Present Value Calculator
Determine how much a future sum is worth in today's dollars. Use the present value formula to compare investment options, evaluate annuities, or assess any future cash flow against your required rate of return.
Present Value Results
Understanding Present Value
The time value of money says a dollar today is worth more than a dollar in the future. Present value quantifies exactly how much more — by discounting future cash flows at your opportunity cost rate.
Lump sum PV: PV = FV ÷ (1 + r)n
Annuity PV: PV = PMT × (1 − (1+r)-n) ÷ r
When to Use Present Value
- Comparing two investments with different payout timelines
- Evaluating whether a pension lump sum beats monthly payments
- Pricing bonds or other fixed-income instruments
- Business capital budgeting and NPV analysis
Choosing a Discount Rate
The discount rate represents your opportunity cost — what you could earn on the money elsewhere. Common choices include the current Treasury yield (risk-free rate), your expected investment return (7–10% for equities), or a company's hurdle rate. A higher discount rate shrinks present value, making distant money worth less today. Use a rate that reflects the actual risk of the cash flows being discounted.
Worked Example: Pension Lump Sum vs. Monthly Payments
Your employer offers a choice: receive a $250,000 lump sum, or $1,500/month for life starting at age 65. You expect to live 25 years in retirement (to age 90). Using a 6% discount rate, the present value of $1,500/month for 25 years = $1,500 × 12 × PV annuity factor = $18,000 × 12.783 = $230,094. At 6%, the monthly annuity is worth about $230,000 in today's dollars versus the $250,000 lump sum — the lump sum is more valuable. At a 4% discount rate, the monthly annuity's present value rises to $18,000 × 15.622 = $281,196, making it the better choice. Your life expectancy and chosen discount rate together determine which option wins.
Present Value at Different Discount Rates
| Future Sum | Years Away | PV at 4% | PV at 7% | PV at 10% |
|---|---|---|---|---|
| $100,000 | 5 | $82,193 | $71,299 | $62,092 |
| $100,000 | 10 | $67,556 | $50,835 | $38,554 |
| $100,000 | 20 | $45,639 | $25,842 | $14,864 |
| $100,000 | 30 | $30,832 | $13,137 | $5,731 |
Frequently Asked Questions
What is present value used for?
Present value is used to compare money received at different points in time on equal footing. It answers: "How much is a future payment worth in today's dollars?" This is fundamental to bond pricing, capital budgeting, retirement planning, and any decision involving cash flows spread across time.
What is net present value (NPV)?
Net present value is the sum of all present values of future cash flows minus the initial investment. A positive NPV means the investment is worth more than it costs — accept it. A negative NPV means it destroys value — reject it. NPV is the standard tool for capital investment decisions in business finance.
How does the discount rate affect present value?
Present value moves inversely with the discount rate. A higher rate produces a lower present value — future money is worth less when better alternatives exist. This is why rising interest rates tend to lower the value of bonds, real estate, and other long-duration assets.
A bond's price is the present value of all its future cash flows: coupon payments and the principal repayment at maturity. Discount those cash flows at your required yield (yield to maturity). If your required yield equals the coupon rate, the bond trades at par ($1,000). If rates rise above the coupon, the PV falls and the bond trades at a discount. If rates fall below the coupon, the bond trades at a premium. This inverse relationship between price and yield is a fundamental bond pricing principle.
Present value is the current worth of a single future cash flow (or series of flows). Net present value (NPV) subtracts the initial cost of an investment from the sum of all present values of future cash flows. If NPV is positive, the investment creates value above your required rate of return — a good investment. If negative, it destroys value. PV is a component used in NPV calculations.