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Finance Functions

The financial functions are a powerful tool in making business or personal

financial decisions. To use the financial functions, select Finance from the Mode

menu, or use the keyboard shortcut Ctrl-F, or use shift then the Fin button..

The financial functions allow you to perform all kinds of financial calculationsincluding the value of investments, the cost of financing a loan, the discounted

value of a future payment or cash flow, and the equivalent rate of return of a

series of payments. There are also buttons to allow you to quickly add tax,

compute a discount or add a mark-up. The meaning of some of the functions,

and the input values needed, are easily forgotten. If you allow the cursor to hover

over a button, or in the case of pen devices if you do a "tap and hold" with the

stylus, a tool tip will appear which gives the full name of the function and a hint at

the order of arguments.

In finance mode the number of decimal places is automatically set to two,

irrespective of the settings in the Option/Display dialog. The display settings

can be modified to change the decimal separator and digit group (thousands)

separator if required. You can select "," or "." for the digit group character or set

it to "no" to disable digit grouping. The scientific and engineering decimal

display settings also have no effect.

The example below assume that you are using Algebraic logic. For RPN logic

you will need to alter the keystrokes slightly. So for example if the key sequencegiven is 100 func 200 = , for RPN you would use 100 Ent 200

func .

Whilst we have taken every care to ensure that these calculator functions and

the descriptions are accurate, we must remind you that you use them at your

own risk. If you are in any doubt, you are urged to seek professional financial

advice before making major financial decisions.

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Using the percent key

The percent key is available in most modes and works in exactly the same way.

In this section we show how you might use it for financial calculations. To get the

percent key use the shift and = buttons. This displays the result of an

arithmetic operation as a percentage.

Examples:

Calculate the tax at 17.5% on 25.00:

250 x 17.5 shift % Result: 43.75

Calculate 12% mark-up on $250

250 + 12 shift % Result: $ 280

Give 5% discount on goods costing $125

125 - 5 shift % Result: $ 118.75

Using the tax , before tax b/t , discount d/c

and mark-up m/u functions.The percentage calculations described above can be performed more

conveniently using the special keys available in finance mode. The tax, discount

(d/c) and mark-up (m/u) functions all do this automatically, without needing a

percentage to be entered. The percentage rates you regularly use will typically

not change frequently and these can be programmed in to the calculator. Any

time you need to use an ad-hoc percentage in a calculation you can revert to

using the percentage key.

First, here is how to change the percentages. Click on the rate button to

bring up the financial rates dialog box. We will look at this dialog further in the

following sections. It shows you the rates used by various functions. To change

the tax, discount or mark-up rates, select the appropriate edit box and enter the

new percentage (on Pocket PC devices the input window should come up

automatically). So, supposing that the sales tax (or value added tax) rate is

17.5%, we would enter this value for the tax rate. Similarly, if we regularly offer

customers a 20% discount, we would enter that value as the discount


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To choose the various percentage rates used in financial calculations, use the

Rate button which brings up the Financial Rates dialog box. The dialog box

can also be used to convert between nominal and effective rates for different

interest payment schedules.

The bank interest rate is applied to the loan calculations ( Loan , Savg ,

TM , TMa , PV , PVa , FV and FVa ) and the discount rate to

the Net Present Value calculations ( NPV and VFl ). Typically these will be

assigned different values which prevail at the time of the calculation and to the

relevant field of commerce. The rates also vary between financial institutions,

and depending on whether you are dealing with a loan or savings, and between

different financial products from the same institution.

By default it is assumed that the period in these calculations is annual. In this

case there is no difference between the nominal interest rate and the effective

interest rate. If a different period is required then the Period: drop-down list box

can be used to select biannual, quarterly, monthly, weekly or daily interest

payments. The nominal or effective annual rate can be used to specify the

interest rate by entering a value in the input box - if the nominal rate is entered

the effective rate is automatically calculated and displayed in the adjacent edit

box and vice versa. The effective rate is the annual rate of interest taking intoaccount the compounding of the individual payments over the year, and is

sometimes referred to as the Annual Effective Rate (AER) or Annual

Percentage Rate (APR - this sometimes is used to include additional related

finance charges). Because of compounding this rate will be slightly higher than

the nominal annual rate. Banks may quote both rates, and lenders are often

legally obliged to display an APR as well as the lower nominal rate which they

tend to give prominence.


