Net
Worth
Most economic analyses require the evaluation
of an equivalent value for a complex cash flow. Again there are
several ways to do this.
For applications we compute the present
worth and uniform worth of a complex
cash flow.


As an example we use the cash flow at
the left.
Present Worth 
P = 30 + 10(P/A, i, 10) + 5(P/G, i,
7)(P/F, i, 3) 
Uniform series over 10 periods: 
A = P(A/P, i, 10) 
Future Worth at time 10: 
F = P(F/P, i, 10) = A(F/A, i,
10) 
For our illustration we use i = 10%. 


Tables 

The traditional way to evaluate equivalent values of cash
flows is through tables. We repeat part of the 10% factor table
below.
We compute the equivalent of the cash flow by substituting
the factor values from the table. In the calculations below have
used accurate factor values, but we rounded the results to two
decimal places.
Present Worth 
P = 30 + 10(P/A, i, 10) + 5(P/G, i,
7)(P/F, i, 3)
P = 30 + 10(6.14457) + 5(12.7631)(0.7513)
P =  30 + 61.45 + 47.94
P = 79.39 
Uniform series over 10 periods: 
A = P(A/P, i, 10)
A = 79.34(0.1627)
A = 12.92 
Future Worth at time 10: 
F = P(F/P, i, 10)
F = 79.34(2.59374)
F = 205.91 


Factor Calculator 

Rather than use the tables, we could have used the factor
calculator to provide the factor values in the computations above.
To compute the net worth, the results of the several component
calculations must be added.
Click on the tool icon to open the factor
calculator.


Cash Flow Calculator 

We provide a convenient calculator for simple net value problems.
The figure below shows the calculator with data entered for the
example problem. Enter the individual amounts in the fields below
the graph. Enter interest rate, periods for the uniform worth
and periods for the future worth at the lower left. When the enter button
is clicked the cash flow appears and the associated present,
uniform and future worth are computed.
Problems are restriced to ten of fewer periods and individual
cash flow amounts must be between 99 and +99. Click on the tool icon to
open a live version of the cash flow calculator.


Economics Addin 

The example is easily evaluated with our recommended
tool, the Economics
addin. This addin is fully described on the ORMM site.
The addin can solve problems of arbitrary complexity and will
be used throughout the remainder of this course.
This addin is fully described on the ORMM site.
Click the icon to go to that site.
In order to use the addin, you will have to download it from
that site. The link below takes you to the download page. Before
attempting to install and use the addin read the instructions
on that page.


BuiltIn Excel Functions 

Excel has several financial functions that are always available
when Excel is loaded. The figure below shows part of the Financial
Functions list. The list is accessed through the Insert/Function menu
item or the insert function icon on the Standard
Toolbar. The PV, NPV, FV and PMT functions
are useful for computing equivalent values. The Excel financial
functions are shown in the dialog from Excel. The funtion call,
PV(rate, nper, pmt, fv, type), appears below the function list
and the purpose of the funciton appears below that. The help
file defines the arguments.
The Builtin functions are useful for
computing equivalent values of some cash flows. Cash flow
components are limited to three types.

a single pv at time 0

a periodic
pmt payment than occurs for nper periods.

a single payment fv at time nper.
The equivalent value is computed at interest rate specified
by the rate parameter. For periodic payments, the type parameter
indicates whether the payments at the end of each period, true,
or at the beginning of each period false. If the parameter
is left out, the endofperiod payments are assumed.
There are no Builtin functions that include the
gradient component so our example cannot be evaluated.


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