Download TIME VALUE OF MONEY

TIME VALUE OF MONEY
Analogy to Calculator Financial Keys
All financial calculators have five financial keys, and Excel's basic time value functions
are exactly analogous. The table below shows the equivalency between the calculator
keys and Excel functions:
Calculator
Key
Excel Function
Solve for
Number of
Periods
N
NPer(rate, pmt, pv, fv, type)
Solve for
periodic
interest rate
I/Yr
Rate(nper,pmt,pv,fv,type,guess)
Purpose
Solve for
PV
present value
PV(rate,nper,pmt,fv,type)
Solve for
annuity
payment
PMT
PMT(rate,nper,pv,fv,type)
Solve for
future value
FV
FV(rate,nper,pmt,pv,type)
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FUTURE VALUE OF LUMP SUMS – FV( )
Suppose that you received money for a birthday/graduation/special event, and now
have $1,000 to invest for a period of 5 years. How much will you have accumulated at
the end of this time period if your money earns 5%
interest?
Where can you invest this money, and what is the
interest rate you’ll receive for your investment? For
CD rates, savings/checking bank rates, go to:
www.bankrate.com
To find the future value of this lump sum investment, use the FV function, which is
defined as:
FV(rate,nper,pmt,pv,type)
In this problem:
 Rate is 5%,
 NPer (total number of payment periods) is 5 years (compounded annually),
 the $1,000 is the present value (PV).
Open a new workbook and enter the data as shown below, but leave B5 blank for now.
Select cell B5 and then type: =FV(B3,B2,0,-B1)
and then press Enter.
Every ‘time value of money’ problem has either 4 or 5 variables (corresponding to the 5
basic financial variables). In this case, we have a 4-variable problem and were given 3 of
them (Nper, Rate, and PV) and had to solve for the 4th (FV). Be sure that any variables
not in the problem are set to 0, otherwise they will be included in the calculation. In this
case, we did not have an annuity payment (PMT), so the third argument in the FV
function was set to 0.
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Note that we left out the optional Type argument. The Type argument tells Excel when
the first cash flow occurs (0 if at the end of the period, 1 if at the beginning). When
solving lump sum problems such as this, the argument has no effect.
Note that, unlike most financial calculators, there is no argument to set the
compounding frequency. In Excel functions, you must set NPer to be the total number
of periods, Rate to be the interest rate per period, and PMT to be the annuity payment
per period. So, if this problem had said that the compounding was monthly (annual was
implied), then we would have typed =FV(B3/12,B2*12,0,-B1). The annual percentage
yield (APY), is compounded monthly, would be 5.116%
Notice that we entered -B1 (-1,000) for the PV argument in the function. Cash inflows
are entered as positive numbers and cash outflows are entered as negative numbers. In
this problem, the $1,000 was an investment (i.e., a cash outflow). Had you entered the
$1,000 as a positive number no harm would have been done, but the answer would
have been returned as a negative number.
It is important that you always use cell references in your formulas. Never type a
number directly into any formulas or Excel functions (unless that number will never
change).
REAL RATE OF RETURN FORMULA
A REAL RATE OF RETURN is a return on an investment that is adjusted for inflation,
taxes or other external factors. An example of the real rate of return formula would be
an individual who wants to determine how much goods they can buy at the end of one
year after leaving their money in a money market account that earns interest.
A Money Market Account (MMA) is a type of savings account that usually earns a higher
amount of interest than a basic savings account. The minimum deposit and balance for
this account is often considerably higher than the minimum balance of a basic savings
account.
For this example of the real rate of return formula, we must assume that the individual
wants to purchase the exact same goods and same proportion of goods that the
consumer price index uses considering that it is used often to measure inflation.
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SCENARIO:
The money market yield is 5%, inflation is
3%, and the starting balance is $1,000.
Using the real rate of return formula, this example would show a real rate of 1.942%.
With a $1000 starting balance, the individual could purchase $1,019.42 of goods based
on today's cost.
In Excel: r = (1+R) / (1+h) – 1
r = real rate of return R = nominal rate
h = inflation
WHY IT MATTERS:
It is critical to consider the real rate of return on an investment before investing.
