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)
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