SESSION 1-2 [Autosaved] [Autosaved].pptx

NATURE OF
FINANCIAL
MANAGEMENT
DR HARITIKA CHHATWAL

LEARNING OBJECTIVES
 Explain the nature of finance and its interaction with other management functions
 Review the changing role of the finance manager and his/her position in the management
hierarchy
 Focus on the Shareholders’ Wealth Maximization (SWM) principle
 Discuss agency problems
 Illustrate the organization of finance function

FINANCIAL MANAGEMENT
 Financial management can be defined as the
management of flow of funds + deals with the financial decision making.
 Areas = financing and investing.
 Financing deals with the management of sources of capital, type, size
and composition
 Investing, on the other hand deals with management of uses of capital.

SCOPE OF FINANCE FUNCTION
 (i) Overall financial planning and control,
 (ii) Raising funds from different sources,
 (iii) Selection of fixed assets,
 (iv) Management of working capital, and
 (v) Any other individual financial event

 Finance manager has to operate as intermediary between the firm’s
operations one hand and the capital market on the other.
 The firm raises funds by selling ownership securities or debt securities
or borrowings in the capital market. The funds raised in this way
become the pool of the investible funds which are committed to
investment decisions of the firm.
 The investment projects generate profit which are either distributed
to the suppliers of investible funds or retained in the business for
reinvestment in the future projects.

ROLE OF FINANCE MANAGER AND TWO-WAY CASH
FLOWS TO CAPITAL MARKET

The finance manager is usually faced with the following distinct scenarios :
size of firm and growth
 Size of the firm =value of its total assets as shown in the balance sheet(yearly percentage change
in the assets of the firm)
 Types of assets to be acquired ? (Investment Decision).
 Pattern of raising funds from various sources

DECISIONS TAKEN BY FINANCE MANAGER
 (i) Investment Decisions :
a) create revenues and profits (e.g., introducing a new product line)
b) assets composition of the firm[Capital Budgeting and Working Capital Management].
c) (1) different alternative options, (2) to buy OR lease, (3) Make or buy, merger of other to avail
the synergies.
d) Working Capital Management
 (ii)Financing Decisions : financing pattern of the firm(equity share capital, preference share capital
and the accumulated profits, Leverage Analysis, EBIT-EPS analysis, Capital structure.

 (iii) Dividend Decision : appropriation of after tax profits. Retained or distributed.
 1. Reinvestment opportunities available to the firm,
 2. The opportunity rate of return of the shareholders.

 Stakeholders in financial decision making of a firm
 1. The shareholders,
 2. The debt investors,
 3. The employees,
 4. The customer and the suppliers,
 5. The public,
 6. The Government, and
 7. The management.

THE OBJECTIVES OF THE FINANCIAL
MANAGEMENT
1. Profits Maximization
 Yardstick for the economic efficiency of any firm.
 Lead to maximization of the welfare of the society.
 Efficient allocation of resources for firm + society

ISSUES WITH PROFIT MAXIMISATION
 1. It ignores the risk.
 Management may undertake all profitable investment opportunities regardless of risk, whereas that
investment may not be worth the risk, despite its potential profitability.
 2. Concentrates on the profitability + ignores the financing aspect of that decision
 3. It ignores the timings of costs and returns and thereby ignores the time value of money.
 4. The profit maximization as an objective is vague and ambiguous.
 5. Widen the gap between the perception of the management and that of the shareholders. Not
directly related to any measure of shareholders benefits, this principle seems to be self-centered at
the cost of loosing attention from the interest of the shareholders, which should be of utmost
importance to any firm.
 6. Concentrate on the immediate effect of a financial decision as reflected in the increase in the profit
of that year or in near future.
 So, the profit maximization fails to be an operationally feasible objective of financial management.


MAXIMIZATION OF SHAREHOLDERS’ WEALTH
 The measure of wealth which is used in financial management is the concept of economic value.
 EV=Present value of the future cash flows generated by a decision, discounted at appropriate rate
of discount (risk).
 Takes into account
 cash flows
 timing of cash flows
 level of risk (discounting process).
 Shareholders’ wealth = Present value of all the future cash flows in the form of dividends or Capital
gain(market value of share).
 As shareholders’ wealth at any time is equal to the market value of all his holdings in shares, an
increase in the market price of firm’s shares should increase the shareholders’ wealth.

