F.A.T.
Financial Analysts Toolchest
USERS MANUAL
Version 1.00
Copyright 1987 by Michael A Brochstein
(minor revisions in 1998)
All rights reserved.
MAB Systems Inc.
March 11, 1987
GENERAL INFORMATION F.A.T. GENERAL INFORMATION
1. General Information
This manual describes F.A.T. (Financial Analysts Toolchest).
F.A.T. is a package of tools (a.k.a. utilities) that assist in the
financial analysis and planning of investments, loans, depreciation
strategies, retirement, and other financial matters.
Effort has been made to make this manual and software package
easily usable by financial laypeople. People trained in financial
analysis or planning may only have to skim the introductory sections
while laypeople are strongly encouraged to read them carefully before
using F.A.T. An introductory textbook in accounting is recommended for
anyone wishing a greater understanding of the subject matter.
The author wishes to express his appreciation to Jay Fridkis and
Sam Saal for their assistance in the development of this product.
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INSTALLATION F.A.T. INSTALLATION
2. Installation for PC/MS-DOS
2.1 Systems with Hard Disks
Insert F.A.T. disk number one into the floppy disk drive (drive
A:). Change your directory (the "cd" command) to the directory on your
hard disk (drive C:) where you want F.A.T. to go (i.e. cd C:FAT). Issue
the following command;
COPY A:*.*
Repeat this process with each of the other diskettes that come
with this software package.
2.2 Systems without Hard Disks
Determine with the DIR command which diskette the tool you
need is located on. You will need to have this disk inserted when
you want to run this tool.
2.3 Notes on Execution Speed
Since most of F.A.T.'s tools use floating point numbers
(numbers with a decimal point), execution speed will be GREATLY
enhanced by the use of a Math Co-Processor (8087/80187/80287 etc.)
in your PC. More information about installation of a Math Co-
Processor can be found in your computer users manual or by
contacting your computer dealer.
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INTRODUCTION F.A.T. INTRODUCTION
3. General Usage of F.A.T. Tools
All of the tools in this package have a standardized user
interface.
In order to see how a tool named "toolname" is used, enter the
name of the individual tool in response to the system prompt (indicated
in the example by a "$", your computer prompt may be C> or A>,...);
$toolname
Usage: toolname p
toolname v
toolname
toolname
In response to entering just the name of the tool, the tool
gives you a "synopsis" of how to use it. According to the example above
there are four ways to use this command. Starting with the third option
mentioned, you would enter in response to the system prompt the toolname
followed by your monthly income and your monthly expenses. If my monthly
income was $25. and my monthly expenses were $23. I would enter the
following;
$toolname 25 23
If I wanted to use the tool with the fourth option shown above I
would have to mention four items on the "command line"; monthly income,
monthly expenses, checking balance, and savings account balance. If my
checking account balance was $450. and my savings account balance was
$2500. I would enter the following;
$toolname 25 23 450 2500
You must enter the numbers in the order mentioned by the
synopsis above. The tool can not tell if you mixed up the order since
it does not have intuition into what the numbers (monthly income, etc.)
should be. Using methods three and four requires you to enter either
two or four "arguments" after the toolname. You can not enter any other
number of arguments.
The tool mentioned above responds differently depending on the
option chosen. Method three asks for two arguments while method four
asks for four. The reason why there may be different ways to invoke the
tool (different number of arguments) is because the same tool will do
different things according as to how it is used. The later pages in
this manual will explain the function of each tool in detail.
The first method mentioned above of invoking the tool asks you
only to enter a "p" after the tool's name. This "p" stands for
"prompt". When the tool is used in this manner it will prompt you
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INTRODUCTION F.A.T. INTRODUCTION
"interactively" with questions. Your responses will provide the program
with the same information as you could have put on the command line as
shown above in the examples using methods three and four. Since there
are two different amounts of arguments that the tool may request, enter
a "carriage return" (the "Enter" key) in response to questions that ask
for information not required by the particular option to use the tool.
The following is an example of using the tool with the fourth method and
the "p" command:
$toolname p
Enter your monthly income <$>............. 25
Enter your monthly expenses <$>........... 23
Enter your checking account balance <$>... 450
Enter your savings account balance <$>.... 2500
Below is an example of how to use the tool with the third
method;
$toolname p
Enter your monthly income <$>............. 25
Enter your monthly expenses <$>........... 23
Enter your checking account balance <$>...
Enter your savings account balance <$>....
Notice that I did not enter any amounts in response to the third
and fourth questions, but entered a "carriage return" only.
The second method of the using the tool is to enter a "v" after
the tool's name. This will provide you with the version number of the
tool, its author, and a copyright notice. Use this information when
contacting the author to notify him of a comment, suggestion, or bug in
the tool. Below is an example of the use of this second method;
$toolname v
toolname: Version 0.01
Copyright 1987 by Michael Brochstein
All rights reserved.
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INTRODUCTION F.A.T. INTRODUCTION
4. Introduction to Financial Analysis
4.1 Compound Interest and Future Value
Future value is a method of calculating how much you would have
at some future time if you invested a certain amount once or the same
amount at regular intervals.
If you invested X dollars today and received 12 % compounded
interest annually for 8 years, the tool "compound" will tell you how
much you will have at the end of 8 years.
Compounding interest annually means that interest is calculated
and added to your account one time a year. Monthly compounding is where
interest is calculated twelve times a year. The amount of interest that
is added each month is the annual interest (12%) divided by the number
of months (12) or 1 % (12 % annual interest divided by 12 months). If
there was daily compounding (365 times a year), the amount of interest
added daily would be the annual interest (12 %) divided by the number of
days in the year (365) or 0.032876 % (12 % annual interest divided by
365 days). The tool "compound" gives you the option of stating the
number of compounding periods per year (the default is 1 = annually).
The tool "fv" is similar to "compound" except that it works in
terms of asking for interest per compounding period and the number of
periods that the investment will run for. For daily compounding in the
above example you would have to use the daily interest (0.03876) and the
number of days (8 years times 365 days = 2920).
