Present Value of Money in 17 Minutes
Present value answers a simple question: what is money you will receive in the future worth today? You find it by discounting, which strips out the interest the money could have earned. It is the core of NPV, bond pricing and stock valuation.
What you will learn
- What present value means and why future money is worth less today
- The present value formula for a single future amount
- What discounting and the discount factor are
- How present value feeds into NPV and valuation
The formulas
- PV
- present value, worth today
- FV
- future amount
- r
- discount rate per period
- n
- number of periods
- DF
- what $1 received in n periods is worth today
Worked example
You will receive $1,000 in 3 years. If the discount rate is 5% a year, what is it worth today?
- Inputs: FV = $1,000, r = 0.05, n = 3.
- Growth factor: (1.05)³ = 1.157625.
- Divide: PV = $1,000 ÷ 1.157625 ≈ $863.84 (rounded to the cent).
Answer: About $863.84 today.
Common questions
What is the present value formula?
For a single future amount, PV = FV ÷ (1 + r)ⁿ, where FV is the future amount, r is the discount rate per period and n is the number of periods. It is the future value formula rearranged.
How do you calculate present value step by step?
Turn the rate into a decimal, add 1, raise it to the number of periods, then divide the future amount by that number. For $1,000 in 3 years at 5%, divide $1,000 by 1.05³ to get about $863.84.
Why is present value less than future value?
Because money today can be invested to earn a return. To have $1,000 in three years at 5%, you only need about $863.84 today. The higher the rate or the longer the wait, the lower the present value.
What discount rate should I use for present value?
Use the return you could earn elsewhere on an investment of similar risk, often called the opportunity cost of capital. In exam questions the rate is usually given. For company projects it is often the WACC.