Page 13 - Economic Damage Calculations

Chapter 2

Overview Of Time Value Of Money

Discounting and present value concepts are based on the idea that a dollar invested today will grow to be
worth more in the future. A dollar invested today can earn interest at an interest rate and be worth more
in the future, or a future dollar can be discounted with a discount rate to conclude the present value of
that future dollar. This idea reflects the notion that there is some value to the use of money for a period
of time, as well as the notion that its present value is affected by the risk that the future value will actual-
ly occur at the expected level. The calculation of the future value in one year of $1.00 at a 10 percent in-
terest rate (or rate of return) is shown as follows:

1
$1.00 × (1 + 10%) = $1.10
Present Value × (1 + Interest Rate) number of compounding periods = Future Value

The discounting of a future value for one year to a present value is illustrated as follows:

$1.00 = $1.10
(1 + 10%) 1

Present Value = Future Value
(1 + Discount Rate) number of compounding periods

In this instance, the discount factor to convert the future value to a present value for one year at a 10
percent discount rate is 1/1.10, or 0.9091, when the present value is equal to the future value multiplied
by the discount factor. fn 1

The formula for the conversion of the value of money in one period to the value of money in another pe-
riod is affected by the number of compounding periods (time). In the previous examples, the 10 percent
interest rate was applied to an investment period of one year. Similarly, the 10 percent discount rate was
used to discount the $1.10 future value one period to a present value of $1.00. With an increased number
of compounding periods, the amount of growth in the money value increases. The future value of $1.00,
assuming a constant 10 percent interest rate for two years, is calculated as follows:

fn 1 The discount factor can also be referred to as the "present value factor." Additionally, some practitioners work with the reciprocal
of the discount factor, such that it grows as the discounting increases, and the present value is the future value divided by this version
of a discount factor. This is a functionally equivalent calculation.

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