4.2 Future Value of an Ordinary Annuity
An "ordinary annuity" is where equal deposits are made at equal
time intervals. An example is where you make a deposit of a dollar at
the beginning of each year for five years and the investment earns 2 %
annually (annual compounding). At the beginning of the fifth year right
after you make the fifth deposit, you will have $5.20. The tool "fvoa"
figures the value at this point which is referred to as the future value
of an ordinary annuity.
4.3 Future Value of an Annuity Due
An "annuity due" is similar to an ordinary annuity except that
in this case the last deposit is not made. In the example given in the
section above, "Future Value of an Ordinary Annuity", the last deposit
of one dollar is not made which then tells us that at the beginning of
the fifth year you would have $4.20. The tool "fvad" figures the value
at this point which is referred to as the future value of an annuity
due.
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INTRODUCTION F.A.T. INTRODUCTION
4.4 Compound Interest and Present Value
Suppose someone offered to give you $100. in ten years if you
gave him $40. today. Would you take the money ?
Being promised to get paid $100. in ten years is not the same as
having it in your pocket today. If you had a $100. today you could
invest it to earn interest and then have more than $100. in ten years.
If the interest that your investment earns is 10 % annually, then in ten
years you would have $259.37 assuming you did not touch either the
principal (the amount you invested or the interest earned during the ten
years). The use of the tool "compound" will tell you this. The tool
calculates the amount of interest an investment will earn given that you
make a one time investment and let the interest "compound", (i.e.
letting the interest itself earn interest). Another tool, "comptbl",
will tell you the same information as "compound" but will also print a
table showing each years interest earned and how much your investment
will have grown in that time.
Now if $100. today is worth $259.37 in ten years (at 10%
interest), how much do you need today to invest so that in ten years you
will have $100. ? You would need $38.55 today. This concept of how
much money in your hand today (presently) would be needed in order to
have a certain amount of money in the future is called "present value".
The tool "pv" figures present value.
From the analysis above we find that $100. in ten years is
equivalent to $38.55 today, if you can earn 10% interest. Under these
conditions I wouldn't think that the person's offer was very generous
since all you would need to have $100. in ten years is $38.55 today. An
alternative analysis using the "fv" tool shows that $40. invested at 10%
is worth $103.75, or more than the $100 promised.
4.5 Present Value of an Ordinary Annuity
An ordinary annuity can be defined as a set of withdrawls of the
same amount made at equal intervals from an investment so that even with
the amount not withdrawn earning interest (until it is taken out), at
the end of this set of withdrawls the balance of the investment
(principal) is zero. With an ordinary annuity it is assumed that
withdrawls are made at the end of each time period. At the end of the
last time interval when the last withdrawl is made, the annuity balance
is zero.
An example of the use of this concept are calculations used for
retirement planning. If you you will need to spend one dollar per year
after retirement age for four years with the dollar withdrawn at the end
of each year and your investment will earn 2 % annually (annual
compounding) then at the beginning of the first year you will need to
invest $3.81. This amount is called the present value of an ordinary
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INTRODUCTION F.A.T. INTRODUCTION
annuity. The tool "pvoa" does the calculation of this amount.
4.6 Present Value of an Annuity Due
An annuity due is similar to an ordinary annuity talked about in
the section above "Present Value of an Ordinary Annuity". However the
present value of annuity due refers to the amount needed on deposit at
the end of the first period that is just before the first withdrawl is
made for the annuity.
In the example used in the section "Present Value of an Ordinary
Annuity", $3.88 is needed in the investment account just before the
first withdrawl of one dollar is made. The tool "pvad" figures the
amount needed on deposit at the end of the first period just prior to
withdrawl.
4.7 IRA Investments
An IRA type investment is an investment where the (usually) same
amount of money (currently up to $2000.) is made each year for a number
of years. There are a few tools in F.A.T. to calculate the future
amount that an IRA type investment will yield. The tool "ira" will tell
how much you will have after investing the same amount for a number of
years at a certain interest rate. "ira2" does the same except it takes
into account an opening balance (maybe a rollover). "iratbl" does the
same as "ira" except that it prints out a table showing how much you
would have each year instead of just the total at the end of the period.
"ira2tbl" does the same as "iratbl" except it takes into account an
opening balance. All four tools mentioned above give you the option of
specifying the number of compounding periods per year for your
investment. The larger the number of compounding periods per year, the
faster your principal will grow.
4.8 Amortization Loans
An amortization loan (also known as a self-amortizing loan) is
one which is structured so that the periodic payments are equal even
though the portions of each payment that goes for interest and principal
repayment vary each period.
If you take out a mortgage of $100,000. for 30 years at 12 %
annual interest and make equal monthly payments then at the end of the
first month you will owe interest on $100,000. outstanding for one
month. At 12 % annual interest this works out to an interest rate of 1%
per month. This means that after one month you will owe $1,000 in
interest. If this was the total monthly loan payment then at the end of
the second month you would owe another months interest on the $100,000
principal which again is $1000. At this rate you will need to pay off
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INTRODUCTION F.A.T. INTRODUCTION
the loan forever since you will never be decreasing the principal amount
($100,000.) at all.
A amortization loan is structured so that in the first month you
will pay this interest payment of $1000. plus a little more which will
go towards decreasing the loan principal. Lets say $1028.61 was paid
instead of just $1000. In this case $1000. goes towards the interest
due on the principal of $100,000. and $28.61 goes towards decreasing the
principal. At the end of the first month the new principle loan balance
will be $99,971.39.
Now at the end of the second month our same payment of $1028.61
will be split up differently. Since the principal is now only
$99,971.39 we only owe $999.71 in interest payments. This leaves $28.90
as the principal part of the monthly payment. At the end of the second
month $99,971.39 - $28.90 or $99,942.49 of principle is owed. If these
payments are kept up for the full 360 months (30 years) then after the
last monthly payment the loan principal will have been decreased to
zero.
