Green Energy ROI and Electricity Cost Calculator

Overview – This calculator is designed to output various forms of ROI (Return on Investment), payback time, cost savings, etc., resulting from installing green or “clean” electricity generators, such as solar PV (photo-voltaic), wind turbines and energy conservation measures (solar water heaters and energy-efficient appliances). But contrary to standard mortgage calculators, which start with a given term to pay back a bank loan, this calculator assumes that the generated average annual “clean” electricity reduces the electricity bill of the consumer or generator owner, and that this dollar amount, calculated for the first year, is equal to the “fixed,” annual loan-repayment thereafter.   All costs are based on actual, rather than constant 2010 dollars, i.e. the effect of inflation is not explicitly included, but the interest on the bank loan is one of the inputs. In its revised version, this Calculator now accounts for inputs of electricity price escalation rates and bank loan compounding frequency.

All these and other needed Calculator inputs are detailed in the Appendix. Some illustrative Calculator results are described further down. Click here to launch the Calculator.  The default values listed under “Calculator Inputs” correspond to the author’s home PV system, installed in Kona, Hawaii, Nov. 2009[5]. After entering the desired inputs and pressing the “Calculate” button, the new outputs appear on the right side of Table 1. The Calculator can “Memorize inputs,” so that after the user presses that button, that set of inputs can later be retrieved by pressing the ”Reset inputs” button, after running different scenarios.

General Comments – Use of this Calculator assumes that the consumer/owner:
  1. Electricity Credits – Can get credit for all of the electricity produced by the green generator (such as solar PV, wind, etc), at a $/kWh rate or cost entered as input, and corresponding to the one the user would pay if the investment in clean or conservation energy had not been made. This version of the Calculator provides no means to account for excess electricity generated beyond what is consumed, which would be subject to provisions stated in the FIT (Feed-in-Tariff) or NEM (Net Energy Metering) agreement with the local utility. The Calculator does account for the Minimum Monthly Charge (MMC) some NEM agreements impose when the net electricity used from the grid is or approaches zero.
  2. Capacity Factor – Knows the value of the local wind or solar capacity (or use) factor, F. In the case of PVs, F can be calculated from average daily insolation, x, in cal/cm2/day[4]: F =  x*4.184/360/24*100 in % or from average daily peak sun hours, H, in h/d (hours/day): F = H/24*100 in %. For wind generators, and depending on location and altitude, F can range from 10 to 50%. For energy conservation based on installing higher efficiency appliances such as a window air conditioners,, the ~1000 annual hours of power-saving operation would be represented by F = 1000/8760 = 11.41%.
  3. Installation – In the case of PVs, the panels are not shaded by trees or other buildings. In the case of wind generators, the higher the elevation of a wind generator, the higher will be the local capacity factor.
  4. Tax Credits – Knows how much tax credit to enter as input, e.g. for PVs: Federal: 30% with 0 $ cap, and Hawaii State: 35% with a cap of $5000, or refundable credit of 24.5%[1], in case of insufficient tax liability. If a tax credit exceeds a cap, the Calculator adjsts the % input for state refund. The percentages for wind or for “conservation” generators are different.
  5. Return on Investment (ROI) – Wants to compare the rewards from investing in clean or conservation energy with those from placing funds into a savings account. The Calculator therefore calculates “fixed” bank-loan repayments with interest during the payback period, as described above, and outputs:
a)  TROI or total ROI in %, i.e. based on “the total, escalating electricity cost saved” minus “the initial bank loan and interest paid” and divided by that same bank loan and interest.
b)   AAROI or (linear) average, annual ROI in %/year, which is simply based based on TROI divided by the equipment life.  However, this ROI should not be compared to the interest or yield of a typical savings account, because its value is higher than that of a savings account resulting in the same TROI. This higher value could mislead an investor to make a poor choice.
c)   CAROI, or compounded annual ROI in %/year, is equivalent to the interest yield of a compounding savings account, which would generate the same TROI over the same time period (equipment life). It is the same as CAGR (Compound Annual Growth Rate[8]) used by many economists. Note that this value is always smaller than the AAROI. But it is not close to the IRR (Internal Rate of Return) used to compare investment alternatives, which may not include cost of capital; IRR is the value at which the investment is balanced by the sum of future discounted cash flows, so that the Net Present Value or NPV = 0.
Illustrative Calculator Results: We included these here to help new users with inputs and interpretation of outputs. They also serve to illustrate the versatility of the Calculator. We assume the Calculator default inputs can serve as reference conditions. These are:
Peak generator output                 2.0       kW (AC)
Capacity or use factor                  15       %
Generator product life                   25       years
Loan Interest                                 4       %/year
Num. compounding periods          365      per year
Fuel-based electricity cost          0.40       $/kWh
Electricity cost escalation               3        %/year
Capital investment                   15895       $
Max. fed tax credit/refund            30       % or ____   $ (cap; leave blank if there is none)
Max state tax credit/refund           35       % or  5000 $ (cap)
Crude oil cost                               80       $/barrel
Util. min. monthly charge (MMC) 22.16   $/month
Utility MMC escalation                   1       %/year

