How to Determine the Cumulative Present Value
Present value is the current worth or value of a future cash amount or stream of cash flows given a set rate of return. In short, a dollar today will not be worth a dollar a year from now. Accordingly, present value allows for finding out how much that same dollar would be worth later. The actual formula is: PV = PMT x [(1 - (1 / (1 + i) ^ n) ) / i] where PMT is payment, "i" is the interest or discount rate and "n" is the number of periods (i.e., weeks, months or years).
Other People Are Reading
Instructions
-
-
1
Add 1 to the discounted rate (or rate of interest) for the series of payments or cash flows, in the form of a decimal. For simplicity, we will call this the interest multiplier. For instance: if the discount rate is 12 percent, it would be 1 + .12 or 1.12.
-
2
Raise the interest multiplier by the number of payment periods. If there are six future annual cash flows, this example would be 1.12 (the interest multiplier) raised to the sixth power, or 1.12 multiplied by itself five additional times. We will call this the period multiplier. For example: 1.12^6 = 1.9738.
-
-
3
Divide 1 by the period multiplier then subtract this number from 1. We will call this the number multiplier. For example: (1 - (1 / 1.9738)) = (1 - (.5066)) = .4934.
-
4
Divide the number multiplier by the interest rate. This number is the present value interest factor. For example: (.4934) / .12 = present value interest factor = 4.112. In the example, we use .12 as the interest rate because the payments are compounded annually. If the payments were monthly over a series of six years, we would use .01 as the interest rate because they are compounded over 12 monthly periods. Accordingly, we would have had 72 periods (6 years x 12 months) instead of 6 in that scenario. If our original discount rate was 14 percent and compounded monthly, we would use .14 / 12 or .012.
-
5
Multiply the payments by the present value interest factor to determine the cumulative present value for an annuity or series of cash flows. This is another way to figure out how much future payments are worth in today's money. For example: annual payments of $500 over six years ($3,000 in future payments) = $500 x 4.112 = $2,053.83 present value.
-
1
Tips & Warnings
There are several present value calculators available online for easy calculation
Some sites have present value tables that give an easy multiplier based on periods and discount rate.
For finding the present value of one future lump sum, instead use the formula PV = PMT / (1 - t x i) where PMT is the lump sum payment, "i" is the interest rate and "t" is the length of time until the payment is made.
References
- Photo Credit piggy bank image by pershing from Fotolia.com
More Like This
Comments
-
How would you adjust the above calculation to consider annual payments of $500 between 2 years and 5 years i.e. we would not pay any thing in the first year.