Inflation, which is often 2% or 3% per year, reduces the value of money as time passes,
and taxes certainly take a chunk away too. What's left -- the real rate of return -- often
can be unimpressive after considering these adjustments. Accordingly, investors must
consider whether the risk associated with the investment is appropriate given the real
rate of return.
SOLVING FOR THE NUMBER OF PERIODS – NPER( )
Sometimes you know how much money you have now, and how much you need to have
at an undetermined future time period. If you know the interest rate, then you can solve
for the amount of time that it will take for the present value to grow to the future value
by solving for N.
SCENARIO:
Suppose that you have $1,250 today and you would like to know how long it will take
you double your money to $2,500. Assume that you can earn 9% per year on your
investment.
You can easily find the exact answer using the NPer function. This function is designed
to solve for the number of periods and is defined as: NPer(rate, pmt, pv, fv, type)
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Create a new worksheet and enter the data shown below:
Select B5 and type:
=NPER(B3,0,-B1,B2)
You can see that it will take 8.04 years to double your money. One important thing to
note is that you absolutely must enter your according to the cash flow sign convention.
If you don't make either the PV or FV a negative number (and the other one positive),
then you will get a #NUM error instead of the answer. That is because, if both numbers
are positive, Excel thinks that you are getting a benefit without making any investment.
If you get this error, just fix the problem by changing the sign of either PV or FV. In this
problem it doesn't really matter which one is negative. The key is that they must have
opposite signs.
Solving for N answers the question, "How long will it take..." Let's look at an example:
Imagine that you have just retired, and that you have a nest egg of $1,000,000. This is
the amount that you will be drawing down for the rest of your life. If you expect to earn
6% per year on average and withdraw $70,000 per year, how long will it take to burn
through your nest egg (in other words, for how long can you afford to live)? Assume that
your first withdrawal will occur one year from today.
In this problem, we know the present value ($1,000,000), the annual payment
($70,000), and the interest rate (6%). We want to know how long the money that you
have now will last. In other words, we want to solve for the number of periods.
Set up a worksheet to look like the one below:
Select B5 and enter:
=NPER(B3,B2,-B1)
You will see that you can make 33.40 withdrawals. Assuming that you can live for about
a year on the last withdrawal, then you can afford to live for about another 34.40 years.
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Now, let's change the problem slightly:
Suppose that you would like to leave an inheritance of at least $100,000 to your favorite
charity. How does this affect the number of periods in which you can withdraw the
$70,000 per year?
It should be obvious that the answer will be less than before because you aren't going to
withdraw the entire $1,000,000. However, be aware that this is not the same as
investing only $900,000 today because the $100,000 is a future value.
Modify your worksheet so that it looks like the one below:
The formula in B6 needs to be changed to: =NPER(B4,B3,-B1,B2). Note that the future
value argument (B2) should be entered as a positive number. In this case, saving
$100,000 to give as an inheritance will reduce the amount of time that you can draw on
your savings to 31.86 years.
SOLVING FOR THE INTEREST RATE – RATE( )
Maybe you have recently sold an investment and would like to know what your
compound average annual rate of return was. Or, perhaps you are thinking of making an
investment and you would like to know what rate of return you need to earn to reach a
certain future value.
SCENARIO:
Suppose that you are planning to send your child to college in 18 years. Furthermore,
assume that you have determined that you will need $100,000 at that time in order to
pay for tuition, room and board, etc. If you have $20,000 to invest today, what
compound average annual rate of return do you need to earn in order to reach your
goal?
Finding the interest rate in a time value of money problem requires the use of the Rate
function, which is defined as:
Rate(nper,pmt,pv,fv,type,guess)
(Note that the Guess argument is rarely required and is optional.)
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Create a new worksheet and enter the data as shown below.
Select B5 and enter the Rate function: =RATE(B3,0,-B1,B2).
As before, you need to be careful when entering the PV and FV into the function. In this
case, you are going to invest $20,000 today (a cash outflow) and receive $100,000 in 18
years (a cash inflow). Therefore, enter -20,000 for PV, and 100,000 into FV.
