# Present Value of Discounting Principles

*How much should be deposited in a safe investment today to compensate for future income lost due to an injury or wrongful death?*

Once the economic damage period is determined, the earnings loss for each year of the period can be calculated. In most cases, an award for economic damages is made in a lump sum which consolidates the amounts for all future years of lost earnings. To arrive at an accurate award, future year dollar amounts representing projected lost income are converted to their current equivalent values.

The current equivalent value, or “present value,” reflects the well-known truism that a dollar received today is worth more than a dollar received in some future time period, as a dollar received today could be safely invested to yield more money in the future. In the following sections, we discuss the process of discounting, or converting future dollar amounts to their present value, in more detail.

*The time value concept of money*

To illustrate the concept of the time value of money, consider an example of a wrongful death lawsuit in which a 62-year-old man was killed in a plant accident. Assume, for the purposes of this example, that there is no issue of liability and the defendant is simply attempting to calculate the total value of the economic damages. Further, assume both sides have agreed that the deceased worker was earning $50,000 per year at the time of his death and would have earned that exact amount each year until retirement at the age of 65.

One way to determine the economic value of the lost wages in this example would be simply to multiply the amount the person was earning at the time of his death by three years, which would mean that the defendant caused a total of $150,000 in economic damages to the family of the deceased. This simplistic calculation is, of course, incorrect because the deceased would have earned the money over the course of three years. A lump sum of that amount would earn interest over the three years, resulting in an award greater than the amount needed to replace the lost future income.

The process of discounting requires an assumption as to how much interest the lump sum award would earn. As will be discussed later, this is a key assumption because the higher the assumed interest rate, the smaller the present value of the lump sum. Figure 8 and Figure 9 provide two Present value discounting principles The process of discounting requires an assumption as to how much interest a lump sum award would earn. 1 examples to demonstrate this point. The future annual incomes of $50,000 in each year 2007 to 2009 are converted to their present value as of 2006, the assumed date of the award.

In Figure 8, the assumed rate of interest is 5 percent and the amount needed to exactly compensate for the lost annual income payments of $50,000 in each year is $136,162, not $150,000. In Figure 9, the assumed rate of interest is 1 percent, and the amount needed to compensate for the lost income payments is $147,049.

### Figure 8: The time value of money assuming a 5% rate of interest

Year of Earnings |
Amount Earned |
Present Value of Amount Earned |

2007 | $50,000 | $47,619 |

2008 | $50,000 | $45,351 |

2009 | $50,000 | $43,192 |

Present Value of 2007-2009 Earnings |
$136,162 |

### Figure 9: The time value of money assuming a 1% rate of interest

Year of Earnings |
Amount Earned |
Present Value of Amount Earned |

2007 | $50,000 | $49,505 |

2008 | $50,000 | $49,015 |

2009 | $50,000 | $48,530 |

Present Value of 2007-2009 Earnings |
$147,045 |

*Discount factors in the courts*

Few topics in litigation generate more confusion and controversy than the discount rate to be applied to future lost earnings in order to calculate their present value. As shown below and discussed above, the primary reason for this is the simple fact that small differences in discount rates can lead to large differences in damage estimates, especially when the future earnings in question accumulate well into the future.

In litigation, even if both sides have reached an agreement over the exact magnitude of lost future earnings, benefits, etc., a disagreement over discount rates can lead to wide discrepancies in damage estimates.

The further into the future the damages extend, the more contentious the disagreement over discount rates. To see this, imagine the calculation of lost earnings for a single year, and imagine discounting these at two different rates, say 2.5 percent and 5 percent. If the valuation is performed for a loss of $50,000 that will occur in one year, then the first discount rate results in a present value of $48,780.49 ($50,000 divided by 1.025), and the second discount rate results in a present value of $47,619.05 ($50,000 divided by 1.05) or a difference of $1,161.

If, however, the $50,000 loss will occur 10 years into the future, then the present value evaluated at 2.5 percent is $39,059.92 ($50,000 divided by 1.02510). However, the present value evaluated at 5 percent is $30,695.66 ($50,000 divided by 1.0510) a difference of $8,364. Clearly, the further into the future the damages extend, the greater the impact the discount rate will have on the present value.

Fortunately, the one area of litigation where the Supreme Court has offered definitive guidance on the acceptable magnitude of discount rates is wrongful death or personal injury. In their 1983 ruling from Jones & Laughlin Steel Corp. v. Pfeifer, the Court endorsed three standard discounting approaches, but stated that one of the three, would be subject to increased scrutiny when utilized. There have been many additional decisions concerning interest rate factors.

*Choosing a discount rate*

There are many interest rates to choose from, and their differences reflect differences in the perceived risk of payment on the part of the borrower, length of time to maturity, and other factors that are beyond the scope of this discussion. The primary rationale for discounting is to allow damage awards to reflect the “time value of money.”

For example, one may consider using the yield on corporate bonds to discount such cash flows. However, corporate bond yields include a premium, compensating the investor for the risk of corporate bankruptcy or default. Therefore, the use of corporate bond yields overstates the risk and is not appropriate for use in discounting cash flows in personal injury or wrongful death cases.

Most economists utilize the yields on Treasury securities (U.S. Treasury bills, notes, and bonds), which are free of default risk and therefore considered “safe” investments. According to the Supreme Court’s ruling in the Pfeiffer case, “the discount rate should be based on the rate of interest that would be earned on the best and safest investments,” and that an injured worker “is entitled to a risk-free stream of future income to replace his lost wages; therefore, the discount rate should not reflect the market’s premium for investors who are willing to accept some risk of default.”

The next issue involves the choice of maturity. U.S. Treasury securities are available and the adjusted yields are published by the Federal Reserve for maturities ranging from 30 days to 30 years. Typically, longer term rates exceed shorter term rates, so the present value will be different depending on the interest rate chosen. Some economists advocate the use of the maturity that comes closest to the length of time the lost earnings damages extend in a specific case.

For cases in which lost earnings are calculated for a person between twenty and thirty years of age who has decades of work ahead, a long-term rate would be used. For cases in which the person is near retirement, a shorter term rate would be used. While there is nothing fundamentally wrong with this approach, it involves potential difficulties that can be avoided by using short-term rates.

*Calculating present day value*

Finally, it should be noted that once a base earnings level has been established, two things determine its present value: the discount rate and the growth rate of earnings. The discount rate is used to determine the present value of future lost earnings. The growth rate of earnings is used to project the increase in earnings beginning at the time of death or injury. As such, many economists work using a “net discount rate,” i.e., the difference between the actual discount rate and the growth rate of earnings.

*The process of discounting requires an assumption as to how much interest a lump sum award would earn.*

*The further into the future the damages extend, the more contentious the disagreement over discount rates.*

*The one are of litigation where the Supreme Court has offered definitive guidance on the acceptable magnitude of discount rates is wrongful death or personal injury.*

# Guidelines for discounting future losses to present value

*Core disagreement*

While discounting is generally accepted, there may be some disagreement on the actual discount rate used in the calculation.

*Probability approach*

In addition to a work life approach, some analysts may incorporate a probability approach to account for the likelihood of certain events.

*‘Real’ interest rate*

An after-inflation (“real” interest rate) discount rate of between 1 percent and 3 percent is generally a reasonable range in cases that involve injury and wrongful death allegations.

*Inversely proportional*

The higher the discount factor, the lower the economic damage estimates.

*We calculate alleged damages in personal injury and wrongful death cases. Contact us to learn more.*

*Questions or comments*

Dwight Steward, Ph.D. Economist and Director

dsteward@employstats.com www.employstats.com