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xirr

Internal rate of return for nonperiodic cash flow

Syntax

Return = xirr(CashFlow, CashFlowDates)
Return = xirr(CashFlow, CashFlowDates, Guess, MaxIterations,
Basis)

Description

Return = xirr(CashFlow, CashFlowDates) returns the internal rate of return for a schedule of nonperiodic cash flows.

Return = xirr(CashFlow, CashFlowDates, Guess, MaxIterations,
Basis)
returns the internal rate of return for a schedule of nonperiodic cash flows with optional inputs.

Input Arguments

CashFlow

A vector or matrix of cash flows. If CashFlow is a matrix, each column represents a separate stream of cash flows whose internal rate of return is calculated. The first cash flow of each stream is the initial investment, entered as a negative number.

CashFlowDates

(Required) A vector or matrix of serial date numbers the same size as CashFlow, or a cell array of date strings the same size as CashFlow. Each column of CashFlowDate represents the dates of the corresponding column of CashFlow.

Guess

The initial estimate of the internal rate of return. Guess is a scalar applied to all streams, or a vector the same length as the number of streams.

Default: 0.1 (10%)

MaxIterations

The positive integer number of iterations used by Newton's method to solve the internal rate of return. MaxIterations is a scalar applied to all streams, or a vector the same length as the number of streams.

Default: 50

Basis

Day-count basis of the instrument. A vector of integers.

  • 0 = actual/actual (default)

  • 1 = 30/360 (SIA)

  • 2 = actual/360

  • 3 = actual/365

  • 4 = 30/360 (BMA)

  • 5 = 30/360 (ISDA)

  • 6 = 30/360 (European)

  • 7 = actual/365 (Japanese)

  • 8 = actual/actual (ICMA)

  • 9 = actual/360 (ICMA)

  • 10 = actual/365 (ICMA)

  • 11 = 30/360E (ICMA)

  • 12 = actual/actual (ISDA)

  • 13 = BUS/252

For more information, see basis.

Default: 0

Output Arguments

Return

Vector of the annualized internal rate of return of each cash flow stream. A NaN indicates that a solution is not found.

Examples

Find the internal rate of return for an investment of $10,000 that returns the following nonperiodic cash flow. The original investment is the first cash flow and is a negative number.

Cash Flow

Dates

($10000)

January 12, 2007

$2500

February 14, 2008

$2000

March 3, 2008

$3000

June 14, 2008

$4000

December 1, 2008

Calculate the internal rate of return for this nonperiodic cash flow:

CashFlow = [-10000, 2500, 2000, 3000, 4000];
CashFlowDates = ['01/12/2007'
                 '02/14/2008'
                 '03/03/2008'
                 '06/14/2008'
                 '12/01/2008'];
Return = xirr(CashFlow, CashFlowDates)

This returns:

Return =
         0.1006 (or 10.0644% per annum)

References

Brealey and Myers, Principles of Corporate Finance, McGraw-Hill Higher Education, Chapter 5, 2003.

Sharpe, William F., and Gordon J. Alexander, Investments. Englewood Cliffs, NJ: Prentice-Hall. 4th ed., 1990.

See Also

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