This article first appeared in the autumn 1996 issue of the Expert Witness.

The discount rate is the interest rate at which it is assumed plaintiffs will invest their awards in order to replace their future streams of losses. As was explained in the first issue of this newsletter, it is the “real” rate of interest – or observed rate of interest net of the expected rate of inflation – which most financial experts prefer to use for this purpose.

In six provinces, the discount rate has been set by regulation. In the remaining four, including Alberta, however, the expert must provide evidence concerning the forecasted value of the real interest/discount rate. The purpose of this article will be to review a number of techniques for obtaining such a forecast and to provide an estimate of the real rate of interest based on the most reliable of these techniques.

The article will be divided into three sections. In the first, I list the rates in the six provinces which mandate a discount rate. In the second section, I summarise three methods which have been used to forecast real interest (discount) rates and identify the strengths and weaknesses of each of those methods. Finally, I select one method and use it to select a discount rate for use in Alberta.

## Mandated Discount Rates

Province | Discount Rate |
---|---|

British Columbia | 3.5% (cost of care) |

2.5% (loss of income) | |

Saskatchewan | 3.0% |

Manitoba | 3.0% |

Ontario | 2.5% |

New Brunswick | 2.5% |

Nova Scotia | 2.5% |

Prince Edward Island | 2.5% |

The discount rates shown in the previous table have been mandated in Canada.

## Three Methods for Determining Discount Rates

**1. The historical approach:** The approach which, implicitly, has been favoured by those provinces which have mandated their discount rates is to assume that the average rate which has been observed in the past will continue into the future. Typically, those who use this approach rely on the real interest rates which have been reported over the entire post-World War II period. What analysis of these rates indicates is that real rates were fairly stable over the period 1950-1970, at approximately 3 percent. During the oil crisis, of the early 1970s, real interest rates fell, sometimes becoming negative. Towards the end of that decade, however, they began to rise again and it appeared that they would return to their historical level. But the rise continued beyond 3 percent and since 1983 real interest rates have consistently remained above that level. Indeed, real interest rates have remained above 4 percent for so long that it is now difficult to justify the use of a rate lower than that. At the very least, any expert who attempted to rely on the historical 3 percent average to forecast future rates of interest would have to explain why the 1980s and 1990s were such an anomaly.

**2. Forecasting agencies:** There is a small number of consulting firms in Canada which provide forecasts of such economic variables as GNP, the unemployment rate, and inflation. They will also forecast other variables, including the real rate of interest. Extreme caution must be used when employing these firms’ long-term forecasts, however. First, the mathematical models which they employ were built specifically to make short- term forecasts. Second, long-term forecasts cannot be made without imposing assumptions about many factors which are outside the mathematical models developed by these agencies, such as foreign interest rates, exchange rates, and government monetary and fiscal policy. Finally, private forecasters have little incentive to produce accurate long-term forecasts. A consulting firm’s reputation will not hinge in any way on the accuracy of its current forecasts concerning, say, the level of unemployment in 2020. The forecasts which customers use to evaluate the agencies’ accuracy are those which have been made into the near future, not the distant future. Hence, it is forecasts of one or two years on which consulting firms concentrate their resources. The real rate of interest, on the other hand, must commonly be forecast twenty or thirty years into the future.

**3. Market rates:** The third source of information concerning future real rates of interest is the money market. When an investment firm which believes that inflation will average 2 percent per year purchases 20 year bonds paying 6 percent, it is revealing that it expects the real rate of interest will average 4 percent over those 20 years. (The real rate of interest is the 6 percent observed, or “nominal,” rate of interest net of the 2 percent inflation.) Thus, if we knew the rate of inflation which investors were forecasting, that forecast could be used to deflate the nominal rates of interest observed in the market in order to obtain the implicit, underlying real rates. At the moment, such forecasts can be obtained with some accuracy. Not only do surveys of investors conclude that there is considerable agreement among them with respect to their forecasts of inflation – generally between 2 and 3 percent – but we know that the government is strongly committed to maintaining a long-run inflation rate below 3 percent. Thus, we can be confident that investors predict real rates of interest which are no less than the observed, nominal rates less 3 percent. (For information concerning the long-run expected rate of inflation, see Bank of Canada, *Monetary Policy Report,* May 1996.)

Alternatively, the Canadian government has for some time issued bonds which are denominated in terms of real interest rates, (real rate of interest bonds, or RRBs). By observing the rates of return at which these bonds sell, the real rate of interest which investors believe will prevail over the future can easily be determined. There are two drawbacks to the use of market interest rates to forecast future real rates of interest. First, the rate which is obtained from this method has not been stable, but has generally fluctuated between 4 and 6 percent since 1983. Hence, no definitive conclusion can be drawn. Second, as very few RRBs have been issued, the rates of return which they have obtained may not accurately reflect the rates in the market as a whole.

## Forecasting the Discount Rate

Of the three techniques for forecasting real interest rates discussed in the previous section, the least satisfactory is the first one, based on historical rates. As those rates have varied so widely since the early 1970s, they convey little reliable information concerning the future. Of the remaining two, most economists prefer the market-based technique. A simple analogy will explain why.

Imagine that you wished to determine the average price which potential purchasers were willing to pay for twenty-year old, three bedroom bungalows in Edmonton. One approach would be to conduct a telephone survey of Edmontonians, asking them what they would be willing to pay for such homes. A second approach would be to observe the actual prices at which such homes sold in Edmonton. Clearly, the second approach is preferable. Why? Because rather than asking individuals how they think they will behave in some hypothetical situation, it observes how individuals actually behave when they have to commit large sums of money to their decisions.

Similarly, economists who are asked to forecast long-term interest rates recognise that little is at stake should those forecasts be in error. Whereas those who are involved in purchasing long-term bonds recognise that the smallest error can result in losses of tens of thousands, even millions of dollars. For this reason, Economica prefers to rely on the interest rates observed in the money market, rather than on surveys of economic consultants, to determine the long-run discount rate.

The following table summarises money market estimates of the long-run real rate of interest for three series: the rate of return on trust company five year guaranteed investment certificates, the interest rate on Government of Canada 10-year bonds, and the rate of return on RRBs. In each case, the figure represents the average of the rates reported in the second quarter (April-June) of 1996, net of the forecast rate of inflation. Two alternative real rates have been calculated for the GICs and the 10-year bonds: the first uses a forecasted rate of inflation of 2 percent and the second a rate of 3 percent. (The figure for RRBs is the same in both scenarios as the observed, market rate is already net of the rate of inflation.)

Investment | 2% Rate of Inflation | 3% Rate of Inflation |
---|---|---|

Trust Company 5-year GICs | 4.5% | 3.5% |

Government of Canada 10-year bonds | 5.6 | 4.6 |

Real rate of return bonds | 4.7 | 4.7 |

The figures in this table suggest that investors currently anticipate that the real rate of interest will fall somewhere between 3.5 and 5.0 percent. At Economica, we employ the mid-point of this range: 4.25 percent.