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period defaults to one year but can also be set to be biannual, quarterly,

monthly, weekly or daily. The bank rate and period are set in the Rate dialog

box. This dialog can also be used to define whether payments are made or

received at the beginning or end of each period.

Savg Savings Payment

To compute the periodic payment needed to accumulate a given amount, enter

the final amount (future value), click the Savg button, then enter the term (number

of payments). Press = to get the amount of each payment.

Example: You decide to start saving for a holiday in 12 months time. How much

should you save each month in order to have1000 available at the end

(assuming 10% bank rate)? What total amount must you put aside?

Check that the bank rate is set at 10% and that the period is monthly, paymentin advance.

1000 Savg 12 = Result: 78.92

X 12 = Result: 947.10

The total amount saved is 947.10. The interest earned makes the amount up

to 1000.

Loan Loan Payment

To compute the required periodic payments to repay a given loan, enter the

amount of the loan (present value), click the Loan button, then enter the term

(number of payments). Press = to get the amount of each payment.

Usually the term of a mortgage is defined in years, but the repayment periods

and corresponding calculations are carried out monthly.

Example: What is the monthly payment to pay off a loan of $30,000 dollars over

25 years at an interest rate of 10% ?

First click on Rate to check that the interest rate is set to 10% (and change it

if needed), and set the period of the payments to monthly. You can note that the

effective interest rate changes to about 10.47%. You should also set the

payments to "arrears", assuming you will be paying the mortgage at the end of

each month.


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To compute the term required for a series of regular payments to increase to a

given value, enter the payment, followed by TMa followed by the desired

compounded sum at the term.

Example: You plan to buy a boat costing $20000. You can afford to save $300

per month. How long will it take to save for the boat (assuming 7% bank interest

over the period, and monthly compounding, payment in advance)?

First check the rate and period are set correctly in the Rate dialog.

300 TMa 20000 =

Result: 56.20

The number of periods is 56.2, or about 4 years and 9 months.

PV Present Value of an Investment

This function computes the present value of a future amount. This can be used

to find out how much you would need to invest now to be worth some specified

amount in the future. You can also use it to work out the present value of some

future amount. This can be useful if you need to compare alternative

investments which yield amounts at different times in the future.

Example: Which is worth more now; 500 in two years time, or 1000 in tenyears time?

To answer this we need to make a guess of the interest rate over the next ten

years or so. Let's assume this to be 5% and, for argument's sake, compounded

annually. We can then work out the present value of the two future amounts so

that we can make a comparison.

500 PV 2 = Result: 453.51

1000 PV 10 = Result: 613.91

This suggests that the 1000 is worth waiting for. In practice you might take

into account any commercial risk of default on the payment over the longer

period.

Example: You plan to give a four year old child $1000 on their eighteenth

birthday. What amount do you need to invest today (assuming 7% bank interest

over the period, and monthly compounding)?


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First check the rate and period are set correctly in the Rate dialog.

1000 PV ( 14 X 12 ) =

Result: 376.38

One problem with such long term calculations is that the bank rate will very

probably vary a great deal over a long period. In this case it is necessary to usea guess of the likely average rate over time based on historical interest rates. It

would also be wise to choose a fairly conservative value for the expected

interest rate.

PVa Value of Annuity

To calculate the present value of an annuity at maturity, enter the amount of the

payment, then FVa , followed by the term (number of periods). Despite theliteral meaning of the word annuity, it is possible to use a period other than

annual in the calculation, in which case you need to change the value of the

interest rate accordingly, by pressing Rate .

