Present value formula

PV = FV ÷ (1 + r/n)^(n×t)
where:
  FV = future value (amount received in the future)
  r  = discount rate (annual, decimal)
  n  = compounding periods per year
  t  = years until receipt

Why present value matters

The concept of present value (PV) is central to finance: a dollar today is worth more than a dollar in the future because of investment opportunity, inflation, and uncertainty. Discounting converts future cash flows into today's equivalent value, making it possible to compare investments with different timing.

Net Present Value (NPV)

NPV = sum of all discounted future cash flows minus the initial investment. If NPV > 0, the investment creates value; if NPV < 0, it destroys value at the given discount rate. The discount rate used is usually the hurdle rate — the minimum acceptable return.

Discount rate selection guide

The appropriate discount rate depends on the context:

Risk-free rate: US Treasury yield (~4–5% as of 2024) — use for near-certain future cash flows.
WACC (Weighted Average Cost of Capital): use for corporate capital budgeting decisions to reflect the company’s blended cost of equity and debt.
Inflation rate: use for personal financial planning when you want to find the real (inflation-adjusted) equivalent of a future amount.

Using the wrong discount rate is the most common PV calculation error — higher rates shrink PV dramatically.

PV of an annuity

For a stream of equal payments (PMT) received at regular intervals:

PV = PMT × (1 − (1 + r)^−n) ÷ r

Where r is the discount rate per period and n is the number of periods. This is the foundation for valuing bonds, mortgages, and pension streams.

Worked example

Would you rather have $10,000 today or $12,000 three years from now at a 6% discount rate?

PV of $12,000 = $12,000 ÷ (1.06)³ = $12,000 ÷ 1.1910 ≈ $10,075.

The $12,000 future payment is worth ~$10,075 today — slightly more than $10,000, so the future payment is marginally better at this discount rate. At a 7% rate, PV = ~$9,796, making $10,000 today the better choice.