Discount Factor Calculator

Discount rate (% per period)

Number of periods (n)

Discount factor

Use continuous compounding

Discount with e raised to minus r times n instead of period-by-period.

Discount a future cash flow

Enter a future amount to see its present value.

Show the cumulative (annuity) factor

Add up the discount factors for every period through n.

Fill in any two of the discount rate, the number of periods, and the discount factor. The calculator solves for the one you leave blank.

Please input values into the fields

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Show the decay chart

Plot how the discount factor shrinks period by period.

Show the period-by-period schedule

A table of each period's discount factor and running total.

The discount factor calculator converts the interest rate and time period into a single multiplier. Multiplying this factor by future cash flows gives their present value - that is, how much they are worth today.

This version allows for bi-directional calculations. You can input two of the three values (rate, number of periods or discount factor) and the tool will calculate the third value. It is also possible to switch between continuous compounding and actual cash flow or add up the factors for each period to get a cumulative annuity factor.

What is a discount factor?

A discount factor is the present value of a future payment. It's based on the time-value of money. A dollar today is worth more than a dollar to be paid in the future because the dollar today can be invested.

At positive interest rates the factor is always between 0 and 1. The further in the future the cash flows are located and the higher the interest rate, the smaller the factor. This is because waiting means missing out on growth opportunities.

Here's how to use this calculator.

Start with the discount rate and number of periods, then the calculator will instantly return the discount factor, showing the discounted amount for each period as well as the corresponding growth factor.

If a field is left blank it can be calculated backwards. If you enter a factor and the number of periods then you can find the implied interest rate. If you enter a factor and an interest rate then you can find the number of periods.

Turn on the option for cash flows and enter future amounts to check the present value. If you turn on the option for annuities, then the factors for each period are summed to get a cumulative factor. This is the present value if you receive one unit in each period.

Discount factor formula:

If interest is compounded periodically, the discount factor is the inverse of the value obtained by raising (1 + rate) to the power of the number of periods.

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

where r is the interest rate per period expressed as a decimal and n is the number of periods. Some texts will present this formula with a negative exponent but it means exactly the same thing.

DF = (1 + r)^{-n}

The present value can be found with a single calculation. Multiply the future cash flow by this factor.

PV = CF \times DF

Example calculation:

Suppose you will receive $10,000 in three years and the expected annual return is 5 percent.

The discount factor for year three would be as follows:

DF = \frac{1}{(1 + 0.05)^{3}} = 0.8638

When this factor is applied to cash flow, it results in present value.

PV = 10{,}000 \times 0.8638 = 8{,}638.38

So the $10,000 you'll receive in three years is worth about $8,638 today. This calculation uses a 5 percent interest rate. The following table shows examples of inputs and outputs.

Symbol	Meaning	Example
r	Discount rate per period	5 percent
n	Number of periods	3
DF	Discount factor	0.8638
CF	Future cash flow	10,000
PV	Present value	8,638.38

Discrete interest calculation and continuous interest calculation.

The standard discount factors are periodically compounded. When interest accrues continuously the factors change to an exponential form.

DF = e^{-r n}

The factors obtained by continuous discounting are slightly smaller for the same time period with the same interest rate. This method is often used in calculating option prices and other derivative transactions. By enabling continuous compounding, both values can be compared.

Cumulative discount factors (annuities)

The sum of the discount factors from the first period to the nth period is called the cumulative factor. It is also known as the present value factor for a series of equal payments and represents the present value if one unit is received in each period.

P/A = \frac{1 - (1 + r)^{-n}}{r}

It's a bridge that connects a single discount factor to a series of equal payments, and it is also the mathematical principle underlying the pricing of loans and annuities.

Applications of discount factors

The discount factor is a core component of valuation. In the discounted cash flow model there will be a separate factor for each future year with the further out the cash flows are the smaller the corresponding factor will be.

Discount factors are used to calculate the value of bonds by discounting each coupon and principal payment, and to determine the value of annuities by discounting future payments. They are also helpful in creating capital budgets as they bring projects with different time frames onto the same basis of present value.

Tips for reasonable estimates:

Make sure that the interest rate and term use the same time units. For monthly factors, you need a monthly interest rate and a number of months, not an annual interest rate and a number of years.

Choose a rate of interest that reflects the riskiness of the cash flows. More risky and uncertain cash flows require a higher rate of interest which will result in lower factors and a lower present value.

Frequently asked questions

What is a discount factor?

A discount factor is a multiplier that converts future cash flows into present value. It represents the current worth of a sum to be received at some point in the future. With positive interest rates, it will always be between 0 and 1.

Are discount factor and discount rate the same thing?

No, they are not the same thing. The discount rate is a percentage used in a formula while the discount factor is a multiplier between 0 and 1 that is applied directly to future cash flows instead of an interest rate.

Can a discount factor be greater than 1?

This is not possible with positive interest rates. As money today has more value than money tomorrow, the factor will be between 0 and 1. Only negative interest rates can have a factor greater than 1.

How do you use a discount factor to find present value?

To convert future cash flows into present value, multiply them by a factor. For example, if you will receive $10,000 in three years and the interest rate is 5 percent, then the discount factor is about 0.8638, so the present value is about $8,638.

What are the differences between discounted and continuous compounding?

In the case of discounting, for each period interest is compounded by raising the reciprocal of (1 + rate) to the power of n. In the case of continuous compounding, e is used as the base of an exponential function where the exponent is -r multiplied by n. The resulting factors are slightly smaller with the same calculation which is often used in pricing derivatives.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Investopedia: Discount Factor
Definition, formula, and present-value use of the discount factor.
Corporate Finance Institute: Discount Factor
How the discount factor drives discounted cash flow models.