Now we can consider the effect of the following input variations, relative to those above:

1.      Sensitivity to input parameters such as capacity factor, interest rate, electricity price, etc on the payback time and ROI. For example, a capacity factor change from 15 to 19% shortens the payback time from 12.29 years to 8.43 years and increases the AAROI from 9.54(CAROI = 4.88) to  15.36 %/year (CAROI = 6.31 %/year).
2.      Eliminating the MMC from 22.16 to 0 $/month shortens the payback time from 12.29 to 8.57 years and increases the AAROI from 9.54 to 14.00 %/year (CAROI from 4.88 to 6.02 %/year). Both above changes, if realized, would clearly generate a much greater interest by home owners or investors to install PV systems. Presently, the Calculator equates the “Net Present Value” (NPV) of MMC with the simple cumulative value of the MMC over the life of the PV or wind or “conservation” generator, because the present yield of savings accounts are typically between 0.1 and 1%. This magnifies the MMC effect by a small fraction of what its true effect would be, if the NPV value of cumulative MMC were calculated.
3.      Increasing the present crude oil price from 80 to 100 $/barrel (which may also raise electricity prices from 0.40 to 0.45 $/kWh) would shorten the payback time from 12.29 to 10.12 years and raise the AAROI from 9.54 to 12.28 %/year (CAROI from 4.88 to 5.61 %/year)
4.      Reducing the normalized PV capital cost before tax credits to $12,000, i.e. from 7.95 to 6 $/kW(peak), would shorten the payback time from 12.29 to 8.68 years and raise the AAROI from 9.54 to 15.18 %/year (CAROI from 4.88 to 6.27 %/year)
5.      If all of the above changes were to be realized simultaneously (increased capacity factor and crude & electricity price, and reduced capital and MMC) , the payback time would drop from 11.54 years to 4.17 years and the AAROI rise from 9.54 to 32.95 %/year (CAROI from 4.88 to 8.89 %/year)
6.      How far would the installation cost need to drop, so that under above reference conditions but w/o any tax credits the CAROI would again be at 4.88 %/year? Answer: It would need to drop to the same level it was after the above subsidies, or $7,626 or 3.8131 $/W(peak AC). The Calculator then shows again a payback time of 12.29 years and an AAROI of 9.54 %/year, as it should.
7.      Solar-based electricity cost for the reference Case is 0.266 $/kWh. With the changes discussed above in items 1-6, the “clean” electricity cost in $/kWh would be: 0.202 (for Case #1), 0.137 (2), 0.261 (3), 0.223 (4), 0.075 (5), 0.266 (6), respectively, without counting energy storage or standby costs
8.      This Calculator also can serve to analyze the benefits or advantage of investing in equipment of “Improved Energy Efficiency.” Example: What is the CAROI, payback or cost of “conservation electricity” for a new “Energy Star” window (or central) 2-ton (=24,000 Btu/h) air conditioner(AC), with an SEER rated at 13.0, replacing or to be purchased vs. a model rated at SEER=9 ***.  If the
*** SEER = Seasonal Energy Efficiency Ratio or Btu/Wh for heating (heat pump) or cooling (AirCond). For heating, a 100% efficient strip heat has an SEER = 3.414 Btu/Wh, because an efficiency of (3.414 Btu/Wh)(1 Wh/3600 J)(1054 J/Btu) = 3.414/3.414 = 1, i.e. 100%.  An AC with an SEER = 13 would output 13/3.414 = 3.81 times more energy than consumed by the compressor-“pump” and auxiliaries.
higher-efficiency AC is also used as heat pump, the equipment cost may be split, and a separate run made for heating-mode-SEER and hours/year (h/y) use. The difference in power consumption for the above AC is 24,000/9 – 24,000/13 (Btu/h)/(Btu/Wh) = 2667 – 1846 = 820.5 W or 0.8205 kW, which is the first Calculator input. Assuming 1000 h/y operation, these hours correspond to a capacity factor of 1000/8760 = 11.4% (second input). Assuming a service life of 16 y, 4%/y interest, an electricity cost of 0.40 $/kWh, investment of $1300, MMC = 0, and some tax credit rebates (10% each), the output column shows the result in terms of the savings, payback time (3.44 years), AAROI (532.8%/year), CAROI (11.53 %/year) normalized cost of the investment based on peak power after subsidies (1.28 $/W) and electricity “cost” of conservation as 0.086 $/kWh. If the above SEER ratings are used to compare an existing vs. a new AC, the remaining service life and pro-rated cost of the old one should be added to the capital cost. In any case, one would input the difference in kW rating and difference in price as capital investment, AFTER proportioning both inputs for equal Btu/h output, in case the two AC units do not have the same output rating.

