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Life Cycle Costing

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Description

Life Cycle Analysis

Formulas

Description

Doing a life-cycle cost analysis (LCC) gives the total cost of your PV system - including all expenses incurred over the life of the system. There are two reasons to do an LCC analysis: 1) to compare different power options, and 2) to determine the most cost-effective system designs. For some applications there are no options to small PV systems so comparison of other power supplies is not an issue. The PV system produces power where there was no power before. For these applications the initial cost of the system is the main concern. However, even if PV power is the only option, a life-cycle cost (LCC) analysis can be helpful for comparing costs of different designs and/or determining whether a hybrid system would be a cost-effective option. An LCC analysis allows the designer to study the effect of using different components with different reliabilities and lifetimes. For instance, a less expensive battery might be expected to last 4 years while a more expensive battery might last 7 years. Which battery is the best buy? This type of question can be answered with an LCC analysis.

Some might want to compare the cost of different power supply options such as photovoltaics, fueled generators, or extending utility power lines. The initial costs of these options will be different as will the costs of operation, maintenance, and repair or replacement. A LCC analysis can help compare the power supply options. The LCC analysis consists of finding the present worth of any expense expected to occur over the reasonable life of the system. To be included in the LCC analysis, any item must be assigned a cost, even though there are considerations to which a monetary value is not easily attached. For instance, the cost of a gallon of diesel fuel may be known; the cost of storing the fuel at the site may be estimated with reasonable confidence; but, the cost of pollution caused by the generator may require an educated guess. Also, the competing power systems will differ in performance and reliability. To obtain a good comparison, the reliability and performance must be the same. This can be done by upgrading the design of the least reliable system to match the power availability of the best. In some cases, you may have to include the cost of redundant components to make the reliability of the two systems equal. For instance, if it takes one month to completely rebuild a diesel generator, you should include the cost of a replacement unit in the LCC calculation. A meaningful LCC comparison can only be made if each system can perform the same work with the same reliability.

LCC Calculation

The life-cycle cost of a project can be calculated using the formula:

LCC = C + M_pw + E _pw + R _pw - S _pw.

where the pw subscript indicates the present worth of each factor.

• The capital cost (C) of a project includes the initial capital expense for equipment, the system design, engineering, and installation. This cost is always considered as a single payment occurring in the initial year of the project, regardless of how the project is financed.
• Maintenance (M) is the sum of all yearly scheduled operation and maintenance (O&M) costs. Fuel or equipment replacement costs are not included. O&M costs include such items as an operator's salary, inspections, insurance, property tax, and all scheduled maintenance.
• The energy cost (E) of a system is the sum of the yearly fuel cost. Energy cost is calculated separately from operation and maintenance costs, so that differential fuel inflation rates may be used.
• Replacement cost (R) is the sum of all repair and equipment replacement cost anticipated over the life of the system. The replacement of a battery is a good example of such a cost that may occur once or twice during the life of a PV system. Normally, these costs occur in specific years and the entire cost is included in those years.
• The salvage value (S) of a system is its net worth in the final year of the life-cycle period. It is common practice to assign a salvage value of 20 percent of original cost for mechanical equipment that can be moved. This rate can be modified depending on other factors such as obsolescence and condition of equipment.

Future costs must be discounted because of the time value of money. One dollar received today is worth more than the promise of $1 next year, because the $1 today can be invested and earn interest. Future sums of money must also be discounted because of the inherent risk of future events not occurring as planned. Several factors should be considered when the period for an LCC analysis is chosen. First is the life span of the equipment. PV modules should operate for 20 years or more without failure. To analyze a PV system over a 5-year period would not give due credit to its durability and reliability. Twenty years is the normal period chosen to evaluate PV projects. However, most engine generators won't last 20 years so replacement costs for this option must be factored into the calculation if a comparison is to be made.

To discount future costs, the multipliers presented in the tables below can be used. The first table lists Single Present Worth factors. These are used to discount a cost expected to occur in a specific year, such as a battery replacement in year 10 of a project. The second table lists Uniform Present Worth factors that are used to discount annually recurring costs, such as the annual fuel cost of a generator. To use the tables, simply select the column under the appropriate discount rate and read the multiplier opposite the correct year or span of years.

Single Present Worth Factors

Uniform Present Worth Factors

The discount rate selected for an LCC analysis has a large effect on the final results. It should reflect the potential earnings rate of the system owner. Whether the owner is a national government, small village, or an individual, money spent on a project could have been invested elsewhere and earned a certain rate of return. The nominal investment rate, however, is not an investor's real rate of return on money invested. Inflation, the tendency of prices to rise over time, will make future earnings worth less. Thus, inflation must be subtracted from an investor's nominal rate of return to get the net discount rate (or real opportunity cost of capital). For example, if the nominal investment rate was 7 percent, and general inflation was assumed to be 2 percent over the LCC period, the net discount rate that should be used would be 5 percent.

Different discount rates can be used for different commodities. For instance, fuel prices may be expected to rise faster than general inflation. In this case, a lower discount rate would be used when dealing with future fuel costs. In the example above the net discount rate was assumed to be 5 percent. If the cost of diesel fuel was expected to rise 1 percent faster than the general inflation rate, then a discount rate of 4 percent would be used for calculating the present worth of future fuel costs. Check with your local bank for their guess about future inflation rates for various goods and services. You have to make an estimate about future rates, realizing that an error in your guess can have a large affect on the LCC analysis results. If you use a discount rate that is too low, the future costs will be exaggerated; using a high discount rate does just the opposite, emphasizing initial costs over future costs. You may want to perform an LCC analysis with "high, low and medium" estimates on future rates to put bounds on the life-cycle cost of alternative systems.

Formulas

1. The formula for the single present worth (P) of a future sum of money (F) in a given year (N) at a given discount rate (I) is

P = F/(1 + I)^N.

2. The formula for the uniform present worth (P) of an annual sum (A) received over a period of years (N) at a given discount rate (I) is

P = A[1 - (1 + I)^-N]/I.

3. The formula for the modified uniform present worth of an annual sum (A) that escalates at a rate (E) over a period of years (N) at a given discount rate (I) is

P = A{(1+E)/(I-E) *[1 - [ (1+E)/(1+I)]^N]}

4. The formula for the annual payment (A) on a loan whose principal is (P) at an interest rate (I) for a given period of years (N) is

A = P{I/[1 - (1 + I)^-N]}.

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