'Time Value of Money' for SEMSETER VI students of Program: B. Com. of Gujarat University, Ahmedabad, Gujarat, India

1. Time Value of Money
GUJARAT UNIVERSITY
PROGRAM: B. Com.
Semester: VI
CE 301 A MANAGEMENT ACCOUNTANCY II
Asso. Prof. Manesh Gandhi
C. U. Shah Commerce College
Ashram Road, Ahmedabad 380014
E-mail: mmgandhi2011@gmail.com

2. • Why would any rational person rejects
defer payment into the future when he
or she could have the same amount of
money now?
• Everyone knows that money deposited
in a saving / Recurring / Fixed Deposit
account will earn interest. Because of
this universal fact, we would prefer to
receive money today rather than the
same amount in the future.

3. For most of us, taking the money in
the present is just plain instinctive.
So at the most basic level, the Time
Value of Money (TVM) demonstrates
that, all things being equal, it is better
to have money now rather than later.

4. The idea that money available at the present
time is worth more than the same amount in
the future due to its potential earning
capacity.
This core principle of finance holds that,
provided money can earn interest, any
amount of money is worth more the sooner it
is received.
Also referred to as “Present Discounted Value".

5. • The rate of return can be calculated with the
rate of discount, rate of interest, rate of
inflation [Domestic (WPI, CPI) & Imported],
expected rate of return (Rate of Interest +
Return of the Risk involved), cost of equity,
cost of debt, period etc.
• For calculations involving annuities, we must
have the information whether the payments
are to be / being made at the end of each
period, or in the beginning of each period.

6. Abbreviations
• An = Accrued Amount = Investment +
Interest to be received at the end of
the period
• PV = Present Value
• P = Present Investment = A
• r = Rate of Interest / 100
• n = No. of years

7. 01 Present Value of Rs. 1 to be received at the
end of the first year @ the given rate of
interest
PV = વર્તમાન મુલ્ય =
1
1+ 𝑟
To calculate the present value of Rs. 1 to be
received at the end of the second year @
cumulative rate of interest =
PV =
PV of Rs.1 to be received at the end of the First Year
1+ 𝑟

8. Example
• Present Value of Rs. 1 to be received at the end of
the First Year, @ 12 % Rate of Interest / Discount =
વર્તમાન મુલ્ય =
1
1+ .12
• Present Value of Rs. 1 to be received at the end of
the First Year, @ 10 % Rate of Interest / Discount
વર્તમાન મુલ્ય =
1
1+.10
• Present Value of Rs. 1 to be received at the end of
the First Year, @ 8 % Rate of Interest / Discount
વર્તમાન મુલ્ય =
1
1+.08

9. 02 Amount to be received at the end
of the term on One Time Investment
(FD/Deb/PD), for a certain period, @
cumulative rate of interest
An = P ( 1+r )n

10. • Note: If the interest is being calculated / paid twice
in a year = divide ‘r’ by 2 & multiply ‘n’ by 2
• Note: If the interest is being calculated / paid thrice
in a year = divide ‘r’ by 3 & multiply ‘n’ by 3
• Note: If the interest is being calculated / paid four
times in a year = divide ‘r’ by 4 & multiply ‘n’ by 4
• Note: If the interest is being calculated / paid on bi-
monthly basis = divide ‘r’ by 6 & multiply ‘n’ by 6
• Note: If the interest is being calculated / paid on
monthly basis = divide ‘r’ by 12 & multiply ‘n’ by 12

11. Example
• Initial Investment Rs. 1,000; Investment
Period 5 Years; Rate of Interest (Cumulative)
12 %. Amount to be received at the end of
the period =
• An = P ( 1+ r )n
• An = 1,000 ( 1+ .12 )5
• An = Rs. 1,762.34

12. 03 Amount to be received at the end
of the term on Recurring Investment of a
certain amount for a certain period, @
cumulative rate of interest:
When Investment is being made in the
beginning of the year:
An = P[
(1+𝑟) 𝑛+1 −1
𝑟
- 1]

13. Example
• Mr A is maintaining a Recurring Account of 5
Years, deposits Rs. 1,000 in the beginning of each
of the years, Rate of Cumulative Interest is 10 %.
On maturity, he will receive Rs._____
An = P[
(1+𝑟) 𝑛+1 −1
𝑟
- 1]
An = 1,000 [
(1+.10)5+1 −1
.10
- 1] = Rs. 6,715.61

14. 04 Amount to be received at the end
of the term on Recurring Investment for
a certain period, @ cumulative rate of
interest
When Investment is being made at the
end of the year:
An = P[
(1+𝑟) 𝑛 −1
𝑟
]

15. Example
Mr B is maintaining a Recurring Account of 5
Years, deposits Rs. 1,000 in the end of each of
the years, Rate of Cumulative Interest is 9 %.
On maturity, he will receive Rs._____
An = P[
(1+𝑟) 𝑛 −1
𝑟
]
An = 1,000[
(1+.09)5 −1
.09
] = Rs. 5,984.71

16. 05 Present Value of a Fixed Amount to be
received at the end of each of the years,
up to a certain period, @ the cumulative
rate of interest (Present Value of
Annuity):
P = A [ 1+𝑟 𝑛−1
𝑟(1+𝑟) 𝑛 ]

17. Example
Present Value of Rs. 20,000 to be received @ the
end of each of the years; for 5 years; @ 8 %
cumulative rate of interest (Present Value of
Annuity):
PV = A [ 1+𝑟 𝑛−1
𝑟(1+𝑟) 𝑛 ]= 20,000 [ 1+.08 5−1
.08(1+.08)5 ]
= 20,000 [ 1.4693 −1
.08(1.4693)
] = Rs. 79,881

18. 06 Present Value of a Fixed Amount to be
received up to an unlimited period, @
the given rate of interest (Present Value
of Perpetuity):
P =
A
𝑟

19. Example
Present Value of Rs. 60,000 to be received
at the end of each of the years, for an
unlimited period, @ 9 % rate of interest
(Present Value of Perpetuity):
P =
A
𝑟
=
60,000
.09
= Rs. 6,66,666.66

20. THANK YOU