The tool "amort" will tell you how much is needed as a monthly
payment in order to pay off the principal loan in the required amount of
time at an interest rate stated. It will also tell you how much
interest you have paid over the course of the loan (useful for tax
planning).
A growing trend today is the use of what is called "principal
pre-payments". This is the practice of sending a sum in addition to
your monthly loan payment that is used solely towards repayment of the
principal amount. If an additional $25. is sent each month as a
principal pre-payment then the amount would go towards diminishing the
principal faster. This means that the loan would be paid off faster and
less interest paid since the loan period was shortened by these
payments. If $25. extra was sent each month as a principal pre-payment,
then the loan would be paid off in 300 months as opposed to 360 months.
This would have save $54,946.60 in interest payments since the loan was
held for 60 fewer months. The tool "amort" will also let you specify a
principal pre-payment.
The tool "amortbl" is similar to "amort" except that it prints
out a table showing each months progress towards paying off the loan.
4.9 Bonds
A bond is a financial debt instrument where one entity loans
another money in return for interest payments during the term of the
loan and the return of the principal at the end of the loan period. The
bond note represents the owing of these interest payments and the return
of the principal when the life of the loan is over.
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INTRODUCTION F.A.T. INTRODUCTION
Bonds are sold initially to the public by corporations and
governmental agencies and can subsequently be resold by the public in
what is called the secondary market.
There are many different types of bonds. The description below
is for a basic type of bond. The amount of money that is returned to
you at the end of the life of the bond is called the maturity value
(also called the par or face value). The interest rate based upon the
bonds par value is called the coupon rate. Suppose a bond is issued
with a $100. par value and stated annual interest rate of 8%. This
means that the bond issuer would pay the bond holder $8. in interest
each year. If the interest rate in the market place was 12% then the
public would not buy the bond since the bonds "yield" was below the
market rate. In order to sell the bond it would have to be priced at
$66.67. Why is that ? Since 12 % of $66.67 is $8. At this price the
bond will also yield the same interest as the interest rate in the
market.
The bond issuer would pay $8. per year for ten years and then at
the end of the tenth year return the par value to the bond holder. (The
total of all payments would equal $8. per year times ten years plus
$100. for a total of $180. Bonds pay interest typically twice a year
although this practice varies.) The total yield on the bond is based
upon how much we earn from the bond (total interest payments plus par
value minus purchase price) divided by the length of the investment. If
I paid $100. for this bond then I would get a yield of 8 %. If I had
paid $50. for the bond then my yield would be 16 %. If the market
interest rate was 16 % then $50. would be the most I would want to pay
for this bond.
Another way to look at a bond is to use the "present value"
techniques described in the other sections above. Evaluating the payout
of interest payments is equivalent to calculating the present value of
an ordinary annuity. Evaluating the payout of the par value at the end
of the bond term is equivalent to calculating the present value of a
single payment made at some future time. We need to know the market's
interest rate for present value analysis in order to see what the
payouts are worth today under current market conditions. Remember the
stated interest rate (or coupon rate) of the bond is the yield based
only upon the par value of the bond and not upon the purchase price of
the bond.
Assume that the bond above is offered for sale at $75. when the
current market interest rate for similar bonds is 11%. Is the bond
priced "right"? Would you be making a smart investment by purchasing
this bond instead of another? Using present value calculations we find
that the present value of the bond to be $82.07. Then this bond is an
attractive investment since it should cost $82.07 today to purchase an
equivalent bond and you need only $75. to purchase this bond.
The tool "bond" does all the calculations mentioned in this
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INTRODUCTION F.A.T. INTRODUCTION
section and should help guide you in your purchase of a bond. Remember
that interest rates do change and that this tool cannot take that into
account (no crystal ball here !). Changing interest rates can make a
bond that is attractive today into one that is a "dog" under conditions
of different interest rates.
4.10 Planning Your Retirement
With Social Security alone not providing an adequate source of
income on which to retire, many people are planning their own
investments to use during their retirement years. In order to make
plans we need to calculate how much we will require each year after
retirement to live the way we want to. We also need to estimate how
many years we expect to live. (We will assume that there is no inflation
or that interest rates will reflect the inflation rate so we can assume
our investments will earn a higher amount of interest if inflation
rises.)
Let us say you need $50,000 a year from your investments and
expect to live 35 years after your retirement date. You also need to
know how many years there are until retirement day. Assume that you
intend to retire in 30 years. The tool "pvoa" will calculate how much
you will need at retirement if you assume that the interest rates on
your investments will be earning 10 % annually (annual compounding).
"Pvoa" tells us that we need $482,207.95 on our day of retirement.
You now have to figure how much to invest today so that you will
have this amount at retirement. The tool "pv" tells us that if you
invest $27,634.64 today you will have the needed amount on retirement
day. Since most people will not have this amount to commit to this
purpose today, they will usually invest a smaller amount each year that
will build until retirement into the needed amount. The tool "fvoa"
tells us that if we invest $1000. each year for 30 years at 10 % annual
interest we will have $164,494.02 on retirement day. We need
$482,207.95 on retirement day (or $164,494.02 x 2.93146). In other words
we would have to invest $2931.46 per year to get the required amount for
retirement.
An easier way to perform this set of calculations is to use the
tool "retire" which does all the calculations necessary by just knowing
the number of years to retirement, number of years in retirement, the
annual interest rate, and the amount you want to receive in payments
each year. The purpose of the long winded discussion above was to
explain how "retire" works and to guide you if your retirement planning
investment is not as simple as the situation assumed by "retire".
What has been left out of these calculations? We have left out
Social Security payments, taxes on any of your investments (usually not
taken directly from the investments anyway), the knowledge of what
interest rates will actually be compared to inflation, taxes on payouts
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INTRODUCTION F.A.T. INTRODUCTION
from the investment if it was tax exempt during its pre-retirement life,
and the knowledge of how long you will live. The last bit of knowledge
could be a problem if you calculate too short a time. In the above
example if you lived longer than 35 years past retirement you would not
have any money left in your investment and hence no income from it after
the first 35 years of retirement.
