CS - EXECUTIVE
Financial
&
Strategic
Mgt.
3/10, BASEMENT, EAST PATEL NAGAR,
NEW DELHI – 110008
CONTACT NO. 011-45139922, 45719209
INDEX
CHAPTER
NO.
CHAPTER NAME
PAGE
NO.
1
NATURE, SIGNIFICANCE
1-17
2
TIME VALUE OF MONEY
18-23
3
VALUATION OF SECURITY
24-41
4
COST OF CAPITAL
42-91
5
LEVERAGE ANALYSIS
92-120
6
CAPITAL STRUCTURE
121-146
7
CAPITAL STRUCTURE THEORIES
147-167
8
DIVIDEND POLICY
168-195
9
CAPITAL BUDGETING
196-281
10
LEASE OR BUY
282-291
11
WORKING CAPITAL
292-324
12
ESTIMATION & CALCULATIONS
325-340
13
RECEIVABLES MANAGEMENT
341-367
14
INVENTORY MANAGEMENT
368-390
15
MANAGEMENT OF CASH
391-409
16
SECURITY ANALYSIS & PORTFOLIO
410-473
CHAPTER 1
NATURE, SIGNIFICANCE & SCOPE OF
FINANCIAL MANAGEMENT
 CONCEPT 1
MEANING OF FINANCE
Finance may be defined as an Art or Science of managing money & includes activ ites like
investing, borrowing, lending, budgeting, saving and forecasting.
It refers to provisioning of money at the time when it is needed.
 CONCEPT 2
MEANING OF BUSINESS FINANCE
Business finance is that business activity which concerns with the acquisition and
conversion of capital funds in meeting financial needs and overall objectives of a business
enterprise”.
Corporate finance is concerned with budgeting, financial forecasting, cash management,
credit administration, investment analysis and fund procurement for the business needs to
adopt modern technology and application suitable to the dynamic global environment.
 CONCEPT 3
DEFINITION OF FINANCIAL MANAGEMENT
Financial management “is the operational activity of a business that is responsible for
obtaining and effectively utilizing the funds necessary for efficient operations.
It is broadly concerned with raising of funds, creating value to the assets of the business
enterprise by efficient allocation of funds. It is the study of integration of the flow of funds
in the most optimal manner to maximize the returns of a firm by taking proper decisions in
utilizing the funds.
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On basis of above discussion, it can be said that financial management involves following
basic questions.
(i)
(ii)
(iii)
(iv)
From where to raise funds? i.e. Financing Decision.
Where to invest? i.e. Investment Decision
How much earning to be distributed as divided? i.e. Dividend Decision.
How to manage working capital? i.e. Working Capital Management Decision.
Thus Wealth of Company is function of investment, finance, Dividend, Working Capital
 CONCEPT 4
SCOPE OF FINANCIAL MANAGEMENT
Traditional Theory on Finance
Traditionally finance was only limited to procurement of the funds for the organization.
The funds were needed to finance the expansion or diversification. As these activities were
rare and required large amount of funds, the emphasis was on the long-term resources and
as a result only long-term finance was considered as important. Finance function was
generally concern with the issues regarding procurement of funds, administration of funds,
administration of covenants imposed by supplier of funds, etc. Thus finance function was
mainly an outsider looking.
Modern Theory on Finance
Modern Theory of finance considered finance as a separate discipline and have a wider
perspective. It’s not only limited to procurement but increased its limit to cover efficient
allocation and effective administration of fund. In modern days finance man agement has
become an integral part of overall management.
 CONCEPT 5
OBJECTIVES OF FINANCIAL MANAGEMENT
Primary Objectives
Profit Maximization
Wealth Maximization
Other Objectives
Maintenance of Liqudity
Meeting of Financial Commitments
Proper utilization of funds
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Maintenance of
Liquidity
Prof it
Maximisation
Wealth
Maximization
Meeting of
Financial
Commitments
Proper
Utilisation of
f und
 CONCEPT 6
PROFIT MAXIMIZATION VS WEALTH MAXIMIZATION
Profit Maximisation
Wealth Maximisation
Does not consider the effect of future cash Recognizes the effect of all future cash flows,
flows, dividend decisions, EPS etc.
dividends, EPS etc.
A firm with profit Maximization objective A firm with Wealth Maximization objective
may refrain from payment of dividend to its may pay regular dividends to its
Shareholders.
Shareholders
Ignores time pattern of returns.
Recognizes the time pattern of returns.
Focus on Short-Term.
Focus on Medium / Long-Term.
Does not consider the effect of uncertainty / Recognizes the risk-return relationships.
risk.
Comparatively easy to determine the Offers no clear or specific relationship
relationship between financial decision and between financial decisions and share
profits.
market prices.
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 CONCEPT 7
TYPES OF FINANCIAL MANAGEMENT DECISION
The Financial Management can be broken down in to three major decisions or functions of
finance. They are: (i) the investment decision, (ii) the financing decision and (iii) the
dividend policy decision
1. INVESTMENT DECISION
The investment decision relates to the selection of assets in which funds will be invested by
a firm. The assets as per their duration of benefits, can be categorized into two groups: (i)
long-term assets which yield a return over a period of time in future (ii) short-term or
current assents which in the normal course of business are convertible into cash usually
with in a year. Accordingly, the asset selection decision of a firm is of two types. The
investment in long-term assets is popularly known as capital budgeting and in short-term
assets, working capital management.
1. Capital budgeting: Capital budgeting – the long term investment decision – is probably
the most crucial financial decision of a firm. It relates to the selection of an asset or
investment proposal or course of action that benefits are likely to be available in future
over the lifetime of the project. The long-term investment may relate to acquisition of
new asset or replacement of old assets.
2. Working Capital Management: Working capital management is concerned with the
management of the current assets. As we know, the short-term survival is a prerequisite to long-term success. The major thrust of working capital managementis the
trade-off between profitability and risk (liquidity), which are inversely related to each
other. If a firm does not have adequate working capital it may not have the ability to
meet its current obligations and thus invite the risk of bankrupt. One the other hand if
the current assets are too large the firm will be loosing the opportunity of making a
good return and thus may not serve the requirements of suppliers of funds. Thus,
the profitability and liquidity are the two major dimensions of working capital
management. In addition, the individual current assets should be efficiently managed so
that neither inadequate nor unnecessary funds are locked up.
2. FINANCING DECISIONS
The second major decision involved in financial management is the financing decision,
which is concerned with the financing i.e. mix of capital structure to finance a given
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investment opportunity. The term capital structure refers to the combination of debt (fixed
interest sources of financing) and equity capital (variable – dividend securities/source of
funds). The financing decision of a firm relates to the choice of the proportion of these
sources to finance the investment requirements. Debt/implies a higher return to the
shareholders and also the higher financial risk and vice versa. A proper balance between
debt and equity is a must to ensure a trade–off between risk and return to the
shareholders. A capital structure with a reasonable proportion of debt and equity capital is
called the optimum capital structure. The second aspect of the financing decision is
the determination of an appropriate capital structure, which will result, is maximum return
to the shareholders and in turn maximizes the worth of the firm. Thus, the financing
decision covers two inter-related aspects: (a) capital structure theory, and (b) capital
structure decision.
