Course Financial Management

Segment 2 Value of Money

Faculty Ujwal M S
Webinar 1: Introduction to Financial Management
& Planning
Recap

1 Meaning and Definition of Financial Management

2 Goals of Financial Management

3 Organisation of Finance function

4 Financial planning
Webinar 2: Value of Money
Overview of Topics

1 Time Value of Money

2 Compounding Technique & Discounting Technique

3 Future Values & Present Values

 Webinar 2: Value of Money
Learning Objectives
At the end of this session, you will be able to:
Explain the Time Value of Money

Compute the Future Values of Lump Sums and Annuity Flows

Calculate the Present Values of Lump Sums and Annuity Flows

TIME VALUE OF MONEY
 TIME VALUE OF MONEY

MEANING
• Value of rupee received today is different from the value of rupee to be received
after some time in future, say , a year.
• i.e.,. Rupee today has more value than rupee tomorrow.
• There is preference for present value as against the future value
• This preference for present value of money against its future value is called
‘’preference for money ‘’ or ‘’time value of money’’.

PRINCIPLE OF TIME VALUE OF MONEY

The principle of time value of money suggests that since money has time value,
every financial decision must be made on the basis of the present value or
discounted value of cash flow or return from an investment proposal.
 TIME VALUE OF MONEY

FACTORS CONTRIBUTING TO TIME VALUE OF MONEY:

1. Future is uncertain & subject to risk (so people prefer receiving cash today)
2. People prefer current consumption of goods. Same goods may be costly in
future
3. Money can be invested today to get some return in future
4. In a period of continuing inflation, rupee has greater value than rupee in
future. (Inflation reduces the purchasing power of money)
 TIME VALUE OF MONEY

TWO FACETS OF THE TIME VALUE OF MONEY

1. COMPOUNDING: the technique of compounding is the process of

ascertaining the future value of an initial sum of money after a
period of time.

2. DISCOUNTING: the technique of discounting is the process of

ascertaining the present value of cash inflows of a proposal over a
period of time.
 Compounding Technique

COMPOUND INTEREST :
When interest at the end of each fixed period is added to the principal, the
amount thus obtained is taken as the principal for the calculation of the interest
for the next period, the interest so charged is called compound interest.

Compound interest for a number of years can be calculated with following formula:
A = P (1 + i)n
Where,
A = Amount at the end of ‘n’ period.
P = Principal amount at the beginning of ‘n’ period.
i = Rate of interest.
n = Number of payment periods.
 Compounding Technique

Example:
Find out the compound interest on ₹.10,000 for 3 years at 9%.p.a
compound interest.
YEAR OPENING INTEREST CLOSING
Soln: A = P (1 + i) n
BALANCE BALANCE
A = 10,000 ( 1 + 0.09 )3
1 10000 900 (10000X9%) 10,900
A = 10,000 ( 1 .09 )3 2 10900 981 (10900X9%) 11881
A = 10,000 ( 1.29503) 3 11881 1069 (11881X9%) 12950
2950
 A = ₹.12,950
So the compound interest is = 12950 – 10000 = ₹.2,950
 Discounting Technique

This technique is in contrast to the compounding approach where we

convert the present amounts into future amounts.

Mathematically, for the Discounted Technique we have the following formula:

P=A( 1 )
(1 + i)n
Where,
A = Amount at the end of ‘n’ period/Sum to be received in the future.
P = present value for the future sum to be received.
i = Rate of interest.
n = Number of years.
 Discounting Technique

Example:
Mr. Zayn requires ₹.10500 at the end of the first year. Given the rate
of interest as 5%, find out how much Mr. Zayn would invest today to
earn this amount.
Soln: P = A ( 1 )
(1 + 0.05)1
P = 10500 ( 1 )
(1.05)1
 P = ₹.10,000
 FUTURE VALUE

Amount to which an investment will grow after earning interest.