There are many other factors to consider when planning for
financial security during retirement. I have only touched here on a
few. Consult a professional financial planner for more information. A
full discussion on other factors is beyond the scope of this
publication.
4.11 Depreciation
There are numerous methods for calculating the depreciation to
be taken each year on an asset. The most commonly used method is called
"Straight-line Depreciation". This is where the salvage value of the
asset is subtracted from the cost of the asset and the remaining value
is divided by the number of years that the asset is expected to be
useful for. For example, a machine bought for $10000. with a salvage
value of $2000. and a life of 5 years would indicate a yearly
depreciation expense of $1400. ((10000. - 2000.) / 5).
For certain assets it is appropriate to take depreciation at an
accelerated rate, that is more depreciation expense in the earlier years
of the assets life. The two most common methods of figuring accelerated
depreciation are the "Double-Declining Balance" and "Sum-of-Years-
Digits" methods.
In the double-declining balance method, depreciation is taken at
twice the rate of straight-line depreciation. If in the above example
20 % of the assets value was taken every year. With this method 40 % of
the "remaining" value is taken every year. Whereas in straight-line
depreciation the same amount is taken every year, here 40% of the
remaining value (after subtracting the salvage value as in straight-line
depreciation) is taken every year. The above example would yield
depreciation expenses of $4000., 2400, 1440., and 160. with no
depreciation taken in the fifth year since the value of the asset minus
salvage value (10000. - 2000. = 8000.) would be exceeded otherwise.
In the "Sum-of-years-digits" (SYD) method, the number of years
in the life of the asset are added up (five years in the above example =
1 + 2 + 3 + 4 + 5 = 15) and this number is used as the denominator. For
the numerator the years are used in reverse order. These fractions are
multiplied by the value of the asset minus its salvage value ($8000.).
In the first year 5/15 * 8000. or $2667.67 is taken as the depreciation
expense. In the second year 4/15 * 8000. or 2133.33 is taken.
The tool "deprec" does all of the above calculations given the
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INTRODUCTION F.A.T. INTRODUCTION
assets cost, salvage value, and life. It prints out a table of
depreciation expenses over the life of the asset.
4.12 Loan/Investment Analysis
There are a number of tools in this package to help you figure
out the terms of a loan or investment that would fit your situation.
The tools can also be used to analyze a loan or investment where you do
not have all the information generally required.
If you know how much interest you will be paid in a period (say
per year) for an investment and how much you are starting with, you may
wish to know when the investment will grow to a certain amount. Assume
you invest $1000. in an investment yielding 10 % per year; how many
years will it take until your investment grows to $10000. ? The tool
"cterm" will tell you that it would take 24.16 years (or periods in the
terminology of "cterm").
You may know how much you can afford a month for loan payments
on something you want to buy. You may also know what the prevailing
loan rates are and how long you wish to pay out this loan over.
However, you may not know how much you can get a loan for given this
information. Say you are willing to make payments of $200. a month for
60 months and the prevailing loan rate is 10 %. The tool "loanamt"
tells you given this information that you can afford a loan of $9413.07.
Another situation might be that you know how much you can afford
each month in payments, how much the item you want costs, and the loan
rate. What you need to know is given these constraints, how long it
would take to pay off the loan. Lets say that a car you want to buy
costs $25000., you can afford payments of $400. a month, and the car
loan rates are 11 %. Using the tool "loanlen" we find that it will take
93.24 months to pay off the car (it better be a reliable car).
A twist on the problems of the present and future value could be
a situation where you know how much you will put in an investment at its
beginning and how much it will equal in a certain number of periods
(years maybe). What you need to know is what its periodic (say yearly)
interest rate is so that you can compare this investment to another.
For example if you know that an investment of $1000. today will accrue
interest so that in 10 years it will equal $4000. the tool "rate" will
tell you that the yearly interest rate is 14.87 % (not bad !).
4.13 Miscellaneous
Many times we are told that a sum of money is due in a certain
number of days (a note or bill in 90 or 120 days etc.). Instead of
counting this out on a calendar day by day or adding months and then
fractions of a month together the tool "dateplus" will tell you that
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INTRODUCTION F.A.T. INTRODUCTION
date on a given number of days from today. Be sure that today's date is
set correctly on your computer system before using this tool.
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INTRODUCTION F.A.T. INTRODUCTION
5. Tool Reference Manual
The following pages contain reference pages for the various
tools in the F.A.T.
Each Reference Page is divided into a number of sections some of
which may not be present for some tools. The sections and a brief
description of each is given below;
NAME The name of the tool and a very brief description.
SYNOPSIS Summarizes the use of the tool.
DESCRIPTION Describes the tool.
EXAMPLES Gives examples of usage of the tool.
SEE ALSO Names other tools and places to look.
DIAGNOSTICS Discusses diagnostic messages generated by the tool.
WARNINGS Points out things to be aware of.
BUGS Lists any known bugs and known limitations of the tool.
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AMORT F.A.T. AMORT
NAME
amort - amortization loan
SYNOPSIS
amort p
amort v
amort
amort
DESCRIPTION
Amort will calculate the monthly payment and total
interest paid over the course of a loan. An optional input is a
monthly "principal pre-payment" which changes to output somewhat.
EXAMPLE(S)
A loan of $100000. at 11 % annual interest for 30 years (360 months);
$amort 100000 11 360
-Monthly payment.......$ 95.23
-Total interest paid...$ 24283.64
A loan of $100000. at 11 % annual interest for 30 years
(360 months) with a $25. monthly principal pre-payment;
$amort 100000 11 360 25
-Regular monthly payment........$ 952.32
-Monthly principal pre-payment..$ 25.00
-Total interest paid............$ 197708.77
-Length of loan ......... 305
SEE ALSO
amortbl
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AMORTBL F.A.T. AMORTBL
NAME
amortbl - amortization loan payment schedule
SYNOPSIS
amortbl p
amortbl v
amortbl
amortbl
DESCRIPTION
Amortbl generates a payment schedule for an amortization
loan. An optional input is a monthly "principal pre-payment".