3. DIVIDEND POLICY DECISIONS
The third major decision of financial management is relating to dividend policy. The firm
has two alternatives with regard to management of profits of a firm. They can be either
distributed to the shareholder in the form of dividends or they can be retained in the
business or even distribute some portion and retain the remaining. The course of action to
be followed is a significant element in the dividend decision. The dividend pay out ratio i. e.
the proportion of net profits to be paid out to the shareholders should be in tune with the
investment opportunities available within the firm. The second major aspect of the
dividend decision is the study of factors determining dividend policy of a firm in practice.
 CONCEPT 8
INTER-RELATION SHIP BETWEEN INVESTMENT, FINANCING & DIVIDEND DECISION
The finance functions are divided into three major decisions, viz, investment, financing and
dividend decisions. It is correct to say that these decisions are inter -related because the
underlying objective of these three decisions is the same. i.e. maximization of shareholders’
wealth. Since investment, financing & divided decisions are interrelated, one has to
consider the joint impact of these decisions on the market price of the company’s shares
and these decisions should also be solved jointly.
The basic objective of financial management is maximization of shareholders wealth. The
evaluation of each decision in relation to its effect, on the shareholders wealth is to be
considered. The decision to invest in a new project needs the financing for the inve stment.
Hence investment & financing decision are interrelated. The financing decision, in turn, is
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influenced by and influences dividend decision because retained earning used in internal
financing deprive shareholders of their dividends. Hence financing & dividend decisions
are interrelated. Further the company is basically making investments for its equity
shareholders, so as to give them higher dividends. Thus investment & dividend decisions
are interrelated.
The above discussion makes it clear that investment, financing and dividend decisions are
interrelated and are to be taken jointly keeping in view their joint effect on the
shareholders’ wealth.
 CONCEPT 9
VALUE OF FIRM – RISK AND RETURN
Financial decisions incur different degree of risk. An investor’s decision to invest in risk
free government bonds has less risk as interest rate is known and the risk of default is very
less. On the other hand, an investor would incur more risk if he decides to invest in shares,
as the return is not certain. However, the investor can expect a lower return from
government bond and higher from shares. Risk and expected return move in tandem; the
greater the risk the greater would be the expected return. The following figure shows the
risk-return relationship.
As discussed earlier, a finance manager has to take various types of decision - investment
decisions, financing decisions and dividend decisions. A finance manager takes these
decisions in the light of the objective of wealth maximisation as reflected in the market
price of the shares. The finance manager should also know as to what are the factors which
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may affect the market price of the shares. The various decisions will be taken in the light of
these factors, otherwise any attempt to achieve the objective of maximisation of market
price of the shares may not be achieved.
A finance manager cannot avoid the risk altogether nor can he make a decision by
considering the return aspect only. Usually, as the return from an investment increases, the
risk associated with it also increases. In an attempt to increase the return, the finance
manager will have to undertake greater degree of risk also. Therefore, a finance manager is
often required to trade-off between the risk and return. At the time of taking any decision,
the finance manager tries to achieve the proper balance between the consideration of risk
and return associated with various financial management decisions to maximise the
market value of the firm. A particular combination of risk and return where b oth are
optimized may be known as Risk-return trade off and at this level of risk-return, the market
price of the shares will be maximised.
The figure below demonstrates the relationship between market value of the firm, return
and risk, on the one hand and financial management decision on the other.
 CONCEPT 10
LIQUDITY
Liquidity is an important concept in financial management and is defined as ability of the
business to meet its shortterm obligations. It shows the quickness with which a
business/company can convert its assets into cash to pay what it owes in the near future. It
measures a company’s ability to meet expected as well as unexpected requirements of cash
to expand its assets, reduce its liabilities and cover up any operating losses. Liquidity, as a
decision criterion, is widely used in financial management. It is used for managing liquid
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resources or current assets or near cash assets so as to enhance the effectiveness with
which they are utilized with a view to minimising costs. It also focuses attention on the
availability of funds. Enhancement of liquidity enables a corporate body to have more
funds from the market.
Liquidity is assessed through the use of ratio analysis. Liquidity ratios provide an insight
into the present cash solvency of a firm and its ability to remain solvent in the event of
calamities
To conclude, liquidity, as a decision criterion is an important tool in financial management.
Financial decisions are affected by liquidity analysis of a company in the following areas:
1.
2.
3.
4.
5.
6.
Management of cash and marketable securities;
Credit policy of a firm and procedures for realisation;
Management and control of inventories;
Administration of fixed assets;
Taking decisions for efficient use of current assets at minimum cost; and
Decisions to keep the company’s position on sound basis to avoid eventualities.
 CONCEPT 11
PROFITABILITY
Profitability as a decision criterion is another important tool in financial management for
taking decisions from different angles after evaluating the performance of the company in
different spheres.
Because different users look at the profitability of a company from different angles, they
use different ratios. Short-term creditors, long-term lenders, equity shareholders,
investors, etc. all are interested in profitable operations of a concern.
They use the ratios which best suit their requirements. Profitability can be related to sales
or to total capital employed or to net worth of the company. But then different figures for
profits are taken into account.
Profitability to sales ratio, reflects the company’s ability to generate profits per unit of
sales. If sales lack sufficient margin of profit, it is difficult for the business enterprise to
cover its fixed cost, including fixed charges on debt, and to earn profit for shareholders.
From investors point of view profits are compared by the investors as percentage to the
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capital employed in the business enterprise. Absence of adequate profitability ratio on
sales reflects the company’s inability to utilise assets effectively. This is analysed through
the asset turnover ratio.
Return on Investment: This is an important profitability ratio from the angle of
shareholders and reflects on the ability of management to earn a return on resources put in
by the shareholders. The beauty of the ROI ratio is that earning of the company can be
viewed from different angles so as to take decisions on different causes responsible, to
reduce or to enhance the profitability of the company. One way of finding out rate of return
on assets employed in the company is to find the ratio of earnings before interest and taxes
(EBIT) to capital employed. This ratio indicates operating income to the assets used to
produce income.
In this way, we find that profitability as decision making criterion in financial management,
is crucial for business managers.
 CONCEPT 13
PROFITABILITY Vs LIQUDITY
One of the most important problems faced by the finance manager is the dilemma of
liquidity vs. profitability. Liquidity ensures the ability of the firm to honour its short term
commitments, that means, the firm has adequate cash; to pay for its bills, to make
unexpected large purchases and to meet contingencies, at all times. It also reflects the
ability of the firm to convert its assets into cash and pay off liabilities quickly. Generally,
“Liquidity measure a company’s ability to meet expected as well as unexpected
requirements of cash to expand its assets, reduce its liabilities and cover up any operating
losses.” Under liquidity management, the finance manger is expected to manage all its
current assets including near cash assets in such a way as to ensure its affectivity with the
view to minimize its costs. On the other hand, under profitability objective, the finance
manger is expected to utilize the funds of the firm in such a manner as to ensure the highest
return. However, the two objectives of liquidity and profitability have inverse relationship.
