A central question in evaluating the economics of solar, wind, hydrogen, storage, mini-hydro, or just about anything is whether the ultimate long-run production cost — the levelised cost — LCOE, or LCOH for hydrogen, or LCOS for storage — is less than then alternatives measured at their short-term or long-term marginal cost. One way to use the LCOE, LCOH, LCOS or the levelised cost per unit of just about anything is to make an initial evaluation of the business case for different strategies. In using levelised cost per unit to evaluate business strategy, it is effective to first establish the costs of getting back your capital. This depends on the cost of capital, taxes, inflation, the life of the asset and the degradation rate in the productivity of an asset. This page works through how to compute the carrying charge components of the LCOE. With the carrying charge rate, you can put your own capital cost per kW, operating cost, capacity factor and derive the total LCOE. For example, if the renewable LCOE is less the cost marginal cost of energy, then consumer bills will be reduced from using more solar power. The LCOE in turn is driven by the carrying charge rate as these technologies are very capital intensive (much more capital intensive than a refinery).
The carrying charge converts a one-time cost (sometimes referred to as overnight cost) into an annual cost. Carefully establishing carrying charge rates can make the analysis of different alternatives much more effective. The first part below walks through different components of the carrying charge that include evaluating project life, inflation, income taxes, investment tax credit, replacement capital costs, debt financing and maintaining a constant capital structure.
In addition to carrying charges, comparing investments must evaluate the fixed and variable costs that for electricity include fuel cost. The second part of this page describes how make various calculations that establish the fixed costs and the variable costs that are combined with the capital cost to establish the overall levelised cost.
The file that is discussed in this section and the file that includes the equations is attached to the button below.
Using the Levelised Cost Calculator
I have made two files that evaluate the carrying charge that is the real basis for the carrying charge evaluation. As with many different things I do in modelling, after you try it for a few times, you can finally get an analysis that is more transparent and more structured. Often, you just need to get an analysis finished and then after you are finished you can re-do the analysis to make it better. This is what happened to me with the carrying charge analysis. To illustrate how carrying charges work, I use a simple example and gradually work through the more and more complexities including inflation, taxes, tax depreciation, debt financing, degradation, different lives and learning rates.
You may say that computing the LCOE is not a big deal. You can use the PMT function and compute the carrying charge rate and apply that carrying charge rate to the capital investment cost. The manner in which you can use the carrying charge rate is illustrated below.
Carrying Charge Applied to Capital Investment = PMT( Return, Life, -1)
If you want to compute the PMT by yourself, you can use the formula below. In this formula, I use the WACC to represent the rate that is use in the PMT formula. You can try this and assure that it works.
|CCR = WACC/(1-(1/(1+WACC) ^ Life))|
In the carrying charge analysis, you can use the after-tax weighted cost of capital. Computing the weighted average cost of capital is illustrated in the little screenshot below. Note that the inflation rate is used to convert nominal rates to real rates. This screenshot use assumptions from NREL which I thought were generally reasonable. Note that when you compute real rates use the formula:
Real = (1+Nominal Rate)/(1+Real Rate) – 1
Once you have the carrying charge in real or nominal terms, you can multiply the carrying charge by the capital investment and then add the O&M expenses to derive the LCOE. But there are couple of added items. These include the effect of income taxes, tax depreciation shields and degradation.
To do this sort of documentation, you can use the following steps:
- First, use the FORMULATEXT for the long formula
- Next, put the different formula factors in separate places to find the values. In the example above, the 4.28% that comes from =s52.
- You can then put use the FORMULATEXT again to demonstrate (to yourself) that you have taken the correct value
- You can then use CNTL [ and F5 to find the name of the variable
- Note that if you have a keyboard in some languages, finding CNTL [ may be difficult. You can use the generic macros with ALT, u to use instead of the CNLT [.
Adjustment for Taxes and Depreciation
If there was no depreciation, all of the required returns would increase by a factor of (1-tax rate) to recover taxes. This includes both the real and the nominal payment as follows:
Nominal Payment factor After tax = PMT/(1-tax rate)
Real Payment factor After tax = PMT/(1-tax rate)
But this payment factor does not account for the benefit of the depreciation tax shield. To account for the benefit of the tax shield you should compute the PV of the depreciation at the nominal and not the real discount rate. You should use the nominal discount rate rather than the real rate because the tax shield is the same in nominal terms no matter what happens to inflation. You can compute the PV of the tax shield in percentage terms using the depreciation rate. Then compute the NPV of the cost in nominal terms. Note that if the inflation rate and the nominal discount rate are higher, the value of the tax depreciation is less as it should be. Once you compute the PV, you can multiply the PV by the tax rate (if there were no taxes, the value of the tax shield would be zero.) So the value of the tax shield can be computed using the following formulas. When discounting, you use the pre-tax rate as the effects of gearing come into play when you apply the PMT to the net value.