EXAMPLE(S)
A loan of $100000. at 13 % annual interest for 30 years (360 months);
$amortbl 100000 13 360
Monthly payment.......$ 1106.20
Total interest paid...$ 298231.83
Month Principal Paid Interest Paid Remaining loan
----- -------------- ------------- --------------
1 22.87 1083.33 99977.13
2 23.11 1083.09 99954.02
3 23.36 1082.84 99930.66
.
.
358 1071.01 35.19 2176.96
359 1082.62 23.58 1094.34
360 1094.34 11.86 0.00
-------------- -------------
100000.00 298231.83
A loan for $100000. at 13 % annual interest for 360 months
with a monthly principal pre-payment of $25.
$amortbl 100000 13 360 25
Regular monthly payment........$ 1106.20
Monthly principal pre-payment..$ 25.00
Month Principal Paid Interest Paid Prepayment Remaining loan
----- -------------- ------------- ---------- --------------
1 22.87 1083.33 25.00 99952.13
2 23.38 1082.81 25.00 99903.75
3 23.91 1082.29 25.00 99854.84
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AMORTBL F.A.T. AMORTBL
.
.
292 1075.98 30.22 25.00 1688.55
293 1087.91 18.29 25.00 575.64
294 575.64 6.24 0.00 0.00
-------------- -------------
100000.00 232023.34
SEE ALSO
amort
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BOND F.A.T. BOND
NAME
bond - bond investment analyzer
SYNOPSIS
bond p
bond v
bond
DESCRIPTION
Bond figures the earnings to the bondholder over the life of the
bond and also analyses the bond using time value of money concepts
in light of the prevailing interest rate in the market.
EXAMPLE(S)
A bond with a par value of $100., stated interest rate
of 8 % annually, being held for 10 years, bought for $95., with a
prevailing interest rate in the market of 10 % annually, and with
the bond paying its interest payments twice a year.
$bond 100 8 10 95 10 2
Total interest payments
over life of bond................. 80.00
Difference between par value
and purchase price................ 5.00
-------------
Net return to bondholder: 85.00
Average return per year........... 8.50
Approximate annual yield.......... 8.95 %
- Using present value analysis techniques;
Present value of Par value of bond.... 37.69
Present value of the annuity of
the interest payments................. 49.85
-------------
TOTAL PRESENT VALUE OF BOND: 87.54
SEE ALSO
pv, pvoa
- 18 -
COMPOUND F.A.T. COMPOUND
NAME
compound - compound interest
SYNOPSIS
compound p
compound v
compound
compound
DESCRIPTION
Calculate how much an investment will accrue to given a certain
initial investment, annual interest rate, length of investment in
years, and the number of compounding periods per year.
EXAMPLE(S)
An investment of $1000. at 11 % annual interest for 25
years.
$compound 1000. 11 25
Total interest paid...... 12585.46
Ending balance........... 13585.46
An investment similar to above except with 12
compounding periods per year.
$compound 1000. 11 25 12
Total interest paid...... 14447.89
Ending balance........... 15447.89
SEE ALSO
comptbl
DIAGNOSTICS
Compound requires at least one compounding period a year and will
use one compounding period a year if the entered value is less than
1.
WARNINGS
Default number of compounding periods annually is one.
- 19 -
COMPTBL F.A.T. COMPTBL
NAME
comptbl - compound interest schedule
SYNOPSIS
comptbl p
comptbl v
comptbl
comptbl
DESCRIPTION
Generate a table showing how an initial investment at a
certain annual interest rate for a set period of years will do. An
optional field lets the user set the number of compounding periods
per year.
EXAMPLE(S)
An investment of $1000. at 11 % annually for 5 year;
$comptbl 1000 11 5
Year Interest Paid Year End Balance
---- ------------- ----------------
0 0.00 1000.00
1 110.00 1110.00
2 122.10 1232.10
3 135.53 1367.63
4 150.44 1518.07
5 166.99 1685.06
---- ------------- ----------------
TOTAL: 685.06 1685.06
An investment of similar to above except with 12
compounding periods per year.
$comptbl 1000 11 5 12
Year Interest Paid Year End Balance
---- ------------- ----------------
0 0.00 1000.00
1 115.72 1115.72
2 129.11 1244.83
3 144.05 1388.88
4 160.72 1549.60
5 179.32 1728.92
---- ------------- ----------------
TOTAL: 728.92 1728.92
- 20 -
COMPTBL F.A.T. COMPTBL
SEE ALSO
compound
DIAGNOSTICS
User input of less than 1 compounding period per year results in
usage of 1 compounding period per year by comptbl.
WARNINGS
Default number of compounding periods annually is 1.
- 21 -
CTERM F.A.T. CTERM
NAME
cterm - find compounding term
SYNOPSIS
cterm p
cterm v
cterm
DESCRIPTION
Cterm finds the length of a investment necessary for the investment
to grow from a present value to a future value at a given interest
rate per compounding period. The answer given is in terms of
periods.
EXAMPLE(S)
To find how long it would take $1000. to increase to $10000. at an
annual interest rate of 7.5 %.
$cterm 1000 10000 7.5
It will take 31.84 periods.
SEE ALSO
rate
- 22 -
DATEPLUS F.A.T. DATEPLUS
NAME
dateplus - todays date plus some days
SYNOPSIS
dateplus p
dateplus v
dateplus
DESCRIPTION
Dateplus tells the user the date it will be in a given number of
days from today.
EXAMPLE(S)
If today is 12/14/86 and I want to know what the date will be in
125 days;
$dateplus 125
Sunday December 14 1986 plus 125 days is Saturday April 18 1987.
DIAGNOSTICS
Dateplus will tell the user when it has asked for a date beyond
what it can see into the future.
