Present Value (PV)

Time Value of Money
Updated Apr 2026 • Has calculator

The current worth of a future sum of money, discounted at a required rate of return.

What is Present Value?

Present value (PV) answers a fundamental question in finance: how much is a future cash flow worth in today's dollars? A dollar received in the future is worth less than a dollar today because of the opportunity cost — money available now can be invested to earn a return. The PV formula discounts a future amount by a rate of return over a given number of periods. PV is the foundation of bond pricing, equity valuation, capital budgeting, and virtually every discounted cash flow (DCF) analysis used in corporate finance and investing.

Formula

PV = FV ÷ (1 + r)^n

Worked Example

Worked example — US Treasury STRIP (Zero-Coupon Bond)

10-year maturity, 2024

Step 1  Face value (FV): $1,000
Step 2  Discount rate: 4.25% (10-year Treasury yield, 2024)
Step 3  Maturity: 10 years
Step 4  PV = $1,000 ÷ (1.0425)^10 = $1,000 ÷ 1.5154 = $660.07
Step 5  → You would pay $660.07 today to receive $1,000 in 10 years at a 4.25% yield

Source: US Treasury — Daily Treasury Par Yield Curve Rates (2024-12-31)

Calculate Present Value

The amount to be received in the future

Annual discount / required rate of return

Number of compounding periods

Present Value

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Not investment advice.

How to Interpret Present Value

< 0
Zero or Negative PV — re-check inputs
0 – 500
Low PV — high discount rate or distant horizon
> 500
Substantial PV — near-term or low-rate discount

📚 Time Value of Money — Complete the path

  1. Present Value
  2. Future Value
  3. PV of Annuity
  4. FV of Annuity
  5. Growing Perpetuity
Sources
  1. CFA Institute — Fixed Income & Time Value of Money, 7th ed.
  2. Brealey, Myers & Allen — Principles of Corporate Finance, 13th ed.
  3. US Treasury — Yield Curve Rates