=88. Cost Comparisons of Different Designs.=—In the design of a pumping station and its equipment the relative costs of different designs should be compared, and the least expensive design selected, due consideration being given to serviceability, reliability, and other factors without definite financial value. In comparing the costs of different types of machinery, all items in connection with the pumping station should be considered. For example, the cost of an electrically driven centrifugal pump and equipment may be less than the total cost of a steam driven reciprocating pump and equipment because of the saving in the cost of boilers, boiler house, etc., but a comparison of the capitalized cost of the two might show in favor of the reciprocating steam pump because of the lower cost of operation. The total cost of a plant, or any portion thereof, may be considered as made up of three parts: (1) The first cost, (2) operation and maintenance and, (3) renewal. The total cost S can be expressed as _S_ = _C_ + _O_⁄_r_ + _R_, in which _C_ = the first cost; _O_ = the annual expenditure for operation and maintenance; _R_ = the amount set aside to cover renewal; _r_ = the rate of interest. _S_ is called the capitalized cost of a plant. The annual payment necessary to perpetuate a plant is _A_ = _Sr_ = _Cr_ + _O_ + _Rr_. The value of _R_ is useful when expressed in terms of the life of the plant or machine and the current rate of interest. It is sometimes called the depreciation factor or capitalized depreciation. If it is borne in mind that _R_ is the amount to be set aside at compound interest for the life of the plant, at the end of which time the accrued interest should be sufficient to renew the plant, it is evident that _R_(1 + _R_)^n − _R_ = _C_ or _R_ = _C_⁄((1+_r_)^n − 1) in which _n_ is the period of usefulness, or life of the plant, expressed in years, no allowance being made for scrap value. A comparison of the annual expense of three different plants is shown in Table 32. It is evident from this comparison that the machinery with the least first cost is not always the least expensive when all items are considered. A sinking fund is a sum of money to which additions are made annually for the purpose of renewing a plant at the expiration of its period of usefulness. The annual payment into the sinking fund is equivalent to the term _Rr_ in the expression for annual cost, or in terms of _C_, _r_, and _n_, the annual payment is _Cr_⁄((1 + _r_)^n − 1). It is the same as the capitalized depreciation multiplied by the rate of interest. The expression _r_⁄((1 + _r_)^n − 1) is sometimes called the rate of depreciation.