WARNINGS
Dateplus can only "see" until January 19, 2038.
BUGS
In addition to only seeing until 1/19/2038, dateplus CAN see
backwards until about the year 1900 if you enter a minus number as
input to dateplus.
- 23 -
DEPREC F.A.T. DEPREC
NAME
deprec - depreciation method analyzer
SYNOPSIS
deprec p
deprec v
deprec
DESCRIPTION
Deprec generates a table showing yearly depreciation expenses for
an asset over its life. It shows the expenses for the "straight-
line", "double-declining balance" and "sum-of-years-digits"
methods.
EXAMPLE(S)
For an asset with a cost of $10000., a salvage value of $2000., and
a life of 5 years;
$deprec 10000 2000 5
Double-Declining Sum-of-the-years
Year Straight Line Balance Digits
---- ------------- ---------------- ----------------
1 1600.00 4000.00 2666.67
2 1600.00 2400.00 2133.33
3 1600.00 1440.00 1600.00
4 1600.00 160.00 1066.67
5 1600.00 0.00 533.33
---- ------------- ---------------- ----------------
TOTAL: 8000.00 8000.00 8000.00
SEE ALSO
none
- 24 -
FV F.A.T. FV
NAME
fv - future value
SYNOPSIS
fv p
fv v
fv
DESCRIPTION
Fv finds the future value of an investment (principal) which is
invested for a number of compounding periods at a certain rate per
compounding period.
EXAMPLE(S)
For an investment of $1000. which earns 12 % per year (period) for
a length of 15 years (compounding periods);
$fv 1000 12 15
Future value........... 5473.57
For an investment similar to above except that interest is
compounded monthly;
$fv 1000 1 180
Future value........... 5995.80
SEE ALSO
compound, comptbl
- 25 -
FVAD F.A.T. FVAD
NAME
fvad - future value of an annuity due
SYNOPSIS
fvad p
fvad v
fvad
DESCRIPTION
Fvad finds the future value of an annuity due where the same amount
is deposited regularly at a certain amount of interest per
compounding period for a number of periods. The last deposit is
never made since this is an annuity due but is counted when
entering the number of deposits as an argument to this tool.
EXAMPLE(S)
For a deposit of $2000. made every year for 20 years at the
beginning of the year and the last deposit is not made. How much
is there at the beginning of the 20th year ? The annual interest
rate is 11 %.
$fvad 2000 11 20
Future value........... 126405.66
SEE ALSO
fvoa, ira, ira2
- 26 -
FVOA F.A.T. FVOA
NAME
fvoa - future value of an ordinary annuity
SYNOPSIS
fvoa p
fvoa v
fvoa
DESCRIPTION
Fvoa find the future value of a set of equal deposits made one to a
period for a given number of periods at a given interest rate per
period.
EXAMPLE(S)
Find the value of an annuity where $2000. is deposited each year
for 20 years at an annual interest rate of 11 %.
$fvoa 2000 11 20
Future value........... 128405.66
SEE ALSO
fvad, ira, ira2
- 27 -
IRA F.A.T. IRA
NAME
ira - IRA investment
SYNOPSIS
ira p
ira v
ira
ira
DESCRIPTION
Ira will figure how much an yearly investment of equal amounts will
grow into in a given amount of years at a given interest rate.
Optionally the number of compounding periods per year can also be
set.
EXAMPLE(S)
For an investment of $2000. per year for 35 years yielding 10 %
annually.
$ira 2000 10 35
Total amount invested......... 70000.00
Total interest earned......... 526253.61
Ending Balance................ 596253.61
For an investment similar to above except with monthly compounding.
$ira 2000 10 35 12
Total amount invested......... 70000.00
Total interest earned......... 597569.61
Ending Balance................ 667569.61
SEE ALSO
ira2, iratbl, ira2tbl, fvoa, retire
DIAGNOSTICS
Ira will reject investments with less than one compounding period a
year, it will default to one compounding a year under these
circumstances.
WARNINGS
- 28 -
IRA F.A.T. IRA
Ira will default to one compounding period per year.
- 29 -
IRA2 F.A.T. IRA2
NAME
ira2 - IRA investment with an opening balance
SYNOPSIS
ira2 p
ira2 v
ira2
ira2
DESCRIPTION
Ira2 calculates how much an investment will yield on an investment
of equal amounts for a given period of years and at a given
interest. An opening balance must be specified. Optionally the
number of compounding periods per year can be varied.
EXAMPLE(S)
For an investment of $2000. per year for 35 years at 8 % interest
with an opening balance of $5000.
$ira2 2000 8 35 5000
Opening Balance............... 5000.00
Total amount invested......... 70000.00
Total interest earned......... 371131.02
Ending Balance................ 446131.02
For an investment similar to above except with 12 compounding
periods per year.
$ira2 2000 8 35 5000 12
Opening Balance............... 5000.00
Total amount invested......... 70000.00
Total interest earned......... 405545.22
Ending Balance................ 480545.22
SEE ALSO
ira, iratbl, ira2tbl, fvoa, retire
DIAGNOSTICS
Ira2 requires at least one compounding period per year and an
opening balance of at least year. Diagnostic messages will tell
- 30 -
IRA2 F.A.T. IRA2
the user if these requirements are not met and will default to a
zero opening balance and one compounding period per year.
WARNINGS
Use at least one compounding period per year and an opening balance
>= 0.
- 31 -
IRA2TBL F.A.T. IRA2TBL
NAME
ira2tbl - IRA investment schedule with an opening balance
SYNOPSIS
ira2tbl p
ira2tbl v
ira2tbl
ira2tbl
DESCRIPTION
Ira2tbl prints a table showing the progress of an IRA type
investment. The investment is of equal deposits made once a year
at a given interest and for a given number of years. An opening
balance must be specified and the number of compounding periods per
year can be varied from the default of one.
EXAMPLE(S)
For an investment of $2000. a year at 7 % interest for 35 years
with an opening balance of $3500.
