Module 2 Time Value of Money

Module 2-Time value of Money
Unit 2: Time Value Of Money.
 Introduction – Meaning & Definition – Need – Future Value (Single Flow – Uneven
Flow & Annuity) – Present Value (Single Flow – Uneven Flow & Annuity)–
Doubling Period .
 Money has time value. A rupee today is more valuable than a year hence. It is on
this concept “the time value of money” is based. The recognition of the time
value of money and risk is extremely vital in financial making.
Most financial decisions such as the purchase of assets or procurement of funds, affect
the firm’s cash flow in different time period. For example, if a fixed asset is
purchased, it will require an immediate cash outlay and will generate cash flows
during many future periods. Similarly if the firm borrows funds from a bank or from
any other source, it receives cash and commits an obligation to pay interest and repay
principal in future periods. The firm may also raise funds by issuing equity shares.
The firm’s cash balance will increase at the time shares are issued, but as the firm
pays dividends in future, the outflow of cash will occur. Sound decision making
requires that the cash flows which a firm is expected to give up over period should be
logically comparable. In fact, the absolute cash flows which differ in timing and risk
are not directly comparable. Cash flows become logically comparable when they are
appropriately adjusted for their differences in timing and risk. The recognition of the
time value of money and risk is extremely vital in financial decision making. If the
timing and risk of cash flows is not considered, the firm may make decisions which
may allow it to miss its objective of maximizing the owner’s welfare. The welfare of
owners would be maximized when Net Present Value is created from making a
financial decision. It is thus, time value concept which is important for financial
decisions.
Thus, we conclude that time value of money is central to the concept of finance. It recognizes
that the value of money is different at different points of time. Since money can be put to
productive use, its value is different depending upon when it is received or paid. In simpler
terms, the value of a certain amount of money today is more value tomorrow. It is not
because of the uncertainty involved with time but purely on account of timing. The difference
in the value of money today and tomorrow is referred as time value of money.
Financial Management , BBA & B.com, School of Commerce , Presidency University Page 1
Meaning :
 The difference in the value of money today and tomorrow is referred as Time value of
money.
 The time value of money (TVM) is the concept that money you have now is worth
more than the identical sum in the future due to its potential earning capacity.
Need or Reason for time value of money
 Risk and uncertainty: Future is always uncertain and risky. Outflow of cash is in our
control as payments to parties are made by us. There us no certainty for future cash
inflows. Cash inflows are dependent out on our creditors, Bank etc. As an individual
or firm is not certain about future cash receipts, it prefers receiving cash now.
 Inflation: In an inflationary economy, the money received today has more purchasing
power than the money to be received in future. In other words, a rupee today
represents a greater real purchasing power than a rupee a year hence.
 Consumption: Individuals generally current consumption to future consumption.
 Investment opportunities: An investor can profitably employ a rupee received today,
to give him a higher value to be received tomorrow or after a certain period of time.
Thus, the fundamental principle behind the concept of time value of money is that, a sum of
money received today, is worth more than if the same is received after a certain period of
time. For example, if an individual is given an alternative either to receive 10,000 now or
after one year, he will prefer 10,000 now. This is because today, he may be in a position to
purchase more goods with this money than what he is going to get for the same amount after
one year. Thus, time value of money is a vital consideration in making financial decision. Let
us take some examples:
Valuation concepts
The time value of money establishes that there is a preference of having money at present
than a future point of time. It means that a person will have to pay in future more for a rupee
received today. For example: suppose your father gave you 100 on your tenth birthday. You
deposited this amount in a bank at 10% rate of interest for one year. How much future sum
would you receive after one year? You would receive 110.
Future sum = Principal + Interest
= 100 + 0.10 × 100 = 110
What would be the future sum if you deposited 100 for two years? You would now receive
interest on interest earned after one year.
Future sum = 100 × 1.10 = 121
We express this procedure of calculating as Compound Value or Future Value of a sum. A

person may accept less today, for a rupee to be received in the future. Thus, the inverse of
compounding process is termed as discounting. Here we can find the value of future cash
flow as on today.
Techniques of time value of money
There are two techniques for adjusting time value of money. They are:
 Compounding Techniques/Future Value Techniques

 Discounting/Present Value Techniques
Compounding Techniques/Future Value Technique
In this concept, the interest earned on the initial principal amount becomes a part of the
principal at the end of the compounding period.
Formula to Calculate Future value :

FV=PV(1+r)n
FV=Future Value
PV =Present Value
r = Rate of Interest
n= Number of Years
The value of money at a future date with a given interest rate is called future value. Similarly,
the worth of money today that is receivable or payable at a future date is called Present
Value.
Case 1 : Annual Compounding
1.Find out the value of a sum of Rs.2000 after a year with a time Preference of 12%
(Ans :2240)
Soln: Formula to Calculate Future value :

FV=PV(1+r)n
FV=2000(1+0.12)1
FV =2000 (1.12)1
FV=2000 (1.12)
FV=2240
2. Mr.X a Finance Manager in ABC Limited invests surplus funds of Rs.10,000 in a

nationalized bank at 10% compound interest per annum .How much Mr.X Will have after 5
years .

FV=PV(1+r)n
FV=10,000(1+0.1)5
FV =10,000 (1.1)5
FV=10,000 (1.6105)
FV=16,105
3.Mr.ABC a Fund Manager in xyz Limited invests funds of Rs.50,000 in a MF Company at

12% compound interest per annum .How much Mr.ABC Will have after 6 years .

FV=PV(1+r)n
FV=50,000(1+0.12)6
FV =50,000 (1.12)6
FV=50,000 (1.9738)
FV=98,691 +99 or -99
4.X invests Rs.3000 for 3 years in a savings account that pays 10% interest p.a .Calculate the
future value

FV=PV(1+r)n
FV=3,000(1+0.1)3
FV =3,000 (1.1)3
FV=3,000 (1.331)
FV=3993
6.Find out the future value of Rs.1600 ,received after 2 years at 10% preference rate .

FV=PV(1+r)n
FV=1600(1+0.1)2
FV =1600 (1.1)2
FV=1600 (1.21)
FV=1936
7. Calculate the future value for 20,000 deposited in bank for a period of 5 years @ 12% p.a .

FV=PV(1+r)n
FV=20,000(1+0.12)5
FV =20,000 (1.12)5
FV=20,000 (1.7623)
FV=35,246
8.Arun makes a deposit of Rs.10,000 in a bank which pays 8% interest compounded annually
for 8 years . You are required to find out the amount which is to received by him after 8 years

