present value
/ abbreviated PV /
Suppose someone signs a solid promise to pay you 1,000 exactly three years from now. That promise is worth something today — but clearly not a full 1,000, because you have to wait, and waiting has a cost. The amount that future promise is worth right now is its present value: the future cash flow shrunk back to today's terms.
Present value is the value today of an amount of money to be received or paid in the future, calculated by discounting it at a chosen interest rate. The formula for a single future amount is present value = future amount / (1 + r) raised to the power n, where r is the discount rate per period and n is the number of periods. For example, 1,000 due in three years discounted at 8 percent is 1,000 / (1.08 x 1.08 x 1.08), which is about 794. The higher the rate or the longer the wait, the smaller the present value. When several future payments are involved (like a stream of bond interest), you find the present value of each and add them up.
Present value is the workhorse of valuing anything that pays out over time. Bonds are priced as the present value of their future interest and principal; long-term notes, leases, and pension obligations are recorded at present value; and investment decisions compare the present value of expected returns against the cost today. It turns the abstract time value of money into a single, comparable number, letting a business line up cash flows arriving at different dates on the same footing.
A bond will pay 1,000 in five years. Discounted at 6 percent, its present value is 1,000 / (1.06 to the fifth power), about 747. If the market instead demands 9 percent, the present value drops to about 650 — the same future cash is worth less when investors want a higher return.
A higher discount rate means a smaller present value for the very same future payment.
Present value depends entirely on the discount rate you choose — there is no single 'true' present value; change the rate and the answer changes, which is why the rate assumption deserves scrutiny.