Yesterday, Dan Phaneuf outlined the steps in a benefit-cost analysis. He said:

If we want to compare benefits and costs occurring at different time scales

discountingis needed to express future costs or benefits at today’s equivalent value. Discounting is mechanically easy, but no agreement exists on what the correct discount rate is. Controversy over discounting lies at the heart of the debate on CBA, in that the choice of discount rate can often determine whether net benefits are found to be positive or negative.

We've also seen examples of the impact of discount rates (1) of 3% or 7% on CAIR benefits and costs and (2) 10% and 2% on the benefits and costs of drilling in the ANWR.

So how and why are discount rates chosen? Here are some quick and dirty answers.

The real rate of interest is the appropriate discount rate for benefit cost analysis. Market interest rates should be used for discounting because they reflect the rate at which those in the economy are willing to trade present for future consumption. Market rates reflect social preferences. Nominal market interest rates are equal to the sum of the real rate of interest (i.e., the rate of return on capital) and inflationary expectations. Most variations in nominal rates are due to changes in inflationary expectations since the rate of return on capital (e.g., factories, equipment) is fairly stable over time. The real rate of interest is equal to the market interest rate minus inflationary expectations.

Most discount rates used for benefit cost analysis are based on U.S. Treasury borrowing rates since they are virtually default risk free. The 10 year U.S. Treasury note is considered a benchmark market interest rate by many financial institutions. In the week ending August 5, 2005 the interest rate (i.e., actually the "yield to maturity") on the 10 year U.S. Treasury note was 4.34% (see WSJ: Key Interest Rates). Assuming expected inflation is equal to the inflation rate from the June 2005 Consumer Price Index (2.6%), the real rate of risk-free interest is 1.74%.

Another estimate of the real rate of risk-free interest is the interest rate on a 10-year Treasury Inflation Protected Security (TIPS). The interest rate on a TIPS that matures in July 2015 is 2.01% (see WSJ: US Gov't Bonds and Notes). Compare this to the nominal rate on a regular Treasury note that matures in August 2015 -- 4.44%. The TIPS rate more appropriately incorporates market *expectations* about the future inflation rate, 4.44% - 2.01% = 2.43%, rather than the historical inflation rate.

The discount rate derived from the TIPS is biased upward since TIPS are less marketable than ordinary Treasury bonds. The lower demand drives their price down and interest rate upwards. This may explain much of the difference between the two estimates of the real interest rate: 1.74% and 2.01%.

Different government agencies may require different discount rates. The two most prominant U.S. government agencies involved in benefit-cost analysis are the Congressional Budget Office (CBO) and the Office of Management and Budget (OMB). The CBO recommends a rate of 2%. This rate is based on a CBO estimate of the long-term cost of borrowing for the federal government and is generally considered a conservative estimate of the long-term real market risk-free interest rate (i.e., the Treasury rate).

The OMB recommends that the real rate should be based on the rate of return to private investment. The 7% rate “approximates the marginal pretax rate of return on an average investment in the private sector in recent years.” This rate is generally considered to be an upper bound for federal projects because the rate of return to public sector projects is lower than private sector projects.

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