A generalised procedure of calculating the future value of a

single cash flow compounded annually is as follows:

FV = 𝑃𝑉 × 1 + 𝑖 𝑛
Where,
FV = future value of the initial flow in n years hence,
PV = initial cash flow
i = annual rate of interest
n = life of investment
 FUTURE VALUE

Example:
What is the future value of $100 if interest is compounded
annually at a rate of 6% for five years?

FV = 𝑃𝑉 × 1 + 𝑖 𝑛

𝐅𝐕 = $100 × 1 + 0.06 5 = $133.82

 FUTURE VALUE

Future value of series of cash flows

An investor may be interested in investing money in instalments
and wish to know the value of his or her savings after n years.

ANNUITY
It is a series of equal amounts payable or receivable at regular
or equal intervals of time, say, yearly, half yearly, quarterly,
monthly or any other period for a specified period of time or
forever.
 FUTURE VALUE
CALCULATION OF FUTURE VALUE OF AN ANNUITY

In an annuity having future value, a person goes on paying or receiving

equal installments for a certain number of years.

Under future value, there are two types of annuities, viz.,

Annuity Immediate & Annuity Due.

Annuity immediate – Cash flow at end of the year

Annuity due – Cash flow at beginning of the year

 FUTURE VALUE
CALCULATION OF FUTURE VALUE OF AN ANNUITY

❖ FORMULA FOR FUTURE VALUE OF ANNUITY IMMEDIATE:

F = A [(1 + i)n – 1]
i

❖ FORMULA FOR FUTURE VALUE OF ANNUITY DUE:

F = A [(1 + i)n – 1] (1+i)
i

WHERE , F = FUTURE VALUE, A = ANNUITY (PERIODIC PAYMENT), i = RATE OF

INTEREST, n = NUMBER OF INSTALMENTS/PERIODS.
 FUTURE VALUE
CALCULATION OF FUTURE VALUE OF AN ANNUITY
ILLUSTRATION:
A depositor deposits in a bank ₹.1,000 at the end of every year for 5 years at
an interest of 10% p.a. Calculate the future value of the annuity at the end
of five years.
Soln: F = A [(1 + i)n – 1]
i
= 1,000 [(1 + 0.10)5 – 1]
0.10
= 1,000 [(1.10)5 – 1]
0.10
= 10,000 [1.61051– 1]
= 10,000 [0.61051]
= ₹.6,105
 FUTURE VALUE
A depositor deposits in a bank ₹.1,000 at the end of every year for 5 years at
an interest of 10% p.a. Calculate the future value of the annuity at the end of
five years.
ALTERNATIVELY,
In this case, the future value of the annuity will be,
= 1000(1.10)4 + 1000(1.10)3 + 1000(1.10)2 + 1000(1.10)1 + 1000
= 1000(1.4640) + 1000(1.3310) + 1000(1.2100) + 1000(1.10) + 1000
= 1,464 + 1,331 + 1,210 + 1,100 + 1,000
= ₹.6105
OR
As per future value annuity table, value of annuity at 10% interest for 5 years is
6.105.
So the compound value of an annuity of ₹.1,000 at 10% interest p.a for 5 years
will be
FUTURE VALUE
CALCULATION OF FUTURE VALUE OF AN ANNUITY
 FUTURE VALUE
CALCULATION OF FUTURE VALUE OF AN ANNUITY
ILLUSTRATION:
Ravi deposits ₹.5000 at the beginning of every year into a bank in a recurring deposit
account for 6 years at 8% compound interest per annum. Calculate maturity value of the
deposit.
Soln: F = A [(1 + i)n – 1] (1 + i)
i
= 5,000 [(1 + 0.08)6 – 1] (1 + 0.08)
0.08
= 5,000 [(1.08)6 – 1] (1.08)
0.08
= 5,000 [1.58687– 1] (1.08)
0.08
= 5,000 [0.58687 x 1.08]
0.08
= 62,500 x 0.63382
= ₹.39,614
 PRESENT VALUE

‘Present value’ can be simply defined as ‘the current value of a future

sum’.

