Concept of Time Value of Money

Learning Outcomes Concept of Time Value of Money Techniques of Time Value of Money Effective Rate of Interest Annuity Concept Concept of Perpetuity Loan Amortization Abstract The time value of money is the concept that shows the importance of money currently more than in future. FV = PV (1+ r/m) mt Discounting / Present Value Techniques PV = FV / (1+r) n Effective Rate of Interest It evaluates all of the various compounding bases, such as annually, semi - annually

Learning Outcomes
⮚ Concept of Time Value of Money
⮚ Techniques of Time Value of Money
⮚ Effective Rate of Interest
⮚ Annuity Concept
⮚ Concept of Perpetuity
⮚ Loan Amortization
Abstract
The time value of money is the concept that shows the importance of money currently more
than in future. To identify the time value of money we have to follow two techniques. They
are the Compounding Technique (Future Value Technique) and the Discounting Technique
(Present Value Technique). In future value techniques we move the cash flows forward in
time. It is called compounding when interest is earned on interest. In present value technique,
we move the cash flows back in time. It is called as the process of moving cash flows back in
time is called discounting when interest is earned on interest. Then we consider the Annuity
concept. An annuity is a series of fixed sums of payment made at equal intervals. According
to the time that the cash flow occurs we identified two concepts as ordinary annuity and
annuity due. There are four formulas to determine the present values and the future values of
a cash flow with regard to concepts, ordinary annuity and annuity due. After we consider the
effective rate of interest and perpetuities concept. Finally, we get an understanding about the
loan amortization concept and amortization schedule steps.

Time Value of Money
The time value of money is the concept that money you have now is worth more than the
identical sum in the future due to its potential earning capacity. It means money has more
value and utility to the beneficiary than receiving in the future due to the opportunity costs
associated with the wait. So, we can identify four main reasons for the time value of money.
● Risk & Uncertainty
● Current Consumption
● Inflation
● Investment Opportunities
Techniques of Time Value of Money
In order to have logical and meaningful comparisons between cash flows that result in
different time periods it is necessary to convert the sums of money to a common point in
time. There are two approaches for adjusting the time value of money.
1. Compounding Techniques / Future Value Techniques
FV = PV (1+r) n
Interest Rate can be compounding daily, monthly, quarterly and half year. Then, the
compounding technique identified below.
FV = PV (1+ r/m) mt
2. Discounting / Present Value Techniques
PV = FV / (1+r) n

Effective Rate of Interest
It evaluates all of the various compounding bases, such as annually, semi - annually,
quarterly and monthly, so that we may choose the most advantageous one. That means if any
interest rates are given under different bases like semi – annually, monthly, quarterly etc. to
calculate the highest interest rate, the effective rate of interest has to be taken.
reef = (1 + i/n) n-1
Annuity
Series of equal payments made at fixed intervals or specified number of periods is called an
annuity.
Ex: Insurance Payments
Ordinary Annuity
Annuity Due
A series of level cash flows that occur at the end of
each period for some fixed number of periods is
called as ordinary annuity.
A series of level cash flows that occurs at beginning
of each period some fixed number of periods is
called as annuity due.
i = Nominal Rate of Interest of year
n = Frequency of compounding per
year

Ordinary Annuity Annuity Due
Present Value PV = A ⌊ 1
r − 1
r ¿ ¿ PV = A ⌊ 1
r − 1
r ¿ ¿
Future Value FV = A ⌊ ¿ ¿ FV = A ⌊ ¿ ¿
Perpetuity
An infinite series of equal cash flows occurring at regular intervals for an infinite time period
is called perpetuity.
PV = A
r
Loan Amortization
A loan that is to be repaid in equal amounts on a monthly, quarterly or annual basis is called
an amortized loan.
Amortization schedule steps
● Find the required payments.
A = Payment Amount
r = Interest Rate

● Find interest charge for Year 01.
● Find repayment of principal in Year 01.
● Find ending balance after Year 01.
Summary
● The time value of money is the concept that money you have now is worth more than
the identical sum in the future due to its potential earning capacity.
● There are two approaches to adjusting the time value of money.
● Series of equal payments made at fixed intervals or specified number of periods is
called an annuity.
● There are four formulas to determine the present values and the future values of a
cash flow with regard to concepts, ordinary annuity and annuity due.
References
https://www.investopedia.com/terms/t/timevalueofmoney.asp
https://www.geektonight.com/time-value-of-money/
Stephen A. Ross, Randolph W. Westerfield, & Bradford D. Jordan. (2010).
FUNDAMENTALS OF CORPORATE FINANCE. McGraw-Hill/Irwin