If liquidity increases profitability decreases and vice- versa. Thus, in almost all the
decisions taken by the finance manger, profitability and liquidity goals conflict. For
example, the finance manger may follow a liberal credit policy with the view to push-up its
sales and thus generate higher revenue, but its liquidity position will affect adversely.
Hence the finance manger has to strike a balance between these two conflicting objectives.
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 CONCEPT 14
FINANCIAL DISTRESS AND INSOLVENCY
Generally the affairs of a firm should be managed in such a way that the total risk –
business as well as financial – borne by equity holders is minimized and is manageable,
otherwise, the firm would obviously face difficulties. In managing business risk, the firm
has to cope with the variability of the demand for its products, their prices, input prices,
etc. It has also to keep a tab on fixed costs. As regards financial risk, high proportion of debt
in the capital structure entails a high level of interest payments. If cash inflow is
inadequate, the firm will face difficulties in payment of interest and repayment of principal.
If the situation continues long enough, a time will come when the firm would face pressure
from creditors. Failure of sales can also cause difficulties in carrying out production
operations. The firm would find itself in a tight spot. Investors would not invest further.
Creditors would recall their loans. Capital market would heavily discount its securities.
Thus, the firm would find itself in a situation called distress. It may have to sell its assets to
discharge its obligations to outsiders at prices below their economic values i.e. resort to
distress sale. So when the sale proceeds is inadequate to meet outside liabilities, the firm is
said to have failed or become bankrupt or (after due processes of law are gone through)
insolvent.
Failure of a firm is technical if it is unable to meet its current obligations. The failure could
be temporary and might be remediable. When liabilities exceed assets i.e. the net worth
becomes negative, bankruptcy, as commonly understood, arises. Technical bankruptcy can
be ascertained by comparing current assets and current liabilities i.e. working out current
ratio or quick ratio. On the other hand, solvency ratios indicate long term liquidity i.e. the
ability of the firm to discharge its term-liabilities. Examples of solvency ratios are Debt to
Equity ratio, Debt to total Funds Ratios, and Interest coverage ratio. Trend analysis should
be made for the past three to five years to pick up signals of bankruptcy, if any.
 CONCEPT 15
FUNCTIONS OF FINANCIAL MANAGER
To achieve the objective of the financial management i.e. to maximise the owner’s wealth,
the financial executives have to perform variety of tasks to discharge their responsibilities.
When the Financial Manager is involved in management of asset, he is performing the role
of the decision-maker and when he is managing funds, he is performing the staff function.
In the light of different responsibilities of the financial manager, he performs mainly the
following duties.
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1. Forecasting of Cash Flow: it involves matching cash inflow against outflows.
2. Raising Funds: The Financial Manager has to plan for mobilising funds from different
sources so that the requisite amount of funds are made available to the business enterprise
to meet its requirements for short term, medium term and long term.
3. To Facilitate Cost Control: The Financial Manager is generally the first person to
recognise when the costs for the supplies or production processes are exceeding the
standard costs/budgeted figures. Consequently, he can make recommendations to the top
management for controlling the costs.
4. To Facilitate Pricing of Product, Product Lines and Services: The Financial Manager
can supply important information about cost changes and cost at varying levels of
production and the profit margins needed to carry on the business success fully. In fact,
financial manager provides tools of analysis of information in pricing decisions and
contribute to the formulation of pricing policies jointly with the marketing manager.
5. Forecasting Profits: The Financial manager is usually responsible for collecting the
relevant data to make forecasts of profit levels in future.
6. Measuring Required Return: The acceptance or rejection of an investment proposal
depends on whether the expected return from the proposed investment is equal to or more
than the required rate of return. An investment project is accepted if the expected return is
equal or more than the required rate of return.
7. Managing Funds: Funds may be viewed as the liquid assets of the firm.The manager is
responsible for having sufficient funds for the firm to conduct its business and to pay its
bills. Money must be located to finance receivables and inventories, to make arrangements
for the purchase of assets, and to identify the sources of long-term financing. Cash must be
available to pay dividends declared by the board of directors. The management of funds
has therefore, both liquidity and profitability aspects. If the firm’s funds are inadequate, the
firm may default on the payment of liabilities and may have to pay higher interest. If the
firm does not carefully choose its financing methods, it may pay excessive interest costs
with a subsequent decline in profits.
8. Managing Assets:
(i) Find out total amount of assets needed by firm to carry out its operations
(ii) Determine composition or mix of asset that will help firm to achieve its goals.
(iii) Identify ways to use existing asset more effectively & unwarranted expenses.
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MULTIPLE CHOICE QUESTIONS
1. Which of following if financial management decision
a) Investment decision
b) Financing decision
c) Dividend decision
d) All of above
2. In investment decision we decide
a) Where to invest
b) From where to borrow
c) How much dividend to be distributed
d) None of above
3. In financing decision we decide
a) Where to invest
b) From where to borrow
c) How much dividend to be distributed
d) None of above
4. In dividend decision we need to decide
a) Where to invest
b) From where to borrow
c) How much dividend to be distributed
d) None of above
5. What are objectives of financial management
a) Profit maximization
b) Wealth maximization
c) Both A & B
d) None of above
6. Which objective of financial management focus on short term
a) Profit maximization
b) Wealth maximization
c) Both of A & B
d) None of above
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7. Which objective of financial management recognize risk-return relationships
a) Profit maximization
b) Wealth maximization
c) Both of A & B
d) None of above
8. Which objective of financial management the effect of all future cash flows, dividend
EPS etc.
a) Profit maximization
b) Wealth maximization
c) Both of A & B
d) None of above
9. Which objective of financial management offers clear & specific relation-ship between
financial decision & profit
a) Profit maximization
b) Wealth maximization
c) Both of A & B
d) None of above
10. Does investment, financing, dividend decisions are inter-related to each other
a) True
b) False.
11. Ability of the business to meet short term obligation is known as
a) Liquidity
b) Profitability
c) None of above
d) Bothe of above
12. Liquidity & profitability are related to each other
a) Directly
b) Inversely
c) Either A or B
d) Not related at all
13. Financial distress is due to
a) Financial risk
b) Operating risk
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c) Both risk
d) None of above
14. Which of following position is goods for a business
a) High risk
b) High return
c) Risk-return
d) No risk
15. varies inversely with profitability.
a) Liquidity.
b) False.
c) Blue.
d) Risk.
16. _________ is concerned with the acquisition, financing, and management of assets with
some overall goal in mind.
a) Financial Management
b) Profit Maximization
c) Agency Theory
d) Social Responsibility.
