Choose discount rate method for Net Present Value

Net Present Value (NPV) is a financial analytical method that aggregates a series of discounted cash flows into present day values. It recognizes that, given a choice, a “rational” person would rather have a dollar, pound or Euro today rather than one year from now. This preference of course derives from the fact that a dollar today can be used to satisfy a need immediately, or can be invested. In addition, the risk of not collecting the dollar in one year’s time is much higher than today.

The following equation sets out a typical NPV calculation:

NPVn = NPV0 + (d1NPV1) +(d2NPV2) + (d3NPV3) + …. + (dnNPVn)

Where NPVn represents the investment (cost or benefit) made at the end of the “nth” year, and “dn” is the discount rate factor in the “nth” year.

d(n) = 1/(1+r)n where r = the discount rate

Typically, discounting assumes that all costs and benefits accrue at the end of each year (yrs 0,1,2,3 …). Generally, the capital cost of the project is assumed to accrue at the start of year zero in the analysis period.

Determination of an appropriate discount rate is a key component in any NPV analysis. The use of a discount rate takes account of the changing (declining) value of money over time. It recognizes that $1 collected in one year will be worth less than the same $1 collected today due to opportunity cost (it could have been invested) and risk.

The first issue to resolve is whether a “private” or “social” discount rate is to be used. By definition, benefit cost analysis that is executed by a governmental agency always determines the benefits and costs of a project from a society at large basis. The social discount rate, then, is always used in governmental benefit cost analysis.

However, if the costs and benefits are to be considered only from the perspective of a private utility, then the private discount rate may be used. This rate is used by most private companies when evaluating projects since the only thing they are concerned with is the cost and benefit to them and no one else.

Deriving a social (governmental) discount rate

Generally speaking, a government discount rate should be derived from the same two elements that affect an individual’s discount rate:

While no method is without theoretical flaws, several specific methods are typically used to set the governmental discount rate (each has many variations):

Deriving a private discount rate

Private discount rates have the advantage of being derived solely from the perspective of the organization itself, not society in general as in governmental analysis. Private discount rates are typically set based on opportunity costs, using short to mid term investment rates that the organization would have earned reflecting investment earnings actually available in the market for the period under analysis and at risk levels the organization is willing to tolerate

Inflation and the discount rate

How to handle inflation is a common question for the analyst. The answer depends on the question under consideration. Where understanding the impact in actual (budget) dollars at a point in the future is relevant to the decision, then an inflation component should likely be part of the discount rate. However, where the analyst is focused on understanding the interaction over time of the relationship between costs and benefits and the interactions among the elements that comprise each (often characterized as “current dollars”), then the inflation component should be left out of the rate.

Declining discount rates

The final determination to be made is whether to use declining discount rates over time. Where a constant discount rate of say 10% is used, the present value of $1 spent on a project in year 20 is only $0.15 so has only a minimal influence on the overall NPV and the ultimate project decision. Declining rates reduce the impact of discounting in the more remote out years. Declining rates should only be used where logic substantiates there applicability.

The effort and knowledge required to select an appropriate discount rate should not be underestimated. Extensive literature has been developed to guide the user is selecting an appropriate rate. The tool links to several sites that assist this process (See “Links and Additional Readings” on the Tool’s navigation bar)