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### Cumulative Discount Factor Tables

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:-

YearDFCDFPVCPV
10.95240.9524\$4,762\$4,762
20.90701.8594\$4,535\$9,297
30.86382.7232\$4,319\$13,616
40.82273.5459\$4,114\$17,730
50.78354.3294\$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)
• Input the number of periods required
• Press "Create The List"

Cumulative Discount Table Web DateDial.com

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