Decision Rules

Abstract

Capital investments yield social benefits over a period of time. For purposes of analysis these benefits cease at the end of the project’s ‘economic life’. The physical life of a dam may be hundreds of years, but silt deposits behind the dam tend to limit its economic life to perhaps a hundred years. Technically, benefits and costs need to be estimated over the complete economic life, which sets the ‘time horizon’ of the project. But future benefits and costs are not treated as being of equal importance as present benefits and costs. The general rationale for ‘discounting’ future gains and losses in public investment projects is that society expresses a preference for the present over the future. The derivation of society’s rate of ‘time preference’ and the other arguments for discounting are dealt with in Section 6 below. If, for the moment, the validity of discounting is accepted, it is necessary to revise the simple decision rule of maximising the difference between benefits and costs. In formal language, we require the net present value of benefits (NPV(B)) to be greater than zero before any project is accepted as being potentially worthwhile. Symbolically,

$$\sum\limits_{t = 0}^{t = T} {{B_t}} \;.\;{d_t} - \sum\limits_{t = 0}^{t = T} {{K_t}} \;.\;{d_t} = {\rm{GPV}}\left( {\rm{B}} \right){\rm{ - GPV}}\left( {\rm{K}} \right){\rm{ = NPV}}\left( {\rm{B}} \right)$$

where B _t is the benefit in period t, K _t the cost in period t, T is the time horizon and d _t is the ‘discount factor’. The discount factor can also be written

$${d_t} = {1 \over {{{\left( {1 + i} \right)}^t}}}$$

where i is the social rate of discount, yet to be derived.