17. ________is concerned with the maximization of a firm's earnings after taxes.
a) Shareholder wealth maximization
b) Profit maximization
c) Stakeholder maximization
d) EPS maximization
18. What is the most appropriate goal of the firm?
a) Shareholder wealth maximization.
b) Profit maximization.
c) Stakeholder maximization.
d) EPS maximization
19. The_________ decision involves determining the appropriate make-up of the right-hand
side of the balance sheet.
a) Asset management
b) Financing
c) Investment
d) Capital budgeting
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20. To whom does the Treasurer most likely report?
a) Chief Financial Officer.
b) Vice President of Operations.
c) Chief Executive Officer.
d) Board of Directors.
21. Which of the following is a financial statement that states items on a cash basis?
a) The income statement
b) The balance sheet
c) The statement of cash flows
d) None of the above
22. The ability of a firm to convert an asset to cash is called________.
a) Liquidity
b) Solvency
c) Return
d) Marketability
23. Which of the following financial statements is also known as a statement of financial
position?
a) Balance sheet
b) Statement of cash flows
c) Income statement
d) None of the above
24. The long-run objective of financial management is to:
a) Maximize earnings per share.
b) Maximize the value of the firm's common stock.
c) Maximize return on investment.
d) Maximize market share.
25. The decision function of financial management can be broken down into the decisions.
a) Financing and investment
b) Investment, financing, and dividend decision
c) Financing and dividend
d) Capital budgeting, cash management, and credit management
26. The controller's responsibilities are primarily _________ in nature, while the treasurer's
responsibilities are primarily related to.
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a) Operational; financial management
b) Financial management; accounting
c) Accounting; financial management
d) Financial management; operations.
27. The primary goal of the financial management is ____________.
a) to maximize the return
b) to minimize the risk
c) to maximize the wealth of owners
d) to maximize profit
28. ___________ are financial assets.
a) Bonds
b) Machines
c) Stocks
d) A and C
29. Which of the following is not an objective of financial management?
a) Maximization of wealth of shareholders
b) Maximization of profits
c) Mobilization of funds at an acceptable cost
d) Ensuring discipline in the organization.
30. The objective of financial management in long run is ______________.
a) generate the maximum net profit
b) generate the maximum retained earnings
c) generate the maximum wealth for its shareholders
d) generate maximum funds for the firm at the least cost.
31. Financial management is indispensable in any organization as it helps in______________.
a) taking sound financial decisions
b) proper use and allocation
c) improving the profitability of funds
d) all the above
32. The decision function of financial management can be broken down into the__________
decisions.
a) financing and investment
b) investment, financing, and dividend
c) financing and dividend
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d) capital budgeting, cash management, and credit management
33. __________ is concerned with the maximization of a firm's stock price.
a) Shareholder wealth maximization
b) Profit maximization
c) Stakeholder welfare maximization
d) EPS maximization
34. What is the most appropriate goal of the firm?
a) Shareholder wealth maximization
b) Profit maximization
c) Stakeholder maximization
d) EPS maximization
35. Which of the following is a function of the finance manager?
a) Mobilizing funds
b) Risk returns trade off
c) Deployment of funds
d) Control over the uses of funds
e) All of above
Answer:
1
D
9
B
17
B
25
B
33
A
2
3
A
B
10
11
A
A
18
19
A
A
26
27
D
C
34
35
A
E
4
C
12
B
20
A
28
D
5
6
C
A
13
14
A
C
21
22
C
A
29
30
D
C
7
B
15
A
23
A
31
D
8
B
16
A
24
B
32
B
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CHAPTER 2
TIME VALUE OF MONEY
One of the essential features of a sound appraisal method for capital expenditure proposals
is the consideration of the time value of money. A project and many other financial
problems involve cash flows occurring at different points of time. For evaluating such cash
flows an explicit consideration of time value of money is required. In order to decide
whether the project is viable a mere matching of present outlays (Cash outflows) and the
benefits (cash inflows) in future period is not sufficient. For a meaningful comparison the
two variable must be strictly comparable. One basic requirement of comparability is the
incorporation of the time element in the calculation. It is necessary to convert the sums of
money to a common time. The net inflows of the future periods have to be discounted to
ascertain their present values. These then have to be compared with the present values of
investment. Thus, time value of money is an important factor to be considered in
investment decisions.
This time value of money principle is based on the following four reasons:
 Inflation – under inflationary conditions the value of money, expressed in terms of
its purchasing power over goods and services, declines
 Risk – Rs 1 now is certain, whereas Rs 1 receivable tomorrow is less certain. This
‘Bird-in-the-hand’ Principle is extremely important in investment appraisal.
 Personal Consumption Preference- Many individuals have a strong preference for
immediate rather than delayed consumption. The promise of a bowl of rice next
week counts for little to the starving man.
 Investment opportunities- Money like any other desirable commodity, has a price,
given the choice of RS 100 now or the same amount in one year ’s time, it is always
preferable to take the Rs 100 now because it could be invested over the next year at
(say) 18% interest rate to produce Rs 118 at the end of one year. If 18% is the best
risk-free return available, then you would be indifferent to receiving Rs 100 now or
Rs 118 in one year’s time. Expressed another way, the present value of Rs 118
receivable one year hence is Rs 100.
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 CONCEPT I
COMPUTATION OF PRESENT VALUE WHEN CASH FLOW ARE NOT CONSTANT
𝑷𝑽 =
𝑪𝒇𝟏
𝑪𝒇𝟐
𝑪𝒇𝟑
+
+
(𝟏 + 𝒊)𝟏 (𝟏 + 𝒊)𝟐 (𝟏 + 𝒊)𝟑
 i = opportunity Cost
Or
𝑷𝑽 = 𝑪𝑭𝟏 (𝑷𝑽𝑭)𝒏=𝟏 + 𝑪𝑭𝟐 (𝑷𝑽𝑭)𝒏=𝟐 + 𝑪𝑭𝟑 (𝑷𝑽𝑭)𝒏=𝟑
𝒓=𝒊
𝒓=𝒊
𝒓=𝒊
Example:Find Present Value of inflows of a project if Cash inflows for
Year 1
10000
Year 2
15000
Year 3
20000
Opportunity Cost = 10%
Answer:
𝑷𝑽 = 𝟏𝟎𝟎𝟎𝟎(𝑷𝑽𝑭) 𝒏=𝟏
𝒓=𝟏𝟎%
+ 𝟏𝟓𝟎𝟎𝟎 × (𝑷𝑽𝑭) 𝒏=𝟐
𝒓=𝟏𝟎%
+ 𝟐𝟎𝟎𝟎𝟎(𝑷𝑽𝑨𝑭) 𝒏=𝟑
𝒓=𝟏𝟎%
= 𝟏𝟎𝟎𝟎𝟎 ×. 𝟗𝟎𝟗 + 𝟏𝟓𝟎𝟎𝟎 ×. 𝟖𝟐𝟔 + 𝟐𝟎𝟎𝟎𝟎 ×. 𝟕𝟓𝟏 = RS 36500.