 Assumption in this approach is that shares are traded in efficient capital market (the effect of
a decision is truly reflected in market price of a share).
 The market price of a share reflects all expected future benefits flowing from the firm to its
shareholders, hence long term perspective of management.
 Market price of a share linked to the investment decision, the financing decision and the
dividend decision.
 Investors form expectations about future cash flows based on current cash flows and
expected future growth reflected in mkt price of the share

PROBLEM WITH THE IMPLEMENTATION OF MAXIMISATION OF
SHAREHOLDERS WEALTH
1. Assumption of efficient capital market wherein the effect of a decision is truly
reflected in the market of share. The market price of a share is influenced by
the overall economic and political scenario in the country. More often than
not, the market price of a share may also fluctuate because of speculative
activities. All these factors are assumed to be given and constant in this
objective.
2. Stakeholders - the shareholders, the professional managers and the creditors.
The objectives of these three stakeholders in the firm are often very different
resulting in conflict among them.

PROFIT MAXIMIZATION VS WEALTH MAXIMIZATION
1. Objective - profit maximizations - does not consider
the risk –no effect of earnings per share, dividends
paid or any other return to shareholders
2. Market price of a share, - reflects shareholders
expected return -long term prospects of the firm-
differences in timing of the returns, considers risk
and recognizes the importance of distribution of
returns.
1. Objective - maximization of shareholder’s wealth -
all future cash flows, dividends, earnings per share,
risk of a decision, etc. -operational and objective .
2. The profit maximization can be considered as a part
of the wealth maximization strategy, but should
never be permitted to over-shadow the latter.

CONFLICT AMONG GOALS:
 The internal goal of department in conflict with the goal of the firm(Systems approach to
Management).
 Concentration- attainable and measurable goals -increase in sales revenue or production, etc-
ignore impact -market price of a share.
 Management -forced by the external factors –objectives - give less than maximum results.
 Differing view points of the ownership and the management.

RISK AND RETURN : BASIC DIMENSIONS OF FINANCIAL
DECISION
 Risk is defined as the variability of expected returns from an investment.
 Risk exists when the decision maker is able to estimate the probabilities associated with the different outcomes.
 Uncertainty exists when the decision maker has no historical data to develop the probabilities associated with the outcome.
 Return associated with a decision is measured as the total gain or loss expected over a given period of time by the decision maker.
 There are numerous factors which may influence the market price of a share. Some of these factors may be political conditions,
economic conditions, investment scenario, company considerations, promoter groups, etc.
 A finance manager is often required to trade off between the risk and return. At the time of taking any financial decision, the finance
manager has to optimize the risk and return.

THE MATHEMATICS OF FINANCE
 The concept of TVM refers to the fact that the money received today is different in its worth from the money receivable at
some other time in future.
 For example, if an individual is given an option to receive 1,000 today or to receive the same amount after one year, he will
definitely choose to receive the amount today (of course he is presumed to be a rational being).
 Therefore, TVM becomes an important consideration for any financial decision

 Reasons for Preference for current money
1.Future Uncertainties
2. Preference for Present Consumption
3. Reinvestment opportunities
Say, a firm is selling a machine for 25,000. The buyer offers to pay 25,000 either now or after one year. The seller firm will
naturally accept the first offer i.e., to receive 25,000 now. In this case, if the firm reinvests the amount of 25,000 in fixed deposit
account for one year at 10% p.a. interest, then after one year the firm will be having total money of 27,500 ( 25,000 + interest of
2,500). In the second option, the firm will receive only 25,000 after one year. Therefore, in the first option the firm will be better
off by 2,500. On the other hand, if the buyer of the machine is ready to pay 27,500 instead of 25,000 after one year, then the
firm may be indifferent. In this situation, the firm will be having 27,500 after one year either (i) by receiving 25,000 now and
reinvesting to get interest of 2,500 or (ii) to get 27,500 from the buyer after one year. This interest amount of 2,500 is the TVM.
TVM is the rate of return which an investor can earn by reinvesting its present money. This rate of return can also be expressed as
a required rate of return to make equal the worth of money of two different time periods.

