# The Importance of Discounting Future Solar Savings

On May 7, 2016, Pearlie Mae Smith, the winner of the New Jersey Lottery Powerball, had an enviable decision to make: Should she accept \$429 million in payments over 30 years or accept a smaller amount, \$284 million, up front? Though it was 34% lower, Ms. Smith chose the up-front payment. While Ms. Smith was more than 70 years old at the time she won the Powerball, her choice was not unique. Powerball data show that all five winners in 2016 chose the up-front payment versus taking payments over time, forfeiting more than a third of their nominal earnings.

Going back as far as 2003, you will find cases where Powerball winners were willing to sacrifice half their winnings to claim them up front versus spreading them out over time. If sacrificing almost half of one’s nominal winnings in exchange for an up-front payment does not sound totally crazy, you already have an intuitive understanding of the concept of the time value of money, also known as discounting.

Time Value of Money

The time value of money means that a dollar promised at a future date is worth a discounted amount compared to a dollar guaranteed today. This is because there is no guarantee that whoever promised you the dollar will be around or will deliver it in 25 years. Even if the person does deliver the dollar, due to inflation, it will not buy as much in 25 years as it does today. In addition, if you get a dollar today, you can invest it and grow that dollar over time. For all of these reasons, money promised in the future is worth less than money guaranteed today.

Discount rate. In the context of solar, the value of electric bill savings in the future should be similarly discounted relative to cash in hand today. The amount that a dollar in the future is discounted relative to a dollar today is referred to as the discount rate, which the American Heritage Dictionary defines as “the interest rate used in determining the present value of a future payment or series of payments.” In plain English, this is the rate of return at which it makes no difference to you whether you receive the payment today versus sometime in the future.

For the mathematically inclined, you can calculate the discount of future to current savings using Formula 1:

where d is the discount rate, Sn is the savings in year n, S0 is the current value of these savings and n is the year of evaluation. The discount rate is typically expressed as a percentage.

Modeling Financial Returns

If you are not applying a discount rate, or if the software you are using does not do so, you are likely misrepresenting the financial returns of going solar. You may also be making suboptimal solar design decisions or recommending the wrong financing option to your client. Let us examine what the application of a discount rate does to some of the more commonly quoted solar financial metrics—lifetime savings, internal rate of return (IRR), levelized cost of energy (LCOE) and payback period—across two financing options: cash and loan-financed purchase.

Case study. For this example, I used Aurora (aurorasolar.com) both to design the 10 kW system in Figure 1 and to perform the financial analysis. The case study assumes the following: The customer is on PG&E’s E-1 baseline utility rate for Region S; the assumed utility inflation rate is 3%; the system cost is \$3.50 per watt; the loan terms require 20% down and 4.9% interest; incentives are limited to the 30% Investment Tax Credit; and the project service life is 25 years. The financial results presented in Table 1 show that applying a discount rate leads to a reduction in the present value of lifetime savings and the LCOE, as well as a slightly longer payback period. These results have implications for both the recommended financing option and the optimal system design.

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