19 | P a g e
 CONCEPT II
COMPUTATION OF PRESENT VALUE WHEN CASH FLOW ARE NOT CONSTANT
𝑷𝑽 = 𝑪𝑭 (𝑷𝑽𝑨𝑭)𝒏=
𝒓=𝒊
PROOF;
𝑷𝑽 =
𝑪𝒇𝟐
𝑪𝒇𝟑
𝑪𝒇𝟏
+
+
𝟐
𝟏
(𝟏 + 𝒊)
(𝟏 + 𝒊)𝟑
(𝟏 + 𝒊)
𝟏
𝟐
𝟑
= 𝑪𝑭 [
+
+
]
(𝟏 + 𝒊)𝟏 (𝟏 + 𝒊)𝟐 (𝟏 + 𝒊)𝟑
= 𝑪𝑭 [(𝑷𝑽𝑭)𝒏=𝟏 + (𝑷𝑽𝑭)𝒏=𝟐 + (𝑷𝑽𝑭)𝒏=𝟑 ]
𝒓=𝒊
= 𝑪𝑭 (𝑷𝑽𝑨𝑭)𝒏=𝟑
𝒓=𝒊
𝒓=𝒊
𝒓=𝒊
Example:
Find Present value of inflows of a project if project generate Rs 10000 P.A. for 3
Consecutive Years. Opp. Cost = 10%
𝑃𝑉 = 𝐶𝐹 (𝑃𝑉𝐴𝐹) 𝑛=3 = 10000 (𝑃𝑉𝐴𝐹) 𝑛=3
𝑟 =10%
𝑟=10%
= 10000 (2.4868 ) = 24868
 CONCEPT III
COMPUTATION OF PRESENT VALUE OF PERPETUITY
𝑷𝒗 =
𝒄𝒇
𝒊
20 | P a g e
PROOF;
𝑷𝑽 =
𝑪𝒇𝟏
𝑪𝒇𝟐
𝑪𝒇𝟑
+
+
± −− −− ∞
(𝟏 + 𝒊)𝟏 (𝟏 + 𝒊)𝟐 (𝟏 + 𝒊)𝟑
𝟏
𝟐
𝟑
= 𝑪𝑭 [
+
+
+ − − − − −∞]
(𝟏 + 𝒊)𝟏 (𝟏 + 𝒊)𝟐 (𝟏 + 𝒊)𝟑
= 𝑪𝑭 [𝑺𝒖𝒎 𝒐𝒇 𝑮𝒆𝒐𝒎𝒂𝒕𝒓𝒊𝒄 𝒑𝒓𝒐𝒈𝒓𝒆𝒔𝒔𝒊𝒐𝒏 𝒖𝒑𝒕𝒐 ∞]
= 𝑪𝑭 [
𝒂
]  𝒂 = 𝟏𝒔𝒕 𝑻𝒆𝒓𝒎
𝟏−𝒓
𝟏
r = common ratio =
𝟏+𝒊
𝟏
𝟏
= 𝑪𝑭 [ + 𝒊 ]
𝟏− 𝟏
𝟏+𝒊
𝑪𝑭
=[ ]
𝒊
For Example
Find Present value of cash inflows related to a project, that will generate Rs 20000 P.A.
forever if opportunity cost = 10%
 CONCEPT IV
𝑃𝑉 =
𝐶𝐹 20000
=
= 𝑅𝑠 200,000
0.10
𝑖
An annuity where first payment is delayed beyond one year, the annuity is called as
deferred Annuity
PV of deferred Annuity
21 | P a g e
Example
Assume that a Rs.20,00,000 plant expansion is to be financed as follows: The firm makes a
15% down payment and borrows the remainder at 9% interest rate. The loan is to be
repaid in 8 equal annual installments beginning 4 years from now. What is the size of the
required annual loan payments?
ANSWER
Amount required
Down payment
Loan Amount
Rate of Interest
No. of Instalments
1St Instalment
=
=
=
=
=
=
Rs 20 Lakhs
15% i.e. Rs 3 Lakhs
17 Lakha
9% P.A.
8
End of 4th Year
(Step I)
Computation of PV at end of 3rd Year
1
3
2
4
5
6
7
8
9
10
11
x
x
x
x
x
x
x
x
𝑷𝑽 (𝒂𝒕 𝒆𝒏𝒅 𝒐𝒇 𝟑𝒓𝒅 𝒀𝒆𝒂𝒓 ) = 𝒙 × (𝑷𝑽𝑨𝑭) 𝒏=𝟖
𝑷𝑽 = 𝒙 × (𝑷𝑽𝑨𝑭) 𝒏=𝟖 × (𝑷𝑽𝑭) 𝒏=𝟑
𝒓=𝟗%
𝒓=𝟗%
𝒓=𝟗%
𝟏𝟕𝑳𝒂𝒌𝒉 = 𝒙 × 𝟓. 𝟓𝟑𝟒𝟖 × . 𝟕𝟕𝟐𝟐
𝟑𝟗𝟕𝟕𝟓𝟔 = 𝒙
UNSOLVED QUESTION
Question 1.
Assume that a deposit is to be made at year zero into an account that will earn 8%
compounded annually. It is desired to withdraw Rs.5,000 three years from now and
Rs.7,000 six years from now. What is the size of the year zero deposit that will produce
these future payments.
22 | P a g e
Answer:
8380
Question 2.
A potential investor is considering the purchase of a bond that has the following
characteristics: the bond pays 8% per year on its Rs.1,000 principal, or face value. The
bond will mature in 20 years. At maturity, the bondholder will receive interest for year 20
plus the Rs.1,000 face value. What is the maximum purchase price that should be paid for
this bond if the investor requires a 10% rate of return?
Answer:
830.12
Question 3.
An investor deposits a sum of Rs.1,00,000 in a bank account on which interest is credited @
10% p.a. How much amount can be withdrawn annually for a period of 15 years?
Answer:
13148)
Question 4.
What is the present value of cash flows of Rs.750 per year forever (a) at an interest rate of
8% and (b) at an interest rate of 10%?
Answer:
(a) Rs.9,375, and (b) Rs.7,500.]
Question 5.
What is the present worth of operating expenditures of Rs.1,00,000 per year which are
assumed to be incurred continuously throughout 8 years period if the effective annual rate
of interest is 12%?
Answer:
Rs.4,96,800.]
23 | P a g e
CHAPTER 3
VALUATION OF SECURITY
 CONCEPT 1
CONCEPT OF VALUATION
Valuation is the process of determining the worth of an assets. Any assets, physical or
financial, has value to the extent that it can satisfy desires, needs or wants of the holder.
The physical assets refer to the tangible assets such as land, building, stock, furniture, etc.
The financial assets refer to the financial claims such as bonds, preference share and equity
share etc. In this chapter, the valuation of only financial assets has been discussed. So, the
process of estimating the value of these financial asset is called valuation for the purpose of
this chapter. Every investor and finance manager must understand how to value the
financial assets to judge whether these are a good buy or not.
A number of concepts of valuation have been used in the literature. These different
concepts of valuation discussed here, have specific uses and purposes and therefore the
same assets may be valued differently by different person with different perspective.
