Present Value Formula: Discount a Future Cash Flow

The present value formula tells you what one future cash flow is worth at an earlier date. Divide the future amount by one plus the periodic discount rate raised to the number of periods between the two dates.

What each input means

FV is one amount at one future date. If a contract promises $28,750 six years from now, that entire amount is FV. The single-sum formula does not value a sequence of annual coupons, monthly rent payments, or uneven project cash flows in one step. Discount each distinct cash flow to the same date and add the present values, or use an annuity shortcut when its equal-payment assumptions fit.

i is the rate for one period. The rate represents the return required for waiting and, when appropriate, the cash flow's risk. A semiannual period needs a semiannual rate. If a problem gives a nominal annual rate of 5.8% compounded semiannually, divide by two to obtain 2.9% per half-year. If it gives an effective annual rate, do not automatically divide it by two; convert it to an equivalent semiannual rate.

n counts the same periods described by i. Six years with semiannual compounding means 12 periods. The units are a pair: a half-year rate goes with a count of half-years. This alignment is more important than memorizing a second version of the formula.

What discounting means

Discounting reverses compounding. Compounding asks what money today can grow to; discounting asks how much would need to be invested today to reach a stated future amount at the chosen rate. The denominator is a growth factor. Dividing by it removes the growth that would occur between the valuation date and the future date.

At a positive discount rate, present value is below the future amount. A higher rate or a longer wait reduces present value because a smaller amount today could grow to the same future amount. A zero rate makes present and future value equal. Negative rates can reverse the usual relationship, so “PV must always be smaller” is a shortcut with a positive-rate assumption.

The cash flow's present value is $20,401.09 at a 5.8% nominal annual rate compounded semiannually. Economically, $20,401.09 invested for 12 half-years at 2.9% per period would grow to $28,750. The check is useful because it tests both the direction of the calculation and the period conversion.

Suppose you mistakenly used six as n while retaining the 2.9% half-year rate. You would discount for only six half-years, equivalent to three years. The resulting present value would be too high because half of the waiting time disappeared. If you instead used 5.8% as a semiannual rate, you would overstate the discounting and produce a value that is too low.

Choosing the discount rate

The arithmetic cannot choose r for you. In a classroom problem, the rate is usually supplied. In practice, it should match the cash flow's risk, currency, and timing. A contractual government payment and an uncertain startup payoff should not generally be discounted at the same rate simply because they occur in the same year. Nominal cash flows should be paired with a nominal rate that includes inflation expectations; real cash flows should be paired with a real rate.

When a sequence has different risk or market rates by maturity, a single flat rate may be an approximation. A more precise valuation discounts each cash flow with a rate appropriate to its date. The single-sum formula still works; the chosen i changes by cash flow.

Multiple cash flows

For uneven cash flows, calculate one present value per date and sum them. The valuation date must be identical for every result. For example, a payment at the end of year 2 is discounted two years, while a payment at the end of year 5 is discounted five years. Adding amounts that sit at different dates is like adding dollars in different currencies without conversion. Discounting places them in the same time unit.

An annuity formula is only a shortcut for equal, regularly spaced payments under a consistent periodic rate. A perpetuity is a different shortcut for payments continuing indefinitely. Start by identifying the cash-flow pattern before selecting a formula.

Common mistakes

Multiplying instead of dividing. Multiplication moves value forward in time. Present value moves a future cash flow backward, so it divides by the growth factor.

Mixing annual and periodic inputs. Convert the rate and count periods using the same frequency. Label the units beside both inputs before calculating.

Using a percentage as a whole number. Enter 5.8% as 0.058, not 5.8. After dividing by two, the periodic rate is 0.029.

Discounting to the wrong date. “Present” means the selected valuation date, which may not be calendar today. Count periods between that date and the cash flow.

Rounding the discount factor early. Keep calculator precision through the exponent and division. Round the final money amount to cents unless the question specifies otherwise.

Treating PV as guaranteed market price. Present value is conditional on the cash-flow forecast and discount rate. Changing either input changes the estimate.

Spreadsheet check

In Excel or Google Sheets, PV(rate, nper, pmt, [fv], [type]) can handle a lump sum by setting pmt to zero. For the example, use a 2.9% rate, 12 periods, zero payment, and a future value of -28750. The negative future value follows the spreadsheet cash-flow sign convention and returns a positive present value. You can also calculate the denominator directly with ordinary arithmetic, which makes the period assumptions easier to audit.

By the FinanceBrain Team · Last verified July 12, 2026 · How we produce and verify articles