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
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.
This post is part of the series: 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.