Four Levelised Cost Methods

This page attempts to take mystery away from computing the levelised cost of electricity, the levelised cost of hydrogen or the levelised cost of just about anything else. I demonstrate that you can compute the levelised cost using four different methods that I name (1) the carrying charge method; (2) the NPV(revenue)/NPV(generation) method; (3) the NPV(cost)/NPV(generation) method; (4) the weighted average price method. All of these methods produce the same result when you make the correct calculation. The idea of levelised cost is not some kind of economic analysis that is unique to the energy industry and it is not some kind of specialised measurement technique. It is just measuring the cost per unit of something on a consistent basis. The levelised cost of just about anything fundamentally depends on a few variables — the capital investment you make for the project; the fixed and variable operating costs; the efficiency of the machine (or horse or person) and a range of variables associated with translating the up-front capital costs into costs over time. Examples on this page and the associated spreadsheets illustrate how all of the levelised cost methods should produce the same result. In discussing the different techniques, I emphasize that the real cost rather than the nominal cost is the appropriate benchmark for comparing technologies that have different capital and operating costs.

When computing the levelised cost of electricity or the levelised unit cost of something else like the oil price necessary to break even on an investment, the ultimate objective is to compare the levelised cost to something else, in particular a different technology or perhaps a different bid. In this page I compute the real LCOE which is the LCOE adjusted for inflation. This means that a flat unit cost in nominal terms is not computed, but the cost is in real terms. This real cost can be compared to things like the cost of your electricity bill per kWh or the cost of natural gas. If you use the nominal LCOE that is in a sense the price at the middle of the life of a solar or other project, you would have to compare your electric bill in 10 or 15 years to the LCOE of the solar project. To compute the real LCOE, I show some techniques that use the PMT function with the real cost of capital rather than the nominal cost of capital. As with other issues, I have included a file with the examples and methods discussed on this page.

I received an email with the following comment on LCOE

I am surprised you have a bee in your bonnet about LCOE. The math is actually straightforward, even my fellow colleague who has a History of Arts degree from the university of southern Uzbekistan knows the math behind this. By the way most developers don’t give a rats arse about LCOE. All they care is getting their equity IRR, get out of the equity lockdown period, take the cash and use it somewhere else. Only policy makers and self-aggrandizing politicians give a hoot about LCOE.

I like the way this comment is written but I must disagree. LCOE is simply the complement of a financial model when done correctly, meaning that the inputs to the LCOE calculation are like putting factors into a financial model and then doing a goal seek to find the price. When computed correctly, the LCOE can be used to do an analysis of what strategies make most sense such as batteries and hydrogen. If the math is so easy, then why do people not know that the only way to make the formula using costs sensible is to use

The evaluations of the LCOE are included in the file that you can download by clicking on the button below.

Excel File that with Levelised Cost per Unit Template with Case Study for Hydrogen Transport Trucks

Introduction to Concepts: Levelised Cost of Beethoven’s Horse

When listening to a story about Beethoven, I found out that he had a horse that he did not take care of very well. Instead, he liked better to drink some cheap wine apparently while he composed the most remarkable music when he was deaf. When I heard about Beethoven’s horse I immediately thought about the levelized cost of a horse. Beethoven’s horse had a capital cost and a fixed operating cost to feed the horse even when the horse was not transporting Beethoven around (Beethoven apparently did not do well in feeding his horse). You can divide these fixed costs of the horse by the amount of distance the horse travels and then add the variable cost of feeding the horse you could compute a cost per km or the cost per mile. You can even account of externalities of the horse pooping in the road. I hope this makes you can compute the levelised cost of just about anything. I suggest when making an evaluation of something like a solar project or hydrogen, you should begin with levelised cost analysis. As I could not find a picture of Beethoven’s horse, I show a picture of a garbage truck that was driven by horses. We could in theory compare the levelised cost of this to the levelised cost of a diesel truck and then a hydrogen truck.

Introduction with Simple Example with No Inflation; No Taxes; No Degradation; No Asset Replacement and Proof with Financial Model

On this page I introduce a generic levelised cost calculator where I hope you can fill in capital costs, operating costs, efficiencies along with some financial parameters to easily compute the levelised cost. This excel sheet computes levelised cost from your defined inputs for capital costs, operating costs and amount of production. The program then ties the levelised cost calculation to a simple financial model and proves that the target return in the levelised cost parameters is equal to the resulting equity IRR in the financial model. You can download the financial model by clicking on button below.

In the example below you just need to know how to use the PMT function to compute the carrying charge. Tis is in line 21. Then you can compute the annual costs and divide them by the kWh production. You can clearly see the drivers of the cost.

Once you have the LCOE you can prove that it really works with a simple financial model

Next, you can prove the formulas for LOCE — NPV Revenues/NPV Generation and NPV cost/NPV Generation product the same result if the pre-tax IRR is used as the discount rate.