FV=PV(1+r)n
FV=10,000(1+0.08)8
FV =10,000 (1.08)8
FV=10,000 (1.8509)
FV=18,510
Case 2 : Multiple compounding or Intra Compounding
When interest is compounded more than once a year, this affects both future and present-
value calculations. With intra-year compounding, the periodic interest rate, instead of being
the stated annual rate, becomes the stated annual rate divided by the number
of compounding periods per year.
Interest can be compounded monthly, quarterly and half yearly. If compounding is quarterly,
annual interest rate is to be divided by 4 and the number of years is to be multiplies by 4.
Similarly, if monthly compounding is to be made, annual interest rate is to be divided by 12
and number of years is to be multiplied by 12.
Formula to be used under Multiple Compounding or Intra compounding are as follows :
a)When Interest is payable half yearly (Semi-annually i.e 2 )
FV =PV(1+r/2)2n
a)When Interest is payable Quarterly (4 )
FV =PV(1+r/4)4n
a)When Interest is payable monthly (12 )
FV =PV(1+r/12) 12n
a)When Interest is payable Daily (365 )
FV =PV(1+r/365)365n
Problems :
1.Calculate the Future value of Rs.4000 which is invested for 4 years and the interest on it is
compounded at 12% p.a Find out the compounded value for half yearly and quarterly .
Given (1.06)8 =1.594
Soln: Formula= a)When Interest is payable half yearly
FV =PV(1+r/2)2n
FV=4000(1+0.12/2)2x4
FV=4000(1+0.06)8
FV=4000(1.06)8
FV=4000(1.594)
FV=6376
FV =PV(1+r/4)4n
FV=4000(1+0.12/4)4x4
FV=4000(1+0.03)16
FV=4000(1.03)16
FV=4000(1.6047)
FV=6419
2.Calculate the future value of Rs.7000 invested for 5 years at a rate of interest of 15%
compounded half yearly .According to Compound table , compound value factor for Re.1 in
5 years at rate 15%.
Soln: Formula= a)When Interest is payable half yearly
FV =PV(1+r/2)2n
FV=7000(1+0.15/2)2x5
FV=7000(1+0.075)10
FV=7000(1.075)10
FV=7000(2.061)
FV=14,427
3.Mrs,Paru deposited Rs.6000 in bank for 5 years and the interest on it is compounded at
10% p.a . if interest is calculated quarterly (Given (1.025)20 = 1.637
Calculate the future value quarterly .
FV =PV(1+r/4)4n
FV=6000(1+0.1/4)4x5
FV=6000(1+0.025)20
FV=6000(1.025)20
FV=6000(1.637)
FV=9822
4.Calculate the future value of Rs.9000 is invested for a period of 5 years at 12% p.a Interest
Compounded quarterly .Find out FV . Given (1.03)20 =1.806
FV =PV(1+r/4)4n
FV=9000(1+0.12/4)4x5
FV=9000(1+0.03)20
FV=9000(1.03)20
FV=9000(1.806)
FV=16,254
5.Indian bank pays 12% interest compounded Quarterly if Rs.1,000 is made as an initial
Deposit , How much it will be in terms of growth at the end of 5th year.
FV =PV(1+r/4)4n
FV=1000(1+0.12/4)4x5
FV=1000(1+0.03)20
FV=1000(1.03)20
FV=1000(1.806)
FV=1806
Case 3 : The future value of annuity of cash flows or series of equal cash flows
Even Cash flows of a certain period of time is known as “Annuity”.
In other words Annuity is a fixed payment or receipt each year for a specified number of
years .
The future value of Annuity can be calculated by using Annuity table as well as by adopting a
formula :
FVA =A x CFA (r,n)
OR
FVA =R(1+i)n-1 + R(1+i)n-2+ R(1+i)n-3+ R(1+i)n-4+ R(1+i)n-5 …………
FVA = Future value of Annuity
R= Principal Amount
i= rate of Interest
n=Number of years
FVA = Future value of Annuity
1.Calculate the FVA of Rs.5000 deposited at the end of each year at 6% for a period of 5
years .
Soln:
FVA =R(1+i)n-1 +R(1+i)n-2+R(1+i)n-3+R(1+i)n-4+R(1+i)n-5
FVA =5000(1+0.06)5-1 +5000(1+0.06)5-2+5000(1+0.06)5-3+5000(1+0.06)5-4+5000(1+0.06)5-5
FVA =5000(1.06)4 +5000(1.06)3+5000(1.06)2+5000(1.06)1+5000(1.06)0
FVA =5000(1.26) +5000(1.19)+5000(1.12)+5000(1.06)+5000(1)
FVA =6300 +5950 +5600 +5300 +5000
FVA =28,150
2.Mr.Kumar deposits Rs.6000 at the end of every year for 5 years and the deposit earns
compound interest at 12% p.a. Determine how much money will he have at the end of five
years under Future value of Annuity Method .(Ans : 38,040)
Soln:
Formula : FVA =R(1+i)n-1 + R(1+i)n-2+ R(1+i)n-3+ R(1+i)n-4+ R(1+i)n-5
FVA= 6000(1+0.12)5-1 + 6000(1+0.12)5-2+ 6000(1+0.12)5-3+ 6000(1+0.12)5-4+

6000(1+0.12)5-5
FVA= 6000(1.12)4 + 6000(1.12)3+ 6000(1.12)2+ 6000(1.12)1+ 6000(1.12)0
FVA= 6000(1.57) + 6000(1.40)+ 6000(1.25)+ 6000(1.12)+ 6000(1)
FVA= 9420 + 8400+ 7500+ 6720+ 6000
FVA=38,040
3.Calculate the future value of annuity of Rs.4000 deposited at the end of each year at 6% for
a period of five years .
Soln:
FVA= 4000(1+0.06)5-1 + 4000(1+0.06)5-2+ 4000(1+0.06)5-3+ 4000(1+0.06)5-4+

4000(1+0.06)5-5
FVA= 4000(1.06)4 + 4000(1.06)3+ 4000(1.06)2+ 4000(1.06)1+ 4000(1.06)0
FVA= 4000(1.26) + 4000(1.19)+ 4000(1.12)+ 4000(1.06)+ 4000(1)
FVA= 5040 + 4760+ 4480+ 4240+ 4000
FVA=22,520
4.Mr.Manju deposits Rs.3000 at the end of every year for five years in his savings account
paying 6% interest compounded annually .He wants to determine how much money he will
have at the end of 5 years under FVA .
Soln:
FVA= 3000(1+0.06)5-1 + 3000(1+0.06)5-2+ 3000(1+0.06)5-3+ 3000(1+0.06)5-4+

3000(1+0.06)5-5
FVA= 3000(1.06)4 + 3000(1.06)3+ 3000(1.06)2+ 3000(1.06)1+ 3000(1.06)0
FVA= 3000(1.26) + 3000(1.19)+ 3000(1.12)+ 3000(1.06)+ 3000(1)
FVA= 3780 + 3570+ 3360+ 3180+ 3000
FVA=16,890
UNEVEN CASH FLOWS
5.Calculate the future value at the end of 4 years of the following series of payments at 9%
rate of interest
Rs.1000 at the end of first year
Rs.2000 at the end of second year
Rs.3000 at the end of third year
Rs.4000 at the end of fourth year.
Soln:
Formula : FVA =R1(1+i)n-1 + R2(1+i)n-2+ R3(1+i)n-3+ R4(1+i)n-4
FVA =1000(1+0.09)4-1 + 2000(1+0.09)4-2+3000(1+0.09)4-3+4000(1+0.09)4-4
FVA =1000(1.09)3 + 2000(1.09)2+3000(1.09)1+4000(1.09)
FVA =1000(1.29) + 2000(1.18)+3000(1.09)+4000(1)
FVA=1290+2360+3270+4000
FVA=10,920
6.Calculate the future value at the end of 4 years of the following series of deposits at 8% rate
of interest
Rs.8000 at the end of fourth year.(21,620)
7.Calculate the future value at the end of 5 years of the following series of deposits at 9% rate
of interest
Rs.4000 at the end of fourth year.
Rs.5000 at the end of fifth year.(16,920)
Discounting or present value concept
Present value is the exact opposite of future value. The present value of a future cash inflow
or outflow is the amount of current cash that is of equivalent value to the decision maker.
Determining the present value :
The process of determining present value of a future payment or receipts or a series of future
payments or receipts is called discounting.
The compound interest rate used for discounting cash flow is also called the discount rate.
The formula used to determine the Present value as follows :
Present Value :
Case 1:Present value of Single Cash flows
PV=FV/(1+r)n
1.Find out the present value of Rs.3000 received at the end of the year, if the discount rate is
9% p.a.
Soln : PV=FV/(1+r)n
FV =3000
r=9% or 0.09
N=1
PV=3000/(1+0.09)1
PV=3000/1.09
PV=2752/-
2.Calculate the present value of a sum of Rs.50,000 received after two years , if the discount
rate is 8% p.a.
Soln : PV=FV/(1+r)n
FV =50,000
R=8% or 0.08
N=2
PV=50,000/(1+0.08)2
PV=50,000/1.17
PV=42,735/-
3.Calculate the present value of a sum of Rs.25 ,000 to be received after 4 years at a discount
of 10%.
PV=25,000/(1+0.10)4
PV=25,000/1.46
PV=17,123/-
Ans : 17,123/-
Case 2: Multiple Compounding or Intra Compounding
PV=FV/(1+r/m)mn
PV =Present Value
R=Rate of Discount
M=Maturity/Multiple
N=Number of years
1.Find out the present value of Rs. 10,000 receivable after 3 years at the rate of 12% interest.
Calculate semi-annually (Half Yearly).
Soln : PV=FV/(1+r/m)mn
PV=10,000/(1+0.12/2)2x3
PV = 10,000/(1+0.06)6
PV=10,000/(1.42)
PV=7042/-
2.Find out the present value of Rs. 10,000 receivable after 3 years at the rate of 10% interest
quarterly and semiannually.
Quarterly =7462/-
Semiannually =7462/-
3.Find out the present value of Rs.12,000/- receivable after 3 years at the discount rate of
12% . Calculate quarterly and semi annually.
Quarterly :8,451/-
Semi Annually :8,451/-
Soln : PV=FV/(1+r/m)mn
PV=12,000/(1+0.12/2)2x3
PV=12,000/(1+0.06)6
PV=12,000/(1.06)6
PV=12,000/1.42
PV=8451/-
Case 3 : Present value of Annuity or A Series of equal or even future cash flows
If a Investor expect uniform cash flows over a period of time at a definite discount rate , such
cash flows present value which will always be less , when compared to the future cash flows
.It can be determined by using the following formula :
𝑃1 𝑃1 𝑃1 𝑃1
PVA : (1+𝑟)1+(1+𝑟)2+(1+𝑟)3+(1+𝑟)4…….to the n numbers
PVA =Present value of Annuity
P1 =Uniform series of Payments
r = Discount rate or Interest rate
1.Find out the present value of Annuity receipt of Rs.4000 received for 4 years at the rate of
8% discount rate.
𝑃1 𝑃1 𝑃1 𝑃1
PVA : (1+𝑟)1+(1+𝑟)2+(1+𝑟)3+(1+𝑟)4
4000 4000 4000 4000

