## Present Worth And Levelized Costs

Money increases or decreases with time, depending on interest rates for borrowing or saving and inflation. Many people assume energy costs in the future will increase faster than inflation. The same mechanism of determining future value of a given amount of money can be used to move money backward in time. If each cost and benefit over the lifetime of the system were brought back to the present and then summed, the present worth can be determined:

_ (cost total for year S) - (financial benefit total for year S)

(1 + d f where cost total = negative cash flow, S = specific year in the wind system lifetime, M = years from the present to year S, and d = discount rate.

The discount rate determines how the money increases or decreases with time. Therefore, the proper discount rate for any life cycle cost calculation must be chosen with care. Sometimes the cost of capital (interest paid to the bank, or alternately, lost opportunity cost) is appropriate. Possibly the rate of return on a given investment perceived as desirable by an individual may be used as the discount rate. Adoption of unrealistically high discount rates can lead to unrealistic life cycle costs. The cost of capital can be calculated from

CC _ 1 + loan interest rate 1 1 + inflation rate

If the total dollars are spread uniformly over the lifetime of the system, this operation is called levelizing.

where P = number of years in the lifetime.

One further step has been utilized in assessing renewable energy systems versus other sources of energy such as electricity. This is the calculation of the annualized cost of energy from each alternative. The annualized cost calculated from Equation 12.8 is divided by the net annual energy production of that alternative source;

COE = annualized cost/AEP

It is important that annualized costs of energy calculated for renewable energy systems are compared to annualized costs of energy from the other sources. Direct comparison of annualized cost of energy to current cost of energy is not rational. Costs of energy calculated in the above manner provide a better basis for the selection of the sources of energy.

RETFinance is an internet-based cost of electricity model [8] that simulates a 20-year nominal dollar cash flow for a variety of renewable energy power projects. It is difficult to compare cost and COE for different years without taking into account the effects of inflation. There are a number of sites on the Web for calculating inflation from past years to the present [9]. As an example, installed costs for wind farms in 2003 were \$1,000/kW, which is equivalent to \$1,160/kW in 2008. Of course, the amount of inflation in the future is a guess.

## Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

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