How to Calculate the FV of Uneven Cash Flow

by Bryan Keythman

The future value (FV) of a stream of cash flows is the total value of the cash flows at a point in the future after the cash flows have earned a return. The FV shows the effect of compounding, which is the process of earning returns on previously earned returns. Some investments may generate the same amount of cash flows each year, while others may produce uneven cash flows. You can calculate the FV of an investment with uneven cash flows by calculating the future value of each cash flow, then the sum of those future values.

Determine the uneven cash flow that the investment produces at the end of each year, and determine the last year in which you received this cash flow. For example, assume an investment generates $500 of cash flow at the end of year one, $400 at the end of year two and $600 at the end of year three, which is the last year of cash flow.

Estimate the investment's discount rate, or required rate of return. This is your opinion of the minimum acceptable percentage return you would require to make the investment and is the same return you could earn on a similar investment. You would require a higher rate of return on a higher-risk investment than on a lower-risk investment. In this example, assume you would require an 8 percent rate of return, or discount rate.

Subtract the number of each year of the investment --1, 2 and 3-- from the number of the last year that you receive the cash flows -- 3. This calculates the number of years for which each cash flow will compound into a future value. In this example, you would receive the first cash flow at the end of year 1, and it would compound until the end of year 3, the last year. So subtract 1 from 3 to get 2, which is the number of years the first year's cash flow will compound. Also, subtract 2 from 3 to get 1 year of compounding for the second year's cash flow, and subtract 3 from 3 to get 0 for the third year's cash flow.

Plug each cash flow and the respective number of years for which the cash flow will compound into the future value formula: CF(1 + i)^t. In the formula, "CF" represents cash flow, "i" represents the discount rate and "t" represents the number of compounding years for each cash flow. In this example, the first, second and third year's cash flows yield the formulas $500(1 + 0.08)^2, $400(1 + 0.08)^1 and $600(1 + 0.08)^0, respectively.

Solve the future value formula of each cash flow. In this example, solve the numbers in parentheses in the first year's FV formula, which simplifies to $500(1.08)^2. Then raise the number in parentheses to the power of 2, which results in $500(1.17). Then multiply the remaining numbers to get a FV of $585 for the first year's cash flow. Solve the second and third year's cash flow to get $432 and $600, respectively. The third year's cash flow does not change because it is received at the end of the third year, which is the end of the holding period. Therefore it does not have any time to compound.

Calculate the sum of each cash flow's future value to get the future value of the uneven cash flows. In this example, calculate the sum of $585, $432 and $600 to get $1,617. This represents the investment's future value at the end of the holding period.

Tip

  • An uneven stream of cash flows that has greater cash flows in the beginning has a higher FV because those larger cash flows have more time to compound.