PVA =(1+0.08)1+(1+0.08)2+(1+0.08)3+(1+0.08)4
4000 4000 4000 4000
PVA=(1.08)1+(1.08)2+(1.08)3+(1.08)4
4000 4000 4000 4000

PVA= 1.08 + 1.17 + 1.26 + 1.36
PVA=3,704 +3,419+3,175 +2,941
PVA=13,239/-
2.Find out the present value of a 5 years annuity of Rs.10,000 discounted at 9%.
Soln : 38,927/-(38,828-39,026)
3.Find out the present value of an annuity receipt of Rs.7000 received for 5 years at the rate
of 12 % discount rate .
Soln:25,285/-
In case of multiple compounding period or intra compounding
𝑃1 𝑃1 𝑃1 𝑃1
PVA : (1+𝑟/𝑚)𝑚𝑛+(1+𝑟/𝑚)𝑚𝑛+(1+𝑟/𝑚)𝑚𝑛+(1+𝑟/𝑚)𝑚𝑛
Mn= mn in the outer column is power
1. An Investor deposits Rs.10,000 at the end of each year for 5 years at the rate 8% p.a ,
interest compounded half yearly. Find out the present value of an annuity .
PVA =?
P1=10,000
R=8%
N=5 year
M=2 times
𝑃1 𝑃1 𝑃1 𝑃1 𝑃1
PVA : (1+𝑟/𝑚)𝑚𝑛+(1+𝑟/𝑚)𝑚𝑛+(1+𝑟/𝑚)𝑚𝑛+(1+𝑟/𝑚)𝑚𝑛+(1+𝑟/𝑚)𝑚𝑛
10,000 10,000 10,000 10,000 10,000

PVA : (1+0.08/2)1𝑥2+(1+0.08/2)2𝑥2+(1+0.08/2)3𝑥2+(1+0.08/2)4𝑥2+(1+0.08/2)5𝑥2
10,000 10,000 10,000 10,000 10,000

PVA : (1+0.04)2+(1+0.04)4+(1+0.04)6+(1+0.04)8+(1+0.04)10
10,000 10,000 10,000 10,000 10,000

PVA : (1.04)2+(1.04)4+(1.04)6+(1.04)8+(1.04)10
10,000 10,000 10,000 10,000 10,000
PVA : + + + +
1.08 1.17 1.26 1.37 1.48
PVA =9,259 +8,547 +7,936 +7,299+6,756
PVA=39,797/-
2. Mr.Ranga rajan deposits Rs.30,000 at the end of each year for 6 years at the rate 10% p.a ,
interest compounded half yearly. Find out the present value of an annuity. (1,30,138)
3. Mr. Anand will deposit Rs.25,000 at the end of each year for 4 years at the rate 12% p.a ,
interest quarterly . Find out the present value of an annuity. (75,098)
Present value of Uneven future cash flows
It can be determined the present value of uneven cash flows by using the following formula :
𝑃1 𝑃2 𝑃3 𝑃4 𝑃5
PVUECF =(1+𝑟)1+(1+𝑟)2+(1+𝑟)3+(1+𝑟)4+(1+𝑟)5
PVUECF =Present value of uneven cash flows
P1,P2,P3=Uneven cashflows
R= Discount rate
1.Calculate the present value of the following series of payments made at the end of each
year for a period of 5 years at 8% discount rate.
Cash flow at the end of 1st year – Rs.2,000
Cash flow at the end of 2nd year – Rs.4,000
Cash flow at the end of 3rd year – Rs.6,000
Cash flow at the end of 4th year – Rs.8,000
Soln:
𝑃1 𝑃2 𝑃3 𝑃4 𝑃5
PVUECF =(1+𝑟)1+(1+𝑟)2+(1+𝑟)3+(1+𝑟)4+(1+𝑟)5
2000 4000 6000 8000 10,000

PVUECF =(1+0.08)1+(1+0.08)2+(1+0.08)3+(1+0.08)4+(1+0.08)5
2000 4000 6000 8000 10,000
PVUECF =(1.08)1+(1.08)2+(1.08)3+(1.08)4+(1.08)5
2000 4000 6000 8000 10,000

PVUECF = 1.08 + 1.17 + 1.26 + 1.36 + 1.47
PVUECF=1,852+3,419+4,761+5,882+6,803
PVUECF =22,717/-
2. Calculate the present value of the following series of payments made at the end of each
Factors (1.08 ,1.17 ,1.26 ,1.36, 1.47)

