## 10/1/15

### What is present value?

The present value is the value in today's dollars of an asset, benefit, or cost that will occur in the future. Perhaps the easiest way to think of a present value is to ask yourself how much you would be willing to accept to sell your rights to a future asset.

For example, is you were to plant an orange tree today you make expect to get \$50 worth of oranges in the future. Since you have to wait for the oranges (and their \$50 value), the value in today's dollars will be less. If someone is patient and the time they have to wait for the oranges is small, then their willingness to accept amount (the present value) may be \$45 or \$40. If the person is impatient or has to wait a long period of time, then the willingness to accept amount (the present value) may be much lower approaching \$5 or so.

The present value of a future payoff should never be larger than the face value of the payoff. This is a result of the idea of "discounting" which means that people tend to prefer having resources now rather than in the future. For example, imagine you were given the choice between:

A) \$1,000 today
or
B) \$1,000 one year from today

Everyone will probably choose A because they would rather have the money now. This tendency to prefer having things in the present is a result of people's time preference for resources. In economics, we can test someone's time preference by slightly altering the previous choice. We could ask someone to choose from:

A) \$1,000 today
or
B) \$1,100 one year from today

In this set up, people who choose option A have a strong time preference towards the present. Those who choose option B seem to take a longer view towards obtaining assets. For those people who are indifferent between the two choices, we could accurately say that the present value of \$1,100 one year from today is \$1,000 (because the person is indifferent between the two choices).

The present value is calculated using the discount rate. The discount quantifies the time preference that individuals have. For example, is someone is indifferent between having \$1,000 today or \$1,100 on year from today, we would say that their discount rate is equal to 10% because they require a minimum return of 10% in order to delay their decision.

Other posts on this site go through examples of how to calculate various present values with different discount rates and future values.

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