The Discount Rate Revisited

by Christopher Bruce, Derek Aldridge, Kelly Rathje, and Hugh Finnigan

This article first appeared in the summer 2005 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 article is available on our website, at economica.ca/ew53p1.htm.)

That survey was subsequently updated in our Winter 2001/02 and Spring 2003 issues. What we found in both of those updates was that interest rates had begun to fall relative to the historically high levels that had persisted over most of the 1990s.

At the time of our Spring 2003 article, we concluded that the best estimate of the long-run discount rate was 3¼ 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 2¼ percent on the first five years of any investment.

The primary purpose of this article is to examine nine additional quarters (27 months) of data to determine whether the trend we observed in our earlier articles has continued, or whether a revision in our recommended interest rate is appropriate. We also report on recent changes to Ontario’s mandated discount rate; and we revisit the question of whether forecasts of future interest rates should be based on information about past interest rates or on information about current, long-run interest rates.

Revised Data

Instead of providing tables of data comparable to those presented in our earlier articles, we now present a chart that shows the trend in interest rates since 1995. The complete data set can be found on our web site (see www.economica.ca/ew102p1.htm). Figure 1 shows the trend in real interest rates on government bonds of various term lengths, as well as the rate of return on real rate of return bonds.

Figure 1

Note: We deduct two percentage points from the “nominal” or observed interest rates to reflect inflation anticipated by investors. As the Bank of Canada has managed to keep the core rate of inflation within a small band around this target since the early 1990s, and as it has been the stated intention of not only the Bank of Canada but most other central banks (most notably that of the European Union) to keep the inflation rate at that level, there is now virtual unanimity among investors that two percent will be the long run rate of inflation in Canada. Accordingly, it can be concluded that investors have been acting as if the real rate of interest is the observed, nominal rate less two percent.

The data in Figure 1 indicate that real rates of interest have continued the downward trend that began in 1996/97. Whereas we concluded two years ago that long-term real interest rates were approximately 3¼ percent and short-term rates approximately 2¼ percent; it now appears that real rates have fallen substantially below those levels. In particular, note that the rate of return on 10-year Government of Canada bonds, net of the 2 percent expected rate of inflation, is now below 2 percent and has not exceeded 3¼ percent (our earlier prediction of the “long-term” rate) since early 2002. Even the real rate on long-term (30-year) Government of Canada bonds has fallen below 2½ percent in the most recent quarter. And the rate of return on real rate of return bonds is now below 2 percent and has not been above 3 percent since mid-2003.

Although we do not show the comparable interest rates on guaranteed investment certificates (GICs), we have examined them and they are consistently lower that the rates of return on bonds. For example, the real rates on 1-year GICs have been consistently negative since late-2001, meaning that investments in one-year GICs are not keeping pace with inflation. The real rate on 5-year GICs has been below one percent for all but two of the last eight quarters and has not exceeded two percent since early 2002.

Forecasting the Real Rate of Interest

For some time now, Economica has been arguing that current interest rates, net of the two percent expected rate of inflation, provide the most reliable basis on which to predict future interest rates. Some other economic experts in Western Canada disagree with us, and base their forecasts on information about historical interest rates. We consider their position to be unjustified. We explain why here:

The continued dramatic fall in interest rates.

First, as a glance at Figure 1 will indicate, the real rate of interest in the last decade has fallen continuously and dramatically: the long-term rate has fallen from about 7 percent to below 2½, while the short-term rate has fallen from about 6 percent to below 1 percent. Clearly, any prediction that was based on an average of the figures in this period (or any other period extending back to the early 1980s) would seriously overstate the rates that will be available to a plaintiff investing his or her award today.

It is important to note that although rates are low by historic standards, today’s investors who seek the security of investments comparable to government bonds and GICs cannot avoid these low rates. The fact that average interest rates over the last 30 years were much higher does not help today’s plaintiff-investor. Even if one believed that long-term real rates will rebound to (say) 3.5 percent in the next 5-10 years, the best that today’s investor will be able to do is place his funds in 5-10 year investments earning 1.5-2 percent and then hopefully reinvest at the higher 3.5 percent rate. This of course will not yield nearly the same result as if he had been able to invest at 3.5 percent right from the start.

Economic theory.

Second, the fall in real interest rates is consistent with macroeconomic theory. Specifically, many macroeconomists are arguing that the relatively high real interest rates that were observed in the 1980s resulted from the high volatility in expectations concerning the nominal rate of inflation. That is, when inflation is unpredictable, investors who place their funds in long-term bonds face a considerable amount of uncertainty. If inflation proves to be higher than expected, the real rate of return that they realise may be very low or even negative. To compensate for this uncertainty, investors demand a relatively high expected rate of return. Conversely, when inflation becomes predictable, as has happened in the last five to ten years, investors face much less uncertainty and are willing to accept lower real rates of return. Accordingly, there is sound reason to believe that, as long as the Bank of Canada maintains its current course[*] (which it is expected to do), both nominal inflation and real interest rates will remain at the low levels that have been observed recently.

