What is Present Value (PV)?
Present Value (PV) is the current value of a future sum of money or stream of cash flows given a specific rate of return. It is a fundamental concept in finance based on the principle that "a dollar today is worth more than a dollar tomorrow" due to its potential earning capacity.
Why Calculate Present Value?
PV allows investors and businesses to compare the value of money received at different times. For example, it can help you decide whether to accept a lump sum today or a series of payments in the future. It is also the basis for many other financial metrics, such as Net Present Value (NPV).
The Present Value Formula
For a single future sum (lump sum), the formula is:
PV = FV / (1 + r)n
Where:
- FV: Future Value
- r: Interest rate (discount rate) per period
- n: Number of periods
Annuity Present Value
If you are receiving a regular stream of equal payments, you are dealing with an annuity. The formula for the present value of an ordinary annuity (payments at the end of the period) is:
PV = PMT × [(1 - (1 + r)-n) / r]
If payments are made at the beginning of the period (Annuity Due), the result is multiplied by (1 + r).
Discount Rate
The discount rate is the interest rate used in PV calculations to account for the time value of money. It typically represents the rate of return you could earn on an alternative investment of similar risk.