BUILT-IN MATHEMATICA SYMBOL

Cashflow

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

Cashflow

represents cash flows occurring at time intervals q.

Cashflow

represents cash flows occurring at the specified times.

MORE INFORMATION

TimeValue 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, the can be given as numerical values or date expressions.

Cashflow is equivalent to Cashflow.

TimeValue 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:

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

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Specify an interval at which cash flows occur:

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

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

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

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

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

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Scope (4)

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:

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: