What is discounting factor in capital budgeting?

The term “discount factor” in financial modeling is most commonly used to compute the present value of future cash flows values. It is a weighting factor (or a decimal number) that is multiplied by the future cash flow to discount it to the present value. Simply put, it is a conversion factor when computing the time value of money.

Table of Contents Show

Discount Factor – Formula
Discount Factor Example
Discount Factor Formula [Approach 1]
Discount Factor Formula [Approach 2]
Discount Factor Calculator – Excel Template
Discount Factor Calculation Example [Approach 1]
Discount Factor Calculation Example [Approach 2]

The discount factor is used most commonly when doing valuation using DCF analysis to compute the present value of future cash flow of each period or year. It is also used to calculate the net present value (NPV) which can be used to determine the net future value of an investment. The discount factor is also used by investors in the short-term money market, pension, and insurance companies, and to obtain future investment values.

In financial modeling, once we obtain the undiscounted cash flows for the projected years or the years to come, we need to calculate their present value to evaluate whether the investment is profitable or not and how much is that company worth. The advantage of using the discount factor is that it makes financial modeling more accurate.

A discount factor is a weighting factor that helps convert future values into the present
The discount factor is computed through a formula that includes the discount rate (%) and the year or period number (for example year 1 to 10)
The decimal value of the discount factor gets smaller, as we go along from year 1 to 10 due to the effect of compounding that builds over time

Discount Factor – Formula

The discount factor is used by analysts when carrying out financial modeling in excel. The formula to calculate it is stated below:

Discount Factor = 1/1(1*(1 + Discount Rate) ^ Year or Period Number)

If we are given the discount rate (%) then we can use the aforesaid formula in an excel spreadsheet to calculate the discount factor for each period (for example, years 1 to 10).

Once we obtain the discount factor for each period, we can multiply the same with the undiscounted cash flow for each period to obtain the discounted cash flow for each period. Thereafter, we derive the total net present value (NPV) of the cash flows – which can be calculated by adding up the individual discounted cash flows for each period (i.e. years 1 to 10). We can also do this by using the NPA formula in excel.

A key point to remember is that to arrive at or obtain the present value of the individual cash flow of any particular period (or year), we multiply the undiscounted cash flow of that period by the discount factor of that period. The choice of the discount rate (%) greatly affects the discount factor value. The discount rate is the rate of return that a project needs to earn to be acceptable to the investor. Using a discount factor enables the analyst to specify the number of days in each period.

Discounting cash flows enables the investor to assess the opportunity cost of undertaking the investment and take into account the time value of money, financing structure, and the risks involved in investing in a particular company vis-à-visor relative to the market.

The discount factor formula is important, as it makes it easier to verify the DCF analysis and obtain more clarity in the net present value (NPV) when conducting financial modeling in excel. The formula enables analysts to view the impact of compounding more clearly for each period.

Discount Factor Example

Given below is an example, where we first calculate a discount factor for each year (period 1 to 10) and then multiply the same by the undiscounted cash flow value in that year to discount it back to its present value. You will notice that the decimal value of the discount factor gets smaller, as we go along from year 1 to 10. This is due to the effect of compounding that builds over time.

Let us assume that each year a company generates US$130,000 in undiscounted cash flows. We need to calculate the present value for each of these years and then sum them up to get the net present value of the cash flows. For each year we need to use a different discount factor.

In year 5, we use the discount factor formula and obtain the value of the discount factor (0.681). Now, if the undiscounted cash flow in year 5 is $130,000, then we multiply it by 0.681 to get the present value of this cash flow (discounted cash flow), in this case, $88,475.8. We do likewise for all years. Thereafter, we calculate the total NPV ($872, 301.6) by adding all the individual discounted cash flows from year 1 to 10.

Learn to build financial models like an expert with our financial modeling course.

Additional Resources

Weighted Average Cost of Capital

3-Statement Model

DCF Terminal Value Formula

The Investment Banker

Discounted Cash Flow (DCF) Model

Equity Value vs. Enterprise Value

DCF Valuation Interview Questions

Operating Cash Flow Metrics

Dividend Discount Model (DDM)

In This Article

What is the formula for calculating the discount factor?
What is the purpose of the discount factor?
What is the relationship between the discount factor and the present value?
How is the discount factor connected to the discount rate?

