# Cashflow

Cashflow[{c0,c1,,cn}]

represents a series of cash flows occurring at unit time intervals.

Cashflow[{c0,c1,,cn},q]

represents cash flows occurring at time intervals q.

Cashflow[{{time1,c1},{time2,c2},}]

represents cash flows occurring at the specified times.

# Details

• TimeValue[Cashflow[],interest,t] computes the time value of a cash flow as a single equivalent payment at the specified time t. Possible cash flow calculations include net present value, discounted cash flow, and internal rate of return.
• Times and amounts can be given as numbers or arbitrary symbolic expressions.
• In Cashflow[{{time1,c1},}], the timei can be given as numerical values or date expressions.
• Cashflow[{c0,c1,c2,}] is equivalent to Cashflow[{{0,c0},{1,c1},{2,c2},}].
• TimeValue[Cashflow[{{date0,c0},}],r,date] computes the time value of a cash flow at date.
• Cashflow[Annuity[]] converts an Annuity object to a Cashflow object.

# Examples

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## Basic Examples(7)

Compute the present value at 7% of a stream of cash flows occurring at regular time intervals:

Specify an interval at which cash flows occur:

Future value at 9% of a stream of cash flows occurring at irregular time intervals:

Find the net present value of a \$1000 initial investment producing future incoming cash flows:

Internal rate of return of an investment with regular cash flows:

What payment at time 2 will make the net present value of a series of cash flows zero:

Solve for the point in time where a payment of \$400 will make the net present value equal 0:

## Scope(5)

Convert an Annuity object to a Cashflow object:

Cashflow works with date expressions:

Cashflow works with symbolic parameters:

Solutions to equations involving Cashflow can be found in terms of symbolic parameters:

Specify Cashflow with a TimeSeries:

## Generalizations & Extensions(3)

Calculate the duration of a series of cash flows using the derivative function D:

Large cash flow sequences that obey a pattern can be generated through Annuity using a payment growth function:

Large cash flow streams can also be created using Table:

Use Plot and Plot3D to explore the various dependencies a series of cash flows has on a set of variables:

Dependence on interest rate:

Dependence on payment growth rate:

Use Plot3D to view the interest rate/growth rate landscape:

## Applications(3)

In return for receiving \$600 at the end of 8 years, a person pays \$100 immediately, \$200 at the end of 5 years, and a final payment at the end of 10 years. What final payment amount will make the rate of return on the investment equal to 8% compounded semiannually:

Payments of \$100, \$200, and \$500 are due at the end of years 2, 3, and 8, respectively. Find the point in time where a payment of \$800 would be equivalent at 5% interest:

At what effective rate of interest will the present value of \$2000 at the end of 2 years and \$3000 at the end of 4 years be equal to \$4000:

## Properties & Relations(1)

A Cashflow object with one cash flow is equivalent to a simple amount:

## Possible Issues(2)

When specifying a valuation period in between payments of a Cashflow object, TimeValue calculates the future value of all cash flows before the valuation period, and the present value of all cash flows after the valuation period:

This is equivalent to the sum of present and future values here:

Cashflow[Annuity[pmt,n,q]] only works for numeric n and f:

Using numeric n allows Cashflow to convert the Annuity object as desired:

## Interactive Examples(1)

Use Manipulate to explore the various dependencies a series of cash flows has on a set of variables:

## Neat Examples(1)

Plot the cash flows in a "sawtooth"-style cash flow stream together with the accumulated value as a function of time:

Wolfram Research (2010), Cashflow, Wolfram Language function, https://reference.wolfram.com/language/ref/Cashflow.html.

#### Text

Wolfram Research (2010), Cashflow, Wolfram Language function, https://reference.wolfram.com/language/ref/Cashflow.html.

#### CMS

Wolfram Language. 2010. "Cashflow." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Cashflow.html.

#### APA

Wolfram Language. (2010). Cashflow. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Cashflow.html

#### BibTeX

@misc{reference.wolfram_2024_cashflow, author="Wolfram Research", title="{Cashflow}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/Cashflow.html}", note=[Accessed: 14-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_cashflow, organization={Wolfram Research}, title={Cashflow}, year={2010}, url={https://reference.wolfram.com/language/ref/Cashflow.html}, note=[Accessed: 14-September-2024 ]}