Example: You decide to finance the purchase of a car costing $15,000 over a

period of five years, but can only afford a monthly payment of $300. If the

finance company offers an APR of 10% compounded monthly, what down

payment would be required?

Make sure rate is 10%, period is monthly, payment in arrears.

300 PVa ( 5 X 12 ) =

Result: $ 14119.61

- 15000 =

Result: $ -880.39

A down payment of $880 is required.

FV Future Value of an Investment

To compute the value of a single amount invested for a given number of years at

the current interest rate, enter the principal, click FV and the number of

investment periods. Usually the number of periods is the number of years. If you


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wish to use a different period (monthly for example) you need to change the

value of the interest rate accordingly, by pressing Rate .

Example: What is the value of $100 invested for five years at compound

interest (assuming a 10% annual interest rate)?

First check that the Rate dialog is set to the correct bank rate (10%) and period

(annual).

1 0 0 FV 5 =

Result: $ 161.05

You can also compute the value of the same investment if interest is computed

monthly by setting the period to monthly in the Rate dialog and adjusting the

number of periods accordingly:

1 0 0 FV ( 5 X 12 ) =

Result: $ 164.53

FVa Future Value of Annuity

To calculate the future value of an annuity at maturity, enter the amount of the

annual payment, then FVa , followed by the term (number of periods).

Despite the literal meaning of the word annuity, it is possible to use a period

other than annual in the calculation, in which case you need to change the value

of the interest rate accordingly, by pressing Rate .

Example: What is the value at maturity of a 30 year annuity with an annual

payment of $200 (assuming an interest rate of 10%)?

Make sure rate is 10%, period is annual, payment in advance.

2 0 0 FVa 3 0 =

Result: $ 36188.68

Cash Flow Funct ions

Cash flow functions are desi ned to com ute the resent value of an irre ular


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series of payments. These functions use the discount rate in the Rate dialog

box. In order to use the IRR and VFl functions you will need to set the calculator

to array mode. To do this, select the Option/Matrix menu and set the grid to the

desired size, and check the box labelled "Show matrix in all modes". If the array

is two-dimensional, the values corresponding to successive periods are

ordered right to left in rows, and then row by row from top to bottom.

IRR Internal Rate of Return

The internal rate of return is the discount rate at which the present value of a

series of payments would be zero. The practice is to compare this with the bank

rate to decide whether the investment is preferable to simply investing the

capital in a bank. In real situations there is usually an element of risk and

uncertainty in the expected future payments and this should be taken into

account when making investment decisions.

To compute the internal rate of return on an irregular series of payments, first

select the Option/Matrix menu and set the grid to the desired size, and check

the box labelled "Show matrix in all modes". Then enter the values of the

payments into the array (if the array is two-dimensional, remember that the

elements are ordered from left to right and then from top to bottom). The

investments should be entered as negative numbers. Make sure all cells are

selected and then click on the IRR button to get the IRR value.

It is possible for a set of cash flows to exist for which there is no IRR, or for the

value to be too large or negative, in which case an overflow error is displayed.

Example: You plan to invest $1000 and expect to receive nothing in the first

year, $100 in the second year, $200 in the third year, and then $300 in the

fourth, fifth and sixth years. What is the internal rate of return?

Enter the values -1000, 100, 200, 300, 300, 300 into the array (make sure all

cells are selected when you finish). Then click on the IRR button. The array is

filled with the internal rate of return, which is computed as 5.55 .

NPV Calculate Net P resent Value of a Future Cash

Flow

To calculate the present value of an amount to be paid at some time in the

future, enter the value of the amount, followed by NPV and then the number of


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.

determined by the settings in the Rate dialog box, and defaults to one year.

If you wish to use a different period (monthly for example) you need to change

the value of the period accordingly.

The NPV function is exactly the same as the PV function except that it

uses the discount rate instead of the bank rate.

You can enter a negative number of periods, in which case you get the present

value of a payment which was paid at some time in the past. If you require the

net present value of a series of periodic cash flows, use PVa taking care to

set the bank rate to the required discount rate. Alternatively use the VFl

function with equal amounts.