This link opens a new window and takes the reader directly to the Calculator. Its Table 1 lists its input parameters on the left columns and its output parameters on the right side, while allowing the reader to toggle back to this text for instructions. These consist of detailed descriptions of all input and output parameters located below in the Appendix, including the used formulas.

Future Features – Clean or green energy from variable sources such as wind, solar PV of wave power need to be coupled to energy storage and stand-by generators in order for the utility to be able to continue to provide reliably constant grid voltage and frequency. As technology progresses, not only can distributed clean energy sources help the utility to smooth out some of that variability, but even further help could be provided by distributed storage equipment.  In their quest for reliability, utilities may implement time-of-day or grid-load-based electricity rates. Therefore, future analyses and/or additions to this Calculator, may include:

·         Such variable rates,
·         The economic consequences of installing excess PV capacity under NEM or FIT agreements and
·         Means to compare the economics of installing battery back-up vs. the cumulative cost of the MMC.
Other inputs such as equipment performance degradation (e.g. output power) with time, Feed-in-Tariff agreement aspects, and explicitly calculating the effects of inflation, are also features worth considering for future Calculator updates.
Acknowledgments
My Excel spreadsheet algorithms were converted into PHP and html software and uploaded by my son Marc Bonne[2]. This Calculator is supported by a WordPress website at http://alohafuels.com.
References
[1] Hawaii State “Renewable Energy Technologies Income Tax Credit,” Form N-342 Lines 42-46 and 342A (2009)
[2] Marc Bonne, Seattle, WA, Design Nebula, Inc.,   mgbonne@comcast.net, (206) 526-9311
[3] Joe Gates, Kailua-Kona, HI, joe@bluebeachdesign.comwww.bluebeachdesign.com
(808) 990-6164
[4] Global Energy Concepts, LLC, “A Catalog of Potential Sites for Renewable Energy in Hawaii,” December 2006. Web document Fig. 7, p.37 by Hawaii Statewide GIS Program (Geographic Information System) at http://hawaii.gov/dbedt/gis/, with a cal/cm2/day map for solar inputs
[6] Home Equity Loan Line of Credit (HELOC) VISA issued by Endura Financial Fed. Credit Union, in Minneapolis, MN atinfo@email.endurafinancial.com 800.533.4004. Variable loan interest rate: 4 %/year. Also available at TCF Bank. Bank of Hawaii offers home equity variable interest loan rates ranging from 5 to 6.25 and fixed rates ranging from 6.4 to 7.5 %/y.
[7] Andy Black, “Economics of solar electric systems for consumers: Payback and other economic tests,” 2009, © Andy Black. July 2009 – 19 pp. Website - http://www.ongrid.net/papers/PaybackOnSolarSERG.pdf
[8] Compound Return on Investment. When expressed in annual terms, a compound return can be referred to as a “compound annual growth rate”(CAGR). For example, if an investment fund claims to have produced a 10% annual compound return over the past 5 years, this means that at the end of its 5th year, the fund’s capital has grown to a size equal to what it would be if the funds on hand at the beginning had been “invested” and compounded for 5 years in a saving certificate yielding 10%/year.
