# Annual Cost

To compare alternatives by annual cost, all cash flows are changed to a series of uniform payments. Current ex-penditures, future costs or receipts, and gradients must be converted to annual costs. If a lump-sum cash flow occurs at some time other than the beginning or end of the eco-nomic life, it must be converted in a two-step process: first moving it to the present and then spreading it uniformly over the life of the project.

Alternatives with unequal economic lives may be compared by assuming replacement in kind at the end of the shorter life, thus maintaining the same level of uni-form payment.

EXAMPLE:

Compare the value of a partial or full sprinkler sys-tem purchased at 10 percent interest.

Annual cost (partial system) =A + P(A/P, 10%, 15)

= \$1000 + \$8000(0.13147)

= \$2051.75

Annual cost (full system) = A + P(A/P, 10%, 20)

= \$250 + \$15,000(0.11746)

= \$2011.90

The full system is slightly more economically desirable. When costs are this comparable, it is especially important to consider other relevant decision criteria, for example, uninsured losses.