xirr

Internal rate of return for nonperiodic cash flow

Syntax

Return = xirr(CashFlow,CashFlowDates)

Return = xirr(___,Guess,MaxIterations,Basis)

Description

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

Return = xirr(___,Guess,MaxIterations,Basis) adds optional arguments.

Examples

Find Internal Rate of Return for Nonperiodic Cash Flow

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 12-Jan-2007

2500 14-Feb-2008

2000 03-Mar-2008

3000 14-Jun-2008

4000 01-Dec-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)

Return = 
0.1006

Alternatively, you can use datetime input to 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'];
CashFlowDates = datetime(CashFlowDates,'Locale','en_US')';
Return = xirr(CashFlow, CashFlowDates)

Return = 
0.1006

Input Arguments

CashFlow — Cash flow

vector | matrix

Cash flow, specified as a vector or matrix. The first entry is the initial investment. 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, usually entered as a negative number.

Data Types: double

CashFlowDates — Cash flow dates

datetime array | string array | date character vector

Cash flow dates, specified as a vector or matrix using a datetime array, string array, or date character vectors. The size of the input date numbers for CashFlowDates must the same size as CashFlow. Each column of CashFlowDate represents the dates of the corresponding column of CashFlow.

To support existing code, xirr also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | datetime | string

Guess — Initial estimate of the internal rate of return

0.1 (10%) (default) | numeric

(Optional) Initial estimate of the internal rate of return, specified as a scalar or vector. If Guess is a scalar, then it is applied to all streams, and if Guess is a vector, then it is the same length as the number of streams.

Data Types: double

MaxIterations — Number of iterations used by Newton's method to solve the internal rate of return

50 (default) | positive integer

(Optional) Number of iterations used by Newton's method to solve the internal rate of return, specified as a scalar or vector of positive integers. If MaxIterations is a scalar, then it is applied to all streams, and if MaxIterations is a vector, then it is the same length as the number of streams.

Data Types: double

Basis — Day-count basis

0 (actual/actual) (default) | positive integers of the set [1...13] | vector of positive integers of the set [1...13]

(Optional) Day-count basis, specified as a positive integer using scalar or a N-by-1 vector. If Basis is a scalar, then it is applied to all streams, and if Basis is a vector, then it is the same length as the number of streams.

• 0 = actual/actual

• 1 = 30/360 (SIA)

• 2 = actual/360

• 3 = actual/365

• 4 = 30/360 (PSA)

• 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/365 (ISDA)

• 13 = BUS/252

For more information, see Basis.

Data Types: double

Output Arguments

Return — Annualized internal rate of return of each cash flow stream

numeric

Annualized internal rate of return of each cash flow stream, returned as a vector. A NaN indicates that a solution was not found.

More About

IRR for Nonperiodic Cash Flows

The IRR is the discount rate at which the present value of the future cash inflows equals the initial investment (cash outflows) and in the case of nonperiodic cash flows, these inflows and outflows occur at irregular intervals.

References

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

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

Version History

Introduced before R2006a

R2022b: Serial date numbers not recommended

Although xirr supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.