The screenshot below demonstrates that the LCOE (of 213 RM/MWH) in the financial model is confirmed with the other LCOE methods.

It also drives me a little crazy to look at power point slides that discuss levelized cost and make you think that the calculation of levelised cost is some kind of mysterious fancy calculation.

The screenshot below illustrates how the LCOE calculator works.

After defining the operating parameters which can be for a battery, a horse, a hydrogen electrolyzer, a truck, an airplane …., you can input some financial parameters which define how the capital costs are translated over time. Unlike the operating parameters, these parameters are similar for different projects and involve things like inflation, interest rates, plant life, gearing and taxes. Inputs for these factors are illustrated in the screenshot below.

With the capital recovery factors and O&M adjustments for inflation made, the LCOE can be computed. The manner in which these factors are computed is described below. The important point for now is that the IRR target of 7% is consistent with the financial model shown below. This uses a financial model to prove that the levelised calculations are correct. The financial model is illustrated in the screenshot below.

Proofs of the LCOE can be made with revenue, cost and generation items from the financial model. In the next four screenshots I have illustrated the proofs.

The LCOE can also be computed using with a weighted average price. This demonstrates what the levelizing really means — it is just a weighted average. The weighted average could be computed in real or nominal terms. In the screenshot below, the starting point is the real rate, but this price is escalated over time.

Case 1: Nominal Levelised Cost without Degradation, Taxes or Debt

The screenshot below illustrates the starting point for computing levelised cost in a case without inflation, a case that I argue is an inappropriate case. To compute levelised cost in any situation, you need some drivers that include capital expenditures, operating costs, the lifetime of the project and some measure of the units sold. For a solar project, you can enter the capital expenditures per kW, the operating costs per kW-year, the lifetime and the capacity factor.

In this case the levelisation — the word that is the foundation for levelized cost — can be accomplished with the PMT function that levelised payments over time. It is an absolutely essential function in excel that takes a single number and produces an equal payment that produces the net present value over a defined period as long as you give the formula a time period and also a discount rate. The payment formula is computed using the number one and the real discount rate in the above screenshot. As the lifetime of each project is different, the carrying charge rate is different for the four projects. The carrying charge rate is multiplied by the cost to produce the required carrying charges:

Carrying charge/kW-year = Capital Expenditure/kW x Carrying Charge Rate

With this the carrying charge, you can compute the carrying charge per unit. Then, assuming the O&M expense does not inflate — a very bad assumption — you can compute the levelised cost per unit using the following formula:

Hours Operated = 8766 x Capacity Factor

Carrying Charge/MWH = Carrying Charge/kW-year / Hours x 1,000

O&M/MWH = O&M/kW-year/ Hours x 1,000

Levelised Cost/MWH = Carrying Charge/MWH + O&M/MWH

Once the levelised cost is computed, alternative calculations of the LCOE can be demonstrates. These calculations are extremely simple in the case with flat units sold and with flat prices. But I begin the section by demonstrating the alternative formulas. To illustrate the other methods, I first make a very simple model. I have input the LCOE as the price and not put in any inflation, taxes, degradation or debt financing. Note that this model with a simple switch for the life produces and IRR that is the input target IRR. You can look at the details and see that the price is the same as the table above.

With this model you can compute use the classic formula for LCOE shown below. The results of this formula which produce the nominal levelised cost of electricity is shown below the formula in the screenshot. Note that the discount rate used for the NPV is shown next to the calculation. In this case the discount rate does not make a difference.

LCOE Nominal =

NPV(Nominal Rate, Revenues)/NPV(Nominal Rate, Units of Generation)

The third method involves using the NPV of costs rather than the NPV of revenues. If you use the same discount rate with the O&M costs — you can compute this with the PV formula in excel (not the NPV formula). Note that the total cost including the Capital Expenditure Cost plus the present value of the O&M cost over the life of the plant amount to the same value as the revenues.

LCOE Nominal = NPV(Nominal Rate, Costs)/NPV(Nominal Rate, Units of Generation)

The fourth method to compute the LCOE is a method where you compute what levelised cost really is — that is you levelise the price using a weighted average calculation. The weighting of the price so that it is not a simple weighted average price is driven by two things in the weighting. The first weighting factor is the amount of the generation. The second weighting factor is the discount rate where the amount of generation applied to the price is lower in future years. The weighted average calculation is shown in the screenshot below.

Case 2: Real versus Nominal Levelised Cost without Degradation, Taxes or Debt

The screenshot below works through how to compute the real levelised cost. When you think about things, the levelised nominal cost is a silly number. Think about a hydro plant than may last 80 years. The nominal levelised cost is the flat value over 80 (with a minor adjustment for inflation in O&M expenses discussed below). With even a minor rate of inflation like 2%, the real value in 80 years is a very small percent of the value in the first year (divide by 1.02^80) — 4.9 times. It would be much better to compute the current value that, when inflated, gives you the target return. In simple terms this involves using a real cost of capital as described below.