Furthermore, most economists believe that real interest rates will be higher in a period in which governments run large deficits – and, therefore, have to borrow heavily – than in those in which revenues exceed expenditures. As is well known, although the Canadian government ran sizeable deficits in the late 1980s and 1990s, it has now adopted a goal of achieving a balanced (or, even, surplus) budget. Again, this leads us to believe that real interest rates will be lower in the future than they were in the 1980s and 1990s.

The actions of large, institutional investors.

Most of the bonds reported in Figure 1 are purchased by large, institutional investors, such as pension funds. That these investors are willing to purchase, say, ten-year bonds paying a real rate of approximately two percent, or real rate of return bonds that are paying below two percent (as of the second quarter of 2005) indicates that they do not anticipate that they can obtain better rates of return on other secure investments. That is, regardless of whether private investors actually purchase the government bonds identified in Figure 1, the returns on those bonds indicate that the institutions that base millions of dollars of investment on their predictions of the financial markets are forecasting that real rates of return will remain low in the foreseeable future. (If expert institutional investors anticipated that rates on secure investments will average, say 3½ percent over the next ten years, then they would not buy bonds that pay only two percent, and the Government of Canada would be forced to adjust its bond rates.)

A future increase in rates will have little effect on most plaintiffs.

Even if real interest rates were to increase substantially in the next ten years or so, (against expectations), that would have relatively little effect on the investments of many plaintiffs, for two reasons. First, it is the rates of return that are available today that will dictate the average rate that plaintiffs will be able to obtain over at least the first 5-10 years of the period of their loss. As noted above, if rates increase in the future, the best that today’s plaintiff can do is place his funds in 5-10 year investments at today’s low rates and then later reinvest at the (hopefully) higher future rates. Even if rates return to their historical average, this investment approach will still yield an average rate of return that is below the historical average. Second, since most plaintiffs will need to begin consuming their award immediately (to replace their lost income and fund their costs of care), the most substantial portion of the interest that they will earn on the investment of their awards will occur in the first half of their period of loss, before they have drawn down much of their capital (that is, during the period in which they are funding most of their annual losses from interest income). If the period of loss is 20 years or less (like most plaintiffs), then the interest they earn in the first ten years will have a much greater impact on their investments than the interest they earn in the next ten years. Thus a return to higher interest rates after 10 years or so will have only a small impact on these plaintiffs. For plaintiffs with a period of loss that is only ten years or less, future increases in interest rates will have almost no effect on their investments.

Note that one implication of relying heavily on current interest rates is that it requires that we change our discount rate assumption more frequently than if we simply relied on historical averages. However, making changes to our discount rate assumption does not imply a weakness in our methodology. To do otherwise would result in us using interest rates that we know are inconsistent with the rates that are actually available to plaintiffs. Even if one believed that over the long-term, real interest rates will average (say) 3 or 3½ percent, it does not necessarily follow that our discount rate assumptions should remain fixed. This is because (as we explained above), the rates of return over the next ten or so years will have a substantial impact on the investment results of most plaintiffs. Thus, it is important to account for the rates that are available to plaintiffs now, as well as the rates that will be available (on average) over the long-term.

Ontario’s mandated discount rate

Following a detailed review, Ontario (in year 2000) revised its regulations concerning its mandated discount rate. The new methodology that was chosen yields a discount rate of 1.5 percent for the first fifteen years of any award and 2.5 percent for all years beyond that point. Specifically, Ontario’s revised regulation 53.09 states:

53.09 (1) The discount rate to be used in determining the amount of an award in respect of future pecuniary damages, to the extent that it reflects the difference between estimated investment and price inflation rates, is,

(a) for the 15-year period that follows the start of the trial, the average of the value for the last Wednesday in each month of the real rate of interest on long-term Government of Canada real return bonds (Series V121808, formerly Series B113911), as published in the Bank of Canada Weekly Financial Statistics for the 12 months ending on August 31 in the year before the year in which the trial begins, less 1 per cent and rounded to the nearest ¼ per cent; and

(b) for any later period covered by the award, 2.5 per cent per year. O. Reg. 488/99, s. 2; O. Reg. 263/03, s. 4 (1).

