Discounting the Future

Discounting the future occurs when an immediate benefit is systemically valued more highly than a delayed benefit. As with other discounted cash flow projections, the variables are the size of the estimated cash flow, the number of discounted periods in the future, and a relevant discount or interest rate. In a case involving one cash payment or outflow (PV) and one future payment or inflow (FV) at a relevant discount rate (r) for a number of discount periods (n), the present value (PV) can be expressed as

A classic example is an amount of cash placed in a savings account (PV) to be redeemed on a future date (FV). All other things being equal, the present value of a cash flow decreases with a decrease in the size of the future cash flow, an increase in the number of discount periods, or an increase in the discount rate. Alternatively, the present value of a cash flow increases with an increase in the size of the future cash flow, a decrease in the number of discount periods, or a decrease in the relevant discount rate.

Cost-benefit analysis takes into account all present and future cash inflows and outflows expected to occur over the life of the project. The present value [Page 603]equation is at the heart of cost-benefit analysis. The discount procedure is essentially a way of reducing a stream of costs or benefits over time to a single sum. Thus, different projects with different cost streams are comparable.

Future payments and costs should be treated in the same way as future receipts and benefits. When future payments or costs and receipts or benefits are discounted to the present and added together, the resulting amount is the net present value (V0). Therefore, the net present value at time t = 0 of a project, which has a duration of n years, and which has costs and benefits of Ct and Bt for t = 0… n, is given by

The project should be undertaken only if V0 > 0. A value of 0 is the point of indifference with respect to accepting or rejecting the project.

Cost-benefit analysis is based on a number of assumptions that must be valid for the calculation to be accurate and relevant to the decision at hand. First, it is assumed that all costs and benefits can be reduced to monetary amounts. The problem of placing valuations on untraded goods and services or intangible factors such as environmental quality is difficult when market values are not available. The value of intangibles such as historical landmarks, Stonehenge or Mount Rushmore for example, is likely to vary widely among the populace. In the absence of market values, a consensus ranking might be used according to public opinion. However, consensus rankings cannot be expressed meaningfully in the same manner in which a consumer might express his or her preferences among economic goods.

A second assumption is that the costs and benefits in the analysis are the same for each person. Only in rare circumstances is everyone a beneficiary of a project. This situation is especially obvious in projects that are undertaken by a present society to benefit future generations.

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