[9] HELCO NEM Contract (Docket No. 05-0037, D&O No. 22313, Dated March 9, 2006), Section 13.C.3: “… if such amount does not exceed the Minimum Charge, (MMC) the Customer-Generator will be billed the Minimum Charge, plus any rate adjustment that may apply to the Minimum Charge”. Historically, such rate adjustments to the MMC have averaged  TBD %/year
[10]The MMC (Minimum Monthly Charge), as explained by HELCO’s billing staff (Oct.2010), works as follows. If a customer uses less than 33 kWh/month (this amount changes from month to month as electricity cost, energy surcharges and other fees change), he will be charged the MMC ($22.16 at present on the Big Island and ~$18 on Oahu). If he uses more, he will pay $22.16 + (consumed kWh – 33) x price/kWh.
Appendix
All input and output parameters is listed below. For the readers interested in the calculation details, the used formulas are included as well.
Calculator Inputs:
Peak generator output, W, in kilowatts of alternating current, kW(AC). For solar PV and wind generators, this would be the design (or maximum) output after an inverter has converted the DC to AC (direct to alternating current). For equipment comparisons, enter the difference in power use for equal or equivalent output, because that difference is the power of the conservation “generator”
Capacity factor, F,           in %, quantifies the average available power for a given generator. For solar PVs it may be defined as: 1) the average energy input, relative to the maximum possible on a cloudless day, with the sun elevation at 90 degrees; or 2) the average energy output, relative to the rated output of the PVs. As stated above, F can also be calculated from average daily insolation, x, in cal/cm2/day[4] or its average daily peak sun hours, H. H = x*4.184/360 in h/d (hours/day) and F = x*4.184/360/24*100 in %. Conservatively, we use 15% for Hawaii, unless measured values tell us otherwise, e.g. 20% in ref.[5]. For wind, typical F-values range from 30 to 45%, although they may reach 50-60% in high-wind locations and even higher at altitudes above 330 m (1000 ft)
Generator product life, L, in years, is the expected service life or warranty period of the generator, whether composed of solar PVs or wind turbine
Loan interest rate, r,       in %/year, is the interest charged by a bank, e.g. for a home equity loan. As of March 2010, a 4 %/year seems to be common and available[6].
Number of annual compounding periods, n, in number per year. Most banks now do this daily of 365/y
Fuel-based electr. total price, E1, in $/kWh, is the price paid by consumers to the local utility. If applicable, a more meaningful value to enter is the FIT or NEM tariff a utility would pay the consumer for the energy produced by the DG (Distributed Generator)
Electricity cost escalation, dE1, in %/year. According to the EIA (Energy Information Agency) escalation rates run between 2 and 4%, with Hawaii closer to the high range.
Capital investment, Co,    is the total investment cost of installing a solar or wind generator, including connection permit fees, disconnect boxes, inverters and applicable excise or sales taxes
Max. federal tax credit/refund, Tf, i.e. the smaller of 1) max. subsidy expressed as a % of Co, and 2) the max. subsidy expressed in $; if there is no cap the input here may be a zero or a “blank” which the Calculator reads as an infinite dollar amount
