Description
Return discountFactor = exp(-periods*log1p(effectiveRate)), equal to (1+effectiveRate)^(-periods).
Discounting expresses a future amount on a chosen present-value basis. The rate must match the period and compounding convention, while the currency price year and the choice of social or private discount rate remain separate assumptions.
Return discountFactor = exp(-periods*log1p(effectiveRate)), equal to (1+effectiveRate)^(-periods).
When to use this tool
Use Environmental Discount Period Factor when checking one supplied discount, accrual or carry-value contribution.
How to use the tool and how it works
- Enter effectiveRate, periods. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read discountFactor. Use the output convention below.
Require effectiveRate > -1 and periods >= 0. Return discountFactor = exp(-periods*log1p(effectiveRate)), equal to (1+effectiveRate)^(-periods). The rate is a fraction per modeled period and periods uses that same time basis.1
Economic evaluation must account for differences in the timing of benefits and costs. This multiplier performs only the stated rate-period conversion; it does not select an appropriate policy rate.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| effectiveRate | Effective Rate | Required. Finite number; strictly above -1. |
| periods | Periods | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| discountFactor | Discount Factor | Required. Finite number. |
{
"input": {
"effectiveRate": 0,
"periods": 5
},
"output": {
"discountFactor": 1
}
}Limitations and assumptions
- Negative rates above -1 produce factors above one for positive periods. This calculates one deterministic discount multiplier without selecting a social rate, constructing a term structure or valuing an entire cashflow stream.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a justified rate convention and complete cashflow schedule, including uncertainty and timing, when evaluating a real policy or investment.
References
-
Calculation and input contract: environmental-economics/environmental-discount-period-factor — tool.io
-
Guidelines for Preparing Economic Analyses, 3rd edition — U.S. Environmental Protection Agency
Similar or alternative tools
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- Pollution Permit Bank Carry Cost Term
Return presentFutureValue = permits*futurePrice/(1+annualRate)^years and netCarryValue = presentFutureValue-permits*currentPrice-storageCost.