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For the analysis I discussed earlier in the thread, the assumption of an upfront cash purchase was assumed. However, the existence of very low financing rate (<2%) seems attractive and requires some more thought on integration into a model. Let's say you have $10k on hand, and intend to purchase a $10k PV system. Let's look at two choices:
1) Spend $10k cash on the PV system
2) Invest the $10k in a hypothetical risk-free bond yielding 2.2% compounded annually, maturing in 10 years. Finance the PV system for zero-down at 1.99% for 10 years.
In Option 2, the monthly payment amortizes to $91.92. At the end of 10 years, the total spent would be $11030.40. However, you would also collect $12430.93 from your bond that matured, netting about $720 into your pocket after taxes. It is like owning a mint, right?
What that first cut doesn't account for is the fact that the $91.92 monthly payment has to come from somewhere, and has time value as well. To keep the comparison fair, the Option 1 could also be given $91.92 / mo to invest, and although an equivalent risk-free bond maturing in progressively shorter amounts of time would not have the same yield, let's say for now that it would. At the end of 10 years, the interest earned on those monthly investments would total up to about $742 after taxes. Based on that result, Option 1 is better by $20, but requires the work of remembering to make the $91.92 investment each month, unless you set up an auto-invest system. Option 2 would have the $91.92 bill each month, which your lender is unlikely to let you forget.
Even though it isn't a fair comparison, this first cut could probably be a realistic prediction of what someone might do. That extra $91.92 per month might disappear into some soft of discretionary spending that would otherwise have been done without. In other words, by requiring the upfront investment in Option 2 in parallel to the financing, even though it is slightly non-optimal, the expected return might actually be higher.
Another way to guarantee that two scenarios are being compared fairly is to require that the monthly finance payment comes out of the account where the $10k was invested. Since there is less money overall in the system being invested at the 2.2% rate, and there is no way to forget making an investment, Option 1 comes out even further ahead, by about $240.
Of course, investments with some risk might offer a higher return than the risk-free 2.2%, and once the after tax yield exceeds the APR of the loan, Option 2 will come out ahead. For example, with a 6% investment return, and with payments coming out of the investment account, the net benefit would be about $1534 after 10 years.
Ok, so now what? Does that $1534 mean that the PV system is "cheaper" than it seems? On a relative basis, the answer should be yes, if the calculation for the all cash purchase had yielded a positive value, then the financed version will be more positive, or will break even quicker. Using that same 6% discount rate, it could also be said that $1534 in 10 years from now is worth $857 dollars today. In other words, by going the financing route under these assumptions, you could take the original $10k system cash flow analysis, change the year 0 cost of the PV system from $10000 to $9143, and leave the rest of the cash flow unchanged, and see how much more quickly the PV system reaches your desired payback level.
If you work often with discount rates, the scenario above might seem trivial to you. For me, by working through the example, it helps reinforce exactly what it means when a particular discount rate is used for analysis. A key point is that when reductions in utility bills are projected, what is done with the savings? Does it get spent on something else, invested, or used to pay off debt? The answer to that question (and ultimately the follow-through) is essential to determining what discount rate is appropriate for a given situation.
Is it worth trying to figure this out? Aren't there calculators that exist to do it automatically? Certainly, SAM does a lot of heavy lifting. My discussion above is built around the net present value concept, and SAM does a good job calculating that. However, to go deeper into payback analysis, there is a lot to learn from what NREL has published showing a detailed comparison of the different metrics that people might use. The NPV based metrics like profitability index and benefit-to-cost ratio are new to me, and I think generally represent my goals in performing the analysis. I will try to understand them better. LCOE, simple payback, IRR, and other methods people might prefer are also discussed, although in conclusion, IRR is dismissed as a poor decision making tool. There is a section on assumption sensitivity, and they cleverly scale the sensitivity into the equivalent purchase price, as I attempted to replicate in my buy vs finance example above.
Unfortunately, SAM does not generate some of these metrics directly, so it seems that once a cash flow is generated, there is still some work to do (I haven't googled yet to see if there are other calculators). The analysis period in the paper is 30 years, much longer than a typical residential customer is interested in, so it is hard to draw any payback conclusions directly from the paper itself. For anyone who is actually interested in the content of this thread, I thought you might find it interesting in its own right.