It can also be defined as the amount to be invested today (present value)

at a given rate of interest over a specified period to equal the ‘future’
sum.

FV
PV = 𝑛
1+𝑖
 PRESENT VALUE
CALCULATION OF PRESENT VALUE OF AN ANNUITY
ILLUSTRATION :
You just bought a new computer for $3,000. The payment terms are 2
years same as cash. If you can earn 8% on your money, how much money
should you set aside today in order to make the payment when due in two
years?
FV
PV = 𝑛
1+𝑖

3,000
PV = = $2,572
1.08 2
 PRESENT VALUE
CALCULATION OF PRESENT VALUE OF AN ANNUITY
Present value of even series of cash flows
In a business scenario, the businessman will receive periodic amounts (annuity) for
a certain number of years. An investment done today will fetch him returns spread
over a period of time.

The present value of an annuity is the current value of future payments from
an annuity, given a specified rate of return, or discount rate.

❖ FORMULA FOR PRESENT VALUE OF ANNUITY:

P = A [(1 + i)n – 1]
i (1 + i)n
WHERE ,
P= Present Value, A = Annuity (Periodic Payment), i = Rate Of Interest, n = Number Of
Instalments/Periods.
 PRESENT VALUE
CALCULATION OF PRESENT VALUE OF AN ANNUITY
ILLUSTRATION:
A 10 payment of annuity of ₹.5,000 will began 7 year hence. What is the value
of this annuity now, if the discount rate is 12% ?
Soln: P = A [(1 + i)n – 1]
i (1 + i)n
= 5,000 [(1 + 0.12)10 – 1]
0.12 (1 +0.12)10
= 5,000 [(1.12)10 – 1]
0.12 (1.12)10
= 5,000 [3.1059– 1]
0.12 (3.1059)
= 5,000 [2.1059]
0.3727
= 10,529
0.3727
 P = ₹. 28,251
 PRESENT VALUE
CALCULATION OF PRESENT VALUE OF AN ANNUITY
ILLUSTRATION:
A 10 payment of annuity of ₹.5,000 will began 7 year hence. What is the value
of this annuity now, if the discount rate is 12% ?
Soln:
ALTERNATIVELY,
As per present value annuity table, for annuity payment of ₹.1 at 12% discount for
10 years is 5.6502
So the present value of an annuity of ₹.5,000 will be
5,000 x 5.6502 = ₹.28,251
PRESENT VALUE
CALCULATION OF PRESENT VALUE OF AN ANNUITY
 PRESENT VALUE
PRESENT VALUE OF AN PERPETUITY
An annuity for an infinite time period is perpetuity. It occurs indefinitely. A
person may like to find out the present value of his investment assuming he
will receive a constant return year after year.

In case of perpetuity or perpetuity annuity, there is permanent investment in

one lump sum, but there is no withdrawal of an investment.

FORMULA :
P=A
i
WHERE ,
P= Present Value, A = Annuity (Periodic Payment), i = Rate Of Interest
 PRESENT VALUE
CALCULATION OF PRESENT VALUE OF AN PERPETUITY
ILLUSTRATIONS:
1. Kumar wants to get a perpetual pension of ₹.1,000/ month. If the
rate of compound interest is 12% per annum, what is the purchase
price of perpetual pension?
Solution:
P=A
i
P = 12,000
0.12
P = ₹.1,00,000
 Webinar 2: Value of Money
Summary

Key points discussed in this session:

➢ Time Value of Money

➢ Compounding Technique & Discounting Technique

➢ Future & Present Values

Webinar 2: Value of Money
Important Questions

Question 1: Concept of Time Value of Money

Question 2: Problems on the Compounding Technique

Question 3: Problems on the Discounting Technique

Question 4: Problems on Future Value of Annuity Due/Immediate

Question 5: Problems on Present Value of Annuity

 References
E - Book References:

❖ Financial Management – I M Pandey

❖ https://open.umn.edu/opentextbooks/textbooks/principles-of-finance