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:

Introduced in 2010
 (8.0)