ABSTRACT
By multiplying through by a scalar (1+ ρ)T , we obtain the equivalent inequality T∑ t=1
Bt(1+ ρ)T−t > K(1+ ρ)T (29.2)
which may be summarized as TVρ(B) > TVρ(K), where TVρ(B) stands for the terminal value of the stream of benefits when each is compounded forward to terminal date T at rate ρ, and TVρ(K) stands for the terminal value of the outlay K when it also is compounded forward to terminal date T at rate ρ. If and only if PVρ(B) > K does TVρ(B) > TVρ(K); one form of the criterion,
that is, entails the other. But the latter form is far more revealing: it makes clear that, for the criterion to be met, the aggregate of the benefits, B1,B2,BT , when each benefit is wholly and continually reinvested to time T at this same weighted rate of return ρ, must exceed the sum which K amounts to when it also is wholly invested and reinvested to the terminal year T . Such a criterion would, of course, be applicable in the rare case when, in fact, both the benefits and the initial outlay of the project were to be used in exactly this way. It could be justified only if all benefits were encashed and wholly invested and reinvested at ρ, the return to private investment, until the terminal date, and similarly for the amount K . Inasmuch as this implicit requirement is seldom complied with, the use of a
criterion that is valid only if such a requirement is, in fact, assured can be seriously misleading. Certainly, any of these four criteria is misleading when it is applied to a public project without information in the particular case about the disposal of
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of stream that the economy.1
