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Discount Factor

Understand the Discount Factor Concept

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Discount Factor

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:

  1. Discount Rate
  2. 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:

  • 0.91 = 1 / (1 + 10%) ^ 1

Next, the present value can be calculated using:

  • 0.91 = $1 × 0.91

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:

  • 1.1 = (1 + 10%) ^ 1

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

  • 0.91 = 1 / 1.1

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.

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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.

Discount Factor Approach 1

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

Discount Factor Approach 1.2

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.

Discount Factor Approach 2

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.

Discount Factor Approach 2.2

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

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

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Maciej
Maciej
January 6, 2022 11:26 am

‘Discount Factor = (1 + Discount Rate) ^ Period Number’ – the formula is correct?
I mean the correct formula is Discount Factor = (1 + Interest Rate) ^ Period Number.
Interest Rate is not equal to Discount Rate because:
Discount Rate = Interest Rate / (1+Interest Rate)

Best regards

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