deterioration and depreciation which are not the same as discounting. Discounting is NOT a physical concept–it is a valuation concept from the perspective of people who engage in economic activities and transactions. The VALUE of that iron piece declines over time because of the presence of corrosion–a new piece is more VALUABLE today than in the future for two reasons, the first being the deterioration or the iron, but more importantly the foregone opportunity value of the resources used to make the iron today instead of waiting to make it at some point in the future. We could have used the energy, iron ore and coke for a different purpose today instead and we gave up that value for making iron that we will use at some point in the future. This issue has nothing to do with physics and everything to do with human choices and behavior. Your confusing a physical process that is unrelated to discounting with human decisions. Instead address my example of the choice of when to eat pieces of cake.

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