Present Value
Determine what future cash flows are worth today by applying a discount rate, essential for comparing investments and financial planning
Formula
PV = FV / (1 + r)^n
Divide future value by (1 + rate) raised to the number of periods to find what that future amount is worth today.
Worked Examples
Example 1: Retirement Planning
Problem:Need $1,000,000 in 30 years. How much is that worth today at 7%?
Solution:PV = FV / (1 + r)^n\nPV = $1,000,000 / (1.07)^30\nPV = $1,000,000 / 7.612\nPV = $131,367\n\nYou need to invest $131,367 today to have $1M in 30 years at 7%.
Result:PV = $131,367
Example 2: Monthly Compounding Example
Problem:Need $50,000 in 12 years. What present value is required at 6% compounded monthly?
Solution:PV = FV / (1 + r/m)^(m×n)\nPV = $50,000 / (1 + 0.06/12)^(12×12)\nPV = $50,000 / (1.005)^144\nPV ≈ $24,381\n\nThis is the lump sum needed today to grow to $50,000 in 12 years at that monthly-compounded rate.
Result:PV ≈ $24,381
Example 3: Investment Decision
Problem:Investment promises $25,000 in 5 years. Maximum to pay at 8% return?
Solution:PV = $25,000 / (1.08)^5\nPV = $25,000 / 1.469\nPV = $17,014\n\nPay no more than $17,014 for this investment to achieve 8% return.
Result:Maximum price: $17,014
Frequently Asked Questions
What is present value?
Present value is the current worth of a future sum of money. Due to time value of money, $100 today is worth more than $100 in 10 years because today's dollars can earn interest.
Why is present value important?
It helps compare money at different times. Use PV to evaluate investments, compare payment options, value bonds, or decide between lump sum vs. payments.
What is the time value of money?
Money available now is worth more than the same amount in the future due to earning potential. This is why we discount future money to find its present value.
Can PV be higher than future value?
No, with positive interest rates. With negative rates (rare), PV exceeds FV. Inflation can make real PV less useful than nominal PV.