The average month-end rate of return on real rate of interest bonds from September 2003 through August 2004 was 2.58 percent. Deducting one percentage point and rounding to the nearest quarter percent yields a mandated discount rate of 1.5 percent for trials that occur in 2005. Given the rates on real rate of interest bonds since September 2005, we can also be almost certain that Ontario’s mandated discount rate (for the first 15 years of loss) will fall to 1.0 percent for trials that occur in 2006.

As discussed in an earlier article (see “Ontario’s Mandated Discount Rate – Rule 53.09(1)” that appeared in the Autumn 2000 issue of the Expert Witness), we have a concern with Ontario’s policy of deducting one percentage point from the one-year average of the rate on real rate of return bonds. What is perhaps more interesting is their finding that 2.5 percent reflects the long-term real rate of interest. This rate is lower than the long-term rate we have been using, though it is consistent with the current rate on long-term Government of Canada bonds.

Conclusion

Our review of the empirical and theoretical sources suggests that it would be appropriate to adjust our discount rate assumption. We also propose to make a change in how we apply our discount rate assumptions in our calculations. Whereas we previously assumed that the real rate of return on all of a plaintiff’s investments would be 2.25 percent for the first five years and 3.25 percent thereafter, we now assume that for income required in the first few years, an investment will be made at short-term rates, while for income needed in the more distant future, investments will be made that will earn the predicted long-term rates. Below we will further explain the approach we will use for our calculations, and then we will outline the discount rate assumptions we will use.

To illustrate the effect of this approach, note that a child plaintiff who will not experience a loss of income for ten years will manage to earn a relatively high rate of return because he will be able to invest in “long-term” investments, and he will be more likely to benefit from possible future increases in interest rates. On the other hand, an older plaintiff who will experience a loss of income over the next five years only, will not be able to benefit from long-term investments or from possible increases in interest rates. She will face the low rates available on short-term investments.

Consider the following example of a plaintiff who will incur a loss of income of $10,000 seven years from now. If she is compensated for the future loss today, she could use her award to purchase a government bond with a seven-year term, and not touch the award until it is needed in seven years, when the bond matures. We will see in Table 1 (below) that such a bond has been paying about 2.2 percent, net of inflation over the last two years. This plaintiff will not need to invest at the lower rates offered by shorter-term assets, but she will also not benefit from the rates offered on longer-term bonds, nor will she benefit from a possible future increase in interest rates. To invest her award in secure assets she faces two options: she can make successive short-term investments in hopes that the rates will increase in the near future, or she can make a longer-term (seven-year) investment and accept the interest rate that is available to her. Given her investment-obligations as a plaintiff, we would expect that that latter option would be more appropriate. Even if she chose the former option we would not expect her overall return to improve, unless we knew that rates would increase in the near future. (And if it was known that rates will increase in the near future, then this increase would already be reflected in the current rate of return offered on seven-year bonds.)

For our calculations we will choose an average rate of return that will be earned on investments that are held until each future year of the period of loss. For example, we assume that the portion of the plaintiff’s award that is held for seven years to compensate her for her loss in year 7 will earn an average rate of return of 2.2 percent. Similarly, we assume that the portion of the plaintiff’s award that is held for 15 years to compensate her for her loss in year 15 will earn an average rate of return of 3.0 percent. And so forth.

To obtain the discount rates for use in our calculations, we propose to take an average of the most recent two years of quarterly interest rates (using two years of monthly rates would yield the same results), for the Government of Canada benchmark bond yields for 2-, 3-, 5-, 7-, 10-year, and long-term bonds. After deducting two percentage points for anticipated inflation and rounding to the nearest tenth of a percent, this will give us our assumed real interest rates for various future terms. We assume the one-year rate is the same as the reported two-year rate, and for the “in-between” years we simply extrapolate. We assume that the long-term rate applies to year 15 and beyond. The rates that result from this approach are shown in Table 1.

Table 1

Note that we believe that the rates proposed in Table 1 (above) remain conservative (that is, they may understate future losses) since they reflect interest rates that have been available over the past two years, instead of only the rates that are available now (even though only the rates available now can be assured to today’s investor).

Footnotes

* Since approximately December 1993, the Bank of Canada has successfully maintained a policy of keeping inflation at a two percent target (the midpoint of its 1-3 percent target range). [back to text of article]

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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.

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

From 2003 through 2005, Hugh Finnigan was a consulting economist at Economica, with a Master of Arts degree from the University of Calgary.

Estimating the Impact of Mid-Career Retraining

by Christopher Bruce and Derek Aldridge

This article first appeared in the summer 2005 issue of the Expert Witness.

Vocational psychologists commonly recommend that injured plaintiffs retrain for a new occupation. A problem that this creates for the financial expert is that it is not clear what the individual’s starting wage will be once the training period has been completed.

