Calculate present discounted value from future value, discount rate, and years, or solve any missing input with one time-value formula.

One future cash flow; constant effective annual discount rate. Enter 5 for 5%. Fractional years use the same annual compounding model.

Related Calculators

Present Discounted Value Formula

The following equation is used to calculate the Present Discounted Value.

PDV = โˆ‘(CFโ‚œ / (1 + r)โฝแต—โพ)
  • Where PDV is the present discounted value ($)
  • CFโ‚œ is the cash flow at time t ($)
  • r is the discount rate (decimal)
  • t is the time period

To calculate the present discounted value, sum each future cash flow discounted by the discount rate raised to the appropriate time period.

What is a Present Discounted Value?

Definition:

A present discounted value is the current equivalent of future cash flows under a chosen discount rate. A positive rate reduces the present value of a future positive receipt; a zero rate leaves it unchanged, and a negative rate increases it.

How to Calculate Present Discounted Value?

Example Problem:

The following example outlines the steps and information needed to calculate the Present Discounted Value.

First, determine the future cash flows. In this example, there are three payments: $500 in 1 year, $600 in 2 years, and $700 in 3 years.

Next, determine the discount rate. In this case, the discount rate is 5% (0.05).

Finally, calculate the present discounted value using the formula above:

PDV = (500 / (1 + 0.05)^1) + (600 / (1 + 0.05)^2) + (700 / (1 + 0.05)^3)

PDV โ‰ˆ 476.1905 + 544.2177 + 604.6863

PDV โ‰ˆ $1,625.09 (round after summing the unrounded discounted values).

FAQ

Why is money in the future worth less than money today?

This is due to the time value of money, which factors in potential inflation and opportunity costs of not having the money available earlier for investment or other uses.

How do I choose a discount rate?

The discount rate can be based on various factors, such as the risk-free rate of return (e.g., government bonds), the cost of capital for a firm, or the perceived risk of the cash flows.

Can the present discounted value formula handle varying cash flows over time?

Yes. The calculator above handles one cash flow at a time. Calculate each cash flow using its own time period and the same annual discount rate, then add the unrounded present values.