 # Present Value of Uneven Cash Flows By Yuriy Smirnov Ph.D.

## Definition

The present value is a keystone in the time value of money concept because this technique is developed to evaluate any assets from financial instruments (e.g., stocks and bonds) with respect to the value of the entire corporation. A large proportion of assets generate uneven or irregular cash flow, making the process of their valuation cumbersome. Common examples of an uneven cash flow stream are dividends on common stock, coupon payments on a floating-rate bond, or the free cash flow of a business. Since the value of each cash flow in the stream can vary and occur at irregular intervals, the present value of uneven cash flows is calculated as the sum of the present values of each cash flow in the stream.

## Formula

To find the present value of uneven cash flows, we first need to calculate the present value of each cash flow and then add them.

 PV = CF0 + CF1 + CF2 + … + CFN (1 + r)0 (1 + r)1 (1 + r)2 (1 + r)N

The formula above shows the general approach and can be transformed as follows:

 PV = N CFt Σ (1 + r)t t = 0

where N is a number of periods, CFt is a cash flow at period t, and r is an interest rate per period.

## Example

Let’s look at the figure below, which is an example of an uneven cash flow stream. It is expected that \$1,500 will be received at the end of the first year, \$1,850 at the end of the second year, \$2,100 at the end of the third year, \$2,500 at the end of the fourth year, and \$2,950 at the end of the fifth year. Let’s find the present value of the cash flow stream if the discount rate is 15.75%.

The present value of the first cash flow (CF1) amounts to \$1,295.90, CF2 is \$1,380.80, CF3 is \$1,354.12, CF4 is \$1,392.69, and CF5 is \$1,419.77.

PV of CF1 = \$1,500 ÷ (1 + 0.1575)1 = \$1,295.90

PV of CF2 = \$1,850 ÷ (1 + 0.1575)2 = \$1,380.80

PV of CF3 = \$2,100 ÷ (1 + 0.1575)3 = \$1,354.12

PV of CF4 = \$2,500 ÷ (1 + 0.1575)4 = \$1,392.69

PV of CF5 = \$2,950 ÷ (1 + 0.1575)5 = \$1,419.77

Thus, the present value of the uneven cash flow stream will be \$6,843.27.

## Calculator

To calculate the present value of uneven cash flows, you can also use our online calculator.