Discount Factor

What is the Discount Factor?

Discount Factor is a weighing factor that is most commonly used to find the present value of future cash flows and is calculated by adding the discount rate to one which is then raised to the negative power of a number of periods.

Discount Factor Formula

Mathematically, it is represented as below,

DF = (1 + (i/n) )^-n*t

where,

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

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For eg:
Source: Discount Factor (wallstreetmojo.com)

In the case of continuous compounding formulaContinuous Compounding FormulaThe continuous compounding formula depicts the interest received when constant compounding is done for an infinite number of periods. The four variables used for its computation are the principal amount, time, interest rate and the number of the compounding period.read more, the equation is modified as below,

DF = e^-i*t

Calculation (Step by Step)

It can be calculated by using the following steps:

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
Now, determine how long the money is going to remain invested, i.e., the tenure of the investment in terms of several years. The number of years is denoted by t
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)
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
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 formula = e^-12%*2

DF = 0.7866

#2 – Daily Compounding

Since Daily Compounding, therefore, n = 365

= (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

= (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 five 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

Understanding this 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 it decreases over time as the effect of compounding the discount rate builds over time. As such, it is a very critical component of the time value of money.

It is the decimal representation used in the time value of moneyTime Value Of MoneyThe Time Value of Money (TVM) principle states that money received in the present is of higher worth than money received in the future because money received now can be invested and used to generate cash flows to the enterprise in the future in the form of interest or from future investment appreciation and reinvestment.read more 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 this factor to translate the value of future investment returns into present value in dollars.