Discount Factor Formula

Table of Contents

• What is Discount Factor Formula?
• Examples of Discount Factor Formula
• Discount Factor Formula Calculator

What is Discount Factor Formula?

The formula of discount factor is similar to that of a present value of money and is calculated by adding the discount rate to one which is then raised to the negative power of a number of periods. The formula is adjusted for the number of compounding during a year.

Mathematically, the discount factor formula is represented as below,

where,

• i = Discount rate
• t = Number of years
• n = Number of compounding periods of a discount rate per year

In the case of continuous compounding, the equation for discount factor is modified as below,

Explanation of the Discount Factor Formula

The equation for a discount factor can be computed by using the following steps:

Step 1: Firstly, figure out the discount rate for a similar kind of investment based on market information. The discount rate is the annualized rate of interest and it is denoted by ‘i’.

Step 2: Now, determine for how long the money is going to remain invested i.e. the tenure of the investment in terms of number years. The number of years is denoted by ‘t’.

Step 3: Now, figure out the number of compounding periods of a discount rate per year. The compounding can be quarterly, half-yearly, annually etc. The number of compounding periods of a discount rate per year is denoted by ‘n’. (The step is not required for continuous compounding)

Step 4: Finally, in the case of discrete compounding, the discount factor can be calculated using the following formula as,

Discount Factor = (1 + (i/n) )^-n*t

On the other hand, in the case of continuous compounding, the discount factor can be calculated using the following formula as,

Discount Factor = e^-i*t

Examples of Discount Factor Formula (with Excel Template)

Let’s see some simple to advanced examples for the calculation of the Discount Factor Equation to understand it better.

Discount Factor Formula – Example #1

Let us take an example where the discount factor is to be calculated for two years with a discount rate of 12%. The compounding is done:

1. Continuous
2. Daily
3. Monthly
4. Quarterly
5. Half Yearly
6. Annual

Given, i = 12% , t = 2 years

#1 – Continuous Compounding

The calculation of the discount factor is done using the above formula as,

Discount factor = e^-12*2

• Discount factor = 0.7866

#2 – Daily Compounding

Since Daily Compounding, therefore, n = 365

The calculation of the discount factor is done using the above formula as,

Discount factor = (1 + (12%/365))^-365*2

• Discount factor = 0.7867

#3 – Monthly Compounding

Since monthly compounding, therefore n = 12

The calculation of the discount factor is done using the above formula as,

Discount factor = (1 +(12%/12))^-12*2

• Discount factor = 0.7876

#4 – Quarterly Compounding

Since quarterly compounding, therefore n = 4

The calculation of the discount factor is done using the above formula as,

Discount factor = (1 + (12%/4))^-4*2

• Discount factor = 0.7894

#5 – Half Yearly Compounding

Since half yearly compounding, therefore n = 2

The calculation of the discount factor is done using the above formula as,

Discount factor = (1 + (12%/2))^-2*2

• Discount factor = 0.7921

#6 – Annual Compounding

Since annual compounding, therefore n = 1,

The calculation of the discount factor is done using the above formula as,

Discount factor = (1 + (12%/1))^-1*2

• Discount factor = 0.7972

Therefore, the Discount Factor for various compounding periods will be –

The graphical representation of the above table will be as follows –

The above example shows that the formula of a discount factor depends not only on the rate of discount and the tenure of the investment but also on how many times the rate compounding happens during a year.

Discount Factor Formula – Example #2

Let us take an example where the discount factor is to be calculated from year 1 to year 5 with a discount rate of 10%.

Therefore, the calculation of discount factor from year 1 to year 5 will be as follows –

• Discount factor for Year 1 = (1 + 10% )^-1 =0.9091
• Discount factor for Year 2 = (1 + 10% )^-2 = 0.8264
• Discount factor for Year 3 = (1 + 10% )^-3 = 0.7513
• Discount factor for Year 4 = (1 + 10% )^-4  = 0.6830
• Discount factor for Year 5 = (1 + 10% )^-5  = 0.6209

Therefore, Discount Factor of Year 1 to Year 5 is shown in the below figure –

The above example captures the dependence of the equation for a discount factor on the tenure of the investment.

Discount Factor Formula Calculator

You can use the following Discount Factor Formula Calculator.

 

Relevance and Use of Discount Factor Formula

The understanding of discount factor is very important because it captures the effects of compounding on each time period which eventually helps in the calculation of discounted cash flow. The concept is that the discount factor decreases over time as the effect of compounding the discount rate builds over time. As such, a discount factor is a very critical component of the time value of money.

The discount factor is the decimal representation used in the time value of money for cash flow. To determine the discount factor for cash flow, one is required to assess the highest interest rate one can get on an investment of a similar nature. Consequently, investors can utilize the discount factors in the translation of the value of future investment returns into present value in dollars.

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

Recommended Articles

This has been a guide to Discount Factor Formula. Here we discuss how to calculate the Discount Factor using practical examples along with downloadable excel templates. You may learn more about Financial Analysis from the following articles –

• Time Value of Money Formula
• Perpetuity Calculator in Excel
• Calculate Discounted Payback Period
• Dividend Discount Model  or DDM
• Calculate Incremental IRR