Excel Application of Time value of Money

7/30/2019 Excel Application of Time value of Money

1/28

2/9/20

Excel Application of

Time Value of Money

Dr. Manvinder Singh Pahwa

UPES, Dehradun

1Financial Management : Dr. M.S. Pahwa

Concept of Time Value of Money

A rupee today is worth more than a

rupee tomorrow

Therefore it can be concluded that money

can be invested to grow to a bigger

amount, and it has a time value


Future Value


Future Value of Money

Assume Rs. 100 is to be invest in a bank

which is paying 5% interest compounded

annually, then by the end of the year

investor will have:

100 + (5% of 100) i.e., 100 + 5 = Rs. 105

This Rs. 105 received at the end of the year

will be referred to as Future Value ofMoney.



2/28

2/9/20


Further if the money is invested for TWO years,

the calculation will be:

100 + 5% of 100 = 105

Reinvested in the beginning of second year

105 + 5% of 105 = 110.25

Here comes the formula for compound interest:

Amount = Principal (1 + Rate of interest)time


In mathematical sense,

FV = PV (1 + r)n

Where,

FV = Future Value

PV = Present Value

r = rate of interest

n= number of years



Future Value Table

The Future Value Table given at the end of the

book can be constructed using MS Excel in some

clicks only.

For this following steps can be followed:


Put the cursor over here and drag it

horizontally to copy it through all

the rows from C to P.

In year Zero that is present time the

value of Re. 1 will be Re. 1 only



3/28

2/9/20

Now i t will look like this


For inserting the formula come on cell B3

and put the formula as given. And press

enter key.


Drag the cursor horizontally to copy

the formula for all the rates.


Then pull the cursor

from here down

vertically to copy the

formulas throughout

the table.



4/28

2/9/20

The Table is ready.


Using Excel Formulas for Future Value

There is a built in function for future values i.e., FV asfollows:

=FV(RATE, NPER, PMT, -PV, TYPE)

Where,

FV = Future Value

RATE = Interest Rate per period

NPER = Total number of periods

PMT = Either 0 or 1 (i.e., if payment is made every period or ifit is an annuity put 1 if not put 0) [it will be ZER O here)

PV = Present Value (it is taken in minus)

TYPE = Either 0 or 1 (if payment is made in beginning of periodor then (1) and at end of the year (0) [it will be ZERO here)


15Financial Management : Dr. M.S. Pahwa 16Financial Management : Dr. M.S. Pahwa


5/28

2/9/20


Future Value of Annuity


What is an Annuity?

Annuity is an amount given (or taken as the

situation may be) at the beginning or end of

every period for certain or uncertain period of

time.

Annuity may be for present value or for future

value. Appendix A-3 at the end o f the book

shows the Future Value of Annuity.


Future Value of Annuity

In the previous situation the amount was

deposited only one i.e., at the beginning of year

and the future value of it after certain years was

calculated.

But if the same amount is deposited in the bank

at the beginning /end of every year, for certain

years, then it is called Future Value of Recurring

Deposit or Future Value of Annuity.



6/28

2/9/20

Understanding Future Value of Annuity


Verifying Future Value of Annuity with Table 3

Appendix A-3 shows the Future Value of

Annuity.

If 3 year row is seen with 8% column

intersection, the value is 3.246.

Now multiply this value 3.246 by 1.08

We get 3.50568 or 3.50

Why?


Verifying Future Value of Annuity with Table 3


Future Value of Annuity using MS Excel



7/28

2/9/20

What will be the future value of Re. 1 invested

every year for 3 years @ 8% p.a.

Future Value of Annuity using MS Excel


This is assuming the payments

are made at the end of the year

and thats why type is 0

Press enter after bracket.



Assuming the payments of annuityare made at the

beginning, typeis takenas1 insteadof 0.Press enterafter bracket.



8/28

2/9/20


Present Value


Present Value of Money

Present Value is just the vice-versa of

Future Value. It is to find out the present

value of Rs. 110.25 to be received after 2

years if discounted at 5% per annum will

be Rs. 100

100 = 110.25/(1+0.05)2

This Rs. 100 is referred to as Present Valueof Rs. 110.25 to be received after 2 years.



Further if Rs. 100 is receivable after THREE

years, the calculation will be:

100/(1 + 5%)3 = Rs. 86.3837

Here comes the formula for discounting :

Amount = Principal /(1 + Rate of interest)time



9/28

2/9/20



Present Value Table

The Present Value Table given at the end of the

book in Appendix A-2 can be constructed using

MS Excel in some clicks only.

For this following steps can be followed:


Apply the formula and pr ess enter


Drag it horizontally and

vertically further to

prepare the entire table.



