February 18th 2019

Discount Factor Formula (Table of Contents)

Discount Factor Formula
Examples of Discount Factor Formula (With Excel Template)
Discount Factor Formula Calculator

Discount Factor Formula

The Discount Factor is a factor by which future cash flow is multiplied to discount it back to the present value. The discount factor effect discount rate with increase in discount factor, compounding of the discount rate builds with time. One can calculate the present value of each cash flow while doing calculation manually of the discount factor. The discount factor is used in DCF analysis to calculate the present value of future cash flow. The discount factor is one by one plus discount rate to the power period number into one. Formula for discount factor can be written as:-

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Discount Factor = 1 / (1 * (1 + Discount Rate)^{Period Number})

Examples of Discount Factor Formula (With Excel Template)

Let’s take an example to understand the calculation of the Discount Factor formula in a better manner.

Discount Factor Formula – Example #1

We have to calculate the discount factor when the discount rate is 10% and the period is 2.

Discount Factor is calculated using the formula given below

Discount Factor = 1 / (1 * (1 + Discount Rate)^{Period Number})

Put a value in the formula.

Discount Factor = 1 / (1 * (1 + 10%) ^ 2)
Discount Factor = 0.83

So, discount factor is 0.83.

Now, let us take another example to understand discount factor formula better.

Discount Factor Formula – Example #2

We have to calculate net present value and discount factor for a period of 7 months, the discount rate for same is 8% and undiscounted cash flow is $100,000.

Let us calculate discount factor for 7 months.

Discount Factor is calculated using the formula given below

Discount Factor = 1 / (1 * (1 + Discount Rate)^{Period Number})

Discount factor for 1st month = 1 / (1 * (1 + 8%) ^ 1) = 0.93
Discount factor for 2nd month = 1 / (1 * (1 + 8%) ^ 2) = 0.86
Discount factor for 3rd month = 1 / (1 * (1 + 8%) ^ 3) = 0.79
Discount factor for 4th month = 1 / (1 * (1 + 8%) ^ 4) = 0.74
Discount factor for 5th month = 1 / (1 * (1 + 8%) ^ 5) = 0.68
Discount factor for 6th month = 1 / (1 * (1 + 8%) ^ 6) = 0.63
Discount factor for 7th month = 1 / (1 * (1 + 8%) ^ 7) = 0.58

Let us calculate DCF for 7 months period.

Discount Cash Flow is calculated using the formula given below

Discounted Cash Flow = Undiscounted Cash Flow * Discount Factor

DCF for 1st month = 100,000 * 0.93 = 92,592.6
DCF for 2nd month = 100,000 * 0.86 = 85,733.90
DCF for 3rd month = 100,000 * 0.79 = 79,383.2
DCF for 4th month = 100,000 * 0.74 = 73,503
DCF for 5th month = 100,000 * 0.68= 68,058.3
DCF for 6th month = 100,000 * 0.63 = 63,017
DCF for 7th month = 100,000 * 0.58 = 58,349

Let us calculate Net Present Value

Net Present Value is calculated using the formula given below

Net Present Value = Sum of value of DCF

Net Present Value = 92592.6 + 85733.9 + 79383.2 + 73503 + 68058.3 + 63017 + 58349
Net Present Value = 520,637

So, Net present value is 520,637.

Net present value also can be calculated by NPV() and XNPV() functions in excel.

Let us see another example to understand functions.

Discount Factor Formula – Example #3

We have to calculate the net present value with manual formula and excel function and discount factor for a period of 7 months, the discount rate for same is 8% and undiscounted cash flow is $100,000.

We have seen the calculation of discount factor in the above formula but here we have to calculate time by subtracting date and get cumulative time in days and use the same for calculation.

Let us calculate discount factor for 7 months.

Discount Factor is calculated using the formula given below

Discount Factor = 1 / (1 * (1 + Discount Rate)^{Period Number})

Discount factor for 1st month = 1 / (1 * (1 + 8%) ^ 0.5)= 0.96
Discount factor for 2nd month = 1 / (1 * (1 + 8%) ^ 1.5) = 0.89
Discount factor for 3rd month = 1 / (1 * (1 + 8%) ^ 2.5) = 0.82
Discount factor for 4th month = 1 / (1 * (1 + 8%) ^ 3.5) = 0.76
Discount factor for 5th month = 1 / (1 * (1 + 8%) ^ 4.5) = 0.71
Discount factor for 6th month = 1 / (1 * (1 + 8%) ^ 5.5) = 0.65
Discount factor for 7th month = 1 / (1 * (1 + 8%) ^ 6.5) = 0.61

Let us calculate DCF for 7 months period.

Discount Cash Flow is calculated using the formula given below

Discounted Cash Flow = Undiscounted Cash Flow * Discount Factor

DCF for 1st month = 100,000 * 0.96 = 96,194.62
DCF for 2nd month = 100,000 * 0.89 = 89,069.09
DCF for 3rd month = 100,000 * 0.82 = 82,453.99
DCF for 4th month = 100,000 * 0.76 = 76,346.29
DCF for 5th month = 100,000 * 0.71 = 70.691.01
DCF for 6th month = 100,000 * 0.65 = 65,454.64
DCF for 7th month = 100,000 * 0.61 = 60,593.37

Let us calculate Net Present Value

Net Present Value is calculated using the formula given below

Net Present Value = Sum of value of DCF

Net Present Value = 96,194.62 + 89,069.09 + 82,453.99 + 76,346.29 + 70.691.01 + 65,454.64 + 60,593.37
Net Present Value = 540,803

Now, please refer to excel for calculation.

=XNPV(8%, Sum of Discounted Cash Flow, Sum of Time Period)

Discount Factor = 540,803

You can download this Discount Factor Template here – Discount Factor Formula Excel Template

Relevance and Uses of Discount Factor Formula

There are multiple uses of discount factor, they are as follows:-

It used to calculate net present value.
Discount factor uses in DCF analysis.
It is used in financial modeling.

Discount factor used by pension plan and insurance companies for discounting their liabilities. It is also used in short term money market like commercial paper and T-bills etc. It is also used by investors to get future investment values.