Discount Factor Formula [Approach 1]

The present value of a cash flow (i.e. the value of future cash in today’s dollars) is calculated by multiplying the cash flow for each projected year by the discount factor, which is driven by the discount rate and the matching time period.

Generally speaking, there are two approaches to calculating the discount factor, but in either case, the discount factor is a function of the:

Discount Rate
Time Period

The discount rate can be thought of as representing the percentage of return that you could have received by investing that dollar, if you had received it today.

The reason you would prefer to have $1 today than $1 three years from now is because if you received the $1 three years from now, you would have missed out on a full three years where you could have invested that $1 and ended up with more than $1 by the end of that time.

The first formula for the discount factor has been shown below.

Discount Factor = (1 + Discount Rate) ^ (– Period Number)

And the formula can be re-arranged as:

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

Either formula could be used in Excel; however, we will be using the first formula in our example as it is a bit more convenient (i.e., Excel re-arranges the formula itself in the first formula).

To arrive at the present value using the first approach, the factor would then be multiplied by the cash flow to get the present value (“PV”).

Present Value (PV) = Cash Flow * Discount Factor

While the discount rate remains constant throughout the projection, the period number rising is what causes the factor to decrease over time.

Note that the period can be whatever length you want (years, months, days, even hours) – but it is critical to ensure that the period is aligned with the implied period of the discount rate.

Intuitively, the discount factor, which is always calculated by one divided by a figure, decreases the cash flow values. This also ties back to what we discussed in the beginning, where receiving $1 today is more valuable than receiving $1 in the future.

To tie this back to the example using $1, assuming a 10% discount rate and a one-year time horizon – the discount factor would be calculated as:

Next, the present value can be calculated using:

The example implies that $1 dollar received one year from the current period would be worth $0.91 in the present day.

Discount Factor Formula [Approach 2]

The formula for the second approach is virtually identical except for the absence of the negative sign in front of the period number exponent.

Discount Factor = (1 + Discount Rate) ^ Period Number

Unlike the first approach, the present value formula this time around divides the cash flow by the discount factor.

Present Value (PV) = Cash Flow / Discount Factor

By entering the discount factor formula into the PV formula, the formula can be re-expressed as:

Present Value (PV) = Cash Flow / (1 + Discount Rate) ^ Period Number

As opposed to decreasing over time, the factor increases in this case – thereby, the downward adjustment on the present value becomes more apparent in later years.

Returning back to the $1 dollar example with the same 10% discount rate and one-year time frame, the calculation is:

And upon applying this to the $1 in cash flow:

So, as we can see, both methods calculate the same present value for the $1 one year from today ($0.91).

Discount Factor Calculator – Excel Template

We’ll now move to a modeling exercise, which you can access by filling out the form below.

Discount Factor Calculation Example [Approach 1]

In the hypothetical scenario we will be using, the company has the following financial profile:

Cash Flow: $100/Year
Discount Rate: 10%

For example, in 2021, the discount factor comes out to 0.91 after adding the 10% discount rate to 1 and then raising the amount to the exponent of -1, which is the matching time period.

The 0.91 is subsequently multiplied by the cash flow of $100 to get $91 as the PV of the 1st year cash flow.

By the end of Year 5, we can see the discount factor drops in value from 0.91 to 0.62 by the end of the forecast period due to the time value of money.

Discount Factor Calculation Example [Approach 2]

Recall how this time around, the cash flow will be divided by the discount factor to get the present value.

And in contrast to the 1st approach, the factor will be in excess of 1.

For 2021, the discount rate of 10% is added to 1, which is raised to the exponent of 1, as that is the first projected year. From doing so, the output is 1.10.

Conversely, the factor increases over time in the 2nd approach since the cash flows are being divided by this >1 factor.

Then, the 1st year cash flow of $100 is divided by 1.10 to get $91 for the PV of the cash flow.

Here, in the finished output sheet below, the present values of the cash flows calculated under both approaches result in the same figures.

Ultimately, it does not matter which approach you decide to take, because conceptually the rationale and impact of the discount factor are exactly identical.