Page 18 - Economic Damage Calculations

be. In figure 2-4, the standard deviation of Distribution 1 is greater than the standard deviation of Distri-
bution 2. The standard deviation increases as the range of outcomes increases or as the likelihood of out-
comes far from the expected value increases ("heavier tails"). The standard deviation of an investment’s
expected economic income is typically an important input into the rate of return that investors expect
from that investment.

In another example, a biotech company may have a 10 percent probability of making $1 billion, a 40
percent probability of making $10 million, and a 50 percent probability of losing $100 million. Based on
these hypothetical data, the expected value of the income of the biotech company may be estimated as
presented in figure 2-5.

Figure 2-5

Scenario Income Probability Expected
1 $1B 10.00% $100M
2 $10M 40.00% $4M
3 ($100M) 50.00% ($50M)

Total Expected Income $54M

In contrast, a United States Treasury bill with an expected payment of $54 million, given the govern-
ment’s de minimus risk of default, would yield the same expected income as the biotech company. How-
ever, the Treasury bill would be worth more than the example biotech company, even though both in-
vestments have the same expected value. fn 6 The valuation of the biotech company would typically in-
volve a valuation adjustment (or penalty) for variability risk, in addition to the discount to reach the $54
million expected value from the $1 billion income from the success scenario.

As discussed in this practice aid, the variability of the cash flow streams associated with these invest-
ment alternatives is manifested in differing rates of return. In an economic damages analysis, when two
different possible outcomes have the same expected value but different ranges of outcomes, then this dif-
ference normally results in different present values.

The Impact of Time

The time to delivery can also affect the present value beyond just discounting for additional future peri-
ods at the selected discount rate. For example, if the potential economic return is extended farther into
the future, investors may (1) perceive greater uncertainty and (2) conclude a lower present value than is
explained by just discounting for additional future periods at the otherwise selected discount rate. This
conclusion would be seen in a higher discount rate, as well as an increased number of discount periods.
Additionally, the risk-free component will generally be greater simply due to the greater period of time
to use the subject investment. For example, a 30-year Treasury bond typically yields more than a 3-
month Treasury bill.

fn 6 There is no time value component in this example.

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