Time Value of Money formulas allow investors to accurately estimate the present and future values of both one-time cash flows and cash flows which regularly repeat. These formulas are nothing more than short cuts to a more general calculation method not constrained by these criteria. In fact, the method described here will work even for the simpler present and future value calculation and provides a way to more clearly understand the nature of present and future valuations. There are three main complications when calculating the present and future vales of an asset.

The first complication is that it is possible for some cash flows to be negative. Negative cash flows represent an outlay of money for the possibility of positive cash flows in the future. The adage “it takes money to make money” expresses this complication accurately. In fact, most businesses expect to lose money in the first few years as the firm establishes in its markets. Consequently, the need to account for negative cash flows in present and future value calculations is necessary to accurately value an asset or investment decision

The second complication is the regularity of cash flows. Unless the cash flows stem from a contractual agreement such as payment for a large-ticket item or a lawsuit settlement, it is unlikely that the cash flows will be in equal amounts. Changing market and economic conditions such as the fluctuation of currency disrupt not only the regularity of cash flows but their value as well.

The third complication comes from the need to value the asset’s cash flows at different periods. Sometimes, an investor may need to know the value of the asset in the middle of the expected future cash flows. When this occurs, it is necessary to use a calculation method that can account for the cash flows at different times. The example given here is a complicated example that illustrates all three of the complications discussed above.

Suppose that an investor is interested in valuing an asset’s cash flows. The asset will cost the investor $2,000 at time zero and $1,500 in the first period. These costs represent negative cash flows (complication one). The asset will then pay $5,000, $7,000, and $12,000 in periods two, three, and four respectively (complication 2). Finally, the investor wants to know the value of the asset in period three (complication 3). The investor assumes a discount rate of 6%. The cash flows are summarized below:

time 0: -$2,000

time 1: -$1,500

time 2: $5,000

time 3: $7,000

time 4: $12,000

To solve this problem, both present and future value components are needed. Essentially, cash flows in periods zero, one, and two need to be brought forward with a future value component and time period four’s cash flow needs to be brought back to time three with a present value component. The cash flow at time three is unaffected by the discount rate because time three is the period in which the valuation is needed. The equation to solve this problem is given as:

FV_{3} = -2000 * (1 + 0.06)^{3} + -1500 * (1 + 0.06)^{2} + 5000 * (1 + 0.06)^{1} + 7000 + 12000 / (1 + 0.06)^{1}

= -2382.03 + -1685.40 + 5300 +7000 + 11320.75

= $19,553.32

So, the value of these cash flows at time three assuming a 6% discount rate is approximately $19,553.

The example illustrated in this article shows just how complicated present and future value calculations can be when valuing an asset. However complicated, the example does point out how powerful the method is for valuing alternative investment decisions. With a few changes, the value of an asset can be calculated for any time period and for any discount rate. Of course, when different rates need to be evaluated, a spreadsheet or multifunction financial calculator makes setting up the formulas and changing of discount rates and time periods much simpler. You can also learn to calculate the future value of uneven cash flow.

## This post is part of the series: Multiple Uneven Cash Flows: Present and Future Values

- How to Calculate the Present Value of Uneven Cash Flows
- How to Calculate the Future Value of Uneven Cash Flows
- A Complicated Example of Calculating Future Values with Multiple Uneven Cash Flows