When you have solved a problem, always be sure to give the answer a second look and
be sure that it seems likely to be correct. This requires that you understand the
calculations that the functions are doing and the relationships between the variables. If
you don't, you will quickly learn that if you enter wrong numbers you will get wrong
answers. Remember, Excel only knows what you tell it, it doesn't know what you really
meant.
SOLVING FOR THE PAYMENT AMOUNT – PMT( )
We often need to solve for annuity payments. For example, you might want to know
how much a mortgage or auto loan payment will be. Or, maybe you want to know how
much you will need to save each year in order to reach a particular goal (saving for
college or retirement perhaps).
SCENARIO:
Suppose that you are planning to send your child to college in 18 years. Furthermore,
assume that you have determined that you will need $100,000 at that time in order to
pay for tuition, room and board, etc. If you believe that you can earn an average annual
rate of return of 8% per year, how much money would you need to invest at the end of
each year to achieve your goal?
Open a new worksheet and enter the data as shown below:
In this problem you want to solve for an annual annuity payment, so you will use the
PMT function. Select B5 and enter: =PMT(B3,B2,0,B1).
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(Note that you entered 0 for the PV argument because the problem doesn't specify an
initial investment.)
You will find that you need to invest $2,670.21 per year for the next 18 years to meet
your goal of having $100,000.
Now, let's change the problem slightly by including a lump sum investment made today:
Suppose that you have just received a gift from one of your children’s grandparents.
They have given you $5,000 to be invested to help pay for her college tuition. How does
this change the amount that you would have to invest each year?
Since you will now be investing $5,000 today (the PV), the amount that you need to
save in future years will be reduced. To find out the new annual payment that is
required, you need to modify the spreadsheet somewhat. First, select Row 1 and insert
a new row. Now, in A1 type: Present Value and in B1 enter: 5,000.
Finally, you need to change the formula in B6 to: =PMT(B4,B3,-B1,B2).
Notice that the PV argument has been changed from 0 to -B1. It has to be entered as a
negative number because the $5,000 will be invested (a cash outflow). If you had put it
in as a positive number, then you would get the wrong answer ($3,203.72). You should
catch this error because the result is higher than if you didn't have the $5,000 to invest.
Again, you always have to think about the direction of the cash flows when using these
functions.
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PRESENT VALUE – PV( )
YOU'VE WON THE LOTTERY! NOW WHAT?
Friday the 13th was your lucky day. You won the lottery! The lottery officials have given
you a choice. You can either receive the $10 million now in one lump sum, or you can
receive $1 million a year for the next 20 years. Now what do you do?
(The present value of $10 million right now is $10 million.)
=PV(0.1,20,-10000000)
Change the interest rate to 5% and make the same calculations again.
The higher interest rate the less the future sum is worth now. The interest rate
represents the opportunity cost of current consumption versus consumption at a later
date. If the interest rate, which could be earned on the income now, is higher (10% v.
8%) than your potential future income will be higher because your investment will earn
a higher return. Thus at some interest rate of return there will be a decision to make
between taking the lump sum now or receiving payments.
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CALCULATING PAYMENTS – PMT( )
SCENARIO:
Imagine that you are about to take out a 30-year fixed-rate mortgage. The terms of the
loan specify an initial principal balance (the amount borrowed) of $200,000 and an APR
of 6.75%. Payments will be made monthly. What will be the monthly payment? How
much of the first payment will be interest, and how much will be principal?
Your first priority is to calculate the monthly payment amount. You can do this most
easily by using Excel's PMT function. Note that since we are making monthly payments,
we will need to adjust the number of periods (NPer) and the interest rate (Rate) to
monthly values.
Open a new spreadsheet and enter the data as shown below:
You can see that the monthly payment is $1,297.20. (Note that your actual mortgage
payment would be higher because it would likely include insurance and property tax
payments that would be funneled into an escrow account by the mortgage service
company.)