PV of Depreciation = NPV (Nominal pre-tax WACC, Depreciation rate)
Tax Shield Value = PV of Depreciation * Tax Rate
CCR Adjusted for Tax = PMT x (1-Tax Shield Value)/(1-Tax Rate)
The last equation above for the CCR can be applied on either a real or a nominal basis. The next screenshots illustrate calculation of the tax shield. The first screenshot demonstrates that inputs that are required. The second screenshot demonstrates how the depreciation rate can be computed with the VDB formula and how the NPV is computed from the nominal WACC before accounting for the tax shield on the interest. The reason for using this pre-tax WACC is because the tax effects of interest are accounted for separately.
Investment Tax Credit and Government Grants
Debt Financing and Carrying Charge
You can compute the WACC with the pre-tax and the after-tax interest rate. The question is whether this is consistent with project financing. I have reconciled the WACC and the project financing using economic depreciation to compute the capital over time and the debt capital over time. This can be used to compute the implicit debt repayment.
Proving the Carrying Charge Mechanics with a Financial Model
In this section I work through a financial model and demonstrate the LCOE and the results of a financial model are the same thing, just presented in a different way. The LCOE starts with the required IRR and financing assumptions and derives prices. A financial model starts with the price and derives the IRR. When I received an email blasting me for being so worried about LCOE and carrying charges as being too simple to worry about, the person who sent me the delightful and critical email may have been correct. But I have noticed a whole lot of confusion about LCOE in my work. So I have have created a proof of the LCOE with a financial model as part of the LCOE calculator.
Creating a financial model from the LCOE makes you think about some of the fundamental principles of making a financial model. This is to make a well structured, flexible, accurate and transparent model (the FAST letters). Do not worry about silly rules, just keep these ideas in the back of your head somewhere. Flexibility is illustrated by learning how to make time lines in seconds with a differentiation between the pre-COD and post-COD periods. Accuracy is covered by using TRUE/FALSE switches that assure that the balance sheet balances among others. Structured means that you should first compute the project IRR pre-tax; then add taxes; and put the financing in only after the after-tax project IRR is computed. Finally, transparency means that you can see everything with simple formulas using F2 and that you can find the source of the inputs in driver columns to the left and then use the CNTL [.
The first principle of financial modeling with flexibility and transparency is illustrates in the screenshot below. Note how there is a simple timeline and a flag to start everything. In this case the flag just allows you to use different project lifetime. Observe also that there are units to the left and the drivers of the model that come from some kind of inputs are also in a left-hand column.
After establishing the pre-tax and post-tax project IRR, you are ready to work on the financing part of a model. The big issue in modelling is often deriving the method of debt repayment. In this example, I use the economic depreciation to compute the capital associated with the project. This economic capital is used to divide the capital between debt and equity. Once you have the debt balance, you can derive the debt repayment. Then, in any model there should always be a debt balance and an interest computation. Note in this case that the after-tax interest rate is below the after-tax project IRR.
The final part of the model includes a cash flow waterfall and calculation of equity cash flow that includes the initial sources and uses of cash. You can then also derive the DSCR implied by the debt to capital ratio. This last part of the financial model is illustrated in the screenshot below. Note that the target IRR equals the computed IRR and there is a test to confirm the model.
Using the Carrying Charge Calculator
This lesson set works through calculation of the carrying charges that are used for computing levelised cost of investment. You may think the carrying charge rate is some kind of esoteric concept that is not useful in your day to day work. If you go through this lesson set you will see that the finance, modelling and economic concepts in carrying charge rate analysis are closely related to both project finance and corporate finance.
