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Selecting the Discount Rate – An Update

by Christopher Bruce, Derek Aldridge, Kelly Rathje, and Scott Beesley

This article first appeared in the spring 2003 issue of the Expert Witness.

In the Autumn 2000 issue of this newsletter, we conducted an extensive review of the various methods of measuring the real rate of interest, or discount rate, and presented evidence concerning the movement of those measures over the period 1995–2000.

That survey was subsequently updated in our Winter 2001/2002 issue (Vol. 6, No. 4). What we found was that interest rates had begun to fall, relative to the historically high levels that had persisted over most of the 1990s.

At that time, we concluded that the best estimate of the long-run discount rate was 3½ percent. But we also argued that, as interest rates on short-term bonds and GICs were lower than those on longer term investments, it would be appropriate to employ an interest rate of 2½ percent on the first five years of any investment.

The purpose of this article will be to provide five additional quarters (15 months) of data to determine whether the trend we observed at the beginning of 2002 has continued, or whether a revision in our recommended interest rate is appropriate.

Revised data

Tables 1 and 2 provide updates of the information contained in the equivalent tables of the Winter 2001/2002 article. In particular, we have added data for all four quarters of 2002 plus the first quarter of 2003.

Table 1 reports the “raw” data from which some of the real interest rate figures in Table 2 have been calculated. The first column reports the “core rate of inflation” – a measure of the rate of inflation that removes the effects of change in those components of the price index that often move erratically, such as food, energy, and taxes. It is often argued that this measure offers a more reliable predictor of future changes in prices than does the “standard” measure of price inflation. (See the Autumn 2000 article for a detailed description of the core rate of inflation.)

The next three columns in Table 1 report the rates of return on Government of Canada 5-year and 10-year bonds and on 5-year Guaranteed Investment Certificates (GICs). The former represent the minimum rates of return that investors can expect on safe investments. The rate of return on GICs, on the other hand, represents the interest rate available on a mixed, low-risk portfolio of stocks and bonds.

Table 1

Table 2 reports seven measures of the real rate of interest – that is, the rate of interest net of the expected rate of inflation. The first of these is the market-determined rate of return on “real rate of return bonds” – bonds whose value is denominated in terms of the real rate of interest. These bonds are of particular importance because they are purchased by sophisticated investors and because they tend to held for long periods of time.

The second, fourth, and sixth columns report the 5- and 10-year government bond interest rates and 5-year GIC rates net of the core inflation measure.

Finally, columns three, five, and seven report the government bond and GIC rates net of the Bank of Canada’s target rate of inflation of 2 percent. As the Bank has managed to keep the core rate of inflation within a small band around this target for the last eight years, it is widely believed that 2 percent is the rate that is expected by most investors. That is, investors are believed to act as if the real rate of interest is the observed, nominal rate less 2 percent.

Table 2

Interpretation of the data

The data in Table 2 indicate that real rates of interest have continued the downward trend that began in 1996/1997. Whereas we concluded a year ago that long-term interest rates were approximately 3½ percent and short-term rates approximately 2½ percent; it appears that those rates have now fallen to 3 percent and 2¼ percent, respectively.

Note that the latter rate is close to the rates reported in the Bank of Canada’s Monetary Policy Report of April 2003 (Chart 19, p. 24).

In addition, 3 percent is the rate at which the Bank of Canada recently issued a new set of 33-year real rate of interest bonds. As we argued in the Autumn 2000 issue of the Expert Witness, the rate of return on these bonds is a particularly reliable estimate of the expected real interest rate as they are purchased primarily by large institutional investors (like pension funds) that have made considerable investments in the prediction of future rates of interest and inflation.

For this reason, we believe that it would be appropriate to revise our existing 2½ and 3½ percent two-part forecast of real interest rates. Based primarily on the observed rate on 5-year Government of Canada bonds, we propose to use a rate of 2¼ percent for the first five years of all calculations. For all subsequent years we propose to use a rate of 3¼ percent – though we note that a rate as low as 3 percent could be supported based on the most recent observed rates on 10-year Government of Canada bonds and based on the Bank of Canada’s current issue of real rate of return bonds. Our long-term rate is perhaps slightly conservative, but we will re-examine this issue next year and decide then if changes are warranted.

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Christopher Bruce is the President of Economica and a Professor of Economics at the University of Calgary. He is also the author of Assessment of Personal Injury Damages (Butterworths, 2004).

Derek Aldridge is a consultant with Economica and has a Master of Arts degree (in economics) from the University of Victoria.

Scott Beesley is a consultant with Economica and has a Master of Arts degree (in economics) from the University of British Columbia.

Kelly Rathje is a consultant with Economica and has a Master of Arts degree (in economics) from the University of Calgary.

Overview

This article extends the work done by us in issues 5(3) and 6(4) of The Expert Witness, we conclude that it would be appropriate to revise our existing 2½ and 3½ percent two-part forecast of real interest rates. We propose to use a rate of 2¼ percent for the first five years of all calculations. For all subsequent years we propose to use a rate of 3¼ percent.

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