PV of Lump Sum
Calculates the present value of a future amount discounted at an annual rate.
When to use: Use to find how much a future sum is worth today — the foundation of discounted cash flow analysis.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PV | Present Value | The current worth of a future sum | $ |
| FV | Future Value | The value of the investment at a future date | $ |
| k | Interest Rate | Nominal annual interest rate as a decimal | % |
| n | Number of Years | Investment time horizon in years | years |
Real-Life Examples
Example 1: Future Inheritance
You will receive $100,000 in 15 years. What is it worth today at a 6% discount rate?
Given
Step-by-Step
The $100,000 inheritance is worth $41,726.51 in today's dollars.
Example 2: Settlement Offer
A lawsuit offers $250,000 payable in 8 years. At a 5% discount rate, what is the present value?
Given
Step-by-Step
The future settlement is worth $169,205.67 today.
Frequently Asked Questions
The present value of a lump sum is what a future amount of money is worth today, after accounting for the time value of money. It answers the question: how much would I need to invest now to have a specific amount in the future?
A dollar today is worth more because it can be invested to earn interest. This concept — the time value of money — means that receiving money sooner is always preferable, since earlier money has more time to grow through compounding.
A discount rate is the interest rate used to calculate present value. It reflects the opportunity cost of money — the return you could earn on an alternative investment of similar risk. Higher discount rates produce lower present values.
Investors use present value to determine whether an investment is worth its price. If the present value of expected future cash flows exceeds the cost of the investment, it may be a good deal. This is the basis of discounted cash flow (DCF) analysis.