KermMartian at 19:12, 24 February 2016

2016-02-24T19:12:21Z

← Older revision		Revision as of 19:12, 24 February 2016
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	Without a frequency list, the formula for npv( is the following:		Without a frequency list, the formula for npv( is the following:
	~~[[TI-BASIC:Math\|Math]]~~		<math>
	\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}		\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}
	\operatorname{npv}(i,\operatorname{CF}_0,\{\operatorname{CF}_j\})=\sum_{j=0}^N{\operatorname{CF}_j\left(1+\frac{i}{100}\right)^{-j}}		\operatorname{npv}(i,\operatorname{CF}_0,\{\operatorname{CF}_j\})=\sum_{j=0}^N{\operatorname{CF}_j\left(1+\frac{i}{100}\right)^{-j}}
	~~[[TI-BASIC:~~/math~~\|/math]]~~		</math>

	When a frequency list is used, the same formula can be applied if we expand the list with frequencies into a long list without frequencies. However, it's possible to do the calculation directly. We define the cumulative frequency S,,j,, as the sum of the first j frequencies (S,,0,, is taken to be 0):		When a frequency list is used, the same formula can be applied if we expand the list with frequencies into a long list without frequencies. However, it's possible to do the calculation directly. We define the cumulative frequency S,,j,, as the sum of the first j frequencies (S,,0,, is taken to be 0):

	~~[[TI-BASIC:Math\|Math]]~~		<math>
	\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}		\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}
	\operatorname{npv}(i,\operatorname{CF}_0,\{\operatorname{CF}_j\},\{n_j\})		\operatorname{npv}(i,\operatorname{CF}_0,\{\operatorname{CF}_j\},\{n_j\})
	=\operatorname{CF}_0+\sum_{j=1}^N{\operatorname{CF}_j\left(1+\frac{i}{100}\right)^{S_{j-1}}\frac{(1-(1+\frac{i}{100})^{-n_j})}{i}}		=\operatorname{CF}_0+\sum_{j=1}^N{\operatorname{CF}_j\left(1+\frac{i}{100}\right)^{S_{j-1}}\frac{(1-(1+\frac{i}{100})^{-n_j})}{i}}
	~~[[TI-BASIC:~~/math~~\|/math]]~~		</math>


	= Error Conditions =		= Error Conditions =
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	= Related Commands =		= Related Commands =

	* [[TI-BASIC:Irr\|Irr(]][[Category:TI-BASIC]]		* [[TI-BASIC:Irr\|Irr(]]
			[[Category:TI-BASIC]]
	[[Category:TIBD]]		[[Category:TIBD]]

Maintenance script: Initial automated import

2016-02-24T18:02:49Z

Initial automated import

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{{Template:TI-BASIC:Command
|picture=NPV.GIF
|summary=Computes the net present value of money over a specified time period.
|syntax=npv(''interest rate'',''CF0'',''CFList''[,''CFFreq''])
|location=Press:
# 2nd FINANCE (on a TI-83) or APPS (TI-83+ or higher) to access the finance menu
# On the TI-83+ or higher, select the first option "Finance..." from the APPS menu
# 7 or use arrow keys to scroll to it
|compatibility=TI-83/84/+/SE
|size=2 bytes
}}

The npv( command computes the net present value of money over a specified time period. If a positive value is returned after executing npv(, that means it was a positive cashflow; otherwise it was a negative cashflow. The npv( command takes four arguments, and the fourth one is optional:

* '''interest rate''' -- the percentage of the money that is paid for the use of that money over each individual period of time.
* '''CF0''' -- the initial amount of money that you start out with; this number must be a real number, otherwise you will get a [[TI-BASIC:Errors#datatype|ERR:DATA TYPE]] error.
* '''CFList''' -- the list of cash flows added or subtracted after the initial money.
* '''CFFreq''' -- the list of frequencies of each cash flow added after the initial money; if this is left off, each cash flow in the cash flow list will just appear once by default.

= Sample Problem =

Your mom recently opened a bank account for you, with $500 as a gift to start you off. This is welcome news to you, until you find out that the bank charges 5% as the interest rate for the account. So, you get a job at Rocco's Pizzas delivering pizzas, which brings in $1,000-$2,000 each month. For the last five months, in particular, you have earned $1,250, $1,333, $1,575, $1,100, and $1,900. (Assume there are no other expenses, such as gas, car payment, etc.)

Plugging in all of the different values into the npv( command, this is what our code looks like:

:npv(5,500,{1250,1333,1575,1100,1900

= Optimization =

The npv( command's optional fourth argument should be left off if each cash flow of money in the list of cash flows just appears once.

:npv(5,1550,{2E3,3E3,4E3},{1,1,1
can be
:npv(5,1550,{2E3,3E3,4E3

At the same time, if there are cash flows that occur multiple times, it can be smaller to just use the frequency argument:

:npv(8,0,{200,200,300,300,300
can be
:npv(8,0,{200,300},{2,3

= Formulas =

Without a frequency list, the formula for npv( is the following:
[[TI-BASIC:Math|Math]]
\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}
\operatorname{npv}(i,\operatorname{CF}_0,\{\operatorname{CF}_j\})=\sum_{j=0}^N{\operatorname{CF}_j\left(1+\frac{i}{100}\right)^{-j}}
[[TI-BASIC:/math|/math]]

When a frequency list is used, the same formula can be applied if we expand the list with frequencies into a long list without frequencies. However, it's possible to do the calculation directly. We define the cumulative frequency S,,j,, as the sum of the first j frequencies (S,,0,, is taken to be 0):

[[TI-BASIC:Math|Math]]
\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}
\operatorname{npv}(i,\operatorname{CF}_0,\{\operatorname{CF}_j\},\{n_j\})
=\operatorname{CF}_0+\sum_{j=1}^N{\operatorname{CF}_j\left(1+\frac{i}{100}\right)^{S_{j-1}}\frac{(1-(1+\frac{i}{100})^{-n_j})}{i}}
[[TI-BASIC:/math|/math]]

= Error Conditions =

* '''[[TI-BASIC:Errors#datatype|ERR:DATA TYPE]]''' is thrown if you try to use anything other than a real number for the interest rate.
* '''[[TI-BASIC:Errors#dimmismatch|ERR:DIM MISMATCH]]''' is thrown if the list of cash flows and the list of cash flow frequencies have different dimensions.

= Related Commands =

* [[TI-BASIC:Irr|Irr(]][[Category:TI-BASIC]]
[[Category:TIBD]]

TI-BASIC:Npv - Revision history

KermMartian at 19:12, 24 February 2016

Maintenance script: Initial automated import