RatedrillPresent value
Present value is what a future amount is worth today: PV = FV / (1 + r)^n, where r is the discount rate per period and n the number of periods. A higher rate or a longer wait makes the present value smaller. It is the basis of every valuation formula, from annuities to NPV.
Syntax
PV = FV / (1 + r)^n = FV x (1 + r)^-n| Part | What it is |
|---|---|
FV | The amount received or paid in the future |
r | Discount rate per period, as a decimal |
n | Number of periods until the amount is received |
Examples
FV = 1,000 in 3 years, r = 5%
PV = 1,000 / 1.05^3Result: PV = 863.84
Excel: =PV(5%, 3, 0, -1000)
FV = 5,000 in 2 years, 8% compounded quarterly
PV = 5,000 / (1 + 0.08/4)^8Result: PV = 4,267.45
Excel: =PV(8%/4, 8, 0, -5000)
FV = 20,000 in 10 years, r = 7%
PV = 20,000 / 1.07^10Result: PV = 10,166.99
Common mistakes
- Multiplying by (1 + r)^n instead of dividing gives a future value, not a present value; present value is always smaller than the future amount when r is positive.
- Using an annual rate with quarterly or monthly periods without dividing it first.
- Discounting each cash flow of a series separately when the annuity formula or Excel PV with a pmt argument does it in one step.
Practice Present value
These drills check your answer on live data, free, no account needed.
- Present value of a lump sumYou will need $6,000 in 25 years for a down payment. If your savings earn 3.25% per year, compounded annually, how much must you deposit today to have exactly that amount?
Questions
What is the discount factor?
The discount factor is 1 / (1 + r)^n, the number you multiply a future amount by to get its present value. At 5% for 3 years it is 0.8638.
How do I calculate present value in Excel?
=PV(rate, nper, pmt, [fv]). For a single amount set pmt to 0: =PV(5%, 3, 0, -1000) returns 863.84.
Related
- Future valueHow to calculate the future value of a lump sum with FV = PV x (1 + r)^n, step-by-step examples, the Excel FV function with its sign convention, and errors.
- Present value of an annuityHow to find the present value of equal payments with PV = PMT x (1 - (1 + r)^-n) / r. Worked examples, Excel PV and why this is the loan formula in disguise.
- NPV (net present value)Net present value is the sum of discounted cash flows minus the initial investment. Examples at 10% and 8%, the accept rule, Excel NPV and the sign mistake.
- Bond priceA bond price is the present value of its coupons plus the present value of its face value at the yield. Annual and semiannual examples, premium and discount.