Page 14 - Economic Damage Calculations

$1.00 × (1 + 10%) = $1.21
2
Present Value × (1 + Discount Rate) number of compounding periods = Future Value

The future value example assumes that the original dollar is invested for two periods (years), with the
same 10 percent interest rate applied for both years. Thus, the originally invested dollar grows to $1.10
after one year, and then it is compounded at 10 percent again in the second year. At the end of the sec-
ond year, the original dollar is worth $1.10 × 1.10, or $1.21. In this present value calculation, the dis-
count factor is 1.00/1.21, or 0.8264.

In the event that different interest rates are used in different periods in the compounding process, the fu-
ture value formula is similar, only slightly more complex. For example, assuming that 10 percent is the
interest rate for year one and 20 percent is the interest rate for year two, then the future value calculation
performed is as follows:

1
1
$1.00 × (1 + 10%) × (1 + 20%) = $1.32
The impact of a higher discount rate is to reduce the present value of a future amount of money more
than a lower discount rate. fn 2 For example, a $1,000 stream of cash flow for five years will be comput-
ed to have a higher present value if the discount rate used to perform the calculation is lower, all else
equal.

Figure 2-1

Lower Discount Rate Higher Discount Rate
Annual
Cash Discount Discount Present Discount Discount Present
Period Flow Rate Factor Value Rate Factor Value
1 $1,000 10% 0.9091 $909 20% 0.8333 $833
2 $1,000 10% 0.8264 $826 20% 0.6944 $694
3 $1,000 10% 0.7513 $751 20% 0.5787 $579
4 $1,000 10% 0.6830 $683 20% 0.4823 $482

5 $1,000 10% 0.6209 $621 20% 0.4019 $402
Total $5,000 $3,791 $2,991

As a result, the core inputs that define the conversion of value of a single cash flow from one period to
another period are (1) the value in one period, (2) the interest or other rate(s) of return (which may differ
period by period), and (3) the number of compounding periods.

fn 2 For purposes of this practice aid, the terms income and cash flow are both used in describing the development of a present value
analysis. In practice, factors such as additions to working capital may call for adjustments to income in order to accurately model val-
ue to an investor or owner of an asset. However, income metrics may function well in calculating economic damages in some situa-
tions and may be simpler for presentation purposes.

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