$ira2tbl 2000 7 35 3500
Year Amount Invested Interest Paid Year End Balance
---- --------------- ------------- ----------------
0 2000.00 0.00 5500.00
1 2000.00 385.00 5885.00
2 2000.00 551.95 8436.95
.
.
33 2000.00 18785.92 287156.22
34 2000.00 20240.94 309397.15
35 2000.00 21797.80 333194.95
---- --------------- ------------- ----------------
TOTAL: 70000.00 259694.95 333194.95
For a similar investment to above except with 12 compounding
periods per year.
$ira2tbl 2000 7 35 3500 12
Year Amount Invested Interest Paid Year End Balance
---- --------------- ------------- ----------------
0 2000.00 0.00 5500.00
1 2000.00 397.60 5897.60
2 2000.00 570.92 8468.51
.
.
- 32 -
IRA2TBL F.A.T. IRA2TBL
33 2000.00 20375.31 302230.22
34 2000.00 21992.83 326223.05
35 2000.00 23727.27 351950.32
---- --------------- ------------- ----------------
TOTAL: 70000.00 278450.32 351950.32
SEE ALSO
ira, ira2, iratbl, fvoa, retire
DIAGNOSTICS
Failure to specify an opening balance >= 0 will result in an
opening balance of 0 to be used along with a diagnostic message
stating this.
Specification of less than one compounding period per year will
result in one compounding period per year being used in
calculations and a diagnostic message stating this.
WARNINGS
Opening balance must be >= 0. If specified, compounding periods
per year must be >= 1. Defaults are 0 and 1 respectively.
- 33 -
IRATBL F.A.T. IRATBL
NAME
iratbl - IRA investment schedule
SYNOPSIS
iratbl p
iratbl v
iratbl
iratbl
DESCRIPTION
Iratbl will print a table showing how an investment of equal
amounts made yearly for a given number of years and interest rate
will do over its life. Optionally the number of compounding
periods per year can be varied.
EXAMPLE(S)
For an investment of $2000. at 9 % for 35 years;
$iratbl 2000 9 35
Year Amount Invested Interest Paid Year End Balance
---- --------------- ------------- ----------------
0 2000.00 0.00 2000.00
1 2000.00 180.00 2180.00
2 2000.00 376.20 4556.20
.
.
33 2000.00 32364.06 391964.69
34 2000.00 35456.82 429421.51
35 2000.00 38827.94 470249.45
---- --------------- ------------- ----------------
TOTAL: 70000.00 400249.45 470249.45
For an investment similar to above except with 12 compounding
periods per year.
$iratbl 2000 9 35 12
Year Amount Invested Interest Paid Year End Balance
---- --------------- ------------- ----------------
0 2000.00 0.00 2000.00
1 2000.00 187.61 2187.61
2 2000.00 392.83 4580.44
.
.
33 2000.00 36554.20 426229.18
34 2000.00 40170.85 468400.03
35 2000.00 44126.77 514526.79
- 34 -
IRATBL F.A.T. IRATBL
---- --------------- ------------- ----------------
TOTAL: 70000.00 444526.79 514526.79
SEE ALSO
ira, ira2, ira2tbl, fvoa, retire
DIAGNOSTICS
Iratbl requires at least one compounding period per year and will
default to one when presented with less than one.
WARNINGS
Use at least one compounding period per year.
- 35 -
LOANAMT F.A.T. LOANAMT
NAME
loanamt - find amount that can be loaned
SYNOPSIS
loanamt p
loanamt v
loanamt
DESCRIPTION
Loanamt calculates how much one can loan given a certain monthly
payment, loan length, and annual loan interest rate.
EXAMPLE(S)
For a monthly payment of $325. for 48 months with a loan rate of 11
% you can borrow:
$loanamt 335 48 11
Amount that can be borrowed...... 12961.63
SEE ALSO
loanlen
- 36 -
LOANLEN F.A.T. LOANLEN
NAME
loanlen - find loan length
SYNOPSIS
loanlen p
loanlen v
loanlen
DESCRIPTION
Loanlen calculates the length that a loan has to be given a certain
principal to be paid off, a certain monthly payment, and an annual
loan interest rate.
EXAMPLE(S)
For a loan of $18,000. at an 11 % loan interest rate with a monthly
payment of $350. How long will it take to pay off ?
$loanlen 18000 350 11
Number of monthly payments needed...... 69.87
SEE ALSO
loanamt
- 37 -
PV F.A.T. PV
NAME
pv - present value in terms of months and years
SYNOPSIS
pv p
pv v
pv
pv
DESCRIPTION
Pv figures the present value of an amount of money (future value)
based on the number of months into the future the money will be
available, the yearly interest rate and optionally greater than the
default of one compounding period per year.
EXAMPLE(S)
Having $1000. in ten years (120 months) at an annual interest rate
of 9 % is the same as having how much today ?
$pv 1000 9 120
Present value........... 422.41
For an situation similar to above except with 12 compounding
periods per year;
$pv 1000 9 120 12
Present value........... 407.94
SEE ALSO
pv2
DIAGNOSTICS
Specification of less than one compounding period per year results
in a diagnostic message and a one compounding period per year being
used in the calculations.
WARNINGS
If specifying the number of compounding periods per year, it must
be >= 1 of the default will be 1.
- 38 -
PV2 F.A.T. PV2
NAME
pv2 - present value in terms of periods and interest per period
SYNOPSIS
pv2 p
pv2 v
pv2
DESCRIPTION
Pv2 calculates the present value of an amount (future value) in
terms of being able to receive a certain interest rate per
compounding period and a given number of compounding periods.
EXAMPLE(S)
Having $1000. in 7 years with an annual interest rate of 12 % is
that same as having how much today ?
$pv2 1000 12 7
Present value........... 452.35
In a situation similar to above except with monthly compounding of
interest.
