In mathematics, the discount factor is a calculation of the present value of future happiness, or more specifically it is used to measure how much people will care about a period in the future as compared to today.

The discount factor is a weighting term that multiplies future happiness, income, and losses in order to determine the factor by which money is to be multiplied to get the net present value of a good or service.

Because the value of today’s dollar will intrinsically be worth less in the future due to inflation and other factors, the discount factor is often assumed to take on values between zero and one. For example, with a discount factor equal to 0.9, an activity that would give 10 units of utility if done today would give, from today’s perspective, nine units of utility if completed tomorrow.

## Using the Discount Factor to Determine the Net Present Value

Whereas the discount rate is used to determine the present value of future cash flow, the discount factor is used to determine the net present value, which can be used to determine the expected profits and losses based on future payments — the net future value of an investment.

In order to do this, one must first determine the periodic interest rate by dividing the annual interest rate by the number of payments expected per year; next, determine the total number of payments to be made; then assign variables to each value such as P for periodic interest rate and N for the number of payments.

The basic formula for determining this discount factor would then be D=1/(1+P)^N, which would read that the discount factor is equal to one divided by the value of one plus the periodic interest rate to the power of the number of payments. For instance, if a company had a six percent annual interest rate and wanted to make 12 payments a year, the discount factor would be 0.8357.

## Multi-Period and Discrete Time Models

In a multi-period model, agents may have different utility functions for consumption (or other experiences) in different time periods. Usually, in such models, they value future experiences, but to a lesser degree than present ones.

For simplicity, the factor by which they discount next period’s utility may be a constant between zero and one, and if so it is called a discount factor. One might interpret the discount factor not as a reduction in the appreciation of future events but as a subjective probability that the agent will die before the next period, and so discounts the future experiences not because they aren’t valued, but because they may not occur.

A present-oriented agents discounts the future heavily and so has a LOW discount factor. Contrast discount rate and future-oriented. In a discrete time model where agents discount the future by a factor of b, one usually lets b=1/(1+r) where r is the discount rate.

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