Soln :23,429/-
(Factors :1.09 ,1.19 ,1.29 ,1.41 ,1.54)
Soln :11,022/-
year for a period of 5 years at 12% discount rate .
Soln :46,145/-
DOUBLING PERIOD: - The doubling time is the period of time required for a quantity to
double in size or value. It is applied to population growth, inflation and resource extraction,
consumption of goods, compound interest, the volume of malignant turnovers, and many
other things which tend to grow over time. When the relative growth rate is constant, the
quantity undergoes exponential growth and has a constant doubling time or period which can
be calculated directly from the growth rate.
The doubling time formula is used in Finance to calculate the length of time required to
double an investment or money in an interest bearing account.
log⁡(2)
Doubling Time = log(1+r)
r = rate of return
it is important to note that r in the doubling time formula is the rate per period. If one
wishes to calculate the amount of time to double their money in a money market account that
is compounded monthly, then r needs to express the monthly rate and not the annual rate. The
monthly rate can be found by diving the annual rate by 12. With this situation, the doubling
time give the number of months that it takes to double money and not years.
CONCEPT OF VALUATION
valuation is the process of determining the current worth of an asset or company. There
are many techniques that can be used to determine value, some are subjective and others are
objective. Judging the contribution of a company’s management would be more of a
subjective valuation technique, while calculating intrinsic value based on future earnings
would be an objective technique.
Asset valuation is commonly performed prior to the sale of an asset or prior to purchasing
insurance for an asset. Asset valuation may consist of both subjective and objective
measurements. For example, in valuing a company there is no number on the company’s
financial statements that tells how much its brand name is worth; this aspect of asset
valuation must be subjective. On the other hand, net profit is an objective measurement based
on the company’s income and expense figures. Common methods for determining an asset’s
value include comparing it to similar assets and evaluating its cash flow potential.
Acquisition cost, replacement cost and deprival value are also methods of asset valuation.
BOND: - A bond is a long-term security issued by an organization which does not carry a
risk for the investors. The rate of interest is generally fixed and known to investors. Usually,
bonds are issued by government where in will be risk free investments and always honor
obligations on its bonds.
In India, there is no distinction between bond or debenture whereas in U.S.A., bonds are
secured by tangible assets of the company and debentures are secured only by the general
creditworthiness of the company. A company in India can issue secured or unsecured
debentures. The private sector companies also issue bonds which are also called debentures in
India. Bonds issued by public sector companies in India are generally secured but they are
free from risk.
FEATURES OF BOND; -
The bond in denture is the contract between the issuer (the borrower) and the bond holder
(the lender), which sets forth all the obligations of the issuer. It usually specifies the interest
rate, maturity date, convertibility and other terms.
Important features of bonds are:
1.Par value: The value of bond is termed as face value, par value or maturity value. A bond
is generally issued at a par value of Rs. 100, Rs. 500 or Rs. 1000 and interest is paid on face
value.
2.Maturity: A bond is usually issued for a specified period of time. The time specified in the
bond is called the Maturity date or date of re-payment of principal amount. The bonds can be
issued at varying maturity period. It could be for long term, medium term or short term
depending on the requirement of each organization.
3.Call: Bonds have an additional feature of call function. This is a privilege to the issuing
company of re-purchase bonds at a slightly higher price above the Par value.
4. coupon rate: The interest rate is also called as Coupon rate. Interest rates are fixed and
known to bond holders. Interest paid on bond is tax deductible. Interest on bond may be paid
by cheque or coupons are detachable. certificates of interest.
5.Redemption: The value that a bond holder receives at the time of maturity is called
redemption value or maturity value. A bond can be redeemed at par or at a premium (more
than par value).
6.Market value: A bond may be traded in stock exchange. The price at which it is currently
sold or bought is called the market value of the bond. Market value may be different from par
value or redemption value.
TYPES OF BONDS
The following list gives information about the various types of bond giving its importance:
Serial bonds: it is issued by an organization with different maturity dates so that it enables
the company to retire the bonds in instalment rather than altogether. The advantages of this
bond will make bondholder to select a bond of maturity date which will match his financial
portfolio. He has an option of selecting short term bonds or long-term bonds. It is usually
does not have any call feature. It resembles sinking fund and have an effect on the yield of
bond.
Sinking fund bond: A company which issues bond wherein it does not take burden at the
time of retiring bond. This bond has an advantage of using the funds are well as retiring them
without any excessive liquidity problems. The company sets apart an amount annually for
retirement of bonds. The annual instalment is usually fixed and put into sinking fund by
trustees. The funds invested are at trustee’s discretion. He may use the funds to call bonds
year or buy bonds from the
Registered Bond: It protects the owner from loss of principal. The bondholder’s bond
numbers, name, address and type of bond are entered in the register of the issuing company.
The bondholder has to fulfil the firm’s formalities at the time of transfer of bonds. While
receiving interest, registered bondholders usually get their payment by cheque. The main
advantages of registering a bond is that if the bond is lost the bondholder does not suffer loss
unlike the unregistered bonds. However, registered bonds do not offer security of principal at
maturity.
Debenture Bond: debenture bonds are issued by those companies who have an excellent
credit rating but do not have security in the form of assets to pledge to the bondholders. The
debenture holder are creditors of the firm and receive the rate of interest whether the
company makes a profit or not.
In Indian context the debentures can be issued with the specific permission of controller of
capital issues. Bearer debentures are not considered legal and permissible documents in India.
Convertible debentures have lower rate of interest and hence it has become an attractive
investment in recent years. Permission has to be sought for the convertibility for the
individual whereas it is not necessary for financial institutions.
Mortgage Bond: a mortgage bond is a promise by the bond issuing authority to pledge the
real property as additional security. In case if the company fails to pay its bond holders the
interest of the principal, when it falls due, the bond holder has the right to sell the security
and get back their dues. The value of the mortgage bond depends upon the quality of property
mortgage and the kin of charge on property. A first charge is the most suitable and highly
secure form of particular investment since its claims will be priority of the asset. A second
and third charge on security of property is considered to be a weak from of security and is
less sound and is less sound than first charge.
Mortgage bonds may be open end, close end and limited open end. An open end mortgage
bond permits the bond issuing company to issue additional bonds if earnings and asset
coverage make it permissible to do so. In close end mortgage bonds the company can make
only one issue of bonds and when those bonds exist, new bonds cannot be issued. If the
additional bonds are issued they get the ranking of junior bonds and the prior issue gets the
first priority in receiving payments. The limited open end bonds permit the organization to
issue specified number of fresh bonds series distributed over a number of years.
Collateral Trust Bond: it is generally issued when the two companies exist and are in
relationship of parent and subsidiary. The collateral is provided in the form of personal
property of the company which issues the bond. A typical example of bonds is when a parent
company requires funds. It issues collateral bonds by pledging securities of its own subsidiary
company. The collaterals are generally in the form of intangible securities like bonds. These
bonds have a priority charge on the bonds which are used as collaterals.
Equipment Trust Bond: the usual method of using these bonds was to issue 20% equity and
80% bonds. The equity issue is like a reverse to protect the lender in cases where the value of
the asset falls in the market. The trustee also has the right to sell the equipment and pay the
bondholders in caser of default.
Supplemental credit bonds: while issuing bonds an additional pledges is guaranteed to

bondholders and their bonds are categorized as supplemental by an additional nonspecific
guarantee. They are:
a. Guaranteed bond: these type of bonds are bonds which are secured by the issuing
company and they are guaranteed by another company. At times a company takes
asses through a lease. The leasing company guarantees the bonds regarding interest
and principal amount due on bonds.
b. Joint bond: these bonds are guaranteed bonds secured jointly by two or more
companies. Bonds are issued when two or more companies are in need of investment
and decide to raise the funds together through bonds. The company raised funds at
reduced cost. The investor is in a favourable position as he has security by pledge of
two companies.
c. Assumed bond: the bonds issued during merging of two companies wherein
company A decides to merge into company B. A’s issues of bonds prior to merge then
becomes the obligation of company B when merger is affected. These are called
assumed bonds as company A did not originally issue them but as a result of merger
the debt was passed on them. The bondholder receives an additional pledge from
company B. He is more secured as his bonds due to merger get the security of both
companies A and B.
Convertible bond: it is right given to a bondholder to buy a bond at the time of issue and
later exchange it with equity shares of the same company. This gives the bondholder a future
promise by the issuing company to share the growth in capital of the company. The price of
the convertible bonds to share the growth in capital of the company. The price of the
convertible bonds to a great extent depends on the price of equity shares. The bond price
increases if the price of equity shares rises and vice versa. The convertible bond has the scope
of exchange into common stock at a future date the specification regarding date of conversion
into equity and the interest at which it will be converted is usually in the form of written
clause. Generally, convertible bond is considered as a trade-off between “the provision of
security and expected future appreciation.
Debentures: the word ‘debenture’ is used to signify the acknowledgment of a debt given
under the seal of the company and containing a contract for the repayment of the principal
sum at a specified date and for the payment of interest (usually half yearly) at a fixed rate
until the principal sum is repaid and it may or may not give a charge in the assets of the
company as security for the loan.
A debenture is a long-term debt instrument issued by governments and big institutions for
the purpose of raising funds. The debenture has some similarities with bonds but the terms
and conditions of securitization of debentures are different from that of a bond. A debenture
is regarded as an unsecured because there are no pledges (guarantee) available on particular
assets.
Meaning of debentures: debenture refers to a certificate of agreement of loans which is

given under the company’s stamp and carries an undertaking that the debenture holder will
get a fixed return (fixes on the basis of interest rates) and the principal amount whenever the
debenture matures.
Definition: section 2(12) of the companies Act states that “a debenture includes debenture
stock, bonds and any other securities of a company, whether constituting a charge on the
assets of the company or not”.
Features of Debentures
Following are the features of debentures:
1. Debentures holders of the company are the creditors of the company and not the
owners of the company.
2. Capital raised by way of debentures is required to be repaid during the life time of the
company at the time stipulated by the company. Thus, it is not a source of permanent
capital.
3. Debentures are generally secured.
4. Return paid by the company is in the form of interest which is predetermined.
5. Debentures are very risky from company’s point of view for raising long term funds.
6. Risk on the part of debenture holders is very less.
7. Debenture holders do not carry any voting rights.