 The two cash flows will be comparable only after adjusting in any of the two ways:
 (i) By compounding 1,00,000 at the required rate of return of the firm for 1 year and comparing with 1,25,000, or
 (ii) By discounting 1,25,000 at required rate of return of the firm for 1 year and then comparing with 1,00,000.
 TVM is of crucial significance to any finance manager and become important and vital consideration while taking financial
decisions. The concept of TVM helps in converting the different rupee amounts arising at different point of time into
equivalent values of a particular point of time (present or any time in future). These equivalent values can be expressed
future values (FV) or as present values (PV).
 The FV of a sum may be defined as the value of that amount if it was made at some time in future. For example, 1,000 is
deposited in a bank account at 10% interest for a period of one year. This deposit of 1,000 will become 1,100 after one year
(inclusive of interest). This 1,100 is the FV of today’s 1,000 at 10% interest after one year.
 On the other hand, the PV of a future money may be defined as the value of that money if it was received today. For
example, PV of 1,100 receivable after one year is 1,000 considering the interest at 10% p.a. which could be earned by
depositing 1,000 today for one year.
 The relationship between the PV and the FV arises because of the existence of the interest rate and the time gap. The interest
rate and the time gap between the present money and the future money

SESSION 1-2 [Autosaved] [Autosaved].pptx

COMPOUNDING TECHNIQUE
 The compounding technique is used to find out the FV of a present money.
 It is the same as the concept of compound interest, wherein the interest earned in a preceding year is reinvested at the
prevailing rate of interest for the remaining period.
 Thus, the accumulated amount (principal + interest) at the end of a period becomes the principal amount for calculating the
interest for the next period.
 The compounding technique to find out the FV of a present money can be explained with reference to :
 1. The FV of a single present cash flow, and
 2. The FV of a series of cash flows.

THE FV OF A SINGLE PRESENT CASH
FLOWS :
 It is already seen that the FV may be defined in terms of Equation 2.1 as follows :
FV depends upon the combination of three variables i.e., the PV, the r, and the n. If any one of these
three variables changes, the FV will also change.

 For example : FV of 1000 at 10% after 7 years or of 5,000 at 11% after 9 years or 50,000 at 16% after 3 years and so on. The
mathematicians have made these calculations easier by finding out the value of (1+𝑟)𝑛
for various combinations of ‘r’ and ‘n’.
These pre-calculated values of (1+𝑟)𝑛
for different combinations of ‘r’ and ‘n’ are given in Table A-1 in Appendix-III. By
selecting a combination of ‘r’ and ‘n’ in Table A-1, one can read off the amount to which 1 will grow by the end of ‘n’ years at
‘r’ rate of interest. These pre-calculated values taken from this table when multiplied by the relevant PV will give the FV of
that amount at rate of interest ‘r’, after ‘n’ years. For example, to find out the FV of 5,000 invested for 10 years at 5% rate of
interest, one can search the Table A-1 for a combination of 5% and 10 years. The interaction of 5% column and 10 years row
is the relevant figure. This figure is 1.629. This factor 1.629 multiplied by 5,000 will give the future value, FV, of 5,000 at 5%
after 10 years.

NON-ANNUAL COMPOUNDING
 In the above discussion it is presumed that the time period ‘n’ is an annual period and that the compounding is made on
annual basis only. However, the compounding period ‘n’ may be other than a year also. In such a case, the compounding
formula to be adjusted to reflect different number of periods. For example, if the compounding is made every 6 months, then
the time period ‘n’ will become 2 times in a single year. Similarly, the interest rate is also to be adjusted, because the rate of
interest will remain same but the interest amount of any 6 months will be compounded in the next 6 months and so on. The
more frequently the interest is compounded, the faster a FV grows. Further, more frequently the interest is compounded, it
begins in turn to earn further interest and hence higher is the effective annual compound rate of interest.
 For example, a deposit of 1,000 is made to earn interest at 12% p.a. compounded half-yearly.
 the value of 1,000 with half-yearly compounding becomes 1,123.60 (at [12% / 2]=6% rate of interest)
 it would have been 1,120 only if the compounding was made annually.