$pv2 1000 1 84
Present value........... 433.52
SEE ALSO
pv
- 39 -
PVAD F.A.T. PVAD
NAME
pvad - present value of an annuity due
SYNOPSIS
pvad p
pvad v
pvad
DESCRIPTION
Pvad calculates the present value of an annuity that pays a certain
withdrawl amount per period while earning a certain interest rate
during that time for a set number of periods. The value is taken
at right before the first payment.
EXAMPLE(S)
What is the present value of an annuity right before its first
payout where $1500. is paid out per month, the investment earns 18
% a year, and withdrawls are made for 20 years ?
$pvad 1500 1.5 240
Present value........... 98651.50
SEE ALSO
pvoa
- 40 -
PVOA F.A.T. PVOA
NAME
pvoa - present value of an ordinary annuity
SYNOPSIS
pvoa p
pvoa v
pvoa
DESCRIPTION
Pvoa calculates the present value of an ordinary annuity given a
certain withdrawl amount per period, interest per period, and for a
number of withdrawls.
EXAMPLE(S)
What is the present value needed for a annuity that will pay $1000.
per month at 12 % annual interest for 30 years ?
$pvoa 1000 1 360
Present value........... 97218.33
SEE ALSO
pvad
- 41 -
RATE F.A.T. RATE
NAME
rate - find interest rate of an investment
SYNOPSIS
rate p
rate v
rate
DESCRIPTION
Rate calculates the interest rate (per period) of an investment
given its value today (present value), its value at the end of the
investment (future value), and the length of the investment (in
periods).
EXAMPLE(S)
What is the annual interest rate if it takes $1000. 5 years to grow
to $2000. ?
$rate 1000 2000 5
Interest rate per period...... 14.870 %
What is the monthly interest rate for the above situation ?
$rate 1000 2000 60
Interest rate per period...... 1.162 %
SEE ALSO
loanamt, loanlen
- 42 -
RETIRE F.A.T. RETIRE
NAME
retire - retirement planner
SYNOPSIS
retire p
retire v
retire
DESCRIPTION
Retire helps you plan your retirement. If you can predict how much
money you will need in retirement each year to withdraw from your
retirement investment as well as how long you expect to be retired
for and you can predict the interest rate for your investments,
retire can tell you how to get this needed money by either
investing a sum each year until retirement or investing a lump sum
today.
EXAMPLE(S)
How can I in retirement, which is in 30 years, withdraw $50000. a
year from my retirement investment while in retirement if I expect
to need this for 35 years in retirement and the annual interest
rate on my investments is 10 % ?
$retire 30 10 35 50000
Amount needed on retirement day............. 482207.95
Option 1: Lump sum needed to invest today... 27634.64
Option 2: Amount to be invested yearly
until retirement.................. 2931.46
SEE ALSO
pvoa, pv, fvoa
WARNINGS
Consult a professional financial planner, don't rely solely upon
this tool.
BUGS
Ability of tool user to predict inflation rate, years to live in
retirement,...
- 43 -
AFTERWORD F.A.T. AFTERWORD
6. User Feedback
MAB Systems Inc. encourages users of its products to submit
feedback of all sorts (suggestions, criticisms, comments, bugs,...)
since it will be this feedback that will enable us to keep our products
in tune with what you the user wants. This feedback is requested for
both documentation (this manual) and software.
Bugs are a permanent part of the software landscape. All
software in this package has been tested in numerous ways.
Unfortunately it is impossible to test this software for all possible
combinations of input data. Should you find a bug, incorrect answer, or
similar problem please note the exact situation including inputs to the
tool in question, version of the software as found by saying "toolname
v", and the computer and operating system being used. Before sending or
phoning in your bug report please make sure the bug is reproducible by
trying the "error conditions" more than once. Please include your full
name, address, and phone number so that we can reply to your bug report.
Please send all feedback to:
Michael_Brochstein@MABsystems.com
- 44 -
BLANK PAGE F.A.T. BLANK PAGE
- 45 -
CONTENTS
1. General Information............................................. 1
2. Installation for PC/MS-DOS...................................... 2
2.1 Systems with Hard Disks................................... 2
2.2 Systems without Hard Disks................................ 2
2.3 Notes on Execution Speed.................................. 2
3. General Usage of F.A.T. Tools................................... 3
4. Introduction to Financial Analysis.............................. 5
4.1 Compound Interest and Future Value........................ 5
4.2 Future Value of an Ordinary Annuity....................... 5
4.3 Future Value of an Annuity Due............................ 5
4.4 Compound Interest and Present Value....................... 6
4.5 Present Value of an Ordinary Annuity...................... 6
4.6 Present Value of an Annuity Due........................... 7
4.7 IRA Investments........................................... 7
4.8 Amortization Loans........................................ 7
4.9 Bonds..................................................... 8
4.10 Planning Your Retirement.................................. 10
4.11 Depreciation.............................................. 11
4.12 Loan/Investment Analysis.................................. 12
4.13 Miscellaneous............................................. 12
5. Tool Reference Manual........................................... 14
amort - amortization loan....................................... 15
amortbl - amortization loan payment schedule.................... 16
bond - bond investment analyzer................................. 18
compound - compound interest.................................... 19
comptbl - compound interest schedule............................ 20
cterm - find compounding term................................... 22
dateplus - todays date plus some days........................... 23
deprec - depreciation method analyzer........................... 24
fv - future value............................................... 25
fvad - future value of an annuity due........................... 26
fvoa - future value of an ordinary annuity...................... 27
ira - IRA investment............................................ 28
ira2 - IRA investment with an opening balance................... 30
ira2tbl - IRA investment schedule with an opening balance....... 32
iratbl - IRA investment schedule................................ 34
loanamt - find amount that can be loaned........................ 36
loanlen - find loan length...................................... 37
pv - present value in terms of months and years................. 38
pv2 - present value in terms of periods and interest per
period.......................................................... 39
pvad - present value of an annuity due.......................... 40
pvoa - present value of an ordinary annuity..................... 41
rate - find interest rate of an investment...................... 42
- i -
retire - retirement planner..................................... 43
6. User Feedback................................................... 44