Future Value of an Uneven Cashflow

Contents
Time Value of Money
Annuities
Perpetuities
Kinds of Interest Rates
Future Value of an Uneven Cash flow
Probability Distribution
Standard Deviation
CAPM
Security Market Line
Bond Valuation
Stock Valuation
Cost of Capital
The Balance Sheet
Financial Terms
Scientific Terms
Disclaimer

Cash Flow

Cash Flow is money you get a little at a time.

Lets say, for example that for the next 4 years you will get the following cash flow.

Cash Flow
in 1 year	$ 320
in 2 years	$ 400
in 3 years	$ 650
in 4 years	$ 300

If you assume that the interest rate is 6.5% (which means that after you get the money, it will be invested and you will get 6.5% interest from it), compounded monthly, how much money will you have in 4 years? In other words, what will the future value of this cash flow be?

Compounding Formula

FV=PV ( 1 + i / m)^mn

FV = Future Value
PV = Present Value
i = Interest rate (annual)
m = number of compounding periods per year
n = number of years

So you have to figure out the future value of each payment and then add them together.

First Payment

FV = PV ( 1 + i / m)^mn
FV = $320 (1 + .065 / 12 )^{12 X 3} (three years)
FV = $320 (1.0054167)³⁶
FV = $320 (1.2146716)
FV = $388.69

Second Payment

FV = PV ( 1 + i / m)^mn
FV = $400 (1 + .065 / 12 )^{12 X 2} (two years)
FV = $400 (1.0054167)²⁴
FV = $400 (1.1384289)
FV = $455.37

Third Payment

FV = PV ( 1 + i / m)^mn
FV = $650 (1 + .065 / 12 )^{12 X 1} (one year)
FV = $650 (1.0054167)¹²
FV = $650 (1.0669719)
FV = $693.53

Fourth Payment - ( The payment is not compounded. There no time to earn interest)

FV = PV ( 1 + i / m)^mn
FV = $300 (1 + .065 / 12 )^{12 X 0}(0 years.)
FV = $300 (1.0054167)⁰
FV = $300 (1) (remember anything to the power of zero is 1)
FV = $300

Finally, add up all the numbers

$ 388.69
$ 455.37
$ 693.53
$ 300.00
----------
$1,837.59

So after 4 years, you will have $1,837.59. That is the future value of your uneven cash flow.

Detailed Explanation

The present value of an uneven cash flow is a financial concept that is essential to understand for any individual or business that engages in financial transactions. This concept refers to the value of a future cash flow in today's dollars, taking into account the time value of money and the expected rate of return. In simple terms, the present value of an uneven cash flow can be thought of as the amount of money that would need to be invested today to generate the same future cash flow. For instance, if an individual is expecting to receive $10,000 in five years, the present value of that cash flow would be the amount of money that would need to be invested today to generate $10,000 in five years, taking into account the expected rate of return.

The present value of an uneven cash flow is a critical concept in finance because it allows individuals and businesses to compare the value of future cash flows to the value of cash flows that they can receive immediately. This comparison is essential in making informed financial decisions because it enables individuals and businesses to determine whether a particular investment or financial transaction is worth pursuing. In addition, the present value of an uneven cash flow can be used to assess the risk of a particular investment or financial transaction. For instance, if an individual is considering investing in a stock that is expected to pay a dividend of $100 in five years, the present value of that cash flow will be affected by the level of risk associated with the stock. If the stock is considered to be high-risk, the present value of the cash flow will be lower than if the stock is considered to be low-risk.

Calculating the present value of an uneven cash flow requires the use of mathematical formulas and financial models. These calculations take into account the time value of money, which is the concept that money available today is worth more than the same amount of money available in the future because of the potential for investment earnings. The formula for calculating the present value of an uneven cash flow involves three key components: the cash flow amount, the expected rate of return, and the time period over which the cash flow is expected to be received. Once these components are known, the present value of the cash flow can be calculated using a discounted cash flow (DCF) analysis. Discounted cash flow analysis is a financial modeling technique that is commonly used to calculate the present value of an uneven cash flow. This technique involves calculating the future cash flows that are expected to be received and then discounting those cash flows back to their present value using a discount rate that takes into account the time value of money and the expected rate of return. The discount rate used in a DCF analysis is based on the level of risk associated with the investment or financial transaction. The higher the level of risk, the higher the discount rate will be, and the lower the present value of the cash flow will be. Conversely, the lower the level of risk, the lower the discount rate will be, and the higher the present value of the cash flow will be.

One important thing to note about the present value of an uneven cash flow is that it can be affected by changes in the expected rate of return or the time period over which the cash flow is expected to be received. For instance, if the expected rate of return increases, the present value of the cash flow will decrease because the future cash flow is worth less in today's dollars. Conversely, if the time period over which the cash flow is expected to be received increases, the present value of the cash flow will increase because the future cash flow is further away in time and, therefore, worth less in today's dollars.

Bibliography

Brealey, R. A., Myers, S. C., & Allen, F. (2017). Principles of corporate finance. McGraw-Hill Education.

Damodaran, A. (2012). Investment valuation: Tools and techniques for determining the value of any asset. John Wiley & Sons.

Gitman, L. J., & Joehnk, M. D. (2019). Fundamentals of investing. Pearson.

Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2019). Fundamentals of corporate finance. McGraw-Hill Education.

About the author

Author: Mark McCracken is a corporate trainer and author living in Higashi Osaka, Japan. He is the author of thousands of online articles as well as the Business English textbook, "25 Business Skills in English".