Future Value of Single Sum Present value of Single Sum Future value of Annuity Present Value of Annuity Perpetuity

1. Time Value of Money

2. Time Value of Money – Module 1
Time has Value:
• Inflation ( Purchase power of Rs100/- at present day is not
same as Future day )
• Delayed Consumption ( You are opting not to consume now ,
so cost of not using it is attached)
• Opportunity Cost: Money can be employed to get better risk
free return
Value of Money can vary over time keeping points we discussed

3. Time Value of Money – Module 1
Time Value at future point can be calculated by accounting
• Interest or return earned or expected to earn
• Or Inflation Accrued .
Say a person expects 5 % return
For him Rs100/- paid now and Rs105/- paid after one year later
both have same value . So Rs5 /- is Time value of Money he expects.
Y1 Rs100/- --- Y2 Rs105/-

4. Time Value of Money – Module 1
There can be Four Scenarios for Time Value of Money
• Future Value of Single Sum – Compounding
• Present Value of Single Sum – Discounting
• Future value of Annuity Payment
• Present value of Annuity Payment

5. Time Value of Money – Module 1
Future Value of Single Sum .
FV = Future Value
PV= Present Value
r= rate of return
n= time period.
FV= PV(1+r)n

6. Time Value of Money – Module 1
Future Value of Single Sum .
FV= PV(1+r)n
You have invested Rs 1000/- for 5 year at 10% compounded yearly .
What is FV .
PV=1000
N=5
r=10% = 10/100=.10
FV = 1000(1+.10)5
= 1610.51 /-

7. Time Value of Money – Module 1
Future Value of Single Sum . When we are compounding
other than year
FV= PV(1+r)n
--- Compounding yearly
Banker agrees to pay interest rate on a five year certificate of deposit at
a rate of 6% on a quarterly compounding ( Four times a year ) .
What is the future value of a Rs 1000/- CD in five years .
PV= 1000/- , r= 6% , n= 5 years .
We have extra factor called compounding factor m=4
Return is paid 4 times= r/4 (r/m)
It will be paid 4 times a year so time period =n*4(r*m)

8. Time Value of Money – Module 1
Yearly Compounding
FV = PV(1+r)n
= 1000( 1+.06)5 = 1338.22
Quarterly compounding (4)
FV=PV(1+r/m)nm
FV = 1000(1+ .06/4)5*4
= 1346.85
Monthly Compounding (12)
FV=1000(1+.06/12)5*12
= 1348.85

9. Time Value of Money – Module 1
Future Value of Money – Problems– more examples ….
Company A is assuring Rs 5000/- for Rs 1000/- invested for 10 years
Company B is assuring Rs 7000/- for Rs 1000/- invested for 10 years .
Keeping other parameters same which is a better investment .
Company A :
FV=5000 , PV=1000/- , n=10 , r=?
5000=1000(1+r)10 > (1+r)=51/10 = .1746 = .1746*100= 17.46 %
Company B :
FV=7000 , PV=1000/- , n=12 ,r=?
7000=1000(1+r)12 > ??????

10. Time Value of Money – Module 1
Future Value of Money – Problems– more examples ….
Mr Ashwin Wants to go to World Trip , which is costing 5L as of today.
He would be going on the trip 5 years once he retires . He wants to
know what amount he needs to invest in an instrument which gives
12% return , so as to fund his world trip after 5 years. Assume
inflation = 6%.
Mr A , is planning to fund his child education after 10 years , he
expects the cost after 10 years is going to be 10L . He is planning to
invest in FD which is going to give a interest of 10% compounded
half yearly . He wants to understand what amount he need to invest
now for next 10 years in this FD to fund his kids education.

11. Time Value of Money – Module 1
Discounting :
It is reverse of compounding
FV=PV(1+r)n
PV=FV/(1+r)n

12. Time Value of Money – Module 1
What Are Annuities?
Annuities are essentially a series of fixed payments required from
you or paid to you at a specified frequency over the course of a fixed
time period.
• There are two basic types of annuities: ordinary annuities and
annuities due.
Ordinary Annuity: Payments are required at the end of each period.
For example, Interest on FD are paid at end of the Month .
• Annuity Due: Payments are required at the beginning of each
period. EMI is example where u pay starting of the month for that
month . Or even SIP.