Max. state tax credit/refund, Ts, i.e. the smaller of 1) max. subsidy expressed as a % of Co, and 2) the max. subsidy expressed in $; if there is no cap the input here may be a zero or a “blank”
One can now also enter the relevant cap and then let the Calculator determine the lesser of the two inputs
Crude oil price, Eo,          in $/barrel, is only used to calculate the saving of imported fuel. However, a price increase may cause future increases in the above fuel-based electr.total price
Utility minimum monthly minimum charge (MMC), Cmu, the $/month minimum amount charged by some utilities such as HELCO, as per NEM agreement. See ref.[10] about MMC billing details.
Utility MMC escalation, dCu,   in %/year. Assuming that this value might be close to that of inflation, we have used 1% as a preliminary default value.
The input of an MMC escalation, dCu, gives the user a tool to account for annual escalation due to inflation, f, and/or discount future MMC payments according to the cost of money (=loan interest rate, r):
                                      — To ignore escalation or discount by inputting dCu = 0.– To simultaneously account for inflationary escalation and for the “lower present value” of future (discounted) MMCs by inputting dCu = f – r, which would typically be a negative number, which results in Calculator outputs (e.g. E2 in $/kWh, below) representing “net present” values. Or– To only consider inflation, just input dCu = f, such as 1 or 2 %. The Calculator outputs then represent average values for the period L.        But note that the above dCu values need to be consistent with the input chosen for dE1. Because kWh-energy is not subject to inflationary or discounting effects, E2 would not be affected by changes in dE1, if payback time were not. However, the Calculator displays two payback results: The first represents (minimum) payback time resulting from paying down the loan with all profits as they typically increase each year. The second represents the payback resulting from fixing the annual loan repayment at the profit made and amount paid in the first year. All ROIs are based on the former (maximum rate of loan repayment). 
Calculator Outputs
Capital after subsidies, C, is the capital investment after correcting for subsidies = Co*(1-Tf/100 -Ts/100)
Life cumulative utility MMC, Cu, i.e. this is the cumulative MMC payments, over the life of the generator. Without MMC escalation we would have, Cu = Cmu*12*L, but w/escalation: Cu = Cmu*12*(1-(1+(dCu+0.0001)/100)^(L+1))/(1-(1+(dCu+0.0001)/100)). The addition of 0.00001 is to prevent non-convergence when dCu ~ 0. The expression after Cmu*12 is the sum of the geometric series with the annual escalation factor of 1+dCu/100 for L years.
Electric energy saving, Se, in kWh/y, i.e. the electricity not provided by the utility = 8760*W*F/100
Average electricity cost saving, Sc, in $/y, is the cost saving after subtracting the average annual MMC, so that Sc = Se*E1*(1-(1+(dE1+0.0001)/100)^(L+1))/(1-(1+(dE1+0.0001)/100))/L – Cu/L
Crude oil import saving, So, in $/y, allowing for 29% e-generation & distribution efficiency, 80% crude oil refining efficiency and 40 gal/barrel:
So = Se/0.29*3.6E6/1054/120000/0.80*Eo
Average return on assets, Sa, in %/y, cost savings relative to invested capital, C: Sa = 100*S/C
Payback time, t,              in years, is the time needed to pay back the loan, based on equating the annual mortgage payments to the above electric energy cost savings, Sc:

                                                t = (LOG(Sc) – LOG(Sc-C*(r/100))) / LOG(1+(r/100)), if dE1=0 and n=1. To avoid escalation of the mortgage as the electricity rate escalates, we chose the mortgage payments to remain “fixed” to the amounts paid during the first year. However, daily compounding complicates the above equation a bit, to become: t = ((LOG((W*F/100*L*8760-Cmu*12)/n) – LOG((W*F/100*E1*8760-Cmu*12)/n-C*((r+0.00001)/n/100))) / LOG(1+((r+0.00001)/n/100)))/n. Depending on whether to escalate or not the loan payments as energy cost savings escalate with escalating electricity rates, we get:

                                      t1 = t as per above formula, unaffected by dE1, so that the loan payments remain “fixed” and equal to the amounts paid during the first year. However, if we want to minimize payback time, we also calculate
                                      t2 < t1 by letting the loan payments escalate as electricity rates escalate. Note that neither t1 nor t2 would cover payment for MMC between t and L
Loan payments:Fixed, P1, or maximum, averaged, P2, in $/y. For P1, the first year energy cost savings are made identical to P1, the “fixed” annual loan payment, after subtracting the MMC. Therefore, for the duration of the payback time, the owner pays the same amount (minus MMC, which is only imposed when the electric bill would be less than the MMC) as he did before installing the generation or conservation equipment. With known t1=t and C, P1 is the classical payment, compounded annually: P1 = C*(r/100)*(1+(r/100))^t/((1+(r/100))^t-1), and should equal Sc, if n = 1,i.e. compounding is done once per year.  Otherwise, e.g. for daily compounding, n=365, and P1 = C*((r+0.00001)/n/100)*(1+(r+0.00001)/n/ 100)^(t*n)/ ((1+(r+0.00001)/n/100)^(t*n)-1)*n. P1 does not (but t1 does) depend on the bank loan interest. Neither depends on dE1, because they are based solely on the 1st-year cost of electricity. However, P2 increases and t2 decreases with increasing dE1.
Average, annual ROI (AAROI), Ra, in %/year, net return on investment (AAROI) averaged over the life of the generator, calculated as a ratio of the total life-cycle “clean” electric energy value generated minus capital and interest(after tax credits), divided by the same capital and interest, and by the years of equipment life.: Ra = (Sc*L – P*t)/P/t/L *100
Total generator life ROI (TROI), Rt, in %, same as above net return, after multiplying by L: Rt = Ra*L
Total net cost savings, St, in $, simply form St = Rt*P*t, because P*t represents the total capital and interest of the investment.
Compound, annual ROI (CAROI), Rc, in %/year, is equivalent to the interest yield of a compounding savings account, which would generate the same net TROI over the same time period (equipment life); in both cases, the principal is not altered over the time L: It is zero, i.e. a repaid loan for CAROI, and Co before and after the time period L. CAROI therefore needs to satisfy the un-compounding of Rt: Rc = (1+ Rt/100)^(1/L/n)*100*n. CAROI is the same as CAGR (Compound Annual Growth Rate[8]) used by many economists. Note that this value is always smaller than the AAROI. But CAROI is not close or equal to the IRR (Internal Rate of Return) used to compare investment alternatives, whereby IRR is the value at which the investment is balanced by the sum of future IRR-discounted cash flows, so that the Net Present Value or NPV drops to zero within a given number of years.
Normalized cost of installed peak power w/ subsidy, Cp, in $/W(peak), is the capital investment, Co, for each installed peak AC watt, W, after allowing for all subsidies:
                                                Cp = C/W/1000*(1-Tf/100-Ts/100)
Normalized cost of installed average power w/ subsidy, Cv, in $/W(average), is the capital investment, Co, for each installed average watt, 100*W/F, after allowing for all subsidies. This value is 100/F times larger than Cp: Cv = Cp*100/F
Life-cycle cost of renewable electricity, E2, in $/kWh, the cost of electricity as represented by the cumulative minimum meter charge (MMC) during the service life of the generator plus the fixed mortgage payments during the payback period, divided by the cumulative electricity output during the service life of the generator: E2 = (Cu+P*t) / (L*Se)

 

Ulrich Bonne, Kailua-Kona, Hawaii

 

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