10/28

2/9/20

The Table is

ready.


Using Excel Formulas for Present Value

There is a built in function for future values i.e., PV asfollows:

=PV(RATE, NPER, PMT, -FV, TYPE)

Where,

PV = Present Value

RATE = Interest Rate per period

NPER = Total number of periods

PMT = Either 0 or 1 (i.e., if payment is made every period or ifit is an annuity put 1 if not put 0) [it will be ZER O here)

FV = Future Value (it is taken in minus)

TYPE = Either 0 or 1 (if payment is made in beginning of periodor then (1) and at end of the year (0) [it will be ZERO here)


While using single cash flow, pmt and type a re set to ZER O as above.These parameters are to be used only when there are annuities



11/28

2/9/20

Present Value of Annuity


What is an Annuity?

As discussed earlier, annuity is an amount given

(or taken as the situation may be) at the

beginning or end of every period for certain or

uncertain period of time.

Annuity may be for present value or for future

value. Appendix A-4 at the end of the book

shows the Present Value of Annuity.


Present Value of Annuity

In the previous situation the amount accrued

only once i.e., at the beginning of the three and

the present value of it was calculated.

But if the same amount accrues at the beginning

/end of every year, for certain years, then it is

called Present Value of Annuity.


Understanding Present Value of Annuity

If ONE rupee accrues at the end of each year for 3

years at 8% interest, the present value will be:

PV = FV[1/(1+r) + 1/(1+r)2 + 1/(1+r)3 ++ 1/(1+r)n]

For the above example,

PV = 1[1/(1+0.08)+ 1/(1+0.08)2 + 1/(1+0.08)3

PV = 2.5771



12/28

2/9/20

PV of Annuity


Present Value of Annuity using MS Excel


What amount should be invested @ 5% p.a. to

generate Rs. 100 per year for 5 years?

Present Value of Annuity using MS Excel


Pmt (payment per year)

No of years

Rate of Discounting

type parameter tells MS Excel whether the cash flow occurs at the end

(0) or at the beginning. Here it has been assumed that payments occur at

the end of the year regularly.



13/28

2/9/20


Present Value of Annuity for Payments

at the beginning

If the payment of first installment is needed in the beginning of the

year, the type parameter is to be changed from 0 to 1.


Present Value of Annuity for Payments at the Beginning

The PV in Cell B5 is -45 4.60 which is higher than -432.95 as in the previous case.

The reason being that since the first installment is received immediately, we

need to deposit a higher am ount so as to receive 5 installments of Rs. 100.The another way of looking to it is that we are actually depositing Rs. 354.60

(454.60 100) and receiving 4 installments of Rs. 100


Present Value of Growing Annuities

and Real Rate of Interest



14/28

2/9/20

Growing Annuity is referred to as those

annuities which have growth rates.

Suppose Mr. Xs annual salary is Rs. 1,00,000 and

his salary will grow @ 10% each year for 5 years.

If the discount rate is 12%, what is the present

value of his salary?

This can be solved in the following steps:

Growing Annuities




15/28

2/9/20



This is one way of finding working out the PV of salary. The other way is to find out

the Real Rate of Interest and discount the real cash flow with Real Rate Interest.



16/28

2/9/20

Real and Nominal Rate of Interest


Interest Rates and Consumption

An interest rate measures the opportunity cost of immediate consumption. Interest rates fluctuate overtime and in order to understand these fluctuations,consider what influences immediate consumption.

One of the most important determinants of interestrates is expected inflation.

Suppose the consumer price index is expected to jumpbecause the price of goods and services are expected toincrease. Consumers are now likely to accelerateconsumption plansto avoidthelikely price rises.


How would you expect interest rates

to respond to this event?

If inflation expectations increase and there is a shiftfrom savings to consumption.

This will result in decrease in savings and further,the fixed income security prices will fall as there willbe the sell ing / redemption of fixed interest bearingsecurities, therefore with rise in prices, the interestrate falls.

Conversely, if prices falls, the interest rates will

rise. Therefore interest rates increase withexpectations of inflation.


The Fisher Equation



17/28

2/9/20

Fisher Equation.. Contd.


Calculating Real Rate of Interest




18/28

2/9/20


The difference is due to

the approximation in

calculating the real rate

of interest by

1.12 / 1.10 = 1.0181818

only 1.018 as been

taken for discounting.


Future Value of Annuity Revised

The present age of an employee is 30 years and

he will retire at the age of 60 years. The

company has policy of deducting Rs. 11,000 as

Provident Fund Contribution annually. The

interest rate on such account is 9%. What will be

the amount which the employee will be getting

on his retirement on account of his PF?