The carrying charge is a percentage that converts a one time cost that is sometimes called the overnight cost into a level annual cost. (The level cost should be expressed in real terms (i.e. without inflation in constant currency). The lesson set involves using a single capital investment cost and evaluating each of the factors that drive the the conversion of the capital cost into an amount that must be recovered on an annual basis. You can think of this as the amount of revenues necessary to provide a given return to investors. After completing this lesson set I hope you will understand the following things about carrying charge rates:
- 1. Overview of why understanding carrying charges is important
- 2. Definition of Carrying Charge Rates — Annual recovery cost to total cost; EBITDA to gross investment; Amount of annual recovery to carry investment
- 3. Normal Complications in Computing Carrying Charge Rates — Construction Period, Inflation, Required Return on Equity, Tax Policies, Capital Structure
- 4. Addition Complications of Carrying Carrying Charge Rate — Replacement Cost, Decommissioning and Deferred Taxes
- 5. Project Finance versus Traditional Approach to Computing Carrying Charge Rates
- 6. Necessity to Convert to Real (i.e. constant) Currency – Would Need to Compute Present value of the Inflated Fuel Cost using Nominal Currency
- 7. Tax Issues with Carrying Charges and the Concept that Recovery of Equity Returns can be Evaluated with the Formula: Recovery = Recovery + Recovery x t/(1-t)
- 8. Deferred Tax Complications whereby Recovery can be Computed through First Calculating the PV of the Tax Shield and then using this to Compute the Payment
- 9 Adjusting the Overnight Cost for Construction Periods with Both Inflation and Financing Cost. Note the Financing Cost must Include Equity and Debt
- 10. Evaluating the Effects of Future Replacement Cost that can Occur at Different Periods
- 11. Computing the Effects of Debt on the Analysis using a Constant Capital Structure.
There are a series of videos that describe each of the adjustments that you can make to derive the carrying charge. The video begins by describing the simple PMT
Carrying Charges and Economic Depreciation
A big difficulty in computing carrying charges with debt and and equity is keeping the capital structure constant. Debt sculpting, mortgage payments or other forms of project finance debt do not keep the capital structure constant. Instead, for computing the debt repayments and keeping the capital structure the same, you can compute the total capital and then after you compute the total capital associated with the project. The total capital can then be allocated. To compute the total capital, the capital must be based on the cash flows. To do this, I insist that you compute the economic depreciation. This is illustrated in the screenshot below.
The depreciation is backed out. Start by considering a normal simple income statement:
The income is the ROE x the opening balance. Before taxes, this income can be divided by one minus the tax rate.
- Revenues Less Operating Expense
- Less Interest
- Less Taxes
- Less Depreciation
- Equals Income
Or, Depreciation = EBITDA – Interest – After-tax Income/(1-Tax Rate)
Or, Depreciation = EBITDA – Interest – ROE * Opening Balance/(1-Tax Rate)
Videos associated with Computing Carrying Charges
There are a series of videos that describe each of the adjustments that you can make to derive the carrying charge. The video begins by describing the simple PMT function that accounts for rate of return on investment and the asset life. Separate videos then move to inflation, tax, depreciation, construction periods, replacement cost and debt. The final video that includes all of the adjustments is explained below. Other videos that walk through each of the financial issues are listed at the bottom of the page. I hope you see how the videos describe many economic and technical aspects of project finance models and to some extent even corporate models. The videos also explain added features of the generic macros that modify colours, links, and sheet structure.
|Carrying Charge Introduction||https://www.youtube.com/edit?o=U&video_id=z9s06nXh7U4|
|Carrying Charges and Inflation||https://www.youtube.com/edit?o=U&video_id=9uh8ZN_SHN4|
|Taxes in Carrying Charge Rates||https://www.youtube.com/edit?o=U&video_id=n3MWZvnleWg|
|Periodic Analysis in Carrying Charges||https://www.youtube.com/edit?o=U&video_id=zp06ubSxiGQ|
|Completed Carrying Charge Analysis||https://www.youtube.com/edit?o=U&video_id=ho2RnSHOWfk|
Files associated Computing Carrying Charges
There are three files associated with this lesson set. The first file is the completed carrying charge analysis that you can use for economic analyses such as the analysis of batteries, solar and diesel. The second file includes all of the components of the carrying charge beginning with the PMT function and ultimately including effects of inflation, taxes, construction timing, replacement and debt. The third file includes exercises that you can work through in order There are a series of videos that describe each of the adjustments that you can make to derive the carrying charge. The video begins by describing the simple PMT function and moves to inflation, tax, depreciation, construction periods, replacement cost and debt.
This page addresses LCOE — the levelised cost of energy and the associated carrying charge rates. LCOE and carrying charge rates are evaluated with through demonstrating how to find data, how to measure and put together all of the factors that drive the carrying charge, and how to use carrying charge rates in economic analysis. For the electricity industry and other capital intensive industries different investment alternatives that have alternative operating lives, capital costs, variable costs, fixed costs and risks the LCOE can be an effective way effectively summarise different alternatives.