## How to Calculate the Future Value of Uneven Cash Flows

written by: John Garger•edited by: Laurie Patsalides•updated: 10/17/2010

The future value of an annuity formula is not adequate when the future cash flows of an asset are not regular. In this case, each cash flow must be calculated separately and added to the total future value of the asset. Learn how to use a formula to calculate the future value of uneven cash flows.

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The future value calculation of an asset with multiple uneven cash flows is more difficult than a standard annuity. Each cash flow must be evaluated separately to find its incremental contribution to the total future value. In fact, even an annuity can be calculated this way; the formula for the future value of an annuity is simply a short cut to calculating each time period of the annuity’s life.

Suppose that an investor is interested in finding the future value of an asset. The investor estimates the future cash flows and has determined that an 8% required return is necessary given the risk of realizing the cash flows associated with the asset. The estimated cash flows are s follows:

time 0: \$5,000

time 1: \$2,000

time 2: \$500

time 3: \$10,000

Notice that since the cash flows are uneven, the future value of the asset can not be calculated as an annuity because an annuity assumes equal payments at regular intervals. Instead, the future value of each cash flow must first be calculated. All of these future values are then summed to find the future value of all the cash flows over the life of the asset. Using the cash flows above:

FV = 5000 * (1 + 0.08)4 + 2000 * (1 + 0.08)3 + 500 * (1 + 0.08)2 + 10000 * (1 + 0.08)1

= 6802.44 + 2519.42 + 583.20 + 10800

= \$20,705.06

So, the future value of the asset is approximately \$20,705 at an 8% discount rate. This is, of course, assuming that the future cash flows are realized. The legitimacy of the future value formula is dependent on accurate estimates of the future cash flows. Lower or higher realized cash flows as well as a lower or higher required return changes the future value of the underlying asset.

The formula used above is a general method of calculating the future value of multiple uneven expected cash flows. With it, any number of applications is possible for any number of periods and cash flows, even negative cash flows. For example, suppose an investor must payout money (a negative cash flow) for two year before a positive cash flow is possible. The formula is still useful in this case as long as the investor takes care to calculate the individual time periods with a negative number where appropriate. There are also more complicated examples of uneven cash flow.

#### Multiple Uneven Cash Flows: Present and Future Values

Present and future value annuity formulas assume that cash flows will occur in even payments and at regular intervals. However, payments from assets such as stocks and bonds are rarely consistent. Calculating these values requires a more general method.