Discounting calculator

Work out the present value of future cash flows, with the discount factor, a year-by-year breakdown, the effect of inflation and the whole method explained.

What is discounting?

Discounting converts a future amount into what it is worth today. It is the reverse of compounding: where compounding pushes money forward in time, discounting pulls it back to the present. The result is the present value, which is what you would need today to reach that future amount over that time at that return.

The future payment is divided by the compounding factor (1 + i)^N. That quotient is the discount factor, and it is never above one. The higher the rate and the more distant the payment, the smaller the factor and the less that future amount is worth today. With several payments the same step is repeated for each and the results are added up.

Why is money worth more today than tomorrow?

Imagine you can choose: €1,000 today, or €1,000 in a year. Almost everyone takes it today, and there are three good reasons why.

The chance to earn. Money you hold today can be invested. If it earns 5%, in a year it becomes €1,050. A thousand euro in a year is therefore worth less than a thousand today, because it earned you nothing in the meantime.

Inflation. Prices rise over time, so the same amount buys less a year from now. Money loses purchasing power simply by existing.

Uncertainty. A promise of future payment may not be kept. The debtor can go under, the contract can be cancelled. Money in hand carries none of that risk.

Together these three make up the discount rate. The greater the opportunity, the inflation or the risk, the higher the rate, and the less a future payment is worth today.

The formula and where it comes from

Discounting is compounding run backwards. Compounding says that today's amount PV grows into FV over t years:

Compounding: forwards

FV = PV \cdot (1 + r)^{t}

Solving that equation for PV, dividing both sides by (1 + r)^t, gives the formula for discounting:

Discounting: backwards

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

If discounting happens more often than once a year, the annual rate is split into periods (i = r/n) and the number of periods multiplied (N = n · t). With several payments the same step repeats for each and the results are added:

Several cash flows

PV = \sum_{t} \frac{CF_t}{\left(1 + \frac{r}{n}\right)^{n \cdot t}}

What each variable means

The most common mistake is in the units: the rate must be a decimal and the periods must match the discounting frequency.

Variables in the formula:

Table of formula variables
Symbol	Name	Jednotka
$PV$	Present value	€
$FV$	Future value	€
$r$	Annual discount rate
$n$	Periods per year
$t$	Number of years	years
$i$	Rate per period
$N$	Total number of periods
$DF$	Discount factor

A worked example

€10,000 in five years

A friend promises to pay you €10,000 in 5 years. You know your money would earn 6% a year elsewhere. The question is: what is that promise worth today?

First the discount factor. Over five years at 6% the compounding factor is 1.06⁵ ≈ 1.3382, so the discount factor is its reciprocal: 0.7473. One euro received in five years is worth about 75 cents today.

The present value is therefore 10,000 × 0.7473 = €7,472.58. That is the amount you would have to put aside today at 6% to have exactly €10,000 in five years.

The difference of €2,527.42 is the price of waiting. Of the original €10,000 the promise keeps only 75% of its value, which is why it is not worth paying more than €7,472.58 for such a promise.

Try raising the rate in the calculator from 6% to 12%. The present value falls by roughly half: the higher the return you demand, the less you are willing to pay today.

Where discounting is used

Discounting is not an academic exercise: it underpins almost every valuation in finance.

Valuing investments: An investment is only worth buying if its price is below the present value of the future income it will produce.
Pricing bonds: A bond's price is the present value of all its coupons plus the discounted face value due at the end.
Valuing companies (DCF): The discounted cash flow method estimates a company's value as the present value of its future free cash flows.
Retirement planning: How much you need set aside today to cover future retirement spending is a pure discounting problem.
Actuarial science: Insurance reserves are the present value of future claims; without discounting they would be overstated.

Common mistakes

Related calculators

Related terms

Every term used in this calculator has its own encyclopedia entry with a detailed explanation and derivation.

Discounting calculator

Work out the present value of future cash flows, with the discount factor, a year-by-year breakdown, the effect of inflation and the whole method explained.

Input parameters

Results recalculate immediately on every change.

Present value

€7,472.58

75% of the future value

What you need today to reach the future amounts at the rate you have given.

Future value: €10,000.00
The cost of waiting: €2,527.42
Discount factor: 0.7473

Try a ready-made scenario

Future vs. present value

The gap between the bars is the price of waiting for the money.

Future and present value compared

Contribution to the present value

Each bar is one cash flow: the lower part survives discounting, the upper is what it lost.

Each cash flow split into present value and the cost of waiting

The discount factor over time

What one euro received in a given number of years is worth today. The higher the rate, the faster the curve falls.

The discount factor by number of years

Timeline of the cash flows

When the payments fall due, and how much of each survives the trip to today.

The height of the bar is the future amount, the green part its present value. The figure above each bar is what that payment is worth today.

Show as a table

The cash flows on a timeline
Year	Future flow	Present value
5	€10,000.00	€7,472.58

Discounting table

For each cash flow: its discount factor, its present value and the running total.

For each cash flow, its year, future amount, discount factor, present value and the running total of present values
Year	Future cash flow	Discount factor	Present value	Cumulative PV
5	€10,000.00	0.7473	€7,472.58	€7,472.58

Formula used

Each future cash flow is divided by the compounding factor for the time until it falls due; the sum is what the whole stream is worth today.

