# Selecting the Discount Rate

This article was originally published in the Autumn 2000 issue of the Expert Witness.

One of the most important determinants of the lump sum award for future losses is the discount rate, or real rate of interest. Simply put, this is the rate of interest at which the plaintiff is assumed to invest the award, after the effects of price inflation have been removed.

For example, assume that the court has found that if the plaintiff was to incur a loss today, the value of that loss would be \$10,000. But, because the loss will occur one year from now, and the rate of inflation between today and one year from now will be 2 percent, the loss will actually be \$10,200.

The court must determine how much the plaintiff will have to invest today in order to ensure that he or she will have \$10,200 available one year from now. The discount rate is the interest rate that is used to make this calculation. The purpose of this article is to determine the current value of the discount rate.

We proceed in four steps. First, we distinguish between “nominal” interest rates and “real” interest rates and explain why the latter are generally used in preference to the former. Second, we review a number of alternative methods of measuring the interest rate. Third, we review a number of methods of estimating the expected rate of inflation. Finally, we report the values of these alternative measures for the years 1997-2000 and we conclude with a recommendation concerning the appropriate value to be used today.

## Real versus nominal interest rates

There are two methods of calculating the present value of a future loss. The first is to “discount” the loss by the “nominal” rate of interest – that is, by the rate of interest that is observed at financial institutions. The second is to remove the inflationary estimate from the projected loss, to obtain what is called a “real” loss, and then discount that loss by the “real” rate of interest – that is, the nominal rate after the rate of inflation has been removed. The two methods yield identical results.

For example, assume that the nominal rate of interest is 6 percent. The first method of determining the award is to divide \$10,200 by 1.06, (that is, by 1 plus the interest rate). That number is found to be \$9,623. It can easily be confirmed that if 6 percent of \$9,623 is added to \$9,623 one obtains \$10,200. That is, if the plaintiff was to invest an award of \$9,623 at 6 percent, he or she would have \$10,200 at the end of one year.

In the second method, one first “removes” inflation, here 2 percent, from both the future loss and the nominal interest rate. In both cases, this is done by dividing by 1.02, (that is, by 1 plus the inflation rate). Thus, as intuition would suggest, the real level of damages is found to be \$10,200/1.02 = \$10,000. The real interest rate is found to be 1.06/1.02 = 1.0392, or 3.92 percent. (Note that, in the same way that 1.06 is 1 plus the nominal interest rate, 1.0392 is 1 plus the real interest rate.) When \$10,000 is divided by 1 plus the real interest rate, 1.0392, one obtains \$9,623, exactly the same answer that was obtained using the nominal method.

Economists generally prefer to use the real loss/real interest rate approach when calculating lump sum awards for future losses. The primary reason for this is that real interest rates tend to be much more stable and, therefore, much more easily predicted, than either inflation rates or nominal interest rates.

## Alternative measures of the interest rate

Because plaintiffs often have to rely on the investment of their awards to provide a significant portion of their future incomes, it is important that they place their awards in relatively risk-free investments. For this reason, the discount rate is usually based on the rate of return on either long-term government bonds or secure private sector investments. Once a nominal rate has been determined for one of these investments, it is then necessary to determine an expected rate of inflation (over the duration of the investment) in order to calculate the real rate of return.

In this section, we will consider three types of secure investments. In the following section, we will discuss three methods of estimating the expected inflation rate.

Real return bonds The first investment vehicle is Government of Canada real return bonds. These are long-term, secure bonds whose rate of return is denominated in terms of a real interest rate. (That is, the government guarantees that the investor will receive a specified (real) interest rate plus the actual rate of inflation.) There are a number of advantages to using the rate of return on these bonds.

First, when that rate is used, it is not necessary to make a separate projection of the rate of inflation.

Second, these bonds are guaranteed by the government of Canada.

Third, the estimate of the real rate of interest that is obtained by observing the prices at which these bonds are traded in the financial markets provides an objective measure of the real rate of interest that is forecast by sophisticated investors. Note, we are not suggesting that plaintiffs should, or will, invest their awards in real return bonds. Rather, we are arguing that the observed returns on these bonds provides an excellent, objective measure of the expected real rate of return – as these bonds are purchased primarily by individuals who are close observers of money markets and who have a great deal of money at stake when selecting their investments. (Generally, it is pension fund administrators who purchase real return bonds.)

