2. INTRODUCTION
In projects companies invest a sum of money in anticipation of
benefits spread over a period of time in the future
If we borrow `100 today @ 10% (i.e. 09-Aug-10) from SBI than we
will have to pay `110 (08-Aug-11), the additional `10 is called interest
or time value of money
Required rate of return = Risk free rate of return + risk premium
Decision can be made by two methods:
Compounding method
Discounting method
3. FUTURE VALUE OF A SINGLE CASH
FLOW
It is the process of determining the future value
of a lump sum amount invested at one point of
time.
We calculate the future value of a single cash
flow compounded annually by
FV = PV(1+i)n
FV= Future value
PV = initial cash flow
i = interest rate per annum
n = the number of compounding periods
4. EXAMPLE
Suppose ` 1100 are placed in the saving account of
a bank at 5% pa. how much shall it grow after 2
years if interest is compounded annually
5. If compounding is done for shorter compounding
period, then:
FV = PV (1+ )m x n
FV= Future value
PV = initial cash flow
i = interest per annum
m = number of times compounding is done in a year
n = the number of compounding periods
m
i
6. EXAMPLE
Suppose Vijaya Bank gives 10% pa interest and
interest is compounded quarterly then calculate the
return after two years if Harsh deposit ` 1000 today
in Vijaya Bank
7. SOLUTION
FV = PV (1+ )m x n
= 1000(1+0.10/4)4 x 2
= 1000(1+0.025)8
= 1000 x 1.2184
= ` 1,218
FV= ?
PV= 1000
m= 4
n= 2
m
i
8. FUTURE VALUE OF MULTIPLE
FLOWS
Instead of investing lump sum at one time if money is invested in multiple
flows then how value of money will be affected?
Suppose Mr Paw Invests ` 1,000 now (at the beginning of one year), ` 2,000
at the beginning of year 2 and ` 3,000 at the beginning of year 3, how much
these flows accumulate to at the end of year 3 at a rate of 12% pa?
9. SOLUTION
FV3 = ` 1000 x FVIF(12,3) + ` 2000 x FVIF(12,2) + ` 3000 x FVIF(12,1)
=`[(1000x1.405)+(2000x1.254)+(3000x1.120)]
= ` 7273
10. FUTURE VALUE OF ANNUITY
Annuity is the term used to describe a series of periodic
flows of equal amounts.
The example of payment of Life insurance premium (` 2000
per annum) for next 20 years can be classified as an annuity.
The future value of a regular annuity for a period of n
years at a rate of interest ‘i’ is given by the formula:
]
)1)1(
[
i
i
AFVA
n
−+
=
A= Amount deposited at the end of
every year
i= Interest rate
n= Time Horizon
FVA= Accumulation at the end of
n year
),( niAxCVFAFVA =
11. EXAMPLE
Suppose Mr Jain deposits ` 2000 at the end of
every year for 10 years at the interest rate of 10%
per annum, then how much will be his corpus after
20 years?
13. SINKING FUND
It is used when we want to calculate how much
we have to deposit every year for ‘X’ years at the
interest rate of i% pa to receive amount ‘Y’ at the
end of ‘X’ year.
We know that
FVA=A x CVFA(i,n)
A= FVA x 1/CVFA(i,n)
14. EXAMPLE
Suppose we want to accumulate ` 500,000 at the end of 10 years.
How much should we deposit each year at an interest rate of 10%
per annum so that it grows to ` 500,000.
16. PRESENT VALUE OF A SINGLE
FLOW
With this approach, we can determine the present value of a future cash
flow or a stream of future cash flows
This is mostly used for evaluating the financial viability of projects.
Suppose if we invest `1000 today at 10% pa for a period of 5 years, we
know that we will get ` 1000 x FVIF(10,5) =`1000x1.611 =`1,611 at the end
of 5 years
So, the present value of `1,611 is `1000
Formula of calculating present value of a single flow is:
FV= PV x FVIF(i,n) ; PV =FV/FVIF(i,n) PV=
PV = FV x PVIF(i,n)
n
i
FV
)1( +
17. PRESENT VALUE OF AN ANNUITY
The present value of an annuity ‘A’ receivable at
the end of every year for a period of n years at a
rate of interest ‘i’ is equal to:
PVA= A x PVIFA(i,n)
]
)1(
1)1(
[ n
n
ii
i
APVA
+
−+
=
18. EXAMPLE
Suppose Mrs Ravina deposits ` 1000 every year for
8 years with 15% interest rate per annum, then
what is the present value of her deposits?
19. SOLUTION
A = ` 1000
n= 8 years
i= 12%
PVA=?
PVA= A x PVIFA(i,n)
PVA = 1000 x PVIFA(12,8)
PVA = 1000 x 4.968
PVA = 4968
20. CAPITAL RECOVERY AND LOAN
AMORTIZATION
If HDFC housing finance gives home loan to a person then
they will decide the EMIs through this method.
P= A x PVFA(i,n)
Suppose Mr X takes a loan of ` 50,000 today to buy a motor-
cycle for his son. If interest rate is 10%, how much Mr X will
have to pay per year to repay his loan in 3 equal end of year
repayments? [`20104.543]
,
1
=
PVAFn i
A P
= × CRFn,iA P
21. PRESENT VALUE OF PERPETUITY
Perpetuity is an annuity that occurs indefinitely.
It tells that how much shall we invest today so that we can get equal
amount every year for indefinite time
Present Value of Perpetuity = Perpetuity ÷ Interest rate
For example If Hari expects ` 5,000 from his investments then
how much he will have to invest today, if rate of interest is 10% per
annum
Present Value = 5000/0.10 = ` 50,000
22. VALUES OF AN ANNUITY DUE
When annuity is calculated from the beginning of
the year it is called annuity due
In the case of annuity due or when payment is
made at the beginning of the year, which means
last payment has completed one year at the time
of calculation
23. FUTURE VALUE OF ANNUITY DUE
Suppose that you deposit ` 1000 in saving account at the
beginning of each year for 5 years to earn 4% interest rate
Future value of an annuity due= future value of an annuity x
(1+i)
= A x CVFA(I,n) x (1+i)
= 1000 x 5.416 x 1.04
= ` 5632.64
)1](
)1)1(
[ i
i
i
AFVA
n
+
−+
=
24. PRESENT VALUE OF ANNUITY DUE
Suppose you deposit ` 500 at the beginning of each year for 5
years at 10% interest rate. Calculate the present value of
annuity.
Present Value of Annuity due = present value of annuity x
(1+i)
PVA = A x PVFA(I,n) x (1+i)
= 500 x 3.791 x 1.10
= ` 2085.05
]
)1(
1)1(
[ n
n
ii
i
APVA
+
−+
=
25. NET PRESENT VALUE (NPV)
Net Present Value (NPV) of a financial decision
is the difference between the present value of
cash inflows and the present values of cash
outflows.
NPV = PV of Cash Inflows – PV of Cash Outflows
If NPV is negative, it means investment in
project higher than the return. So, project will be
rejected.
26. EXAMPLE
Reliance industries is planning to start a project which
requires ` 1000 Cr at the beginning year and ` 200 Cr at the
beginning of second year. They are expecting to get a return
of ` 250 Cr at the end each year for next 5 years. Suggest
whether reliance should go for the project or not, If interest
rate in the market is 10% per annum.
