# METHODS OF CALCULATION

The concepts of annualized cost and present worth are employed in LCC. Using the annualized cost method, all costs incurred are converted to equivalent annual costs using a baseline and a specified life span. For example, initial costs would be amortized over the life cycle and include principal and interest (similar to home mortgage payments). Replacement costs or rehabilitation costs at various points during the life cycle would also be converted to equivalent annual costs (sinking fund). The following steps can be employed:

1. Annualized initial cost. Tabulate all initial (acquisition) costs. These include the base cost of each of the alternative systems and any other initial cost. Total these initial expenditures to arrive at the total initial cost (IC). Next, amortize the initial costs (IC) by determining the annual payment necessary to pay off a loan equaling the total initial cost. Using a capital recovery table or the following equation, find the periodic payment (PP) necessary to pay off $1.00 at a discount rate of r over a period of n years. Each total initial cost is multiplied by this factor to determine the annualized cost for this element.

r

1 – (1 + r)-n

2. Annual recurring cost. The next step is to tabulate, for each alternative, the average annually recurring costs for operations, maintenance, and other known factors.

3. Annualized nonrecurring cost. Next, determine the replacement or rehabilitation costs for all major items, for each alternative, at appropriate times during the life span. Also determine the salvage value at the end of the life span. Each of the replacement costs is then discounted from the point in time where the funds are to be expended. Multiply each cost by the present worth factor (PW) from a table or calculated by the equation

PW = (1 + r)-n

Then, the present worth of these replacement and salvage costs is reduced to a uniform series of payments by applying the same capital recovery periodic payment factor (PP) used in step 1. Salvage or residual values are treated similarly except that the resulting costs are negative.

4. Total annual cost. Finally, sum the annualized initial cost, annual recurring cost, and annualized nonrecurring cost for each alternative to determine total annual costs. These costs represent a uniform baseline of comparison for the alternatives over a projected life span at a selected interest rate. The annual differences are then determined and used for recommendations.

5. Present worth of annual difference. To determine the real value of an annual cost difference, calculate its present worth. Multiply each cost by the present worth annuity factor (PWA), which shows how much $1.00 paid out periodically is worth today in real dollars. The factor may be obtained from a table or calculated by the equation

1 – (1 + r)-n

r

Thus, one may then compare the present worth of each alternative to assess the bene fit derived.

6. Effect of inflation. The effect of inflation should be considered in the calculations when determining annual recurring cost, replacement cost, and salvage value, If inflation is constant at a rate i, costs at a future date of y years can be found by multiplying the cost by an inflation factor (IF) given by the equation

IF = (1 + i) у

Thus, the calculations can be made using costs that allow for inflation. Using this procedure, different costs can be adjusted for different levels of inflation, if there is information to support such choices. More complex methods for handling inflation are also available.

If the items being compared do not involve different annual costs, it is more direct to make the present worth calculation directly. Future nonrecurring costs over the project design life can be reduced to their present worth value by multiplying by the PW factor given above, PW = (1 + r)“n. These are added to the initial costs to determine total present worth of each system. The present worth of alternative systems can then be compared.

10.10.1 Example of Calculations

A simple example to illustrate the above calculation method is presented in Table 10.4. In this example, inflation is handled by using a net discount rate equal to the nominal discount rate (assumed as 10 percent) minus the rate of inflation (assumed as 5 percent). Two pipe materials are being considered for a drainage application where the project design life is 50 years. Initial costs associated with pipe A are $150,000, and those associated with pipe B are $180,000. Pipe A will require a $37,400 rehabilitation at the end of 40 years, and pipe B a $25,000 rehabilitation at the end of 45 years. Pipe A will have no salvage value, and pipe B will have a salvage value of $30,000. For illustrative purposes, each is assumed to have an annual maintenance cost of $1000. Calculations in part A show that for the assumed conditions, pipe A will have the lower annualized cost and the present worth of the difference in annual cost is $24,900. Calculations in part B show the same difference in present worth, since the annual recurring costs are the same in this example. (For an example of LCC in pavements, see Art. 3.11.)

Life cycle costing is a technique to assess the total cost consequences between alternatives. The potential to optimize value through LCC is only as good as the alternatives being considered. It should be used in proper sequence as part of the VE effort.

(H. G. Tufty, Compendium on Value Engineering, Indo-American Society, Bombay, 1989; “Value Engineering and Least Cost Analysis,” Handbook of Steel Drainage and Highway Construction Products, AISI, Washington, D. C., 1994.)

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