nccmp - time value of money

8/13/2019 NCCMP - Time Value of Money

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Session 03


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Time Value of Money

Money and time have a relationship;if invested in some form, money grows over

time; for the same reason, the value ofmoney decreases when we look at it

backwards.

Time


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Future Value of a Single Amount

If you deposit ` 1,000 in a bank that pays10% interest per annum, what will be its valueat the end of one year ?

FVn = PV(1+r) n

Alternatively you can use an Excel sheet to do thecalculation.

PV = Value of the investment at the beginning of the term,

FV = Value of the investment at the end of the term,r = Rate of interest,n = Number of periods in the term.


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Open an Excel sheet.

Click Formulas
http://time%20value%20of%20money.xlsx/http://time%20value%20of%20money.xlsx/


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Click Financial


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From the menu that drops down, choosefunction FV .

And fill in the data.

Remember to make PV negative.


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Now let us try solving the problem we posed atthe start.

If you deposit ` 1,000 in a bank that pays10% interest per annum, what will be its valueat the end of one year ?

0.10

1

-1000

Let us now enter these values in the formula and get

the Future Value .


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The future value is ` 1,100/-.


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Once you are sufficiently familiar with the Excelformulas, you need not go through the series ofmenus.

You can straight away type the values in theproper format in any cell of the Excel sheet, and onclicking Enter , the cell will show the result.

Do not forget to insert an additional comma after the value of nper to fill the place of pmt .

additional comma


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Now let us try solving the same problem for alonger term (longer period of deposit), say 5 years.

If you deposit ` 1,000 in a bank that pays10% interest per annum, what will be its valueat the end of five years ?

0.10 %

5

1000

Let us now enter the values in the formula and get

the Future Value after 5 years.


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What would happen if our problem wasmodified as follows :

If you deposit ` 1,000 in a bank that pays10% interest per annum, compounded quarterly,what will be its value at the end of five years ?

Here the interest is added to the principal everythree months, that is four times a year; whatdifference will that make to the future value ?

What modifications do we need to make in ourformula to adjust for this fact ?


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To adjust for quarterly compounding we needto make two modifications to the data values weenter in the Excel formula.

rate = 0.10/4 (rate of interest per quarter)

nper = 5*4 (number of compounding periods)



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Future Value of an Annuity

If you deposit ` 1,000 in a bank at the beginningof every year for five years, and if the bank pays 10%interest per annum, what will be its value at the end of five years ?

FVAn = A (1+r)n - 1

r

A = Investment made at the beginning of every period (annuity),

FVA = Value of the investment (annuities) at the end of the term,r = Rate of interest,n = Number of periods in the term.


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To find the future value of an annuity you canuse the same FV formula. Now you leave the value of pv blank, and instead fill in the value of pmt(annuity).

Do not forget to insert an additional comma after the value of pmtto fill the place of pv .

additional comma



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What is this 1 in

the FV formula ?

The 1 denotes that the annuity has beendeposited at the beginning of the period; if theannuity is deposited at the end of the period, 1 should be substituted by 0 .

See the difference in FV by putting 0 in place of 1.


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Sinking Fund

How much should you deposit in a bank at thebeginning of every year for 5 years, if the bank pays10% per annum, and if you wish to receive ` 6,716 atthe end of five years ?

A = FVAn r(1+r) n-1 A = Investment made at the beginning of every period (annuity),

FVA = Value of the investment at the end of the term,r = Rate of interest,n = Number of periods in the term.


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To find the annuity that you need to pay at thebeginning of every year, to get the desired FV afterfive years, you can use the pmt formula.

Do not forget to insert an additional comma after the value of nperto fill the place of pv .

The annuity is ` 1,000/-.


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Finding the Rate of Interest / ReturnYou deposit ` 1,000 in a bank. You are told that

that it will grow to ` 1,611 in five years. What is the rateof interest that the bank is paying you ?

To calculate the rate , given the FV , you need to use the

formula IRR.

Before you begin thecalculation of IRR you haveto enter the investmentvalue ( PV ), receipts at theend of every year and futurevalue ( FV ) in an array ofExcel cells as shown

alongside.


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Then write the IRR formula, selecting the arrayof values already entered, as shown below.


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Click Enter to get the rate of interest.

The rate of interest is 10%.


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Capital RecoveryIf you deposit ` 1,00,000 in a bank which

pays 10% per annum, how much can bewithdrawn annually (at the end of the year) fora period of 10 years ?

A= PVAn (1+r) n -1r(1+r) n n

A = Annuity received at the beginning of every period, PVA = Present value of annuities to be received,r = Rate of interest,n = Number of periods in the term.


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To find how much can be withdrawn annually(at the end of the year) for a period of 10 years fromthe ` 1,00,000 deposited in the bank, we have to usethe PMT formula.

Annual withdrawal is ` 16,275/-.


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Present Value of a Single Amount

You are promised ` 1,000 five years hence.What is the present value of this amount, if therate of interest is 10% ?

PV = Value of the investment at the beginning of the term, FV = Value of the investment at the end of the term,r = Rate of discount (rate of interest),n = Number of periods in the term.

PVn = FVn 11+r n


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To find the present value of the amount you aregoing to receive in future ( FV ), you need to use the PV formula.

The present value is `

621/-.


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Present Value of an AnnuityYou are expecting to receive ` 1,000 at the

beginning of every year for the next five years.What is the present value of these annuities, ifthe rate of discount is 10% ?

PVAn = A(1+r) n -1

r(1+r) nn

A = Annuity received at the beginning of every period, PVA = Present value of annuities to be received,r = Rate of interest,n = Number of periods in the term.


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To find the present value of the annuities youare going to receive in future, you need to use the PV formula.

The present value is ` 4,170/-.


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Now lets us change the problem a little :

You are expecting to receive ` 1,000 at theend of every year for the next five years. What isthe present value of these annuities, if the rate ofdiscount is 10% ?

The change inthe formula that youneed to make issimple :

Replace thevalue of type instead of 1 put 0 .


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Now lets us change the problem a littlemore :

You are expecting to receive ` 1,000 at theend of every year forever (in perpetuity/ ).What is the present value of these perpetual

annuities, if the rate of discount is 10% ?Well, for this you do not need an Excel formula;

the present value of perpetual annuities (constant

amount every year) is given by

PVA = A1r


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Then write the NPV formula, selecting the arrayof values already entered, as shown below.


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See how the present value changes if wechange the timing of flows, keeping the total

amount received the same.

The present value is `

3,935/-.


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nccmp - time value of money

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