That answers your first question. So, you now need to separate that payment into its
interest and principal components. You can do this using a couple of simple formulas
(you will use some built-in functions in a moment):
Monthly Interest Payment = Principal Balance x Monthly Interest Rate
Monthly Principal Payment = Monthly Payment - Monthly Interest Payment
Using these formulas, you can see that the interest component of the first payment
would be:
Interest in 1st Payment = 200,000 x 0.005625 = $1,125
and the principal payment is: Principal in 1st Payment = 1,297.20 - 1,125 = $172.20
Note that the sum of the interest and principal is the amount of the total payment:
1,125 + 172.20 = $1,297.20 That is the case for every single payment over the life of the
loan. However, as payments are made the principal balance will decline. This, in turn,
means that the interest payment will be lower, and the principal payment will be higher
(because the total payment amount is constant), for each successive payment.
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MACROS
An Excel macro is a set of programming instructions stored in what is known as VBA
(Visual Basic for Applications) code that can used to eliminate the need to repeat the
steps of commonly performed tasks over and over again.
ADDING THE DEVELOPER TAB
By default in Excel, the Developer tab is not present on the Ribbon. To add it:
1. Click the File tab to open the drop down list of options
2. On the drop down list, click Options to open the Excel Options dialog box
3. In the left hand panel of the dialog box, click on Customize Ribbon to open
the Customize Ribbon window
4. Under the Main Tabs section in the right-hand window, click on the check box
next to Developer to add this tab to the Ribbon
5. Click OK to close the dialog box and return to the worksheet.
The Developer should now be present - usually on the right-hand side of the Ribbon
RECORD A MACRO
1. On the Developer tab, in the Code group, click Record Macro. Optionally, you can
assign your macro a shortcut key combination so that it's easy to run.
2. Click OK to start the Macro Recorder.
3. In your workbook, perform the actions that you want recorded, which can
include typing words or numbers, clicking cells, clicking buttons, dragging cells,
formatting, and more.
4. When you're done with the actions that you want recorded, click Stop Recording.
RUN A MACRO
1. On the Developer tab, in the Code group, click Macros.
2. In the Macros dialog box, find your macro and click Run.
Note If you assigned your macro a keyboard combination (for example,
CTRL+SHIFT+M) when you started the macro recorder, you can use that shortcut
to run the macro.
ADD A MACRO TO THE QUICK ACCESS TOOLBAR
1.
2.
3.
4.
5.
6.
Click the File tab, and then click Options.
Click Quick Access Toolbar.
Under Choose Commands from, select Macros.
Find and select your macro in the list.
Click Add and then click OK.
To change the name of the macro that's shown on the Quick Access Toolbar,
click Modify and type the name you want displayed in the Display name box.
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ADD A MACRO TO A SHAPE AS A HYPERLINK
1.
2.
3.
4.
Click Insert, Shapes and choose a shape (I’m using rounded rectangle).
Use the mouse to draw a button on the worksheet.
Double-click inside the button and type some text (ie. ‘Click to Copy Rows’).
Right-click on the shape, click Assign Macro, select the name of your VB/macro
and click OK.
5. Click off the button to deselect it.
6. Now you’re ready to try the macro. Click the button and the macro will run.
7. Save the workbook – the VB code will be saved with it. BUT….you must save the
workbook as a macro-enabled workbook.
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VISUAL BASIC FOR APPLICATIONS (VBA)
On your keyboard press the ALT+F11 keys .You now see the Visual Basic Editor. Again,
press ALT/F11 and you are back into Excel. Use the ALT/F11 key to go from Excel to the
VBA and back.
 Go to the menu bar VIEW and click PROJECT EXPLORER.
 Go back to the menu bar VIEW and click PROPERTIES WINDOW.
 To display the CODE WINDOW click on Sheet1 in the PROJECT EXPLORER pane.
A new Excel workbook includes three sheets and another component named
ThisWorkbook. This component is the location where you will store the macros (also
called VBA procedures) for your workbook. The three sheets and ThisWorkbook start
automatically when the workbook is opened.
The PROPERTIES WINDOW shows you the properties of the component that is selected
in the PROJECT WINDOW. For example, if you single click on Sheet1 in the PROJECT
WINDOW you see the properties of Sheet1 in the PROPERTIES WINDOW.
 Return to your spreadsheet and change the name on the tab of Sheet1 to
Introduction. Notice in the PROPERTIES WINDOW that the property NAME has
changed to Introduction.
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The CODE WINDOW is where 90% of the VBA work is done; writing VBA sentences,
testing your VBA procedures and modifying them when needed.
