# Basics on How to Figure Cash Flow Values With Gradients

by Dennis Hartman

The way a business handles its cash is reflected in its annual statement of cash flows. To an investor, this financial statement is valuable because it represents how well a business manages the money it receives and whether it has enough cash inflow to cover the outflow necessary to meet its financial obligations and grow in value. Cash flow analysis involves factoring in gradients, which makes the process more complex but is still within an individual investor's reach.

In cash-flow accounting, a gradient is a trend that shows cash inflow or outflow for a particular item rising or falling by a consistent amount over time. Not every cash flow includes gradients. For example, if a particular source of revenue remains constant, its inflow does not exhibit a gradient. Likewise, if an expense changes radically from year to year, rising in some years and falling in others, it does not have a uniform gradient. Cash-flow gradients can be positive to represent rising amounts or negative to represent amounts moving toward zero.

## Basic Equation

The simplest situation for figuring the value of a cash flow with a gradient occurs when there is a uniform gradient and a defined number of accounting periods over which to measure its impact. In this situation, cash flow for a given year is equal to the present value of cash flow, plus the product that results from multiplying the gradient by the number of years between the present year and the year in question. For example, an organization may receive \$100,000 from a trust in 2012, but the payment from the trust decreases by \$5,000 each year, for a uniform gradient of -\$5,000. The cash flow for 2017, or five years later, is \$100,000 + (-\$5,000 x 5), or \$100,000 - \$25,000, or \$75,000.

## Terminology

Figuring cash flow gradients is often more complex and requires special equations. These equations, which differ based on the regularity and number of cash flow periods (usually measured in years) use specific terminology as well. "G" is the variable for referring to the uniform gradient, which can be positive or negative. "P" refers to the present value of the cash flow at a given point in time. Lower case "i" stands in for the interest rate in cases where a gradient involves interest. Finally, "N" refers to the number of cash flow or accounting periods under observation.

## Interest Example

One of the most common reasons for a cash-flow gradient is compounded interest on an investment. For example, if a business uses an interest-bearing bank account to store its cash reserves, that money will earn an interest payment each year. If the business doesn't spend from its reserves, the next year's interest payment will be larger due to the higher balance in the account from the prior year's interest payment. This will manifest as a constantly rising source of income on the cash flow statement, with a positive gradient based on the account's interest rate.

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