Machinery's Handbook, 31st Edition
152 EVALUATING INVESTMENTS Equivalent Uniform Annual Cost.— This method is applied when the alternatives have unequal periods of life. To avoid unequal periods of time, the present value and future value is converted to an annual value. The alternatives must be mutually exclusive and repeatedly renewed up to the duration of the longest lived alternative. A = ( P )( A given P ) - ( L )( A given F ) + ( G )( A given G ) + AE
i 1 i + ( ) n – 1 -------------- Li AE + + 1 i + ( ) n
With sinking fund depreciation: With sinking fund depreciation and uniform gradient G :
A P L – ( ) =
[
]
A P L – ( ) i 1 i + ( ) n 1 i + ( ) n – 1 =
-------------- Li AE G 1 i -- + + + P L – ( ) n +1 ( ) i 2 n ------------------- + + +
n 1 i + ( ) n – 1 – --------------
Straight line depreciation:
P L – n ------- Li AE
=
A
Example: An investment of $15,000 is being considered to reduce labor and labor-asso ciated costs in a materials handling operation from $8,200 a year to $3,300. This operation is expected to be used for 10 years before being changed or discontinued entirely. In addi tion to the initial investment of $15,000 and the annual cost of $3,300 for labor, there are additional annual combined costs for power, maintenance, insurance, and property taxes of $1,800 associated with the revised operation. Based on comparisons of annual costs, should the $15,000 investment be made or the present operation continued? Solution: The present annual cost of the operation is $8,200 for labor and labor-associ- ated costs. The proposed operation has an annual cost of $3,300 for labor and labor extras plus $1,800 for additional power, maintenance, insurance, and taxes, plus the annual cost of recovering the initial investment of $15,000 at some interest rate (minimum acceptable rate of return). Assuming that 10 percent would be an acceptable rate of return on this investment over a period of 10 years, the annual amount to be recovered on the initial investment would be $15,000 multiplied by the capital recovery factor. Putting this value into ( A given P ) yields: A i 1 i + ( ) n 1 i + ( ) n – 1 -------------- P AE + ( ) 1+ ( ) 10 1+ ( ) 10 – 1 ----------------------- 15000 + 5100 7541.18 = = = 0.10 0.10 0.10 This amount is less than the present annual cost of $8,200. Thus, the investment is jus- tified unless there are other considerations, such as the effects of income taxes, salvage values, expected life, uncertainty about the required rate of return, changes in the cost of borrowed funds, and others. A tabulation of annual costs of alternative plans A, B, C, etc. is a good way to compare costs item by item. For this example: Item Plan A Plan B 1 Labor and labor extras $8,200 $3,300 2 Annual cost of $15,000 investment 2,442 3 Power 400 4 Maintenance 1,100 5 Property taxes and insurance 300 Total annual cost $8,200 $7,542
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