19/28

2/9/20

Solving the Annuity Payment

What will be the payments to be made toaccumulate certain sum of money after certainyears?

For Example:

A person wants to purchase a house of Rs.10,00,000 after 5 years from now and thesavings are to be started one year from today.How much the person should save each year topurchase the house if the savings earn @ 5%?


In this situation, the function called PMT is to be

used.

Following is the format:

PMT(RATE, NPER, PV, FV, TYPE)

Let us do it on MS Excel

Solving the Annuity Payment. Continued


The same concept can be used to find out how much a company needs tosave each year in order to rede em the debent ures of Rs. Ten Lakhs

The amount

available at

present is

shown here.


Further if the person already has Rs. 1,00,000 with him then in such

situation the amount required for house after 5 years will be less.



20/28

2/9/20

Capital Recovery and Loan Amortization


For Example:

How much amount should be recovered each

year from the lender to recover a loan of Rs.

1,00,000 given at 12% interest in 5 years?

CVF = 1/3.605

= 0.27739

=1000000.27739

=Rs. 27,739


MS Excel Calculations:


Solving for Number of Periods in an Annuity

If a person takes a loan of Rs. 10,00,000 and his

payment capacity is Rs. 1,00,000 a year, then in

what period will he be able to pay the principle

and interest, if the interest rate is 10%?

Formula:

NPER(RATE, PMT, PV, FV, TYPE)



21/28

2/9/20


Solving for Interest Rate in an Annuity

A washing machine is costing Rs. 11,000 and the

seller says that an installment of Rs. 1,500 per

year for 10 years. For the interest rate the seller

is showing the following calculations:

1500 10 = 15000

15000-11000 = 4000

So, Rs. 4,000 10 = Rs. 400 per year

And 400 11,000 = 3.6%


Formula for Real Interest Rate

RATE(NPER, PMT, PV, FV, TYPE, GUESS)



22/28

2/9/20


If the first installment is to be paid immediately after the purchase, the

effective rate of interest can be calculated by changing TYPE parameter

to 1 from 0


The same can also be calculated as offering a loan of Rs. 9,500 and taking9 installments as both are one and the same thing. See formula above.



23/28

2/9/20

Alternative Way

If it is assumed that the seller is actuallycharging 4.5% rate of interest then, the presentvalue of the payments for purchasing theproduct should be equal to the price of theproduct.

This means the present value of Rs. 1,500 ifdiscounted @ 4.5% should be equal to Rs.11,000, and if it is not, then seller is charging ahigher rate.


If the present va lue of the installments paid in more than the price of the

product, it means that the seller is charging more than what he is claiming.


Deferred Annuities

Any income flow which is beginning from a

future date, but whose amount is to be

calculated now is called Deferred Annuities.



24/28

2/9/20

Revised Example:What will be the amount available to an employee at the time

of his retirement at the age of 60, if Rs. 11,000 is deducted

annually one year from now when his age is 30 years?


Further

Now the company wants to know that if thisemployee is to be offered Rs. 2 lakh each year afterretirement and his life expectancy is 75 years, itmeans the company has to pay Rs. 2 lakhs to theemployee for 15 years because he will retire at theage of 60 years.

The management of the company wants to knowhow much amount should be deducted from theemployees salary so that the company may be ableto meet out its obligation without incurring anycost. The rate of interest now is 9% and the rate isexpected to drop down to 7%.


This has to be done in TWO steps:

Step 1:

Find out the present value of Rs. 2 lakhs that

will be paid to him for 15 years.

Step 2:

Find out the amount to be deducted each year

to arrive the required amount.

This can be done as follows:



25/28

2/9/20




26/28

2/9/20


Present Value of Uneven Cash Flows

When the cash flow is not uniform, it may be

difficult to find out the present value or the

future value manually.

The Present Value of uneven cash flows can be

calculated using the function NPV as follows:




27/28

2/9/20

There is no in-build function to calculate the

future value of uneven cash flows. but it can be

done by first calculating the present value at

time zero and then take the present value to

future value.

This can be done following the steps from the

previous example as under:

Future Value of Uneven Cash Flows



Solving for Yield in an Uneven Cash Flows

Yield refers to the net rate of interest that aperson will receive.

For Example:

An insurance policy states that if Rs. 7,000 is paid toit every year for 16 years, the insurance companywill return Rs. 20,000 at the end of 4th year, 8th year,12th year, 16th year and in 25th year it will pay Rs.2,00,000.

What is the yield of the investment plan?

It can be calculated with the help of function IRR:



28/28

2/9/20



End of the Session


Documents

Excel Application of Time value of Money