8. Debentures are a cheap source of funds from the company’s point of view.
9. Debentures are instruments in writing acknowledgement of the debt of the company
to the holder of the instrument.
10. Debentures are always made under the seal of the company. However a certificate
that has been signed by two or more directors of the company but carries no seal is
considered a valid debenture document.
11. The owner of the instrument is not an owner of the company but merely its creditor
for the amount mentioned in the acknowledgment.
12. The interest needs to be paid to the debenture holder on a specified rate by a specified
time.
13. The holder of debenture documents is entitled to get regular interest from the
company. This continues even in case where the company has incurred losses.
14. All the debentures ae redeemed on due date. In case of winding up of the company,
debenture holders are repaid after payment to shareholders are made.
15. Debenture can be converted into equity share by the issuing company.
Types of Debentures
Debentures can be classified into the following ways:
1. Non-convertible debentures (NCD): these instruments retain the debt character and
cannot be converted in to equity shares.
2. Party convertible debentures (PCD): a part of these instruments are converted into
equity shares in the future at notice of the issuer. The issuer decides the ratio for
conversion. This is normally decided at the time of subscription.
3. Fully convertible debentures (FCD): these are fully convertible into equity shares at
the issuer’s notice. The ratio of conversion is decided by the issuer upon conversion
the investors enjoy the same status as ordinary shareholders of the company.
4. Optionally convertible debentures (OCD): the investor has the option to either
convert these debentures into shares at price decided by the issuer/agreed upon at the
time of issue.
On basis of security, debentures are classified into the following ways:
5. Secured debentures: these instruments are secured by a charge on the fixed assets of
the issuer company. So if the issuer fails on payment of the principal or interest
amount, his assets can be sold to repay the liability to the investors.
6. Unsecured debentures: these instrument are unsecured in the sense that if the issuer
defaults on payment of the interest or principal amount, the investor has to be along
with other unsecured creditors of the company.
7. Registered debentures: these are those debentures which are registered in the
register of the company. The names, addresses and particulars of holdings of
debenture holders are entered in a register kept by the company. Such debentures are
treated as non-negotiable instruments and interest on such debentures are payable
only to registered holders of debentures. Registered debentures are also called as
debentures payable to registered holders.
8. Bearer debentures: these are those debentures which are not registered in the register
of the company. Bearer debentures are like a bearer cheque. They are payable to the
bearer and are deemed to be negotiable instruments. They are transferrable by mere
delivery. No formality of executing a transfer deed is necessary. When bearer
documents are transferred, stamp duty need not be paid. A person transferring a
bearer debenture need not give any notice to the company to his effect. The transferee
who acquires such a debenture in due course bonafide and for available consideration
gets good title not withstanding any defect in the title of the transferor. Interest
coupons are attached to each debenture and are payable to bearer.
9. Redeemable debentures: these debentures are issued by the company for a specific
period only. On the expiry of period, debenture capital is redeemed or paid back.
Generally the company creates a special reserve account know as “Debenture
Redemption Reserve Fund” for the redemption of such debentures. The company
makes the payment of interest regularly. Under section 121 of the Indian Companies
Act, 1956, redeemed debentures can be re-issued.
10. Irredeemable debentures: these debentures are issued for an indefinite period
which is also know as perpetual debentures. The debenture capital is repaid either at
the option of the company by giving prior notice to that effect or at the winding up of
the company. The interest is regularly paid on these debentures. The principal amount
is repayable only at the time of winding up of the company. However, the company
may decide to repay the principal amount during its lifetime.
11. Mortgage debenture: a mortgage debenture is one which is secured by a mortgage
on the real property of the company. If the company fails to repay the borrowed
amount at a specified period, the debenture holder has a legal right to sell the property
and recovered the loan.
12. Naked debenture: in general the term debenture in British usage designates any
security issued by companies other than their shares, including, therefore, what are in
the united states commonly called bonds. When used in the united states debenture
generally designates an instruments secured by a floating charge junior to other
charges secured by fixed mortgages or specify, one of a series of securities secured by
a group of securities held in trust for the benefit of the debenture holders.
13. Agency debentures: the market place appears to believe that GSE Agency
debentures carry an implicit guarantee from the united states government. This is due
to the GSE’s direct borrowing ability from the U.S. Treasury and the importance of
the GSE’s congressional charters and missions.
Advantages of Debentures
1. Control of co. is not surrendered to debenture holders because they don’t have any
voting rights.
2. Trading on equity is possible as debenture holders get a lower rate of return than the
earnings of the company.
3. Interest on debenture is an allowable expenditure under income tax act, hence
incidence of tax on the company is decreased.
4. Debenture can be redeemed when company has surplus funds.
Disadvantages of Debentures
1. Cost of raising capital through debentures is high of high stamps duty.

2. Common people cannot buy debenture as they are on high denominations.
3. They are not meant for companies earning greater than the rate of interest which they
are paying on the debentures.
DIFFERENCE BETWEEN SHARES AND DEBENTURES
Basis Shares Debentures
Capital A share is a part of equity or A debenture is a part of loan

preference share capital of a capital of the company. The holder
company. The holders of the shares of a debenture is the creditor of the
may be described as part owner of company.
the company.
Return Return on share is known as Return on a debenture is known as

dividend. A company declares interest and the company
divided only when there are profits compulsorily pays it at a fixed rate
and its rate may vary from year. whether there are profits or losses.
Appropriation dividend is an appropriation of profit Interest on debenture is a charge

and is therefore debited in profit & against profits and is therefore
loss appropriation account. debited in profit & losses.
Charge Shares do not create any charge on Debenture create a charge on the
the assets of the company. asset of the company.
Property
Redemption normally the share capital is not The amount of debenture has to be
returned during the lifetime of the returned after a stipulated period of
company. time as per the conditions of issue.
Discount Shares can be issued at discount only There are no restriction on issue of
when the conditions lay down in debentures at a discount.
On issue
section 79 of the companies act 1956
are fulfilled.
Premium on Premium received on issue of shares Premium received on issue of

can be utilised by the company debentures can be utilized by
Issue
subject to the conditions given in company in any manner it likes.
section 78 of the companies Act
1956.
Purchase A company cannot purchase its own A company can purchase own
shares. debentures from the open market.
Convertibility Shares cannot be converted into Debentures can be converted into

debentures. shares according to the conditions
of issue of debentures.
VALUATION OF BONDS OR DEBENTURES
A bond or a debenture is a long-term debt instrument or security. It is issued by business