13. Time Value of Money – Module 1
Future Value of a Annuity :
Lets look at future value of a Ordinary Annuity:
If some one deposits rs1000 at end if every month for 5 years and
you are paid a interest of 5% per annually . What is the corpus you
will have at end of the 5 years.
You are doing a series of payments for next 5 years . This a ordinary
annuity . ( explain it in normal FV calculation )

14. Time Value of Money – Module 1
Future Value of a Ordinary Annuity :
The future value of an annuity formula is used to calculate what the value at a
future date would be for a series of periodic payments.
The future value of an annuity formula assumes that
1. The rate does not change
2. The first payment is one period away
3. The periodic payment does not change
If the rate or periodic payment does change, then the sum of the future value
of each individual cash flow would need to be calculated to determine the
future value of the annuity. If the first cash flow, or payment, is made
immediately, the future value of annuity due formula would be used.

15. Time Value of Money – Module 1
Future Value of a Annuity :
If some one deposits rs1000 at end if every month for 5 years and you
are paid a interest of 5% per annually . What is the corpus you will
have at end of the 5 years.
You are doing a series of payments for next 5 years . This a ordinary
annuity . ( explain it in normal FV calculation –scan copy)

16. Time Value of Money – Module 1
Future Value of a Annuity due :
The future value of annuity due formula is used to calculate the ending value of a
series of payments or cash flows where the first payment is received immediately. The
first cash flow received immediately is what distinguishes an annuity due from an
ordinary annuity. An annuity due is sometimes referred to as an immediate annuity.
The future value of annuity due formula calculates the value at a future date. The use
of the future value of annuity due formula in real situations is different than that of the
present value for an annuity due. For example, suppose that an individual or company
wants to buy an annuity from someone and the first payment is received today. To
calculate the price to pay for this particular situation would require use of the present
value of annuity due formula. However, if an individual is wanting to calculate what
their balance would be after saving for 5 years in an interest bearing account and they
choose to put the first cash flow into the account today, the future value of annuity due
would be used.

17. Time Value of Money – Module 1
Future Value of a Annuity :
Lets look at future value of a Ordinary Annuity:
If some one deposits rs1000 at starting of every month for 5 years
and you are paid a interest of 5% per annually . What is the corpus
you will have at end of the 5 years.
You are doing a series of payments for next 5 years . This a ordinary
annuity . ( explain it in normal FV calculation and also formula)

18. Time Value of Money – Module 1
Future Value of a growing Annuity :
The formula for the future value of a growing annuity is used to calculate the future
amount of a series of cash flows, or payments, that grow at a proportionate rate. A
growing annuity may sometimes be referred to as an increasing annuity.
Ex: A is getting a salary of 5Lac per year and he expects his yearly salary to grow at 10% .
He deposits 50% of his salary in FD which gives a return of 8%. What is the corpus at end
of 5 years . He is gets salary end of every year.

19. Time Value of Money – Module 1
Present Value of a Annuity :
Ordinary Annuity:
The present value of annuity formula determines the value of a series of future
periodic payments at a given time.
The formula shown has assumptions, in that it must be an ordinary annuity. These
assumptions are that
1) The periodic payment does not change
2) The rate does not change
3) The first payment is one period away

20. Time Value of Money – Module 1
Present Value of a Annuity :
Annuity due:
The formula for the present value of an annuity due, sometimes referred to as an
immediate annuity, is used to calculate a series of periodic payments, or cash flows, that
start immediately.

21. Time Value of Money – Module 1
Perpetuity:
Infinite series of equal cash flows occurring at regular intervals. It
has indefinitely long life.
PVp = Cash flow/r
Find out the present value of an investment which is expected to give a
return of rs 2500 p.a indefinitely and the rate of interest is 12 % pa.
= 2500/.12
= 2083.33

22. Time Value of Money – Module 1
Effective Rate of return :
The Annual Percentage Yield (APY), referenced as the effective annual rate in Finance, is
the rate of interest that is earned when taking into consideration the effect of
compounding.
Ex: Bank A gives 12% compounded monthly and bank B gives 12.5% compounded yearly.
Which is better.

23. Time Value of Money – Module 1
Inflation adjusted return or Real Rate of Return :
The real rate of return formula is the sum of one plus the nominal rate divided by the sum
of one plus the inflation rate which then is subtracted by one. The formula for the real rate
of return can be used to determine the effective return on an investment after adjusting for
inflation.
The nominal rate is the stated rate or normal return that is not adjusted for inflation.