Present value

Present value is today's equivalent of a future cash flow, found by discounting it at a required rate: PV = FV / (1 + r)^n. It allows future amounts to be compared on a common today's basis.

ByHoang TruongUpdated June 30, 2026

FrameworkTime value of money

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A project pays €8,000 in three years. At a required return of 6%, that cash flow is discounted by (1.06) cubed, a factor of 1.191, giving a present value of €6,719. The future amount divides by the discount factor: PV equals future value divided by (1 plus r) to the power n. A higher discount rate would shrink the present value further.

Where it fits

TopicTime Value of MoneyCoreSubjectCorporate FinanceCore

The formula

LaTeX

PV = \frac{FV}{(1+r)^n}

Variables

$P V$: Present value (€)
$F V$: Future value (€)
$r$: Discount rate per period (decimal)
$n$: Number of periods (periods)

Converts a future cash flow to its equivalent value in today's money.

Check yourself

PracticeCORE

A contract will pay €9,000 in exactly two years. The required return is 5% per annum, compounded annually. What is the present value of this payment, to the nearest euro?

Select an answer to check your understanding.