Formula

PV = \sum_{t} \frac{CF_t}{\left(1 + \frac{r}{n}\right)^{n \cdot t}}

Substitution

PV = \frac{10000.00}{(1 + 0.060000)^{5}} = 7472.58

What each variable means:

Table of formula variables
Symbol	Name	Jednotka
$PV$	Present value	€
$FV$	Future value	€
$r$	Annual discount rate
$n$	Periods per year
$t$	Number of years	years
$i$	Rate per period
$N$	Total number of periods
$DF$	Discount factor

The calculation, step by step

Every step shows the formula, the numbers put into it, and the intermediate result.

1
Finding the rate for a single period
The annual discount rate is split across the periods. When discounting happens more than once a year, each period uses only its proportional share of the annual rate.
Formula
$i = \frac{r}{n}$
Substitution
$i = \frac{0.0600}{1} = 0.060000$
Rate per period: 6,00 %
2
Working out the discount factor
The discount factor says what one euro received in the future is worth today. It is the reciprocal of the compounding factor, which is why it is never above 1.
Formula
$DF = \frac{1}{(1 + i)^{N}}$
Substitution
$DF = \frac{1}{(1 + 0.060000)^{5}} = 0.747258$
Discount factor: 0,7473
3
Discounting the future payment
The future amount is multiplied by the discount factor. The result is what you would need today for it to grow, at that rate, into exactly that future amount.
Formula
$PV_t = CF_t \cdot DF_t = \frac{CF_t}{(1 + i)^{n \cdot t}}$
Substitution
$PV_{5} = 10000.00 \cdot 0.747258 = 7472.58$
Present value: 7 472,58 €
4
What discounting took off
The difference between the future and present value is the price of waiting, the value a deferred payment gives up.
Formula
$D = FV - PV$
Substitution
$D = 10000.00 - 7472.58 = 2527.42$
The effect of discounting: 2 527,42 €

What is discounting?

Why is money worth more today than tomorrow?

Imagine you can choose: €1,000 today, or €1,000 in a year. Almost everyone takes it today, and there are three good reasons why.

Inflation. Prices rise over time, so the same amount buys less a year from now. Money loses purchasing power simply by existing.

Uncertainty. A promise of future payment may not be kept. The debtor can go under, the contract can be cancelled. Money in hand carries none of that risk.

Together these three make up the discount rate. The greater the opportunity, the inflation or the risk, the higher the rate, and the less a future payment is worth today.

The formula and where it comes from

Discounting is compounding run backwards. Compounding says that today's amount PV grows into FV over t years:

Compounding: forwards

FV = PV \cdot (1 + r)^{t}

Solving that equation for PV, dividing both sides by (1 + r)^t, gives the formula for discounting:

Discounting: backwards

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

Several cash flows

PV = \sum_{t} \frac{CF_t}{\left(1 + \frac{r}{n}\right)^{n \cdot t}}

What each variable means

The most common mistake is in the units: the rate must be a decimal and the periods must match the discounting frequency.

Variables in the formula:

Table of formula variables
Symbol	Name	Jednotka
$PV$	Present value	€
$FV$	Future value	€
$r$	Annual discount rate
$n$	Periods per year
$t$	Number of years	years
$i$	Rate per period
$N$	Total number of periods
$DF$	Discount factor

A worked example

€10,000 in five years

A friend promises to pay you €10,000 in 5 years. You know your money would earn 6% a year elsewhere. The question is: what is that promise worth today?

The present value is therefore 10,000 × 0.7473 = €7,472.58. That is the amount you would have to put aside today at 6% to have exactly €10,000 in five years.

Try raising the rate in the calculator from 6% to 12%. The present value falls by roughly half: the higher the return you demand, the less you are willing to pay today.

Where discounting is used

Discounting is not an academic exercise: it underpins almost every valuation in finance.

Valuing investments: An investment is only worth buying if its price is below the present value of the future income it will produce.
Pricing bonds: A bond's price is the present value of all its coupons plus the discounted face value due at the end.
Valuing companies (DCF): The discounted cash flow method estimates a company's value as the present value of its future free cash flows.
Retirement planning: How much you need set aside today to cover future retirement spending is a pure discounting problem.
Actuarial science: Insurance reserves are the present value of future claims; without discounting they would be overstated.

Common mistakes

Related calculators

Related terms

Every term used in this calculator has its own encyclopedia entry with a detailed explanation and derivation.

Year	Discount factor
0	1.0000
1	0.9434
2	0.8900
3	0.8396
4	0.7921
5	0.7473

Year	Discount factor
0	1.0000
1	0.9434
2	0.8900
3	0.8396
4	0.7921
5	0.7473

What is discounting?

Why is money worth more today than tomorrow?

The formula and where it comes from

What each variable means

A worked example

Where discounting is used

Common mistakes

Related calculators

Related terms

Related topics

Terms that come up in this calculation

Calculators that follow on from this one

Input parameters

Try a ready-made scenario

Future vs. present value

Contribution to the present value

The discount factor over time

Timeline of the cash flows

Discounting table

Formula used

The calculation, step by step

Finding the rate for a single period

Working out the discount factor

Discounting the future payment

What discounting took off

What is discounting?

Why is money worth more today than tomorrow?

The formula and where it comes from

What each variable means

A worked example

Where discounting is used

Common mistakes

Related calculators

Related terms

Related topics

Terms that come up in this calculation

Calculators that follow on from this one

Input parameters

Try a ready-made scenario

Future vs. present value

Contribution to the present value

The discount factor over time

Timeline of the cash flows

Discounting table

Formula used

The calculation, step by step

Finding the rate for a single period

Working out the discount factor

Discounting the future payment

What discounting took off