Recently, Ontario revised its Rules of Court concerning the selection of the discount rate. Whereas the previous rule required that the courts use a fixed rate of 2.5 percent, the new rule bases the rate on current observations of the interest rate on real return bonds. For further analysis of Ontario’s new rule, see the accompanying article “Ontario’s Mandated Discount Rate – Rule 53.09(1).”

Guaranteed investment certificates A second approach to the determination of the real discount rate is to identify a measure of the rate of return on a “safe portfolio” of investments (i.e. the kind of portfolio in which a plaintiff could be expected to invest) and to deduct from that rate the expected rate of inflation. We have long recommended that the rate of return on five year guaranteed investment certificates, GICs, be used for this purpose.

Again, as we commented with respect to real return bonds, we are not suggesting that the plaintiff should use his or her award to purchase GICs. Rather, as the types of investments contained in GICs are similar to those that one would expect a prudent investor to purchase, the rate of return on GICs provides an objective measure of the rate of return that plaintiffs can expect to obtain. (Furthermore, as the quoted rate on GICs is net of investment management fees, there is no need to make a separate calculation of the management fee.)

Long-term Government of Canada bonds The rate of return on long-term government bonds can be used as a benchmark against which to measure the returns on other investments. As these bonds are widely held by private citizens (unlike real return bonds) and as they are among the most secure investments available, it would be expected that plaintiffs would never earn a nominal rate of return less than that obtainable from Government of Canada bonds. (If the plaintiff’s investments began to obtain a lower rate of return, the plaintiff could always, easily, transfer his or her investments to government bonds.) Hence, any suggested discount rate must pass the test that it is not lower than the rate obtainable on government bonds. Conversely, we would suggest that the discount rate used should also not significantly exceed the government bond rate, as that would imply that plaintiffs should place their awards in unacceptably risky investments.

## Estimating the rate of inflation

The real rate of interest is calculated by removing the effects of price inflation from the nominal rate of interest. As the interest rate is to apply to investments that will continue for many years into the future, the relevant rate of inflation is the average rate that is expected to apply over that future. We will discuss three methods of forecasting this rate.

Current rate of inflation One simple method is to assume that the current rate of inflation will continue into the future. Use of this rate is based on the observation that investors appear to adjust their expectations of the future when current conditions change. Often it is assumed that this shift of expectations occurs with a short “lag,” of six months to two years. But, in periods in which the rate of inflation is not changing quickly, only small errors will be produced if the current rate is used.

Core rate of inflation In Canada, the reported rate of inflation is measured as the change in the price level of a representative “basket” of goods over a 12 month period. For example, the rate of inflation reported for January 2001 will be the percentage change in prices between January 2000 and January 2001.

What this means is that if there is a large, one-time increase in prices in January 2000, measured inflation will be relatively high in each month from January 2000 to December 2000 and then will fall significantly in subsequent months. The reason for this is that the increased price level produced by the January 2000 price increase will continue to be in effect in every future month. Hence, in every month between January 2000 and December 2000, prices will be higher than in the corresponding month a year earlier. Inflation in those months will be correspondingly high.

For example, assume that the CPI had been 100 in every month during 1999, had risen to 110 in January 2000, and stayed at that level for the rest of the year. Then, in every month during 2000 the CPI would be 110, in comparison with 100 in the same month the year before. Hence, in every month in 2000 the rate of inflation would be reported as 10 percent – even though there had not been a price increase since January.

But, when calculating the January 2001 inflation rate, the price level for that month will be compared to a price level (January 2000) that already contains the one-time increase of January 2000. Hence, the measured rate of inflation in January 2001 (i.e. between January 2000 and January 2001) will drop back to the long-run maintainable rate.

In our example, if the CPI remains at 110 in January 2001, inflation between January 2000 and January 2001 will be 0 percent. The one time increase in January 2000 will have had only a temporary impact on the rate of inflation.

What this observation implies is that if we wish to use the current rate of inflation to forecast the long-run rate of inflation, we must first remove the effect of one-time price increases. The Bank of Canada attempts to provide such a measure of long-run price inflation with what it calls its core rate of inflation. In particular, this measure removes movements in the costs of food and energy and movements in prices due to the effects of indirect taxes.

For example, the core rate of inflation would not include the effects of the doubling of oil prices during 2000. Why? Because, although a doubling of prices from \$15 a barrel to \$30 (and higher) was not completely unexpected, very few observers expect to see prices rise much higher. Hence, even if prices remain at their current level, within 12 months of the initial increases, inflation (the change in the level of prices) will fall. (The increase in oil prices is an example of the one-time increase we discussed above.)