 CONCEPT 2
BOND VALUATION
A bond or a debenture is a debt security issued by a borrower and subscribed/purchased
by a lender/investor. Bond is a tradition of long term financing used by firms which upon
issuing a bond, promise to make certain cash flows in future (in the form of interest and/or
repayment) under clearly defined terms and conditions. In order to understand the
valuation of bonds, the understanding of the following basic terms is required:
(i)
Par Value : The par value (also called face value or normal value) of a bond is the
principal amount of a bond and is stated on the face of the bond security. The par
value of a bond may be Rs. 100, Rs. 1,000 or any amount. The issue price, however,
may be less than, equal to or more than the par value. Similarly, the redemption
repayment may also be less than, equal to or more than the par value.
(ii) Coupon Rate : This is the rate at which interest on the par value of the bond is
payable as per the payment schedule. The interest may be paid annually, semi24 | P a g e
annually or even monthly. The coupon rate is usually described as % rate and is
applied to the par value to find out the periodic interest amount.
(iii) Maturity : The maturity of a bond refers to the period from the date of issue, after the
expiry of which the redemption repayment will be made to the investor by the
borrower firm.
Assumption : An assumption which may be required while valuing a bond is that the first
interest payment shall become due for payment after one year from the date of
purchase/issue of the bond.
Valuation Model : The value of a bond may be defined as the sum of the present values of
the future interest payments plus the present value of the redemption repayment. The
appropriate discount rate to find out the present value would be the required rate of return
Kd’ which depends upon the prevailing risk free interest rate and risk premium. Equation
17.2 of the basic valuation model may be modified to find out the value of a bond as follows
:
n
B0= ( ∑
−
i=1
Where,
Ii
RV
)+
I
(1 + k d )
(1 + k d )n
B0 = A value of bond at present,
Ii
= Annual interest payment starting one year from now till the end of year
n,
RV
Kd
=
=
Redemption repayment at the end of year n, and
Appropriate discount rate.
Question 1.
A bond of Rs. 1,000 bearing a coupon rate of 12% is redeemable at par in 10 years. Find out
the value of the bond if:
(i) Required rate of return is 12% or 10% or 14%.
(ii) Required rate of return is 14% and the maturity period is 8 years of 12 years.
(iii) Required rate of return is 12% and redeemable at Rs. 950 or at Rs. 1,050 after 10
years.
Answer.
The value of the bond can be ascertained by the Equation 6.3 as follows:
25 | P a g e
B0= ( ∑ni=1 − (
Ii
1+kd ) I
Or B0 =
Where, (PVAF) i, n
(PVF) i, n
RV
) + (1+k )n
d
I (PVAF) i, n + RV (PVF) i, n
=
Present Value Annuity Factor at the rate of interest i, and
number of years, n
= Present Value Factor for a given rate of interest i, and number of
years, n.
These values may be found from the Total A-4 and the Table A-3 respectively.
Now, the value of the bond under different situations can be ascertained as follows:
(1) Basic information
Coupon Rate 12%
Redeemable at par
Maturity 10 years
If the required rate of return is 12%
B0
=
120 (5.650) + 1,000 (.322)
=
678 + 322
=
Rs. 1,000.
If required rate of return is 10%
B0
=
120 (6.145) + 1,000 (.386)
=
737.4 + 386
Rs. 1,123.40.
If required rate of return is 14%
B0
=
120 (5.216) + 1,000 (.270)
=
625.92 + 270
=
Rs. 895.92.
(2) Basic information
Coupon Rate 12%
Redeemable at per
Maturity 8 years
Required Rate of return 14%
If maturity period is 8 years
26 | P a g e
B0
=
=
=
(3) Basic information
120 (4.639) + 1,000 (.351)
556.68 + 351
Rs. 907.68.
Coupon Rate 12%
Required rate of return 12%
Maturity 10 years
If redemption amount is Rs. 950
B0
=
120 (5.650) + 950 (.322)
=
678 + 305.90
=
Rs. 983.90.
If redemption amount is Rs. 1,050
B0
=
120 (5.650) + 1,050 (.322)
=
678 + 338.10
=
Rs. 1,016.10
 CONCEPT 3
BOND VALUE IN CASE OF SEMI-ANNUAL INTEREST
In case, the firm decides to pay the interest on half-yearly intervals, then the Equation 26.3
for bond valuation needs to be modified. The basic equation remains same, however,
following changes are required:
(i) Find out the half-yearly amount of interest by dividing the annual interest by 2.
(ii) The number of years to maturity is multiplied by two to get the number of half-year
periods till maturity.
(iii) The required rate of return is also converted to the half-year required rate of return by
dividing by 2.
𝑖
RV
2
B0= ∑ −
+
I
k 2n
i=1
kd
(1 + 2d )
(1
+
)
(
2 )
n
27 | P a g e
Question 2.
A bond of Rs. 1,000 bearing a coupon rate of 12% p.a. payable half-yearly is redeemable
after five year at par. Find out the value of the bond given that the required rate of return is
14%.
Answer.
Basic information Annual Interest
Kd
n
RV
=
=
=
=
Rs. 120
14%
5 years
Rs. 1,000.
Putting these value in Equation 6.3A, value of the bond is
= 60 (PVAF 7%, 10y ) + 1,000 (PVF 7%, 10y )
= 60 (7.024) + 1000 (.508)
= Rs. 929.
So, the value of the bond is Rs. 929. In the same case if the interest is payab le on yearly
interval, then the value of the bond as per Equation 6.3 is as follows:
=
=
=
120 (PVAF 14%, 5y ) + 1,000 (PVF 14%, 5y )
120 (3.433) + 1000 (.519)
Rs. 931.
Comparing the bond values under semi-annual interest payment (Rs. 929) and annual
interest payment (Rs. 93), it can be seen that the bond value is the less when semi-annual
interest in paid. This will always occur whenever the required rate of return is more than
the coupon rate (hence the bond is being valued to give a discount figure). Fu rther, in case
the required rate of return is less than the coupon rate, the semi-annual value will be more
than the value under annual interest payment.
YIELD TO MATURITY (YTM)
The cash flows in relation to a bond are consisting of regular interest pay ment and the
redemption repayment. The rate of return, K d’ which makes the discounted values of these
cash flows equal to the bond’s market value, is known as the YTM of the bond. So, a bond’s
YTM may be defined as the internal Rate of Return (IRR) for a given level of risk. When an
investor evaluates bonds in order to make a buy or not to buy decision, the evaluates bonds
in order done by finding out the IRR of the bond. is often done by finding out the value of
Kd in Equation 17.3. The YTM i.e., The IRR of a bond may be found by solving Equation 17.3
for the value of Kd’ given the value of B0’ the annual interest, I, the redemption value, RV
28 | P a g e
and time to maturity, n. Thus, the rate of return expected from a bond it is kept till maturity
is called the YTM of the bond.
While finding out the YTM, an implied assumption is that all interest received are
reinvested at a rate of return equal to bond’s YTM.
