Time Value of Money

GUJARAT UNIVERSITYPROGRAM: B. Com.

Semester: VICE 301 A MANAGEMENT ACCOUNTANCY II

Asso. Prof. Manesh Gandhi

C. U. Shah Commerce CollegeAshram Road, Ahmedabad 380014E-mail: mmgandhi2011@gmail.com

• 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.

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.

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".

• 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.

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

01 Present Value of Rs. 1 to be received at the end of the first year @ the given rate of interest

PV = વર્તમાન મલુ્ય =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

Example

• Present Value of Rs. 1 to be received at the end of the First Year, @ 12 % Rate of Interest / Discount =

વર્તમાન મલુ્ય =1

1+ .12

• Present Value of Rs. 1 to be received at the end of the First Year, @ 10 % Rate of Interest / Discount

વર્તમાન મલુ્ય =1

1+.10

• Present Value of Rs. 1 to be received at the end of the First Year, @ 8 % Rate of Interest / Discount

વર્તમાન મલુ્ય =1

1+.08

02 Amount to be received at the endof the term on One Time Investment (FD/Deb/PD), for a certain period, @ cumulative rate of interest

An = P ( 1+r )n

• 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

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

03 Amount to be received at the endof 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]

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

04 Amount to be received at the endof 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]

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

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]

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

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

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

THANK YOU