enterprises or government agencies to raise long-term capital. A bond usually carries a fixed
rate of interest. It is called as coupon payment can be either s=annually or semi-annually.
Valuation of bond refers to a techniques for determining the fair value of a particular
bond. Bond valuation includes calculating the present value of the bond’s future interest
payments, also known as its cash flow and the bond’s value upon maturity also known as its
face value or par value.
Bonds are of two types, viz.,
a) Redeemable bonds
b) Irredeemable bonds
A bond can be irredeemable or redeemable. Redeemable bonds have a fixed maturity date
and irredeemable bonds have perpetual life with only interest payments periodically.
VALUATION OF REDEEMABLE BONDS OR DEBENTURE
1𝐼 2𝐼 I
3 𝐼
4 𝐼5 𝑀 5
1 + (1+𝑑)2 + ⁡ (1+𝑑)3 + (1+𝑑)4 + ⁡ (1+𝑑)5 + ⁡ (1+𝑑)5
PVB =(1+𝑑)
Where,
PVB= present value of the bond
i = interest amount received
d = discount rate
n = number of years
Illustration: 1
Find out the present value of bond if it matures after 4years and yield Rs.80 every year with a
maturity value of Rs.120 and if the capitalization rate is 8%
Solution:
𝐼1 2 𝐼 3 I 4 𝐼 𝑀4
PVB= + (1+𝑑) + ⁡ (1+𝑑) + (1+𝑑) + ⁡ (1+𝑑)4
(1+𝑑)1 2 3 4
80 80 80 80 120
= (1.08)1 + ⁡ (1.08)2 + ⁡ (1.08)3 + ⁡ (1.08)4 + ⁡ (1.08)4
80 80 80 80 120
= 1.08 + 1.17 + 1.26 + 1.36 + 1,36
= 74 + 68 + 63 + 59 + 88
= 352
Illustration: 2
A debenture is available in the market for Rs. 1,000 with Rs.80 as the interest for a year for a
period of 4years with the maturity value of Rs.1,120. The debenture capitalization rate is
10%. Advise Mrs. Mita in her buying decision of this debenture.
Solution:
1 𝐼 2 𝐼 3 4 I 4 𝐼 𝑀
1 + (1+𝑑)2 + ⁡ (1+𝑑)3 + (1+𝑑)4 + ⁡ (1+𝑑)4
= (1+𝑑)
80 80 80 80 1120
= (1.10)1 + ⁡ (1.10)2 + ⁡ (1.10)3 + ⁡ (1.10)4 + (1.10)4
80 80 80 80 80
=1.10 + ⁡ 1.21 + 1.33 + 1.46 + 1.46
=73 + 66 + 60 + 55 + 767
=1,021
VALUATION OF IRREDEEMABLE BONDS OR DEBENTURE
The value of debenture which carries a particular rate of interest for an indefinite period of
time is calculated by using this formula:
𝐼
PVD = 𝐶𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛⁡𝑅𝑎𝑡𝑒
Illustration: 1
What is the value of irredeemable debenture which has Rs.50 as the interest for an infinite
period with the discount rate at 10%.
𝐼 50
Solution: PVD = 𝐶𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛⁡𝑅𝑎𝑡𝑒 = ⁡ 10% = 500
Illustration: 2
What is the value of debenture which has an indefinite period with the interest amount of
Rs.80 per year with the capitalization rate is 6%.
𝐼 80
Solution: PVD = 𝐶𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 = 6% = 1333.33
SHARES
As per the companies Act of 1956, “A Share is a share in the share capital of the
company”.
The total capital of a joint stock company is divided into a number of units of a fixed
value. Each such unit is called a share.
FEATURES OF SHARE
The main features of shares are as follows:
1.Limited liability for shareholders: for each individual shareholders, the maximum value
at risk is the total value of their investment in the shares of the company. This means that,
unlike in a partnership, ordinary shareholders are not personally liable for the debt of a
company in the event of bankruptcy.
2.Loss absorption for other (debt) investors and other creditors: it is important to
understand that shares come last in the ranking of a company’s capital structure and
shareholders only hold a residual claim. This means that in liquidation, shareholders only get
back their money if there is anything left over after creditors have been settled. In most cases,
the shares are usually worthless in the event of bankruptcy or liquidation.
3.Uncertain returns: while many companies pay out dividends to shareholders, there is no
obligation on companies to do so. Indeed, there is no guarantee of returns in any form to
shareholders. However, in return for this degree of uncertainty and risk, shares carry higher
expected returns over the long term than most investments. This forms the basis of the
relationship between risk and return for investors in stocks and shares.
Some other important features of share are given below:
I. A share is not a sum of money. It is only an interest or right, measured in a sum of

money, to participate in the profits of the company during its life and in the assets of
the company when it is wound up.
II. A share is given a face or nominal value, and is paid for in money or money’s worth.
III. The person who holds the share or shares of a company is called a shareholder or
member of the company.
IV. The title of a member to a sharp is evidenced by the share certificate issued by the
company under its common seal.
V. Each share in a company having share capital is distinguished by its specific or
appropriate number.
TYPES OF SHARES
A company issue different types of shares in order to satisfy the requirements of different
classes of investors and to collect more capital. A public company can issue only two types of
shares such as:
1. Preference shares 2. Equity shares
PREFERENCE SHARES
Preference share is a stock with dividend that are paid to shareholders before common
stock dividend are paid out. In the event of a company bankruptcy, preferred stock
shareholders have a right to be paid company assets first. Preference shares typically pay a
fixed dividend, whereas common stocks do not. And unlike common shareholders, preference
shareholders usually do not have voting rights.
Meaning of preference shares
Preference shares are shares, which have preferential rights (i.e., first priority or
preference over other kinds of shares) in respect of payment of dividend during the existence
of the company, and also in respect of repayment or refund if share capital in the events of
the winding up of the company.
FEATURE OF PREFERENCE SHARES
The main features of preference share are as follows:
1. Preference share have been priority over payment of dividend and repayment of
capital.
2. Preferences shares do not hold voting rights.
3. Cumulative preference shares have been a right to claim dividend for those years also
for which there were no profits.
4. The holders of non-cumulating preference shares have no claim for the arrears of
dividend. They are paid a dividend if there are sufficient profits.
5. Redeemable preference shares neither the company can return the share capital nor
can the shareholder demand its repayment.
6. Irredeemable preference shares are the shares which cannot be redeemed unless the
company is liquidates are known as irredeemable preference shares.
Types of preference shares
The preference shares can be classified into the following ways:
1.cummulative preference shares
The holders of cumulative preference share are entitled to receive a fixed percentage of
dividends before anything is given, to other classes of shareholders. Apart from this right in
the case of these shares, if the company has no profits or inadequate profits in any year to
declare dividend, the arrears of dividend would accumulate and become payable out of the
future profits before anything is given to other classes of shareholders.
2.Non-cumulative Preference Shares
Non-cumulative preference shares are entitled to a fixed rate of dividend in the first
instance (i.e., before anything is given to other types of shareholders). But they are entitled to
receive the fixed percentage of dividend in the first instance only for the year or years when
the company earns sufficient profits and dividend is declare dividend , then, the arrears of
dividend do not accumulate and become payable out of future profits in the case of these
shares.
3.Participating Preference Shares
The holders of these shares, in addition to a fixed percentage of dividends are also entitled
to participate in the surplus profits of the company along with the equity shareholders. Only if
there is a specific provision in the articles of association of the company giving the holders of
these shares special rights to participate in the surplus profits. They are also entitled to
participate in surplus assets of the company on its winding up.
4.Non-Participating Preference Shares
The holders of non-participating preference shares will get only a fixed rate of dividend,
of course, in the first instance (i.e., before any dividend is paid to equity shareholders). But
they are not entitled to participate in the surplus profits of the company.
5.Convertible Preference Shares
The holders of convertible preference shares are given the rights to convert their shares
into equity shares later on (i.e., after a certain period).
6.Non-Convertible Preference Shares
The holders of non-convertible preference share are not given the right to convert the
shares into equity shares later on.
7.Redeemable Preference Shares
Redeemable preference shares are those preference shares, which can be redeemed (i.e.,
returned or paid back) even during the existence of the company. These shares can be
redeemed as per the terms of issue either at a definite date after the expiry of a stipulated
(fixed) period or at the option of the company, i.e., whenever the company wants, after giving
proper notice. Redeemable preference shares can. Be redeemed by a company. But their
redemption is subject to the conditions:
i. The articles of association of the company should provide for the issue and
redemption of these shares.
ii. Only fully paid shares can be redeemed. Party paid shares cannot be redeemed.
iii. They can be redeemed only out of the profits of the company which would be
otherwise available for dividend (i.e., out of the divisible profits of the company) or
out of the proceeds of fresh issue of shares made for the purpose of redemption.
iv. Any premium paid on their redemption must be paid out of the profits of the company
or out of the company’s share premium account.
8.Irredemable Preference Shares
Irredeemable preference shares are those share, which are not redeemable (i.e.,
refundable) until the company is wound up.
Advantages of preference shares
1. Helpful in raising long term capital for a company.

