**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:

**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.**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%.**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.**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.**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:

**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:

Max state tax credit/refund 35 % or 5000 $ (cap)

Crude oil cost 80 $/barrel

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

**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).

**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.

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:

**Acknowledgments**

**References**

[5] U. Bonne, “Study of a Newly Installed Home Solar PV System: Actual and Calculated Outputs,” at http://friendsofnelha.org/study-of-a-newly-installed-home-solar-pv-system-actual-and-calculated-outputs/, 6 Dec. 2009

**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

**rate adjustment that may apply to the Minimum Charge”**. Historically, such rate adjustments to the MMC have averaged TBD %/year

**Appendix**

**Calculator Inputs:**

**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”

**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)

**L**, in years, is the expected service life or warranty period of the generator, whether composed of solar PVs or wind turbine

**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].

**n**, in number per year. Most banks now do this daily of 365/y

**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)

**dE1**, in %/year. According to the EIA (Energy Information Agency) escalation rates run between 2 and 4%, with Hawaii closer to the high range.

**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

**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

**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

**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

**Cmu**, the $/month minimum amount charged by some utilities such as HELCO, as per NEM agreement. See ref.[10] about MMC billing details.

**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**

**C,**is the capital investment after correcting for subsidies = Co*(1-Tf/100 -Ts/100)

**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.

**Se,**in kWh/y, i.e. the electricity not provided by the utility = 8760*W*F/100

**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

**So,**in $/y, allowing for 29% e-generation & distribution efficiency, 80% crude oil refining efficiency and 40 gal/barrel:

**Sa**, in %/y, cost savings relative to invested capital, C: Sa = 100*S/C

**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

**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 1

^{st}-year cost of electricity. However, P2 increases and t2 decreases with increasing dE1.

**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

**Rt**, in %, same as above net return, after multiplying by L: Rt = Ra*L

**St**, in $, simply form St = Rt*P*t, because P*t represents the total capital and interest of the investment.

**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.

**Cp**, in $/W(peak), is the capital investment, Co, for each installed peak AC watt, W, after allowing for all subsidies:

**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

**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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