The Mechanics of Discounting and Compounding

The mechanics of discounting are simple, and routines for discounting are now part of any spreadsheet program For the sake of illustration, we present here an example on compounding. Suppose we place US$100 at 10 percent per year for five years in a savings account, where a bank pays interest on the total amount in the account at the end of the year.

Net Present Value Criterion

The present value of the net benefits of a project is the basic economic criterion that we should use to accept or reject a project. Two conditions must be satisfied if a project is to be acceptable on economic grounds, namely

• The expected present value of the net benefits or net present value  of the project must not be negative when discounted at an appropriate rate.

• The project’s expected NPV must be at least as high as the NPV of mutually exclusive alternatives. For investments where no consensus exists on how to value benefits in monetary terms, the analyst should specify alternative project success criteria, yardsticks for monitoring progress during implementation, and measuring success on completion. Such projects must normally be shown to represent the expected least-cost condition for achieving the posited expected benefits.

Comparison of Mutually Exclusive Alternatives

So far, we have discussed the equivalence of the two rules in reference to a single project. When projects are independent, as long as the NPV is not negative, the project is acceptable. The fact that one project may have a higher IRR, though a lower NPV, than another project is irrelevant. However, when choosing among mutually exclusive projects or project designs, in the sense that they are alternative ways of producing exactly the same output—for example, hydroelectric versus thermal power production— differences in ranking are important. To illustrate these concepts, consider a small and a large irrigation scheme for the same site. If the small scheme were built, it would preempt use of the site for the large one; hence, they are mutually exclusive. The NPV, IRR, and total cost of each design appear. If we use the IRR to select between the two options, we would opt for the small-scale irrigation alternative. If we use the NPV to select between alternatives, we would choose the larger project. Which one is correct? Because the NPV criterion maximizes the net benefits accruing to the country, it is preferable. If we choose the smaller project, the country will forgo 241.9 million currency units in net benefits.