# Future Value of Uneven Cash Flows

By Yuriy Smirnov Ph.D.

## Definition

The future value of uneven cash flows is the sum of future values of each cash flow. It can also be called “terminal value.” Unlike annuities where the amount of payment is constant, many financial instruments and assets generate cash flows that can vary from period to period. For example, dividends on common stock and coupon payments of a floating rate bond can vary. Cash flow generated by business activity is another common example of uneven or irregular cash flows.

## Formula

As was mentioned above, the future value of an uneven cash flow stream is the sum of the future values of each cash flow. To determine this sum, we need to compound each cash flow to the end of the stream as shown in the formula below.

FV = CF0 × (1 + r)N + CF1 × (1 + r)N-1 + CF2 × (1 + r)N-2 + … + CFN

The above can be transformed as follows:

 FV = N CFt × (1 + r)N-t Σ t = 0

where N is a number of periods, CFt is a cash flow at period t, and r is an interest rate per period.

## Example

Shown below is an example of an uneven cash flow stream.

\$1,000 is expected to be received at the end of the first year, \$800 at the end of the second year, \$1,100 at the end of the third year, \$700 at the end of the fourth year, and \$1,050 at the end of the fifth year. It may be possible to reinvest received cash flows at an annual interest rate of 12%. To find the future value of the cash flow stream, we need to find the future value of each cash flow. The first cash flow (CF1) will be reinvested for 4 years, CF2 for 3 years, CF3 for 2 years, CF4 for 1 year, but CF5 won’t be reinvested because it is expected to be received at the end of the fifth year.

FV of CF1 = \$1,000 × (1+0.12)(5-1) = \$1,573.52

FV of CF2 = \$800 × (1+0.12) (5-2) = \$1,123.94

FV of CF3 = \$1,100 × (1+0.12) (5-3) = \$1,379.84

FV of CF4 = \$700 × (1+0.12) (5-4) = \$784.00

FV of CF5 = \$1,050 × (1+0.12) (5-5) = \$1,050.00

Thus, the total future value of the uneven cash flow stream is \$5,911.30.

## Calculator

To calculate the future value of uneven cash flows, you can also use our online calculator.