UNSOLVED QUESTION
(A) Bond Valuation
TYPE (I)
WHEN BONDS ARE REDEEMABLE.
Bo
Int.
Int.
Int. s
Int.
Int.+ Rv
Bo = Int (PvAf) + Rv (PVF)
Question 1.
A bond of Rs 1000 bearing a coupon rate of 12% is redeemable at par in 10 years.
Find value of bond if
(i)
(ii)
(iii)
Required return is 12%
Required return is 10%
Required return is 14%
Question 2.
A bond of Rs. 1,000 bearing a coupon rate of 12% p.a. payable half-yearly is redeemable
after five year at par. Find out the value of the bond given that the required rate of return is
14%.
Answer.
Basic information Annual Interest
Kd
n
RV
=
=
=
=
Rs. 120
14%
5 years
Rs. 1,000.
Putting these value in Equation value of the bond is
= 60 (PVAF 7%, 10y ) + 1,000 (PVF 7%, 10y )
= 60 (7.024) + 1000 (.508)
29 | P a g e
=
Rs. 929.
So, the value of the bond is Rs. 929. In the same case if the interest is paya ble on yearly
interval, then the value of the bond as per Equation is as follows:
= 120 (PVAF 14%, 5y ) + 1,000 (PVF 14%, 5y )
= 120 (3.433) + 1000 (.519)
= Rs. 931.
Comparing the bond values under semi-annual interest payment (Rs. 929) and annual
interest payment (Rs. 93), it can be seen that the bond value is the less when semi-annual
interest in paid. This will always occur whenever the required rate of return is more than
the coupon rate (hence the bond is being valued to give a discount figure). Furthe r, in case
the required rate of return is less than the coupon rate, the semi-annual value will be more
than the value under annual interest payment.
Question 3.
A Rs. 1,000 bond matures in 20 years and offer a 9% coupon rate. The required of return is
11%. Compute the bond’s value.
Answer.
The annual interest payment is Rs. 90. At the end of the year 20, the bondholder receives
the Rs. 90 interest payment and the Rs. 1,000 par value. The present value of the interest
payment is obtained by using the present-value annuity factor for 11% and 20 payments:
PV
=
Interest x (PVAF)
=
90 x 7.9633 = 716.67
n = 20
r = 11%
The present value of the Rs. 1,000 principal repayment is obtained by using the presentvalue, single-payment factor for 11% and 20 years:
PV
= Amount x (PVF11%, 20y)
= Rs. 1,000 x (.124) = Rs. 124
Therefore, the bond’s value is Rs. 840.67 (Rs. 716.67 + 124.00).
In this example, the discount rate exceeds the coupon rate. As a consequence, the bond ’s
intrinsic value is less than its par value.
30 | P a g e
Question 4.
The Elu Co. is contemplating a debenture issue on the following terms:
Face Value
=
Rs. 100 per Debenture.
Term to Maturity =
7 years.
Coupon rate of Interest:
Years 1-2
= 8% p.a.
3-4
= 12% p.a.
5-7
= 15% p.a.
The Current market rate of interest on similar debentures is 15% p.a. The company
propose to price the issue so as to yield a (compounded) return of 16% p.a. to the
investors. Determine the issue price. Assume the redemption on debenture at a premium of
5%.
Answer.
The interest payment over the life of the debentures and their present values are given in
the following Table:
Year
Interest
(Rs.)
PVF @
16%
1
2
3
4
5
6
7
8
8
12
12
15
15
15
.862
.743
.641
.552
.476
.410
.354
Total
Present
value
(Rs.)
6.896
5.944
7.692
6.624
7.140
6.150
5.310
45.756
The present value of the redemption amount of Rs. 105 (Rs. 100+Rs.5) @ 16% p.a. is
Rs. 105 x .354 =
Rs. 37.17
Therefore, the present value of the debenture is Rs. 45.76 + Rs. 37.17 = Rs. 82.93. The
company should issue the debentures at this value in order to yield a return of 16% to the
investors.
31 | P a g e
Question for practice
Question 1.
2004 - Dec [2] (b) Blue Ltd. is contemplating a debenture issues on the following terms:
Face value
Rs. 100 per debenture
Terms to maturity
7 years
Coupon:
Year
1-2
8% p.a
3-4
12% p.a
5-7
15% p.a
The current market rate of interest on similar debentures is 15% per annum. The company
proposes to price the issue so as to yield a (compounded) return of 16% per annum to the
investors. Determine the issue price. Assume the redemption of debentures at a premium
of 5%. (10 marks)
(a) 82.926
(b) 85
(c) 80
(d) 90
Answer - A
Question 2.
[Intrinsic Value of Bond – DCF Approach]
Trooper Corporation has a bond issue with a coupon rate of 10% per years and 5 years
remaining until maturity. The par value of the bond is Rs. 1,000. What is the value of the
bond when the required rate of return of Bond – holders is (a) 6% (b) 10% and (12%)
Answer.
(a) Rs. 1,168.20
(b) s. 1,000
(c) 927.50
Question 3.
A firm pays a dividend of 20% on the equity shares of face value of Rs. 100 each. Find out
the value of the equity share given that the dividend rate is expected to remain same and
the required rate of return of the investor is 15%.
Answer.
In this situation, the following information is given:
32 | P a g e
Therefore,
Ke
D
= 15%
= 20(i.e., 20% of Rs. 100)
P0
=
TYPE (II)
20
0.15
= Rs. 133.33
IN-CASE VALUE OF ZERO COUPON BOND
Question 4.
Suppose we are considering investing in a zero-coupon bond that matures in 15 years and
has a face value of Rs. 1000. If these bonds are priced to yield 10% what is the present
value of the bonds?
Answer.
239.40
TYPE (III)
VALUE OF IRREDEEMABLE BOND
Question 5.
A bond pays Rs. 90 interest annually upto perpetuity. What is its value if the yield is (i) 10%
and (II) 8% and (iii) 12% ?
VALUATION OF EQUITY SHARE:
TYPE (I)
WHEN INVESTMENT IS FOR ONE YEAR.
P0
P1
D1
𝑷 +𝑫
𝟏
𝟏
P0 = 𝟏+𝑲
𝒆
Question 6.
Find out current price of equity if, it is expected that price at the end of year 1 will be 10 5&
dividend at end of year 1 Rs. 10 With opportunity Cost of investor 14%.
33 | P a g e
Answer.
P0 = Rs. 100.877
Question 7.
Find out current MP if price & dividend at end of year 1 is expected to be 110 & 10
respectively & opportunity cost of investor  10%.
Answer.
P0 = Rs. 109.09
TYPE (II)
WHEN INVESTMENT IS FOR 2 YEAR.
P0
D1
𝑫
P0 = 𝟏+𝒌𝟏 +
𝒆
D2
P2
𝑫𝟐+𝑷𝟐
(𝒊+𝑲𝒆 )𝟐
Question 8.
Fine out current price of equity share if dividend at end of year 1 & year 2 amounted to Rs
10 & Rs 12 and MP at end of year 2 amount to Rs 105. & opportunity Cost of investor is
10%
Answer.
