AW Value Calculation 

The AW value of an alternative is the addition of two distinct components: capital recovery (CR) of the initial investment and the equivalent A value of the annual operating costs (AOC).

The recovery of an amount of capital P committed to an asset, plus the time value of the capital at a particular interest rate, is a fundamental principle of economic analysis. Capital recovery is the equivalent annual cost of owning the asset plus the return on the initial investment. The A/P factor is used to convert P to an equivalent annual cost. If there is some anticipated positive salvage value S at the end of the asset’s useful life, its equivalent annual value is removed using the A/F factor. This action reduces the equivalent annual cost of owning the asset. Accordingly, CR is

The annual amount (A of AOC) is determined from uniform recurring costs (and possibly receipts) and nonrecurring amounts. The P/A and P/F factors may be necessary to first obtain a present worth amount, then the A/P factor converts this amount to the A value in Equation (5-2).

Lockheed Martin is increasing its booster thrust power in order to win more satellite launch contracts from European companies interested in new global communications markets. A piece of earth-based tracking equipment is expected to require an investment of $13 million. Annual operating costs for the system are expected to start the first year and continue at $0.9 million per year. The useful life of the tracker is 8 years with a salvage value of $0.5 million. Calculate the AW value for the system if the corporate MARR is currently 12% per year.

The cash flows (Figure (5-2a)) for the tracker system must be converted to an equivalent AW cash flow sequence over 8 years (Figure (5.2b)). (All amounts are expressed in $1 million units.) The AOC is A = $ -0.9 per year, and the capital recovery is calculated by using Equation (5-3).

Figure (5-2): (a) Cash flow diagram for satellite tracker costs, and (b) conversion to an equivalent AW (in $1 million), Example (5-2).

The correct interpretation of this result is very important to Lockheed Martin. It means that each and every year for 8 years, the equivalent total revenue from the tracker must be at least $2,576,000 just to recover the initial present worth investment plus the required return of 12% per year. This does not include the AOC of $0.9 million each year. Total AW is found by Equation (5-2).

This is the AW for all future life cycles of 8 years, provided the costs rise at the same rate as inflation, and the same costs and services apply for each succeeding life cycle.

For solution by computer, use the PMT function to determine CR only in a single spreadsheet cell. The format is =  PMT(i%,n,P,-S). As an illustration, the CR in Example (5-2) is displayed when = PMT(12%,8,13,-0.5) is entered. 

The annual worth method is applicable in any situation where PW, FW, or Benefit/Cost analysis can be utilized. The AW method is especially useful in certain types of studies: asset replacement and retention studies to minimize overall annual costs, breakeven studies and make-or-buy decisions (all covered in later chapters), and all studies dealing with production or manufacturing where cost/unit is the focus.