And, of course, if prices should fall back to their pre-2000 levels, short-term inflation will fall even more – perhaps into negative numbers – for the next 12 months. But no one will expect those low levels of inflation to continue any more than they expect the current high levels to continue.

The implication, then, is that the core rate of inflation may be a better indicator of the long-run, expected rate of inflation than is the measure that is usually reported in the press. For this reason, in the tables below, we report both the core rate and the published rate.

The Bank of Canada’s target rate For the last decade, the Bank of Canada’s monetary policy has been directed at producing a rate of inflation of 2 percent (plus or minus 1 percent). As anyone who can remember the 1970s and 1980s can attest, the Bank has been singularly successful in reaching this goal.

Indeed, it has been so successful, that we believe that it can be argued that most investors have come to believe that the long-run rate of inflation will be (approximately) 2 percent. (The Bank itself reports that most financial analysts are predicting inflation rates of approximately 2 percent. See Bank of Canada Monetary Policy Report, November 2000, p. 32.) For this reason, when determining the real interest rate, in the tables below, we report calculations employing an inflation rate of 2 percent.

## The data

We present two tables. Table 1 reports quarterly values of the two nominal interest rates – 10-year Government of Canada bonds and GICs – and two of the measures of expected inflation – the standard version and core inflation – for 1997, 1998, 1999, and the first three quarters of 2000. (We do not report the Bank of Canada target rate of inflation, as it did not change over this period.)

Table 2 reports the real rates of interest obtained, first, from the real return bonds and, second, from adjusting the two nominal interest rates by each of the three measures of expected inflation. This produces seven measures of the real rate of interest.

What these figures suggest is, first, that the interest rate on real return bonds has been remarkably constant over the last three and a half years, rarely deviating very far from the 4.0 to 4.1 percent range until 2000, when it fell to approximately 3.7 percent.

Second, it is seen that the real rate of interest on 10-year government bonds has also fluctuated around 4.0 percent, but with far larger deviations than was seen with respect to the rate on real return bonds. Some of the wider of these deviations can easily be explained, however.

Note, for example, that the low real rates produced in 1998 and 1999 when the 2 percent inflation factor is used may have resulted because a long period of below-2 percent inflation had caused financial markets to believe that the Bank had lowered its target rate. (The conventional measure of inflation exceeded 2.0 percent only once between the first quarter of 1996 and the third quarter of 1999, when it was reported to be 2.1 percent in the first quarter of 1997.) If the markets had come to expect inflation rates of 1.5 percent in 1998 and 1999, for example, most of the real rates in those years would have been close to 4.0 percent.

The relatively high rates found in 2000 when long-run bond rates are discounted by core inflation, and the relatively low rates found in that year when they are discounted by the standard measure of inflation, could both be “explained” if it was found that financial markets had begun to accept the Bank of Canada’s statement that it was targeting a long-run inflation rate of 2 percent.

The consistently low rates found on GICs, however, are disconcerting. Over the entire period reported in Table 2, and for a number of years prior to that, the rates of return on GICs were significantly lower than those on government bonds. This suggests that plaintiffs would be extremely unwise to invest in GICs for the foreseeable future.

We conclude, therefore, that current estimates of the discount rate should be based on the rates observed on real return bonds and on long-term Government of Canada bonds. Arguably, these rates fluctuated around 4.0 percent for most of the last four years. They have, however, fallen slightly during 2000.

This raises the question of whether 2000 is an aberration, or whether the recent decline in real rates is the beginning of a long-term trend. Some evidence that the decline is expected to be short-lived comes from the Alberta government’s Budget 2000 documents. There, it is reported that nine respected forecasting agencies predicted an average interest rate on Government of Canada 10-year bonds of approximately 6.21 percent (over the years 2000-2003). As it is unlikely that those agencies would have forecast an inflation rate in excess of 2 percent, implicitly they have forecast a real rate of interest of approximately 4.1 percent.

In this light, we believe that a rate of 4.0 percent is the best, current estimate of long-run real interest rates. However, Economica will be monitoring movements in the interest rates on real return and 10-year Government bonds closely. If bond rates do not rise relative to the rate of inflation in the near future, we will be revising our real rate of interest forecast downward.

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.