Specifically, all of our data concerning incomes by occupation suggest that individuals’ incomes increase as they age (usually until their mid-40s). If we assume that this increase occurs either because individuals gain valuable experience in their occupations or because they move up “career ladders” as they age, individuals who change careers will find themselves starting at lower wages than would be suggested by their ages.

For example, Table 1 reports incomes by age (for Alberta males) for two occupations that are commonly recommended as retraining possibilities: partsman (NOC-S B572) and drafting technologist/technician (NOC-S C153). It can be seen there that annual incomes rise continuously from the youngest age group, 20-25, to the second oldest group, 45-54, before declining slightly.

Table 1

If it has been recommended that, say, a 40 year-old male retrain to enter one of these occupations, the economic expert is faced with determining which of the income levels from Table 1 best represents the income at which the plaintiff will begin his new career. If experience in the occupation, or movement along a career ladder, are important determinants of income, then we would expect that the newly-trained worker would begin at one of the lower incomes suggested by the census data.

Perhaps with his greater maturity the 40 year-old would not start at the income level of a 20-25 year-old; but with no experience in this occupation, it seems unlikely that he would start at the income of a 40 year-old. Fortunately, statistical evidence has recently become available that can help us to determine the impact of a change in career.

Most importantly, Arthur Goldsmith and Jonathan Veum[*] have used a detailed survey that followed 1400 young workers from 1979 to 1996 to compare the effects of additional years of experience on wages when individuals: remained in the same occupation and industry, remained in the same occupation but moved between industries, remained in the same industry but changed occupations, and changed both occupations and industries.

What they found was that the value that was placed on previous experience was approximately the same for all individuals except those that had changed both occupation and industry. In their words:

…experience acquired while a real estate agent is
valued similarly as tenure at other occupations, such as
accounting, within the real estate industry. In addition, the
experience as a real estate agent is valued similarly to
tenure at other industries, such as the pharmaceutical
industry, if continuing in the occupation of sales. If the
real estate agent becomes an accountant in the pharmaceutical
industry, however, the experience as a real estate agent is
of less value than that within accounting or the
pharmaceutical industry. (p. 442)

Referring to the examples in Table 1, Goldsmith and Veum’s findings suggest that the 40 year-old who retrains as a partsman may be able to earn an income comparable to that of a 40 year-old partsman with 15 years experience, if the retrained individual remains within his previous industry. For example, if an individual who had previously worked on oil rigs becomes a partsman in a shop that provides equipment to oil rigs, he can be expected to obtain a starting salary much higher than he would have obtained if he had become a partsman in an automobile dealership.

We would suggest that Goldsmith and Veum’s findings be interpreted in the following way: First, if the plaintiff’s injuries require that he/she retrain for both a new occupation and a new industry, the starting salary should (normally) be selected from the 25-29 year-old census category. This allows for the finding that previous experience is of limited importance, while avoiding the confounding effect that the incomes of 20-24 year-olds will be biased downwards by issues of immaturity.

Second, if the plaintiff’s injuries require that he/she retrain for a new occupation in the same industry he/she worked in prior to the accident, it should be assumed that the experience gained in the previous occupation will be, in large part, transferable to the new occupation. This does not necessarily mean that a 40 year-old plaintiff should be assumed to start his/her new career at the income level of an experienced 40 year-old in that occupation. Most importantly, plaintiffs often experience residual mental and physical difficulties that will reduce their earning capacity below that of the individuals represented in the census data. Also, however, it must be recognised that Goldsmith and Veum’s results referred to individuals who had changed occupations voluntarily; that is, to individuals who had chosen new occupations that met both their interests and their aptitudes. Plaintiffs often are not provided with that opportunity. As the new occupations for which they are retraining are not those that they had chosen when they were healthy, it is possible that they will not perform as well as individuals who had chosen those occupations voluntarily.

Finally, it must be recognised that Goldsmith and Veum’s findings are only suggestive. They can only be interpreted to indicate that, on average, when uninjured individuals make mid-career changes within a given occupation or industry, they tend not to suffer appreciable losses of earnings. They provide less information about specific individuals, particularly those who make significant career changes because of injury. We strongly suggest, therefore, that counsel request an opinion from a vocational psychologist concerning the impact that the injuries suffered by the particular plaintiff in question will have on that individual’s earning capacity. Specifically, if the psychologist recommends that the plaintiff retrain for a different occupation or industry, does the psychologist believe that that individual will be able to begin the new career at a salary that is comparable to other individuals of his/her age? Or will the plaintiff be forced to enter the new career at a salary lower than that of otherwise comparable individuals?

Footnotes

* Goldsmith, A.H. and J.R. Veum (2002). Wages and the Composition of Experience. Southern Economic Journal, 69(2), 429-443. [back to text of article]

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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.