Figuring out how to apply the different metrics to my small 3 kW system will take more time, although I hope to post the results when I do.
1) Spend $10k cash on the PV system
2) Invest the $10k in a hypothetical risk-free bond yielding 2.2% compounded annually, maturing in 10 years. Finance the PV system for zero-down at 1.99% for 10 years.
In Option 2, the monthly payment amortizes to $91.92. At the end of 10 years, the total spent would be $11030.40. However, you would also collect $12430.93 from your bond that matured, netting about $720 into your pocket after taxes. It is like owning a mint, right?
What that first cut doesn't account for is the fact that the $91.92 monthly payment has to come from somewhere, and has time value as well. To keep the comparison fair, the Option 1 could also be given $91.92 / mo to invest, and although an equivalent risk-free bond maturing in progressively shorter amounts of time would not have the same yield, let's say for now that it would. At the end of 10 years, the interest earned on those monthly investments would total up to about $742 after taxes. Based on that result, Option 1 is better by $20, but requires the work of remembering to make the $91.92 investment each month, unless you set up an auto-invest system. Option 2 would have the $91.92 bill each month, which your lender is unlikely to let you forget.
Even though it isn't a fair comparison, this first cut could probably be a realistic prediction of what someone might do. That extra $91.92 per month might disappear into some soft of discretionary spending that would otherwise have been done without. In other words, by requiring the upfront investment in Option 2 in parallel to the financing, even though it is slightly non-optimal, the expected return might actually be higher.
Another way to guarantee that two scenarios are being compared fairly is to require that the monthly finance payment comes out of the account where the $10k was invested. Since there is less money overall in the system being invested at the 2.2% rate, and there is no way to forget making an investment, Option 1 comes out even further ahead, by about $240.
Of course, investments with some risk might offer a higher return than the risk-free 2.2%, and once the after tax yield exceeds the APR of the loan, Option 2 will come out ahead. For example, with a 6% investment return, and with payments coming out of the investment account, the net benefit would be about $1534 after 10 years.
Ok, so now what? Does that $1534 mean that the PV system is "cheaper" than it seems? On a relative basis, the answer should be yes, if the calculation for the all cash purchase had yielded a positive value, then the financed version will be more positive, or will break even quicker. Using that same 6% discount rate, it could also be said that $1534 in 10 years from now is worth $857 dollars today. In other words, by going the financing route under these assumptions, you could take the original $10k system cash flow analysis, change the year 0 cost of the PV system from $10000 to $9143, and leave the rest of the cash flow unchanged, and see how much more quickly the PV system reaches your desired payback level.
If you work often with discount rates, the scenario above might seem trivial to you. For me, by working through the example, it helps reinforce exactly what it means when a particular discount rate is used for analysis. A key point is that when reductions in utility bills are projected, what is done with the savings? Does it get spent on something else, invested, or used to pay off debt? The answer to that question (and ultimately the follow-through) is essential to determining what discount rate is appropriate for a given situation.
Is it worth trying to figure this out? Aren't there calculators that exist to do it automatically? Certainly, SAM does a lot of heavy lifting. My discussion above is built around the net present value concept, and SAM does a good job calculating that. However, to go deeper into payback analysis, there is a lot to learn from what NREL has published showing a detailed comparison of the different metrics that people might use. The NPV based metrics like profitability index and benefit-to-cost ratio are new to me, and I think generally represent my goals in performing the analysis. I will try to understand them better. LCOE, simple payback, IRR, and other methods people might prefer are also discussed, although in conclusion, IRR is dismissed as a poor decision making tool. There is a section on assumption sensitivity, and they cleverly scale the sensitivity into the equivalent purchase price, as I attempted to replicate in my buy vs finance example above.
Unfortunately, SAM does not generate some of these metrics directly, so it seems that once a cash flow is generated, there is still some work to do (I haven't googled yet to see if there are other calculators). The analysis period in the paper is 30 years, much longer than a typical residential customer is interested in, so it is hard to draw any payback conclusions directly from the paper itself. For anyone who is actually interested in the content of this thread, I thought you might find it interesting in its own right.
Figuring out how to apply the different metrics to my small 3 kW system will take more time, although I hope to post the results when I do.
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