 An easy way to calculate the FV of half-yearly compounding in the above situation is to interpret the situation as that 1,000 is
deposited for two periods at rate of interest 6% per period. In this way, this problem becomes a FV problem with interest rate r
= 6% and number of periods n = 2. If the compounding is made ‘m’ number of times per year, then the FV at the end of ‘n’
years with rate of interest ‘r’ p.a. may be expressed are as follows :
In Equation 2.3, it may be noted that (i) the exponent has been increased from ‘n’ to ‘m.n’ to reflect
the increased number of compounding periods, and (ii) the interest rate per annum has also been
adjusted by dividing ‘m’, to correspond to the shorter compounding periods. Table 2.1 shows the
effect of frequent compounding on the FV 1,000 at rate of interest 12% p.a

 Table 2.1 shows that more frequently the compounding is made, the faster is the growth in the FV. It also shows that the rate
of interest is 12% p.a. but effectively it has helped earning an effective rate of 12.36% if compounded half-yearly and at
12.55% if compounded quarterly and so on. The rate of interest 12% p.a. is also known as the normal rate of interest and the
rate of interest 12.36% or 12.55% etc. are known as the effective rate of interest.
 EFFECTIVE RATE OF INTEREST : The effective rate of interest is the annually compounded rate of interest that is equivalent to
an annual interest rate compounded more than once per year. The effective rate of interest and the nominal rate of interest
are equal whenever they generate the same FV. Mathematically,
In case, m = 1 i.e., annual compounding, then re = r i.e., the effective rate of interest is equal to the nominal
rate of interest. The effective rate of interest is very useful in financial decision making particularly in
investment decisions where different optional opportunities have different compounding intervals. The
effective rate of interest of various options will help the finance manager in selecting the best alternatives.

 For example, a deposit of 10,000 is made in a bank for a period of 1 year. The bank offers two
options Receive interest at 12% p.a. compounded monthly or (ii) to receive interest at 12.25%
p.a. compounded half-yearly. Which option should be accepted? In this case, the two options
can be evaluated as follows

 In this case, the normal rate of return is higher in option (ii) i.e., 12.25% but the effective rate of interest is higher in option (i)
i.e., 12.68%. Therefore, the depositor should select the option (i) i.e., interest at 12% p.a. compounded monthly.
 FUTURE VALUE OF A SERIES OF EQUAL CASH FLOWS OR ANNUITY OF CASH FLOWS : Quite often a decision may result in
the occurrence of cash flows of the same amount every year for a number of years consecutively, instead of a single cash flow.
For example, a deposit of 1,000 each year is to be made at the end of each of the next 3 years from today. This may be referred
to as an annuity of deposit of 1,000 for 3 years. An annuity is thus, a finite series of equal cash flows made at regular intervals.
Calculation of the FV of an annuity can also be presented graphically as in Figure 2.1 (rate of interest 10% compounded
annually).

 The FV of an annuity also depends upon three variables i.e., the annual amount, the rate of interest and the time period.
 For example, the FV of an annuity of 1,000 for 3 years at 10% may be calculated as follows : (i) Find out the relevant figure in
Table A-2, which is 3.310. (ii) Multiply this figure by 1,000 to give value of 3,310. This is the FV of the annuity of 1,000 and it
is equal to the value already calculated in Figure 2.1. This factor 3.310 is also known as Compound Value of Annuity Factor for
a given combination of ‘r’ & ‘n’. This may be expressed as CVAF(r, n)’ and Equation 2.1 may be written as Equation 2.1B

DISCOUNTING TECHNIQUE
 This process is in fact the reverse of compounding technique and is known as the discounting
technique. As there are FVs of sums invested now, calculated as per the compounding
techniques, there are also the present values of a cash flow scheduled to occur in future. The
present value is calculated by discounting technique.
The discounting technique to find out the PV can be explained in terms of : (i) The PV of a future sum, (ii) The PV
of a future series.

