# Calculating the Present Value of Multiple and Uneven Cash Flows with a Formula

An annuity is an asset that will pay equal amounts of money at regular time periods over its life. Essentially, an annuity can be thought of as a security with equal expected cash flows usually paid annually, semi-annually, quarterly, or monthly. The payment of dividends or payments from a lawsuit settlement are typical annuities. However, expected future cash flows from a security with the uncertainty of market and economic conditions rarely follow such a regular schedule.

Investors often calculate the value of an asset such as stocks, bonds, options, etc. by evaluating the expected future cash flows the asset will bring to its owner. For example, suppose that a corporation pays regular dividends to its stock holders each quarter of the year. These four payments represent cash flows to the stock holders for each share of stock owned at the time of the dividend payment. However, dividend payments made in the past are no guarantee of payments in the future. Furthermore, even corporate policies that guarantee dividend payments can’t be enforced if a company goes bankrupt and is forced to default on its promise to pay.

Suppose that an investor has determined that the expected future cash flows of an asset will follow the following schedule:

time 0: $5,000

time 1: $2,000

time 2: $500

time 3: $10,000

Although the payment of these cash flows is quite regular, the amounts differ from time period to time period. The standard annuity formula for determining the present value of this asset is insufficient because it assumes that payments are equal. Calculating the present value of these cash flows is a bit more complicated.

Suppose that the discount rate from the cash flows above is 8%. This means that a required return of 8% is necessary to make the investment worthwhile. What is the present value of the cash flows at 8%? To calculate the present value, each cash flow must be considered to be a component of the total present value of the asset. Then, simply adding up the components gives the total present value. For example:

PV = (5000 / (1 + 0.08)0) + (2000 / (1 + 0.08)1) + (500 / (1 + 0.08)2) + (10000 / (1 + 0.08)3)

= 5000 + 1851.85 + 428.67 + 7938.32

= $15,218.84

So, the present value of the asset is approximately $15, 219. Using the more complicated set of steps above, the present value of any asset can be calculated provided that the expected future cash flows have already been estimated. The next article in the series will consider calculating the future value of uneven cash flows.

## 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.