Discounting Future Benefits and Costs

CHAPTER 6: DISCOUNTING FUTURE BENEFITS AND COSTS

Purpose: This chapter deals with the practical issues one must know in order to compute the net present value of a project. It assumes the social discount rate is given, which is reasonable as the rate is often set by an oversight agency, such as the Office of Management and Budget. The chapter covers: the basics of discounting (two-periods); compounding and discounting over multiple periods (years); the timing of benefits and costs; horizon (terminal) values; comparing projects with different time frames; inflation and the difference between nominal and real dollars; relative price changes; and sensitivity analysis in discounting. Appendix 6A provides shortcut formulas for calculating the present value of annuities and perpetuities.

BASICS OF DISCOUNTING

Projects with Lives of One Year

Discounting takes place over periods not years. However, for expositional simplicity, we assume that each period is a year. This section discusses projects that last one year.

There are three possible methods to evaluate potential projects: future value analysis, present value analysis and net present value analysis. Each gives the same answer.

Future Value Analysis – Choose the project with the largest future value, FV, where the future value in one year of an amount X invested at interest rate i is:

FV = X (1 + i) (6.1)

Present Value Analysis – Choose the project with the largest present value, PV, where the present value of an amount Y received in one year is:

PV = Y/(1 + i) (6.2)

Note that if the PV of a project equals X, and the FV of a project equals Y, both equations (6.1) and (6.2) imply:

This equation shows that discounting (the process of calculating the present value of future amounts) is the opposite of compounding (the process of calculating future values).

Net Present Value Analysis – Choose the project with the largest net present value, which calculates the sum of the...