2. There is no need to mortgage property on these shares.
3. Redeemable preference shares have the added advantages of repayment of capital
whenever there is surplus in the company.
4. Rate of return is guaranteed.
Disadvantages of Preference shares
1. Permanent burden on the company to pay a fixed rate of dividend before paying
anything on the other shares.
2. Not advantageous to investors from the point of view of control and management as
preferences shares do not carry voting rights.
3. Compared to other fixed interest bearing securities such as debentures, usually the
cost of raising the preference share capital is higher.
EQUITY SHARES
Equity shares are those, which are not preference shares. In other words, these are shares,
which do not enjoy any preferential right either in respect of payment of dividend or in
respect of the repayment of capital at the time of the winding up of the company. These
shares are know as equity shares, as they are the ‘ownership shares’ conferring the ownership
of the company on the holders of these shares, i.e., the holders of these shares are the real
owners of the company.
Meaning of Equity Shares
Equity share refers to the stock of a business entity which represents the original paid into
or invested in the business by its founders. It serves as a security for the creditors of a
business since it cannot be withdrawn to the detriment of the creditors.
Differences between Preference Shares and Equity Shares
There are many differences between preference shares and equity shares are as follows:
Preference Shares Equity Shares
Meaning Preference shares are those shares Shares which bear the risk and
which enjoys preference regarding provide permanent finance are
dividend and repayment of capital. called equity shares.
Repayment Preference shareholders get back Equity capital is not repaid during
their finance during life time of the the life of company.
company and before the equity
shareholders.
Nature of Preference shares enjoys preferential Equity shares do not carry such
preference rights as regards the payment of preferential rights over preference
dividend and return of capital. shares.
Rate of Rate of dividend is fixed at the time Rate of dividend is not fixed but
dividend of issue and changes are not made in flexible. In changes every as per
this rate in due course. the net profit of the company.
Voting Preference shares do not carry Equity shares carry normal voting
rights normal rights, but only under rights.
exceptional circumstances.
Types There are different types of All equity shares are of one type or
preference shares like cumulative, category. They are always
redeemable, irredeemable, irredeemable.
participating and non-participating.
Appeal to Preference shares appeal to relatively Equity shares appeal to

investors less adventurous investors, interested adventurous investors willing to
take risks in their investment.
in fixed, but regular return on

investment.
Face value Relatively higher. Usually Rs.100 Relatively less. Usually Rs.10
capital No capital appreciation is possible Capital appreciation is possible due

to prospects of rising dividends.
Redeemable Preference shares, i.e., redeemable But equity shares are not
preference shares are redeemable redeemable during the life of the
during the existence of the company. company.
BONUS SHARES
Bonus shares are shares issued by a company out of its accumulated reserves or profits
to the existing equity share holders either as fully paid shares or partly paid shares free of
cost.
A bonus share is a free share of stock given to current shareholders in a company, based
upon the number of shares that the shareholder already owns. While the issue of bonus shares
increases the total number of shares issued and owned, it does not increase the value of the
company. Although the total number of issued shares increases, the ratio of number of shares
held by each shareholder remains constant. An issue of bonus shares is referred to as a bonus
issue. Depending upon the constitutional documents of the company, only certain classes of
shares may be entitled to bonus issues, or may be entitled to bonus issues in preference to
other classes.
A bonus issue is a stock spilt in which a company issues new shares without charge in
order to bring its issued capital in line with its employed capital (the increased capital
available to the company after profits). This usually happens after a company has made
profits, thus increasing its employed capital. Therefore, a bonus issue can be seen as an
alternative to dividends. No new funds are raised with a bonus issue.
Unlike a rights issue, a bonus issue does not risk diluting your investment. Although the
earnings per share of the stock will drop in proportion to the new issue, this is compensated
by the fact that you will own more shares. Therefore the value of your investment should
remain the same although the price will adjust accordingly. The whole idea behind the issue
of Bonus shares is to bring the Nominal Share Capital into line with the true excess of assets
over liabilities.
VALUATION OF SHARES
The method of valuation depends on the purpose for which valuation is required.
Generally, there are three methods of valuation of shares.
1.Net Assets Methods of Valuation of Shares
In this method, the net value of assets of the company are divided by the number of shares
to arrive at the value of each share. For determination of net value of assets; it is necessary to
estimate the worth of the assets and liabilities. The goodwill as well as non-trading assets
should also be included in total assets. The following points should be considered while
valuing of shares in this method.
a) Goodwill must be properly valued.

b) The fictitious assets like preliminary expenses, discount on issue of shares and
debentures accumulated losses etc. should be eliminated.
c) Goodwill must be properly valued.
d) The fixed assets should be taken at their realizable value.
e) Provision for bad debts, depreciation etc., must be considered.
f) All unrecorded assets and liabilities if any should be considered.
g) Floating assets should be taken at market value.
h) The external liabilities like sundry creditors, bills payable, loan, debentures etc.,
should be deducted from the value of assets for the determination of net value.
The net value of assets, determined so as to be divided by number of equity shares for
finding out the value of share. Thus the value per share can be determined by using the
following formula:
Value per share = (Net Assets – Preference Share Capital) / No of equity shares.
2.Yield or market value method of valuation of shares
The expected rate of return in investment is denoted by yield. The term rate of return
refers to the return in which a shareholder earns on his investment. Further it can be classified
as
(a) Rate of earning
(b) Rate of dividend
In other words, yield may be earning yield and dividend yield.
(a) Earning yield
In this method, shares are valued on the basis of expected earning and normal rate of
return. The value per share is computed by using the following formula.
Value per share = (Expected rate of earning\normal rate of return) *paid up value of equity
share.
Expected rate of earning = (profit after tax\paid up value of equity share) *10
(b) Dividend yield
In this method shares are valued on the basis of expected dividend and normal rate of
return. The value per share is computed by using the following formula.
Expected rate of divided = (profit available for dividend\paid up equity share capital) *100
4.Earning capacity method of valuation of shares
In this method, the value per share is computed on the basis of disposable profit of the
company.
The disposable profit can be determined by deducting reserves and taxes from net profit.
The following steps are applied for the determination of value per share under earning
capacity.
Step 1: find out the profit available for dividend
Step 2: compute the capitalized value using the formula
Capitalized value = (profit available for equity dividend \ normal rate of return) * 100
Step 3: compute value per share
Value per share = capitalized value \ no. of shares
Illustration – 1
A company is planning to raise finds by making rights issue of equity shares to finance its
expansion. The existing equity share capital of the company is Rs.50,00,000. The market
value of its share is Rs.42. the company offers to its share the right to buy 2 shares at /rs.11
each for every 5 share held. You are required to calculate:
1. Theoretical market price after right issue

2. The value of right
3. % increase in share capital
Solution:
Market value of 5 share already held by a shareholder @ Rs.42 = 210
Add the price to be paid by him for acquiring 2 more shares
@ Rs.11 per share = 22
Total Rs. 232
1. Theoretical market price of one share = 232\7 = Rs.33.14

2. Value of right = market price – theoretical market price = 42 – 33.14 = 33.86
3. % increase in share capital
Present capital = 50,00,000
Right issue Rs.50,00,000 × 2\5 = 20,00,000
% increase in share capital = 20,00,000 \ 50,00,000 × 100 = 40%
Review questions
Conceptual type
1. What is time value of money?