To begin the discussion, the screenshot below demonstrates how I have input an inflation rate and also computed a required real return. The required real return is computed as:

Real Return = (1+Nominal Return)/(1+Inflation Rate) -1

You can then use the real return instead of the nominal return in the carrying charge calculation with the PMT function. You can also then compute the total carrying charges and the LCOE with the inflation rate.

Note in the above screenshot that the O&M cost is different for the real LCOE than for the nominal scenario. This is because the O&M cost should increase with inflation. After you levelize the O&M cost, it should be higher in the nominal case where it is (inappropriately) held flat. To compute the equivalent levelised O&M cost, you can apply the formula:

Inflated O&M Factor = PV(Real Rate, Life, -1)/PV(Nominal Rate, Life,-1)

Note that this is not the NPV formula; it is a formula that allows you to input a payment (-1) and produces the present value, The PV using the real rate is higher than the nominal rate. So, the value of this factor is above 1.

As with the first case, I have made a little financial model that proves the approach. I compute a little model for both the nominal case where the absurd assumption is made that the price never changes. But this time I allow the O&M cost to increase with inflation. With the price computed using the increased O&M, the financial model produces the correct IRR that is input as the target IRR.

In the screenshot with the simple model, I also show how the model in the real case. In this case (the bottom part of the screenshot), the computed real LCOE is increased by the inflation rate as shown in the orice line (27.8 followed by 28.50, followed by 29.21 etc.). The O&M is inflated in both case starting with the real level (this is the value of 6/kW-year multiplied by 1,000 to put the values in terms of MW.) With these values, both the real value and the nominal value produce the target return of 5.5% that is input as the target in the above screenshot.

Using this model, one can demonstrate that the other LCOE methods produce the correct result, both in nominal terms and in real terms. However, when computing the real LCOE using the PV of revenue and PV of generation formula, you should use the real target return rather than the nominal target return in the denominator of the formula as shown in the equations below. The screenshot illustrates the results:

LCOE Nominal =

NPV(Nominal Target IRR, Revenues)/NPV(Nominal Target IRR, Units of Generation)

LCOE Real =

NPV(Nominal Target IRR, Revenues)/NPV(Real Target IRR, Units of Generation)

In the screenshot below, the computation of the real and the nominal LCOE is exactly the same as the computation using the carrying charge formula.

Now we can move to the third method, which is the NPV of costs divided by the NPV of generation. In this case the formula for the real case must again be adjusted for the real discount rate. This time, you can compute the NPV of operating expenses using the real amount with the real rate or the nominal amount (discussed above with the PV formula) using the nominal rate. I the screenshot, I demonstrate computation of the PV of the operating costs using the PV formula with nominal amounts and the nominal rate. With the nominal amount and the nominal O&M cost, you can compute the LCOE with the cost formula.

LCOE Nominal =

(Capital Expenditures + NPV(Nominal Rate, Costs))/NPV(Nominal Rate, Units of Generation)

LCOE Real = NPV(Nominal Rate, Costs)/NPV(Real Rate, Units of Generation)

Where

Real Rate = (1+Nominal Rate)/(1+Inflation) -1

I am going through all four methods in this page and I am not going to stop. In the last method which is again intended to demonstrate that levelised cost is just a weighted average, I compute a weighting factor with the present value of the generation and then compute the LCOE. The screenshot illustrates that when you make this weighted calculation, the inflated real amounts produce the nominal LCOE.

Case 3: Inclusion of Degradation in the Levelised Cost

The next section evaluates levelised cost when the quantity of the units change. Different amount of units affects the weighting of the levelised price. For example, if the number of units is half of the units when the units start and if the price changes, then weighted average price changes. Without discounting, the screenshot below is 13.33.

I have included degradation as the change in units after inflation because degradation can be modelled in a similar manner to negative inflation. In the example below I illustrate

When you think about things, the levelised nominal cost is a silly number. Think about a hydro plant than may last 80 years. The nominal levelised cost is the flat value over 80 (with a minor adjustment for inflation in O&M expenses discussed below). With even a minor rate of inflation like 2%, the real value in 80 years is a very small percent of the value in the first year (divide by 1.02^80) — 4.9 times. It would be much better to compute the current value that, when inflated, gives you the target return. In simple terms this involves using a real cost of capital as described below.

Case 4: Inclusion of Income Taxes and Tax Depreciation

The next section evaluates levelised cost when the quantity of the units change. Different amount of units affects the weighting of the levelised price. For example, if the number of units is half of the units when the units start and if the price changes, then weighted average price changes. Without discounting, the screenshot below is 13.33.