PRESENT VALUE OF A FUTURE SUM
 The present value of a future sum will be worth less than the future sum because one foregoes the opportunity
to invest and thus foregoes the opportunity to earn interest during that period.
 As the length of time for which one has to wait for the future money increases, the cost attached to delay also
increases reflecting the compounded value of the lost opportunities. In order to find out the PV of a future
money, this opportunity cost of the money is to be deducted from the future money. Say, 1,080 is receivable at
the end of one year from now and the expected rate of interest which a person can earn on his investment is 8%
p.a. then the PV can be calculated
This means that 1,080 receivable after 1 year is just equal in worth to 1,000 receivable today. In the latter case,
1,000 if received today will earn interest of 80 (at 8% p.a.) and becomes 1,080 at the end of 1 year from now. In
other words, a person will be indifferent between receiving 1,000 now or receiving 1,080 after a year. It can be seen
from Equation 2.2 that the PV of a future money depends upon the three variables i.e. the FV, the rate of interest and
the time period.

 These values are known as Present Values of a future sum for a given rate of interest and time-period and is denoted as PVF(r,
n). These values have been given in Table A-3 in Appendix-II. The figure given at the intersection of a particular rate of
interest, ‘r’ and time period, ‘n’, when multiplied by the future amount will give the PV of that amount for the given
combination of ‘r’ & ‘n
For example, in order to find out the PV of Rs, 1,500 receivable after 3 years and the rate of interest after 10%,
the PV factor in Table A-3 (10% column and 3 years row) is .751. Now, 1,500 × .751 = 1,126.50 is the PV of
1,500. It means that an amount of 1,126.50 invested at 10% p.a. for 3 years will accumulate to 1,500. Thus, the
PV of a future money is the amount that makes a person exactly as well off today as the money received in
future.
Two observations can be made on the basis of the values given in the pre-calculated Table A-3 i.e., (i) for a given
period the higher the interest rate, the lower will be the present value factor and therefore, the lower will be the
PV, and (ii) for a given rate of interest, the longer the time period the lesser will be the present value factor and
therefore, the lower will be the PV. The reason for this behaviour is obvious. As the length of waiting time to
receive the future money increases, the discount factor also decreases reflecting the continuation of the lost
opportunities to earn interest for a longer period.

THE PV OF A SERIES OF EQUAL FUTURE CASH FLOWS OR
ANNUITY
 A decision taken today may result in a series of future cash flows of the same amount over a period of number of years. For example,
a service agency offers the following options for a 3-year contract: (i) Pay only 2,500 now and no more payment during next 3 years,
or (ii) Pay 900 each at the end of first year, second year and third year from now. A client having rate of interest at 10% p.a. can
choose an option on the basis of the present values of both options as follows :
 Option I : The payment of 2,500 now is already in terms of the present value and, therefore, do not require any adjustment. Option II
: The customer has to pay an annuity of 900 for 3 years
 Calculation of PV of Annuity at r=10%

 PV of series of Payments :
 The PV of different amounts accruing at different times are to be calculated and then added. For the above example, as shown
in Figure 2.2, the total PV is 2,238. In this case, the client should select the option II, as he is paying a lower amount of 2,238 in
real terms as against 2,500 payable in option I. It may be noted that the PV of a future series i.e. the annuity also depends upon
upon 3 variables i.e., the annuity amount, the rate of interest and the time period. In order to calculate the PV of an annuity, the
pre-calculated mathematical tables are available for different combinations of ‘r’ and ‘n’. These tables are known as Present
Value of Annuity Table, and is given as Table A-4 in Appendix-II. In this table, any combinations of ‘r’ and ‘n’ will give a value
which if multiplied by the annuity amount will give the PV of the annuity for that particular rate of interest and time period. For
example, the relevant value for rate of interest 10% and 3 years is 2.487. Now, multiply this value by the annuity amount of 900.
The present value is 900 × 2.487 = 2,238. This is the same as found in Figure 2.2. The values taken from Table A-4 are known as
as the Present Value of an Annuity Factor for a given combination of ‘r’ and ‘n’, and may be denoted as PVAF(r, n)

 So, the present value in option II is 1,119.40 and therefore, the option II is still better than the option I. It may be noted that
the PV of the option II has changed from 1,125.50 to 1,119.40 only because of change in the payment schedule.