Example: What is the net present value of $100 to be paid in five years time

(assuming 5% discount rate).

First check that the discount rate is set to 5%; period to annual.

1 0 0 NPV 5 =

Result: $ 78.35

VFl Net Present Value of Cash Flows

To calculate the net present value of a series of uneven cash flows, first select

the Option/Matrix menu and set the grid to the desired size, and check the box

labelled "Show matrix in all modes". Next enter the cash flow for each period

into the array. Make sure that all cells are selected and press the VFl button.

The array is now filled with the net present value for each corresponding period.

The value corresponding to the last entry is the present value of the whole cash

flow.

Typically the period is annual. If you wish to use a different period (monthly forexample) you need to change the value of the discount rate accordingly, by

pressing Rate .

Example: A project requires an initial capital expenditure of $1,000,000. After

five years the capital equipment is to be written off. The expected annual

revenue stream at the end of each year, less running costs, is: year 1 -

$100,000; year 2 - $200,000, year 3 - $300,000, year 4 - $300,000, year 5 -

$300,000. The net revenues exceed the initial capital cost, but is the investment


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a good one, assuming a discounting rate of 5% per annum?

Input the values, with a value of zero for year 1:

0.00

100000.00

200000.00

300000.00

300000.00

300000.00

VFl

Result:

0.00

95238.10

276643.99

535795.27

782606.01

1017663.86

The result shows that, taking into account the time value of money, the revenue

flows have a net present value of $1017663.86, so that the project is just

profitable (but probably not worth the risk!).

Depreciation Functions

The depreciation functions compute a depreciation factor for a given asset life

(in periods) and number of periods. For example, the depreciation factor for an

asset with a life of 10 years after 5 years with straight line depreciation would

be computed as 1 0 SLD 5. The resulting factor, 0.5, can be applied to the

value of the asset less any salvage value at the end of the period.

SLD Straight Line Depreciation

To calculate the fraction of the value of an asset which is depreciated after a

given time using straight-line depreciation, enter the initial cost less any salvage

value, then X , followed by the useful asset life, then SLD , followed by the

number of periods after which the depreciation is to be calculated, followed by

= . The result is the total cumulative de reciation char e.


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Usually the number of periods is the number of years. If you wish to use a

different period (monthly for example) you need to change the value of the

discount rate accordingly, by pressing Rate .

Example: What is the depreciation after five years on a capital asset costing

$10,000 with a ten year life and a salvage value of $1000 at the end of its life?

1 0 SLD 5 =

Result: 0.50 (the depreciation factor)

X ( 1 0 0 0 0 - 1 0 0 0 ) =

Result: 4500.00

The depreciation is $4500, therefore the value of the asset after 5 years is

$10000 - $4500 = $5500.00

Using RPN logic, you would enter:

10000 Ent 1000 - 10 Ent 5 SLD X

DDB Double declining Balance Depreciation

The double-declining balance method of depreciation is an accelerated

depreciation method which provides more rapid depreciation charges in the

early part of the lifetime of the asset. This method is often preferred when

calculating depreciation charges for tax purposes, for example. To calculate the

fraction of the value of an asset which is depreciated after a given time using

the double-declining balance method of depreciation, enter the initial cost

(ignoring the residual value), then X , followed by the useful asset life, then

DDB , followed by the number of periods after which the depreciation is to

be calculated, followed by = . The result is the total (cumulative) depreciation

charge.


different period (monthly for example) you need to change the value of the

discount rate accordingly, by pressing Rate .



( 1 0 DDB 5 ) X 1 0 0 0 0 =


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Result: 6723.20


$10000 - $6723 = $3277

Applying the depreciation to the whole of the asset value, rather than the value

less the residual value, results in a faster rate of depreciation (which is usuallyadvantageous). This does mean that the depreciation charge may bring the

depreciated value below the residual value near the end of the life of the asset.

When this happens the usual practice is to reduce the depreciation charge to a

value which leaves the residual value and allow the asset to remain at this value

until it is sold or disposed of.

