The cumulative discount factor is a multi-period discount factor. It is the sum of the present value factors for each of a series of periods at a given discount rate.

For example, the discount factors for a 5-year flow of $5,000 discounted starting at the end of year 1 at 5% is as follows:-

Year

DF

CDF

PV

CPV

1

0.9524

0.9524

$4,762

$4,762

2

0.9070

1.8594

$4,535

$9,297

3

0.8638

2.7232

$4,319

$13,616

4

0.8227

3.5459

$4,114

$17,730

5

0.7835

4.3294

$3,917

$21,647

DF = Discount Factor

CDF = Cumulative Discount Factor

PV = Present Value

CPV = Cumulative Present Value

Investment : $5,000

4.3294 - This is the Cumulative Discount Factor.

$5,000 * 4.3294 = $21,647

In the above example, we calculated the Present Value of $5,000 at 5% over a 5 year period. Note when we summed the individual present values for each of the 5 years we get $21,647. When we multiply $5,000 x 4.3294 (the cumulative discount factor) we also get $21,647, not by coincidence.

The Cumulative Discount Factor formula used is (1 - (1 + r)^{ -t }) / r where r is the period interest rate expressed as a decimal and t is the specific year. For example, 6% is expressed as 6/100 or 0.06; t is the number of periods.

This calculator allows you to create a table of Cumulative Discount factors derived from a range of interest rates over any time periods of your choosing. To produce a table (single-column or multiple):-

Input the number of columns

Input the starting percentage rate

Input the steps in percent change (if not consecutive)