How to Calculate the Future Value of Uneven Cash Flows Compounded Semi-Annually

by Bryan Keythman

An investment that generates different cash flows each year generates uneven cash flow. The future value of a cash flow is its value at a point in the future after it has earned interest. A cash flow that compounds semi-annually adds interest twice a year. This increases a cash flow’s value at a faster rate than annual compounding, which adds interest once a year. You can calculate the future value of a stream of cash flows by determining the future value of each cash flow and calculating the sum of the future values.

Determine the uneven cash flows you receive at the end of each year from an investment. Determine the holding period, or number of years, of the investment, and the annual interest rate you earn on the investment. For example, assume a three-year investment generates $100 in cash flow at the end of the first year, $150 at the end of the second year, and $125 at the end of the third year; assume a 5 percent interest rate.

Count the number of years between the time you receive each cash flow stream until the end of the investment’s holding period to determine the number of years each cash flow will earn interest. In this example, the first cash flow will earn interest for two years -- from the end of the first year until the end of the third year. The second cash flow will earn interest for one year. The third cash flow does not earn interest because you will receive it at the end of the holding period.

Substitute each uneven cash flow into the future value formula: CF(1 + i/m)^(mn). In the formula, CF represents cash flow, i represents the interest rate, m represents the number of compounding periods per year and n represents the number of years each cash flow earns interest. In this example, the first formula is $100(1 + 0.05/2)^(2 x 2). The second formula is $150(1 + 0.05/2)^(2 x 1). The third cash flow’s future value is the same as the cash flow because it does not earn interest.

Solve the first formula to calculate the first cash flow’s future value. In this example, calculate the numbers in each set of parentheses to get $100(1.025)^4. Raise the number in parentheses by the exponent, and multiply the result by $100 to get $110.38.

Solve the second formula to calculate the second cash flow’s future value. In this example, calculate the numbers in each set of parentheses to get $150(1.025)^2. Raise the number in parentheses by the exponent, and multiply the result by $150 to get $157.59.

Add each cash flow together to calculate the future value of the investment. Continuing with the example, add $110.38 plus $157.59 plus $125 to get $392.97. This means that, at the end of three years, the cash flows will be worth $392.97 after compounding semi-annually at a 5 percent interest rate.