2. What to you mean by future value?
3. Define annuity?
4. What is present value?
5. What is doubling period?
6. State two techniques for adjusting the time value of money.
Analytical type
1. Explain the concept of time value of money.

2. Explain the needs for time value of money.
3. Explain the types of annuities.
PRATICAL PROBLEMS
1. Find out the future value of Rs.4,800 received after two years at 10% time preference
rate.
2. Calculate the future value for 10,000 deposited in bank for a period of 5 years at 12%
p.a. given (1.12)5 = 1.762
3. Calculate the future value of Rs.38,000 invested for 5 years at a rate of interest of
15% compounded half yearly. According to compound table compound value factor
for Rs1 in 5 years at rate 12%.
4. Calculate the future value of Rs.18,000 is invested for a period of 5 years at 12% p.a.
interest compound quarterly. Find out FV given (1.03)20 = 1.806
5. Calculate the future value of annuity of Rs.66,000 deposited at the end of each year at
8% for a period 5 years.
6. Mr. Satish Roy deposited Rs.23,000 at the end of every year for five years and the
deposit earns compound interest @10% p.a. Determine how much money he will
have at the end of 5 years. FVA
7. Calculate the future value at the end of 5 years of the following series of payments at
12% rate of interest.
Rs.2,000 at the end of first year.
Rs.4,000 at the end of second year.
Rs.6,000 at the end of third year.
Rs.8,000 at the end of fourth year.
Rs.10,000 at the end of fifth year.
8. Mr. Saha is to receive Rs.12,000 after 5years from now. His time preference for
money is 2% p.a. calculate the present value. According to discount factor table, the
present value discount factor at 12% p.a. for 5 years for Rs.1 is 0.567. calculation of
present value.
9. Calculate the future value of money at the end of five years of the following series of
payments at 9% rate of interest.
Rs.22,000 at the end of first year.
Rs.23,000 at the end of second year.
Rs.24,000 at the end of third year.
Rs.26,000 at the end of fourth year.
10. Find out the present value of annuity receipt of 7,000 received for 5 years at the rate
of 12% discount rate.
11. Calculate the present value of the following series of payments made at the end of
each year for a period of 5 years at 9% interest rate.
Cash flow at the end of 1st year Rs.1,000
Cash flow at the end of 2nd year Rs.2,000
Cash flow at the end of 3rd year Rs.3,000
Cash flow at the end of 4th year Rs.4,000
12. Calculate the present value of the following series of payments made at the end of
each year for a period of 4 years at 12% interest rate.
Cash flow at the end of 1st year Rs.11,000
Cash flow at the
end of 2nd year Rs.12,000
Cash flow at the end of 3rd year Rs.13,000
13. Determine the present value of perpetuity Rs.2,20,000 per year for infinite period at
an effective rate of interest of 8% p.a.? PVD =2,20,000/8%
14. Determine the present value of perpetuity Rs.50,000 for infinite period at an effective
rate of interest of 6% p.a. if steady rate is 5% per year. PVD=50000/6%
15. A company has raised a loan amount of Rs.3,00,000 from bank at 12% per annum rate
of interest. The amount has to be paid back in 5 equal annual installments. What shall
be the size of installment?
?? FV=PF(1+r)^n.
********************

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Module 2-Time value of Money

Unit 2: Time Value Of Money.

Need or Reason for time value of money

Future sum = Principal + Interest

= 100 + 0.10 × 100 = 110

Future sum = 100 × 1.10 = 121

We express this procedure of calculating as Compound Value or Future Value of a sum. A

Techniques of time value of money

 Compounding Techniques/Future Value Techniques

Compounding Techniques/Future Value Technique

Formula to Calculate Future value :

Case 1 : Annual Compounding

Soln: Formula to Calculate Future value :

2. Mr.X a Finance Manager in ABC Limited invests surplus funds of Rs.10,000 in a

Soln: Formula to Calculate Future value :

3.Mr.ABC a Fund Manager in xyz Limited invests funds of Rs.50,000 in a MF Company at

Soln: Formula to Calculate Future value :

FV=98,691 +99 or -99

Soln: Formula to Calculate Future value :

Soln: Formula to Calculate Future value :

Soln: Formula to Calculate Future value :

Soln: Formula to Calculate Future value :

Case 2 : Multiple compounding or Intra Compounding

Formula to be used under Multiple Compounding or Intra compounding are as follows :

a)When Interest is payable half yearly (Semi-annually i.e 2 )

a)When Interest is payable Quarterly (4 )

a)When Interest is payable monthly (12 )

a)When Interest is payable Daily (365 )

Given (1.06)8 =1.594

Soln: Formula= a)When Interest is payable half yearly

a)When Interest is payable Quarterly (4 )

Soln: Formula= a)When Interest is payable half yearly

Calculate the future value quarterly .

a)When Interest is payable Quarterly (4 )

a)When Interest is payable Quarterly (4 )

a)When Interest is payable Quarterly (4 )

Even Cash flows of a certain period of time is known as “Annuity”.

FVA =A x CFA (r,n)

FVA =R(1+i)n-1 + R(1+i)n-2+ R(1+i)n-3+ R(1+i)n-4+ R(1+i)n-5 …………

FVA = Future value of Annuity

FVA = Future value of Annuity

FVA =R(1+i)n-1 +R(1+i)n-2+R(1+i)n-3+R(1+i)n-4+R(1+i)n-5

FVA =5000(1+0.06)5-1 +5000(1+0.06)5-2+5000(1+0.06)5-3+5000(1+0.06)5-4+5000(1+0.06)5-5

FVA =5000(1.06)4 +5000(1.06)3+5000(1.06)2+5000(1.06)1+5000(1.06)0

FVA =5000(1.26) +5000(1.19)+5000(1.12)+5000(1.06)+5000(1)

FVA =6300 +5950 +5600 +5300 +5000

Formula : FVA =R(1+i)n-1 + R(1+i)n-2+ R(1+i)n-3+ R(1+i)n-4+ R(1+i)n-5

FVA= 6000(1+0.12)5-1 + 6000(1+0.12)5-2+ 6000(1+0.12)5-3+ 6000(1+0.12)5-4+

FVA= 6000(1.12)4 + 6000(1.12)3+ 6000(1.12)2+ 6000(1.12)1+ 6000(1.12)0

FVA= 6000(1.57) + 6000(1.40)+ 6000(1.25)+ 6000(1.12)+ 6000(1)

FVA= 9420 + 8400+ 7500+ 6720+ 6000

Formula : FVA =R(1+i)n-1 + R(1+i)n-2+ R(1+i)n-3+ R(1+i)n-4+ R(1+i)n-5

FVA= 4000(1+0.06)5-1 + 4000(1+0.06)5-2+ 4000(1+0.06)5-3+ 4000(1+0.06)5-4+

FVA= 4000(1.06)4 + 4000(1.06)3+ 4000(1.06)2+ 4000(1.06)1+ 4000(1.06)0

FVA= 4000(1.26) + 4000(1.19)+ 4000(1.12)+ 4000(1.06)+ 4000(1)

FVA= 5040 + 4760+ 4480+ 4240+ 4000

Formula : FVA =R(1+i)n-1 + R(1+i)n-2+ R(1+i)n-3+ R(1+i)n-4+ R(1+i)n-5

FVA= 3000(1+0.06)5-1 + 3000(1+0.06)5-2+ 3000(1+0.06)5-3+ 3000(1+0.06)5-4+

FVA= 3000(1.06)4 + 3000(1.06)3+ 3000(1.06)2+ 3000(1.06)1+ 3000(1.06)0