Present Value Calculator
PV Formulas
Lump Sum:
PV = FV / (1 + r)^n
Annuity:
PV = PMT x [1-(1+r)^-n] / r
Perpetuity:
PV = PMT / r
Common Discount Rates
Understanding Present Value
What is Present Value?
Present Value (PV) is the current worth of a future sum of money or stream of cash flows given a specified rate of return. It answers the question: How much is future money worth today?
The Time Value of Money
Money available today is worth more than the same amount in the future because of its potential earning capacity. This core principle underlies all present value calculations.
Types of Present Value Calculations
Lump Sum PV
Discounts a single future amount back to today. Used for one-time payments like bond face values or settlement amounts.
Example: What is $100,000 in 10 years worth today?
Annuity PV
Discounts a series of equal payments. Used for loan analysis, lease valuation, and retirement income planning.
Example: What is $1,000/month for 20 years worth today?
The Discount Rate
The discount rate reflects the opportunity cost of money and includes factors like risk, inflation, and alternative investment returns.
| Scenario | Typical Rate | Why |
|---|---|---|
| Government guarantee | 2-4% | Very low risk |
| Corporate investment | 8-12% | Moderate risk |
| Personal goals | 6-10% | Expected portfolio return |
| High-risk venture | 15-25% | High uncertainty |
Practical Applications
Investment Decisions
Compare different investment opportunities by converting all future cash flows to present value terms.
Loan Analysis
Determine the true cost of financing by calculating the PV of all future payments.
Business Valuation
Value a business by discounting its expected future cash flows to present value.
Settlement Analysis
Compare lump sum settlements to structured payment options by calculating present values.
Example: Lottery Winnings
$1 Million Jackpot: Lump Sum vs Payments
Option A: Lump Sum Today
Receive $600,000 now
Option B: $50,000/year for 20 years
Total: $1,000,000
PV at 5%: $623,111
At a 5% discount rate, the annuity option has a higher present value. But at 8%, the lump sum becomes more valuable.
Impact of Time and Rate
| Future Amount | Years | PV at 5% | PV at 10% |
|---|---|---|---|
| $100,000 | 5 | $78,353 | $62,092 |
| $100,000 | 10 | $61,391 | $38,554 |
| $100,000 | 20 | $37,689 | $14,864 |
| $100,000 | 30 | $23,138 | $5,731 |
Key Insight
The further away a cash flow and the higher the discount rate, the less it is worth today. This is why early cash flows are more valuable than distant ones, and why high-risk investments require higher expected returns.
Frequently Asked Questions
What is present value?
Present value (PV) is what a future sum of money is worth today, given a specific rate of return. It's based on the time value of money principle: money available now is worth more than the same amount later because it can be invested. PV helps compare cash flows occurring at different times.
How do I calculate present value of a lump sum?
Use the formula: PV = FV / (1 + r)^n, where FV is future value, r is the discount rate per period, and n is the number of periods. For example, $100,000 in 10 years at 5% discount rate: PV = $100,000 / (1.05)^10 = $61,391. The higher the rate or time, the lower the present value.
What discount rate should I use?
Use a rate reflecting your opportunity cost or required return. Common choices: risk-free rate (3-5%) for guaranteed cash flows, expected portfolio return (6-10%) for personal goals, company cost of capital (8-12%) for business decisions, or higher rates (15-25%) for risky ventures.
What is the difference between present value and net present value?
Present value calculates what a single future amount is worth today. Net present value (NPV) is the sum of all present values of cash inflows minus the initial investment. Positive NPV means the investment creates value; negative NPV means it destroys value. NPV is the key metric for investment decisions.