Incorporation of adjustments to the levelised cost for degradation are addressed on this page. In some cases like solar and batteries, the entire plant degrades and you can adjust the recovery of the total capital cost. In other cases such as for hydrogen, the degradation applies only to one cost item — the purchase of electricity. On this page I show you how to apply both types of degradation. I emphasize again that the you should worry much more about getting the levelised cost number right and less about your financial model which just proves that the levelised cost numbers are correct. The effects of degradation on levelised cost can include degradation only in input or fuel expense. The LCOE calculator attached to the button below can be used to evaluate degradation in the entire project or only the operating expense. Formulas and technical details are explained below.
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Summary of Degradation Formulas
There is degradation of the total output which requires a kind of reverse inflation. This can be done by making a separate calculation of the real or nominal IRR just for the calculation of O&M expenses.
For inflation analysis when adjusting the O&M from real to level nominal, then you use PV of O&M with real/PV of O&M with nominal. You can use the PV formula in excel, not the NPV formula.
PV(real rate, life, O&M)/PV(nominal rate, life, O&M).
This factor will be above 1.0 if the inflation rate is positive and the real rate is below the nominal rate.
The same adjustment can be made for real degradation where the real discount rate is computed from (1-real rate)/(1+cost degradation) – 1.
I wrote some notes, but here is the step by step approach. Note that there are different calculations for nominal LCOE and Real LCOE. Note that when you make adjustments to the rates for PMT and for PV calculations, you should be careful with the denominator.
Note that the tax adjustment — divided by (1-t) is made to the PMT function using the nominal IRR adjusted for degradation.
Part 1: Adjustments to Nominal LCOE for Overall Output Degradation
Step 1: Compute the adjusted nominal IRR for degradation as
Adjusted Nominal Rate = (1+Nominal Rate)/(1-Degradation Rate)
Step 2: Apply the Adjusted Nominal Rate in the PMT function
Step 3: Adjust the Initial O&M. This is confusing. The O&M goes up because it should inflate and it goes up further because of degradation. So there are two adjustments to the O&M for nominal levelization. You compute a PV factor adjustment and use the real rate in the numerator and the nominal rate adjusted for degradation in the denominator
Compute the nominal rate adjusted for degradation. This produces a higher rate
Nominal Adjusted IRR = (1+Nominal IRR)/(1-Degradation) – 1
If you have not computed it, compute or find the real unadjusted rate. This will be the rate adjusted for inflat
Real IRR = (1+Nominal Unadjusted IRR)/(1-Inflation Rate) – 1
Step 4: Then you can compute an adjustment factor using the PV function. To do this, compute the PV factor using the PV of at the Real Rate on the top and using the adjusted nominal rate at the bottom.
Adjustment Factor = PV(Real rate, life, O&M)/PV(Nominal Adjusted Rate, Life, O&M).
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Step 5: Apply the adjustment factor to the O&M
Starting O&M in financial Model subject to adjustment = base O&M x (inflation index) * (degradation index)
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Part 2: Adjustments to Real LCOE for Overall Output Degradation.
Step 1: Compute Real Rate as (1-Nominal Rate)/(1+Inflation Rate) – 1
Step 2: Compute Real Rate with overall degradation effect:
Real rate with degradation = (1+real rate)/(1-degradation) – 1
This adjusted rate is applied to the PMT function and to the O&M function for overall degradation.
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Inclusion of Degradation in the Levelised Cost using adjustments to both Carrying Charges and O&M Costs
The formulas below evaluate 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. The price is not the average of 15.00 because you should give less weight to the price when there is less generation.
You should make changes to both nominal and real LCOE and you should make operating expense adjustments. The adjustments are represented by the following equations:
Adjusted Target IRR for Degradation = (1+Nominal IRR)/(1-Degradation)
Adjusted Real IRR for Degradation = (1+Real IRR)/(1-Degradation)
O&M Factor Nominal = PV(Real IRR,Life,-1)/PV(Adjusted Nominal IRR,life,-1)
O&M Factor Real = PV(Real IRR,Life,-1)/PV(Adjusted Real IRR,life,-1)
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 how the real and nominal discount rate (target project IRR) is adjusted for degradation. The formulas to apply when adjusting the carrying charge include an adjustment to discount rates:
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.
Degradation with for a Single Expense Rather than the Entire Project
As stated above, for an electrolyzer the degradation can be for the quantity of electricity purchased rather than for the entire project.