To illustrate what you can do in the CODE WINDOW, start by creating a small macro in
an empty workbook.
 Switch to the VBE. Double-click on Sheet 1 in the PROJECT WINDOW. On the
right is the CODE WINDOW for Sheet 1.
 Click anywhere in the CODE WINDOW and type the text below:
Sub myFirst()
Range(“A1”).Value = 34
Range(“A2”).Value = 66
Range(“A3”).Formula = “=A1+A2”
Range(“A1”).Select
End Sub



Click on any line of the macro, go to the menu bar at the top of the VBE screen
and click Run; then click Run Sub/Userform. Go back to Excel (ALT/F11) and see
what has happened to cells A1, A2 and A3.
Go back to Excel and clear the cells A1, A2 and A3 of Sheet1. On the menu bar go
to Tool and click on Macros. In the dialog window select myFirst and click Run.
In the VBE, retype sub myFirst() without using a capital S as the beginning of
sub. After entering the closing parenthesis click Enter. The VBE capitalizes letters
appropriately when the word is spelled correctly.
o This is one interesting feature that you should always use when writing
macros. Make it tour habit never to use capital letters when writing code.
In this way, whenever VBE fails to capitalize a letter, you will know that
something is wrong.
Function SumCode(rng As Range)
sumx = 0
For Each cell In rng
sumx = sumx + cell.Value
Next
SumCode = sumx
End Function
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1. Open a spreadsheet in Excel.
2. Copy the following macro code:
Sub Test()
Dim Destrange As Range
Dim Smallrng As Range
Dim Newsh As Worksheet
Dim Ash As Worksheet
Dim Lc As Long
Application.ScreenUpdating = False
Set Ash = ActiveSheet
Set Newsh = Worksheets.Add
Ash.Select
Lc = 1
For Each Smallrng In Selection.Areas
Smallrng.Copy
Set Destrange = Newsh.Cells(1, Lc)
Destrange.PasteSpecial xlPasteValues
Destrange.PasteSpecial xlPasteFormats
Lc = Lc + 1
Next Smallrng
Newsh.Columns.AutoFit
Newsh.PrintOut
Application.DisplayAlerts = False
Newsh.Delete
Application.DisplayAlerts = True
Application.ScreenUpdating = True
End Sub
3. From the Excel Developer tab, click Visual Basic:
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4. In the Visual Basic screen, click Insert, Module and then paste the code in the
window:
5. You can close this Visual Basic window. When prompted to Save, make sure you
now save your spreadsheet as a macro-enabled spreadsheet (i.e.
My_Spreadsheet.xlsm). The macro-enabled spreadsheet option is available in
the Save As dropdown:
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6. To use the macro, select an area in your spreadsheet that you’d like to print.
From the Developer tab, click Macro, Test, Run (if you’d like a different name,
change the code on the 1st page of this document before you paste it into the
Visual Basic window).
7. This is how your report will print:
8. If you don’t want to click Macro and run Test, you can change the macro to run
from a keyboard shortcut or add as a button to the Quick Access Toolbar. Choose
Modify instead of Run when you click Macro from the Developer tab.
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If your Excel workbook contains multiple worksheets and you’d like to combine all the
sheets onto just one sheet, follow the steps below:
1. Open the Excel workbook and add a new sheet. Make sure to place this new
sheet as the first sheet in the workbook.
2. Copy the code below. Press ALT + F11 to open the VBA window, click Insert,
Module and paste the code.
Sub CombineAllSheets()
Dim osheet As Object
For Each osheet In Sheets
If osheet.Index > 1 Then
osheet.Activate
Range("A1", osheet.UsedRange.Cells _
(osheet.UsedRange.Cells.Count)).Select
Selection.Copy
Sheets(1).Activate
Cells(Sheets(1).UsedRange.Cells _
(Sheets(1).UsedRange.Cells.Count) _
.Row + 1, 1).Select
ActiveSheet.Paste
Application.CutCopyMode = False
End If
Next
Sheets(1).Cells(1, 1).Select
End Sub
3. Click the Play button to run the code and copy all the spreadsheets to the first
spreadsheet.
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