 On the basis of the above discussion of the future values and the present values, two observations can be made as follows:
(1) That both the FV and the PV are two sides of the same coin. This is evident from the basic Equations 2.1 and 2.2 also i.e.,
In this situation, either the FV or the PV can be made the dependent variable and can be found by taking
the other variable as the independent variable. (2) For a single cash flow, the future value factor i.e. CVF(r,
n) will be greater than one, while the present value factor i.e. PVF(r, n) will be less than one. The future
value is the compounded value and is inclusive of the interest for the interval period. However, the present
value is the discounted value and is exclusive of the interest for the interval period.

FV=17,00,000X
1.295029=22,01,550
PV=Annuity Amount X (1.09/=
8times and GT =5.535)

SINKING FUND(FUTURE VALUE)
 Sinking fund is a fund, which is created out of fixed payments each period to accumulate to a future
sum after a specified period. For example, companies generally create sinking funds to retire bonds
(debentures) or loan on maturity. The factor used to calculate the annuity for a given future sum is
called the sinking fund factor (SFF). SFF ranges between zero and 1.0. It is equal to the reciprocal of
the compound value factor for an annuity.How much should we deposit each year at an interest rate
of 6 per cent so that it grows to `21,873 at the end of fourth year?
 CVFA of 4.3746 for 4 years at 6%

CAPITAL RECOVERY AND LOAN AMORTIZATION
 Capital recovery is the annuity of an investment made today, for a specified
period of time, at a given rate of interest. The reciprocal of the present value
annuity factor is called the capital recovery factor (CRF).

You plan to invest `10,000 today for a period of four years. If your interest rate is 10 per cent,
how much income per year should you receive to recover your investment?
It would be thus clear, that the term 0.3155 is the capital recovery factor and it is reciprocal of the
present value factor of an annuity of `1. The annuity is found out by multiplying the amount of
investment by CRF. Capital recovery factor helps in the preparation of a loan amortization schedule or
loan repayment schedule.
Suppose you have borrowed a 3-year loan of `10,000 at 9 per cent from your employer to buy a
motorcycle. If your employer requires three equal end-of-year repayments

OTHER SPECIFIC CASH FLOWS
 Perpetuity: If the first occurrence of the perpetuity takes place after 1 year

 A finance company makes an offer to deposit a sum of 1,100 and then receive a return of 80
p.a. perpetually. Should this offer be accepted if the rate of interest is 8%? Will the decision
change if the rate of interest is 5%?

FUTURE VALUE OF ANNUITY
 Suppose a constant sum of Re1 is deposited in a savings account at the end of each year for four years at 6 per
cent interest. This implies that Re1 deposited at the end of the first year will grow for 3 years, `1 at the end of
second year for 2 years, Re1 at the end of the third year for 1 year and Re1 at the end of the fourth year will not
yield any interest. Using the concept of the compound value of a lump sum, we can compute the value of
annuity. The compound value of `1 deposited in the first year will be: 1 × 1.063 = `1.191, that of `1 deposited in
the second year will be: `1 × 1.062 = `1.124 and `1 deposited at the end of third year will grow to: `1 × 1.061 =
`1.06 and `1 deposited at the end of fourth year will remain `1. The aggregate compound value of `1 deposited at
the end of each year for four years would be: 1.191 + 1.124 + 1.060 + 1.00 = `4.375. This is the compound value
of an annuity of `1 for four years at 6 per cent rate of interest.

2. FUTURE VALUE OF ANNUITY DUE : Savings account at the beginning of each year for 4 years
to earn 6 per cent interest? How much will be the compound value at the end of 4 years? You
may recall that when deposit of `1 made at the end of each year, the compound value at the
end of 4 years is `4.375. However, `1 deposited in the beginning of each of year 1 through year
4 will earn interest respectively for 4 years, 3 years, 2 years and 1 year:
Thus the compound value of `1 deposited at the beginning of each year for
4 years is 1 × 4.375 × 1.06 = `4.637

PRESENT VALUE OF ANNUITY
 For example, an investor, who has a required interest rate as 10 per cent per year, may have an
opportunity to receive an annuity of `1 for four years. The present value of `1 received after
one year is, P = 1/(1.10) = `0.909, after two years, P = 1/(1.10)2 = `0.826, after three years, P =
1/(1.10)3 = `0.751 and after four years, P = 1/(1.10)4 = `0.683. Thus the total present value of
an annuity of `1 for four years is `3.169
A person receives an annuity of `5,000 for four years. If the rate of interest is 10 per cent,
the present value of `5,000 annuity is:

