Cashflow
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
open all close allBasic Examples (4)
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ドル initial investment producing future incoming cash flows:
Scope (6)
Convert an Annuity object to a Cashflow object:
Cashflow works with date expressions:
Specify Cashflow with a TimeSeries :
Cashflow works with symbolic parameters:
Solutions to equations involving Cashflow can be found in terms of symbolic parameters:
Calculate the duration of a series of cash flows using the derivative function D :
Applications (6)
Internal rate of return of an investment with regular cash flows:
Find the payment at time 2 that will make the net present value of a series of cash flows zero:
Solve for the point in time where a payment of 400ドル will make the net present value equal to 0:
In return for receiving 600ドル at the end of 8 years, a person pays 100ドル immediately, 200ドル at the end of 5 years and a final payment at the end of 10 years. Find the final payment amount that will make the rate of return on the investment equal to 8% compounded semiannually:
Payments of 100,ドル 200ドル and 500ドル are due at the end of years 2, 3 and 8, respectively. Find the point in time where a payment of 800ドル would be equivalent at 5% interest:
Find the effective rate of interest at which the present value of 2000ドル at the end of 2 years and 3000ドル at the end of 4 years will be equal to 4000ドル:
Properties & Relations (3)
A Cashflow object with one cash flow is equivalent to a simple amount:
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:
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:
Related Guides
History
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_2025_cashflow, author="Wolfram Research", title="{Cashflow}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/Cashflow.html}", note=[Accessed: 04-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_cashflow, organization={Wolfram Research}, title={Cashflow}, year={2010}, url={https://reference.wolfram.com/language/ref/Cashflow.html}, note=[Accessed: 04-January-2026]}