The total benefit (revenue plus consumer savings) is 14.1 mils per kW-hr for electricity which is sold to Americans. For an SSPS that has a capacity of 10 GW and an assumed utilization of 95 percent, this produces annual benefits of $1.173 billion. Power sold to foreigners yields 13.6 mils of benefits per kW-hr which amounts to $1.132 billion annually for each SSPS. All the power produced in the first 2 years after the initial terrestrial SSPS is built is sold to the U.S. Afterwards one-third of the power produced is sold abroad. An SSPS is assumed to begin to produce power the year after it is completed. As an example, table 6-12 shows that in year 20, 5 terrestrial SSPS's are producing power. The benefits obtained are therefore $5.783 billion.
Subject to certain qualifications discussed below a project should be undertaken if and only if the value of its benefits exceeds the value of its costs (see ref.9). It is important to include all benefits and all costs, even those which are not normally expressed in monetary terms, such as the value of any damage done to the environment. In our society there is usually a positive interest rate. This is a reflection of the fact that society values the consumption of a commodity today at a higher value than the consumption of the same commodity in the future. This fact must be taken into consideration when the value of benefits and amount of costs are determined. To do this the benefits and costs which occur in the future must be discounted. For example, if a project pays as benefits or has costs amounting to $B in every one of n + 1 consecutive years, then the value of the benefits or what is technically called the present value of the benefits is equal to:
Under certain idealized conditions the real discount rate is the same as the real rate of interest. The latter is essentially the rate of interest observed in the marketplace less the rate of inflation. Empirically the idealized conditions needed to make r equivalent to the real rate interest do not hold, resulting in a considerable divergence between these two parameters. The size of this divergence and hence the appropriate value of r is the subject of an extensive, unresolved debate among economists. The value of r which is currently used by the Office of Management and Budget is 10 percent. This is considered by most economists to be reasonable if not conservative.
Having introduced several concepts, it is now possible to be precise about what is meant by the benefit-to-cost ratio. It is the present value of the stream of benefits divided by the present value of the stream of costs. When this ratio is greater than one, then the project, subject to certain qualifications, is worthwhile. It is worth noting that if a benefit-to-cost ratio is, for example, 1.2, then if the costs in every year of the program were increased by as much as a factor of 1.2, the project would break even in the sense that the benefits would equal the costs where the costs include a real rate of interest equal to the real discount rate.
There is no reason why a project cannot be of infinite length having an infinite stream of benefits and costs. Normally, the present value of these streams and hence the benefit-to-cost ratio is finite. In the space colonization program a 70-year period is selected, not because a finite period is needed but for other reasons. In particular, if one goes too far into the future, various assumptions begin to break down. For instance, a 5 percent growth rate in electrical power cannot continue forever, especially since much of this growth rate is due to a substitution of electricity for other forms of energy. An additional consideration is that when employing a real discount rate of 10 percent, whatever happens after 70 years has little impact on the benefit cost ratio.
The term payback has been applied to a number of differing concepts. The most common form of usage is adopted for this study; namely, that payback occurs when the principal of the original investment has been repaid.
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