PRESENT VALUE OF AN ANNUITY DUE
 If the first payment is made immediately, then its present value would be the same (i.e., `1) and
each year’s cash payment will be discounted by one year less. This implies that the present value
of an annuity due would be higher than the present value of an annuity. Thus, the present value
of the series of `1 payments starting at the beginning of a period is
 4-year annuity of `1 each year, the interest rate being 10 per cent. What is the present value of
this annuity if each payment is made at the beginning of the year?
present value of an annuity due is more than of an
annuity by the factor of (1 + i). If you multiply the
present value of an annuity by (1 + i), you would get
the present value of an annuity due.
the present value of `1 paid at the beginning of each
year for 4 years is 1 × 3.170 × 1.10 = `3.487

 Growing Perpetuity : Infinite series of periodic cash flows which grow at a constant rate per
period. For example, an amount is receivable indefinitely in such a way that the amount of a
particular period is 10% more than the amount for the preceding period.
 Note :formula can be used only if the rate of interest > rate of growth i.e. r > g.
 Q. Company is expected to declare a dividend of 2 at the end of first year from now and this
dividend is expected to grow 10% every year. What is the PV of this stream of dividend if the rate
of interest is 15%?

 Growing Annuity : A growing annuity may be defined as a finite series of periodic cash flows
growing at a constant rate every period (truncated growing perpetuity)

 Q. Person opens a recurring deposit account for a period of 10 years earning 12% interest and
accepts the scheme under the condition that for the first year the deposit is 3,150 and for
subsequent years the deposit amount will increase by 5% every year. What is the PV of this
scheme

APPLICATION OF THE CONCEPTS OF TVM
 Finding out the Implicit Rate of Interest : Several financial institutions have issued the Deep
Discount Bonds (DDB) where the investor is required to pay a specific amount per bond at
the time of issue and receives a much larger amount at the end of a specified period. The
interest however, is not given. The technique of TVM can be applied to find out the implicit
interest as applicable to DDBs.

In the CVF Table, the value 4 may be found in the 26% Column for 6 years period. So,
the implicit rate of interest is 26%.
Q DDB is issued for 5,000 today and will mature after 6 years for 20,000. The
implicit rate of interest can be ascertained

 3. Sinking Funds : In case of a business firm, a finance manager may be interested to
accumulate a target amount in order to replace an asset or in order to repay a liability at the
end of a specified period. In this case, the annual accumulation by the finance manager in fact
becomes the annuity for a given period where each of the annual subscription/accumulation
will be invested for the remaining period so that the total accumulation at the end of the given
period is equal to the target amount.
 For example, an amount of 1,00,000 is required at the end of 5 years from now to repay a
debenture liability. What amount should be accumulated every year at 10% rate of interest so
that it ultimately becomes 1,00,000 after 5 years?

4. Capital Recovery : Sometimes, one may be interested to find out the equal annual amount
paid in order to redeem a loan of a specified amount over a specified period together with the
interest at a given rate for that period.
1,00,000 borrowed today is to be repaid in five equal instalments payable at the end of each of
next 5 years in such a way that the interest at 10% p.a. for the intervening period is also repaid.

 5. Deferred Payments : Suppose a person takes a loan of a specified amount at a given rate of interest. He wants to repay this
loan together with interest in such a way that the annual amount being paid is same and further that the first payment be made
a few years from now. In this case, the interest for the period for which the payment has been delayed (i.e. the period from the
date of loan to the date of first payment) should also be considered in finding out the annual payment for the repayment of
loan together with the interest.
A loan of 1,00,000 is taken on which interest is payable @ 10%. However, the repayment is to start only at the end of third year
from now. What should be the annual payment if the total loan and interest is to be repaid in six instalments ?

PRESENT VALUE OF PERPETUITY
 Perpetuity, time period, n, is so large (mathematically n approaches infinity, ∞) that the
expression (1 + i) n in Equation (10) tends to become zero, and the formula for a perpetuity
simply becomes

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