SYD Sum-of-Years-Digits Depreciation

The Sum-of-Years-Digits is another accelerated depreciation method. To

calculate the fraction of the value of an asset which is depreciated after a given

time using sum-of-years-digits, enter the initial cost less any salvage value, then

X , followed by the useful asset life, then SYD , followed by the number of

periods after which the depreciation is to be calculated, followed by = . The

result is the total (cumulative) depreciation charge.


different period (monthly for example) you need to change the value of thediscount rate accordingly, by pressing Rate .



1 0 SYD 5 =

X ( 1 0 0 0 0 - 1 0 0 0 ) =

Result: 6545.45


$10000 - $6545 = $3455

Currency Conversion

You can use the conversion feature to perform conversions between some of

the major currencies and the former currencies of the European Union. Select


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"Currency" as the property and then select the To and From currencies from the

drop-down lists. Apart from the former currencies of countries now using the

Euro (which had a fixed exchange rate) the currency conversions fluctuate and

so the conversions will not be up-to-date. The date at which the conversion was

set is indicated for each currency. You can get updated currency files from time

to time at our web site (http://www.calculator.org/), or you can edit the currency

conversions yourself as needed.

For more information on using the conversion utility see the relevant section.

More examples

Example: You have $100,000 in a savings account, earning 6% annual

interest, credited monthly. In addition, $500 is deposited every month. How long

will the funds last if $1,500 is withdrawn every month?

That's a net withdrawal of $1000/month (the withdrawal and deposit amounts

can be offset). Interest is 0.5%/month (or you could correct for compounding if

appropriate). None of the built-in functions yield a term for an annuity type

investment, but we can use the formula:

Term = - log(1 - PV.rate/pmt) / log(1 + rate)

where PV (present value) is 100000 and pmt (payment) is 1000 so

Term = - log(1 - 100000 x 0.005 / 1000) / log(1 + 0.005)

= 138.975 months, or about 11 1/2 years.

You can check this value using the Mortgage function by computing the

mortgage repayment on a $100000 loan over 139 months, which gives a

payment of about $1000. You can also check using the Annuity function that a

$1000 payment over 139 months yields about $200000, if the rate is set to

0.005%. You can then discount this to the present value (using NPV with a term

of 139) to get back to about $100000.

Example: In the above example, how much can be withdrawn each month to

make equal monthly withdrawals for 10 years?


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.

TMa Term ofAnn.

x 0 x ans B

PVPresentValue

0 ans x x B

PVaPresentValue ofAnn.

x ans x B

FVFutureValue

0 x ans x B

FVaFutureValue ofAnn.

x 0 ans x B

LoanLoanPayment

ans x 0 x B

SavgSavingsPayment

ans 0 x x B

NPVNetPresentValue

0 ans x x D

Int Interest 0 x n/a n/a B

If you need to compute any of the various quantities by hand, the underlying

arithmetic functions are as follows (r = rate):

TM(PV, FV) = log(FV/PV)/log(1+r)

TMa(PMT, FV) = log(1 + FV.r/PMT) / log(1 + r)

PV(FV, term) = FV.(1 + r) -term

PVa(PMT, term) = PMT.(1 - (1+r)-n) / r or PMT.(1 + r).(1 - (1 + r)-n) / r (advance)

FV(PV, term) = PV.(1 + r) term

FVa(PMT, term) = PMT.((1 + r) term - 1) / r or PMT.(1 + r).((1 + r) term - 1) / r

(advance)

Loan(PV, term) = PV.r / (1 - (1 + r) -term) or PV.r / (1 - (1 + r) -term) / (1 + r)

(advance)

Savg(FV, term) = FV.r / ((1 + r) term - 1) or FV.r / ((1 + r) term - 1) / (1 + r)

advance


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NPV(FV, term) = FV.(1 + rd )-term

Vflow (FVn) = FVn.(1 + rd)-n

Int(PV) = PV.r

Copyright Flow Simulation Ltd., 2010

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