Time value of money
◼ Individuals value more the opportunity to
receive money in the present than
receiving the same amount some time in
the future.
◼ There are three reasons that explain the
concept of time value of money:
◼ Investment opportunities: Money can be
productively employed to earn real
returns.
◼ Preference for present consumption: In an
inflationary period, a rupee today has a
higher purchasing power than a rupee in
the future.
◼ Risk or uncertainty: As the future is
characterized by uncertainty, individuals
prefer current consumption to future
consumption. In situations where an
individual forgoes the present
consumption of a particular amount for
future consumption, he expects a risk
premium to be given to him to
compensate for the uncertainty associated
with the future.
◼ Hence, the nominal or market interest rate
can be expressed as
◼ Nominal rate= Real rate of interest +
expected rate of inflation + risk premiums
to compensate for uncertainty.
◼ F.V. = COMPOUNDING
F.V.=P.V.((1+r)^n)
◼ P.V.= DISCOUNTING
P.V.=F.V./((1+r)^n)
Future Value of a Single
Flow
◼ The method of compounding helps us to
find the worth of money at some time in
the future. The future value factors are
used to find the value of money at the
end of year n (in future) at a particular
rate of interest.
◼ Example: Find the value of Rs 1,000
(which we have invested now), at the end
of 3 years given that the rate of interest
earned by it is 4%.
◼ The formula to be used in such a situation
is
◼ Future value = Present value (1+k)n
◼ =1000((1+0.04)^3)
◼ F.V.=1124.864
Future Value of Multiple
flows
◼ The above formula computes future value
for a single outflow of money. Let us
consider another example where we have
to calculate the future value of more than
one cash outflow (i.e multiple flows).
◼ Example: Ram invests Rs 1500 at the
beginning of the first year(or in other
words at the end of 0th year); Rs. 2,000 at
the beginning of the second year and Rs
5,000 at the beginning of third year at a
rate of interest 5% per annum. What will
be the accumulated value of all these cash
outflows at the end of the third year?
◼ CALCULATE F.V. IN EACH STREAM AND
TAKE TOTAL
◼ FV
PV FV
1 1500 =1500((1+0.05)^3)=
2 2000 =2000((1+0.05)^2)=
3 5000 =5000((1+0.05)^1)=
TOTAL=9191.44
◼ F.V.
PV F.V.
1 1500 1500((1+0.05)^3)=1736
2 2000 2000((1+0.05)^2)=2205
3 5000 5000((1+0.05)^1)=5250
TOTAL =9191
◼ 1500 deposited at the beginning of 1st
year
◼ 2000 deposited at the beginning of 2nd
year
◼ 5000 deposited at the beginning of 3rd
year
=1500(1+0.05)^3=1736 Total=9192
=2000(1+0.05)^2=2205
=5000(1+0.05)^1=5250
Present Value of a Single
Flow
◼ We apply the technique of discounting to
the future cash flows in order to find their
present value because the value of an
amount (say Re. 1) in future may be less
than the value of the same amount at the
present moment because of factors like
inflation etc.
◼ Example: Suppose a particular
investment opportunity provides us Rs
2000 at the end of three years. We need
to find out the present value of this cash
inflow of Rs 2000 that is got at the end of
three years with the interest rate being
5%.
◼ Present value = Future value x 1/(1+k)n
◼ =2000/((1+0.05)^3)
◼ =1728
Present Value of Multiple
Cash Flows
◼ A person invested certain amount of
money in a project. The project generates
an inflow of Rs 1500 at the end of the first
year, Rs 2,000 at the end of the second
year and Rs 4,000 at the end of the third
year. What is the present value of these
future cash inflows given that the rate of
interest is 5%?
◼ P.V.
FV P.V.
1 1500 =1500/((1+0.05)^1)=1428
2 2000 =2000/((1+0.05)^2)=1814
3 4000 =4000/(1+0.05)^3)=3455
TOTAL=6697.98
◼ P.V.
F.V. P.V.
1 1500 1500/((1+0.05)^1)=1429
2 2000 2000/((1+0.05)^2)=1814
3 4000 4000/((1+0.05)^3)=3455
=6698
◼ 1500 received at the end of 1 year
◼ 2000 received at the end of 2 year
◼ 4000 received at the end of 3 year
◼ 1500/(1+0.05)^1=1429 Total=6698
◼ 2000/(1+0.05)^2=1814
◼ 4000/(1+0.05)^3=3455
Present Value of an Annuity
◼ Example: A person invested certain
amount of money in a project. The project
generates an inflow of Rs 2000 each at
the end of first, second and third year.
What is the present value of this annuity
of Rs 2000 at 5%?
◼ The formula that has to be used for
computing the present value of an annuity
is
◼ PVIFA (Present Value Investment
Factor of an Annuity) =F.V ((1 + r)n-
1)/[r(1 + r)n].
=2000 {[(1+0.05)^3)-
1]/[(0.05(1+0.05)^3)]}
I am getting in all 6000 so my Ans has to be
less than 6000 as we need to find p.v.
=5446
◼ A person invested certain amount of
money in a project. The project generates
an inflow of Rs 2000 each at the end of
first, second and third year. What is the
present value of this annuity of Rs 2000 at
5%?
FV P.V.
1. 2000 2000/((1+0.05)^1)=1905
2. 2000 2000/((1+0.05)^2)=1814
3. 2000 2000/((1+0.05)^3)=1728
5447
RS.2000 F.V.
F.V. P.V.=F.V./(1+r)^n
1. 2000
=2000/(1+0.05)^1=1905
2. 2000 =2000/(1+0.05)^2=
1814
3. 2000 =2000/(1+0.05)^3=
1728
Sum of 1905+1814+1728=5446
Future value Annuity
◼ Suppose we deposit Rs.30,000 per year in
PPF for 30 years at the end of year. What
will be accumulated amt in PPF at the end
of 30 years if the Interest rate is 11%?
◼ F..V.A= P.V.(({1+r)^n}-1)/r)
=30,000(({1+0.11)^30}-1)/0.11)
=5970600
Future value Annuity
◼ Suppose we deposit Rs.30,000 per year in
PPF for 30 years at the Begining of year.
What will be accumulated amt in PPF at
the end of 30 years if the Interest rate is
11%?
◼ F..V.A= P.V.(((1+r)^n-1)/r)(1+r)
=30,000(((1+0.11)^30-1)/0.11))(1+0.11)
=5970600 (1+0.11)
=6627366
