Formula to Calculate Discount Factor
The formula of discount factor is similar to that of the 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, it 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,
Discount Factor Calculation (Step by Step)
It can be calculated 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, it can be calculated using the following formula as,
DF = (1 + (i/n) )^{-n*t}
On the other hand, in the case of continuous compounding, it can be calculated using the following formula as,
DF = e^{-i*t}
Examples (with Excel Template)
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:
- Continuous
- Daily
- Monthly
- Quarterly
- Half Yearly
- Annual
Given, i = 12% , t = 2 years
#1 – Continuous Compounding
The calculation of the discount factor is done using the above formula as,
= e^{-12%*2}
- DF = 0.7866
#2 – Daily Compounding
Since Daily Compounding, therefore, n = 365
The calculation of the discount factor is done using the above formula as,
= (1 + (12%/365))^{-365*2}
= 0.7867
#3 – Monthly Compounding
Since monthly compounding, therefore n = 12
The calculation of the DF is done using the above formula as,
= (1 +(12%/12))^{-12*2}
= 0.7876
#4 – Quarterly Compounding
Since quarterly compounding, therefore n = 4
The calculation of the DF is done using the above formula as,
= (1 + (12%/4))^{-4*2}
= 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,
= (1 + (12%/2))^{-2*2}
= 0.7921
#6 – Annual Compounding
Since annual compounding, therefore n = 1,
The calculation of the DF is done using the above formula as,
= (1 + (12%/1))^{-1*2}
= 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 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.
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 DF from year 1 to year 5 will be as follows –
- DF for Year 1 = (1 + 10% )^{-1 }=0.9091
- DF for Year 2 = (1 + 10% )^{-2 }= 0.8264
- DF for Year 3 = (1 + 10% )^{-3 }= 0.7513
- DF for Year 4 = (1 + 10% )^{-4 }= 0.6830
- DF for Year 5 = (1 + 10% )^{-5 }= 0.6209
Therefore, DF of Year 1 to Year 5 is shown in the below figure –
The above example captures the dependence of DF on the tenure of the investment.
Discount Factor Calculator
Discount Rate | |
Number of Compounding Periods | |
Number of Years | |
Discount Factor Formula = | |
Discount Factor Formula = | 1 + (Discount Rate / Number of Compounding Periods)^{−Number of Compounding Periods * Number of Years} | |
1 + (0 / 0)^{−0 * 0} = | 0 |
Use and Relevance of Discount Factor Formula
The understanding of this disc. the 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 it is a very critical component of the time value of money.
It 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.
Discount Factor Formula Video
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 –
- Payback Period – Merits
- Examples of Incremental Revenue
- Time Value of Money Formula
- Perpetuity Calculator in Excel
- Calculate Discounted Payback Period
- Dividend Discount Model or DDM
- Calculate Incremental IRR
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