pvvar

Present value of varying cash flow

Syntax

PresentVal = pvvar(CashFlow,Rate)

PresentVal = pvvar(___,CFDates)

Description

PresentVal = pvvar(CashFlow,Rate) calculates present value of a varying cash flow.

PresentVal = pvvar(___,CFDates) adds an optional argument for CFDates.

Examples

Calculate Present Value for Regular and Irregular Cash Flow

Calculate the net present value for a regular and irregular cash flow.

Regular Cash Flow

This cash flow represents the yearly income from an initial investment of $10,000. The annual interest rate is 8%.

Year 1 - $2000

Year 2 - $1500

Year 3 - $3000

Year 4 - $3800

Year 5 - $5000

To calculate the net present value of this regular cash flow:

PresentVal = pvvar([-10000 2000 1500 3000 3800 5000], 0.08)

PresentVal = 
1.7154e+03

Irregular Cash Flow

An investment of $10,000 returns this irregular cash flow. The original investment and its date are included. The periodic interest rate is 9%.

January 12, 1987 - ($10000)

February 14, 1988 - $1500

March 3, 1988 - $2000

June 14, 1988 - $3000

December 1, 1988 - $4000

To calculate the net present value of this irregular cash flow:

CashFlow = [-10000, 1500, 2000, 3000, 4000];

CFDates = ['01/12/1987'
            '02/14/1988'
            '03/03/1988'
            '06/14/1988'
            '12/01/1988'];

PresentVal = pvvar(CashFlow, 0.09, CFDates)

PresentVal = 
-768.1461

The net present value of the same investment under different discount rates of 7%, 9%, and 11% is obtained by:

PresentVal = pvvar(repmat(CashFlow,3,1)', [.07 .09 .11], CFDates)

PresentVal = 1×3
103 ×

   -0.5099   -0.7681   -1.0146

Input Arguments

CashFlow — Cash flow amounts

vector

Cash flow amounts, specified as a vector of varying cash flows. Include the initial investment as the initial cash flow value (a negative number). If CashFlow is a matrix, each column is treated as a separate cash-flow stream.

Data Types: double

Rate — Periodic interest rate

decimal

Periodic interest rate, specified as a decimal. If CashFlow is a matrix, a scalar Rate is allowed when the same rate applies to all cash-flow streams in CashFlow. When multiple cash-flow streams require different discount rates, Rate must be a vector whose length equals the number of columns in CashFlow.

Data Types: double

CFDates — Indicates irregular cash flow

datetime array | string array | cell array of date character vectors

(Optional) Indicates irregular cash flow, specified as a datetime array, string array, or cell array of date character vectors on which the cash flows occur.

Specify CFDates when there are irregular (nonperiodic) cash flows. The default assumes that CashFlow contains regular (periodic) cash flows. If CashFlow is a matrix, and all cash-flow streams share the same dates, CFDates can be a vector whose length matches the number of rows in CashFlow. When different cash-flow streams have different payment dates, specify CFDates as a matrix the same size as CashFlow.

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

Data Types: cell | string | char | datetime

Output Arguments

PresentVal — Present value

numeric

Present value, returns the net present value of a varying cash flow. Present value is calculated at the time the first cash flow occurs.

More About

Present Value

Present value is a fundamental financial concept that refers to the current worth of a sum of money or a stream of cash flows that will be received or paid in the future, discounted at a specific interest rate.

The idea behind present value is that a certain amount of money today is worth more than the same amount in the future due to its potential earning capacity. This concept is crucial in finance for valuing investments, making financial decisions, and assessing the worth of future cash flows.

Version History

Introduced before R2006a

R2022b: Serial date numbers not recommended

Although pvvar 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.