## Present Value Damages Calculator

Any lump sum award granted today will earn interest. If compensation (represented by the "annual deficit") is paid annually, the lump sum award will be depleted by the amount of the "deficit" paid as compensation each year, leaving a declining balance which will accrue interest. The amount of accrued interest depends on the interest rate, or equivalently, the discount rate assumption. "The idea is that the award plus the interest earned on the award should equal the future loss earnings that the plaintiff would have received had s/he not been [interrupted in their career path]."

^{1}This calculator allows for unique refinements not captured by "slide rules", multiplier tables or other present value tools:

- it allows the user to specify the date at which the present value is calculated ("date of valuation") that could precede the current date or be in the future, to simulate when the award will be granted;
- it allows the user to enter his/her own assumed interest rate;
- it allows the user to enter a "growth" rate (or not) for the annual deficit, so that it is not constrained to be constant but could increase over time (slide rules and multipliers do not allow this feature);
- it allows the user choice in selecting the date at which the present value ceases- either by specifying an "end age" explicitly or by incorporating statistical working life expectancy;
- the "statistical working life expectancy" option allows the user to model the earnings stream in the Canadian labour market by incorporating the probability each year -- based on age, gender and education level -- that the person would be working, reflecting contingencies that cause interruptions or absences in work force participation (disability, unemployment, part-time work or the choice for leisure or unpaid work). This field could also be used to simulate other contingency reductions;
- it allows the user to optionally incorporate a mortality contingency in order to reflect that most streams of payment would not be made or required if the recipient died;
- it incorporates an adjustment for timing of payments to reflect that most present value calculations convert periodic payments (monthly, bi-monthly, weekly) into lump sums
Although the user can enter a date that has passed, we recommend using a "date of valuation" that is a current date or in the future. Entering a historical date in the "date of valuation" produces a present value

as at that date, so assumes the lump sum was awarded at that date and applies the present value factors the year following the year of valuation.Converting an annual compensation stream (or "annuity") to present value requires us to discount the lump sum award today by the estimated rate of interest. There is a field below that allows you to enter an assumed rate of interest in the future.

A growth rate field is also provided if you expect the annual deficit to increase in the future at a rate greater than inflation. (If it will increase only in line with inflation, fill in this field with 0%).

Hints on Working Life ExpectancyIncorporating statistical working life expectancy in the present value estimates is an alternative to specifying an "ending age" (the user must choose one approach or the other). Rather than assuming complete withdrawal from the work force at a certain age, the statistical working life expectancy approach incorporates the probability that the person will be in the labour force each year, but this probability is usually less than 100% so compensation is reduced each year for this probability unless the individual is older and working years extend beyond age 65 from the current age. The calculations extend to age 65 as the latest retirement age.

If the user chooses to fill in an ending age, the calculation extends to that age with certainty, i.e., if the income stream represents earned income, it is assumed that the person is working with 100% certainty at each age until the ending age.

Hints on rates (interest rate):"Real" interest rates remove the inflation component. They represent the real rate of return to the investor. All provinces except Alberta, Newfoundland and the Yukon mandate real interest rates by legislation for tort cases, which range from 0% to 2.5% per year. Brown Economic currently uses a "real" interest rate of 2% as a lower risk rate of return for plaintiffs in civil litigation after 5 years. A rate of 1% is used for the first 5 years.

"Nominal" rates reflect the rates advertised by the financial community and by banking institutions. Based on an inflation rate forecast of 2.0% per year, the nominal interest rate ranges from 3% to 4% per year.

For further discussion of interest rates, see the January 2020 edition of Brown's Economic Damages Newsletter,

"Calculating Present Values in Civil Litigation: A Review of Past, Present & Future Interest Rates"Hints on rates (growth rate):If the annual deficit you choose is expected to grow at the rate of inflation, then you can use a "real" interest rate and 0% for the "growth" field (inflation is accounted for but mathematically "cancelled out"). Alternatively, you could use a "nominal" interest rate and 2% for the "growth" field to incorporate inflation in the annual deficit. The magnitude of the present value result will only vary by 1-2% using either the "real" or "nominal" method.

If the annual deficit you choose is expected to grow

abovethe rate of inflation (i.e., by occupation specific growth, such as "steps" between years of experience in a collective agreement), then use a "real" interest rate and enter your value in the "growth" field. An appropriate annual range for a long time period would be 0.5 to 3.0% per year. If a province's mandated discount rate does not allow for any adjustments in order to comply with the legislation, this field can be used to capture growth above inflation. In this way, it modifies the "annual deficit with growth" and thus the discount/interest rate stays intact and complies with legislation.

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1] G.A. Anderson and D.L. Roberts, "Economic Theory and the Present Value of Future Lost Earnings: An integration, Unification, and Simplification of Court Adopted Methodologies" (1985) 39U. Miami L. Rev.723, reproduced from C.L.Brown,Damages: Estimating Pecuniary Loss,Dec 2019 (26th edition), Canada Law Book (a Thomson Reuters Business).