P0 = Rs. 105.78
TYPE (III)
WHEN INVESTMENT IS FOR FOREVER AND THERE IS NO GROWTH.
Po
D
D
D
D
D
Question 9.
Fine value of equity share is dividend of Rs 10 is expected every year & opp. Cost of
investor is 10% or 8% or 15%
Answer.
(i) P0 = 100 (ii) P0 = 125 (iii) P0 = 66.67
TYPE (IV)
GROWTH.
WHEN INVESTMENT IS FOR FOREVER AND THERE IS PERPETUAL
34 | P a g e
𝑷𝐨
Where,
𝐃𝐢
𝐊𝐞 − 𝐠
Di = Expected Dividend i.e. D o(i +g )
Ke= Opportunity cost of investor
g= Growth rate
Question 10.
Compute value of equity share if last year dividend Rs 10, growth rate 8% and opportunity
cost is 10%/12% /14%
Answer.
(i) P0 = 540 (ii) P0 = 270 (iii) P0 = 180
TYPE (V)
WHEN INVESTMENT IS FOR FOREVER BUT GROWTH RATE VARIES
Question 11.
A firm is paying a dividend of Rs. 1.50 per share. The rate of dividend is expected to grow at
10% for next three years and 5% thereafter infinity. Find out the value of the share given
that the required rate of return of the investor is 15%.
Answer.
For the situation, the following information is available:
Ke
= 15%
D0 = Rs. 1.50
G1
= 10% (for 3 years)
g2 =
5% (infinitely)
Now, the value may be calculated as follows:
End of Year
Div. Amt. (Rs.)
PVF (15%, n)
PV
1
1.65
0.870
1.44
2
1.82
0.756
1.38
3
2.00
0.658
1.32
Rs. 414
Rs. 414 is the present value of dividends expected from the company for first three years.
The value of the equity shares at the end of year three will be as follows:
35 | P a g e
P3
=
P3
=
D3 (1 + g)
Ke - g
2(1.05)
15 - .05
= Rs. 21
The value of the share at the end of the year 3 will be Rs. 21. The present value of Rs. 21 is:
=
Rs. 21 x (PVF15%, 3y)
=
Rs. 21 x (.658)
= Rs. 13.82
The value of the share at present is Rs. 4.14 + Rs. 13.82 i.e., Rs. 17.96.
Question 12.
Bharat Ltd. is foreseeing a growth rate of 20% p.a. for next two years. The growth rate is
likely to fall to 15% for the next two years. After that the growth rate is expected to
continue at 10% p.a. The company paid a dividend of Rs. 2 per share last ye ar. Investor’s
required rate of return is 20%. At what price would you as investor be ready to buy the
shares of this company now (t = 0) ?
Answer.
P0 = Rs. 27.94
Question 13.
Bharat Ltd. is foreseeing a growth rate of 20% p.a. for next two years. The growth rate is
likely to fall by 25% for the next year. During fourth year the growth rate will be same as in
the third year. After than the growth rate is likely to fall by 33-1/3% and expected to
continue thereafter. The company paid a dividend of Rs. 2 per share last year. Investor ’s
required rate of return is 20%.
Answer.
P0 = Rs. 27.94
Question 14.
Madhu is considering the purchase of stock X at the beginning of the year. The dividend at
year-end is expected to be Rs. 3.25 and the market price by the end of the year is expected
to be Rs. 25 if she requires a 12% return, what is the intrinsic value o f stock ? If actual
market value of the stock is Rs. 22 what do you advise her?
36 | P a g e
Answer.
Intrinsic Value = Rs. 25.23; Purchase the stock)
Question 15.
D Ltd. is foreseeing a growth rate of 12% per annum in the next two years. The growth rate
is likely to be 10% for the third and fourth year. After that the growth rate is expected to
stabilize at 8% per annum. If the last dividend was Rs. 1.50 per share and the investor ’s
required rate for return is 16%, determine the current value of equity share of the
company. The P.V. factors at 16%
Year
1
2
3
4
P.V. Factor
0.862
0.743
0.641
0.552
Answer.
Rs. 22.41
Question 16.
D Ltd. is foreseeing a growth rate of 12% per annum in the next two years. The growth rate
is likely to be 10% for the third and forty year. After that the growth rate is expected
stabilize at 8% per annum. If the last dividend was Rs. 1.50 per share and the investor ’s
required rate of return is 16%, determine the current value of equity share of the company.
The P.V. factors at 16%.
Year
1
2
3
4
P.V. Factor
.862
.743
.641
.552
Answer.
Value of equity share Rs. 22.43
Question 17.
A large sized chemical company has been expected to grow at 14% per year for the next 4
years and then to grow indefinitely at the same rate as the national economy, i.e. 5%. The
required rate of return on the equity shares is 12%. Assume that the company paid a
dividend of Rs.2 per share last year (D 0 = 2) Determine the market price of the shares
today.
37 | P a g e
Answer.
Rs.40.62.
MULTIPLE CHOICE QUESTIONS
1. If the required rate of return of a particular bond is less than coupon rate, it is
known as
a) Discount Bond
b) Premium Bond
c) Par Bond
d) Junk Bond.
2. Market interest rate and bond price have
a) Positive relationship
b) Inverse relation
c) No relationship
d) Same relationship
3. If a coupon bond is selling at discount, then which of the following is true?
a) Po < Par and YTM < coupon
b) Po < Par and YTM > coupon
c) Po > Par and YTM < coupon
d) Po > Par and YTM > coupon
4. In the formula ke (D1/P0) + g, D 1/P0 refers to
a) Capital gain yield
b) Dividend yield
c) Interest yield
d) None of the above
5. The rate of interest payable on a bond is also called
a) Effective Rate of Interest
b) Yield to Maturity
c) Coupon Rate
d) Internal Rate of Return.
38 | P a g e
6. Rate of Interest on convertible debenture is generally________the rate on nonconvertible debentures
a) Lower than
b) Higher than
c) Same as
d) None of the above.
7. A 16% bond with a face value of Rs. 250 is available for Rs. 200 in the market. They
yield on the bond is
a) 16%
b) 20%
c) 80%
d) 32%
8. Market Price of Bond and Market Rate of Interest
a) Inverse relationship
b) Positive relationship
c) No relationship
d) None of the above.
9. Which of the following is a feature of zero-coupon bonds?
a) Sold at Par
b) Sold at premium
c) Pays no Interest
d) Not Redeemable.
10. Which of the following will cause an increase in bond values?
a) Decrease in Redemption Amount
b) Decrease in Coupon Rate
c) Increase in Redemption Amount
d) Increase in Redemption Period.
11. In a 3 years Bond purchased and held till maturity, the rate earned is called
a) Coupon Rate
b) Yield to Maturity
c) Current Yield
39 | P a g e
d) Holding Period Return.
12. An investor should buy a bond if
a) Intrinsic Value < Market Value
b) Intrinsic Value > Market Value
c) Market Value < Redemption Value,
d) Market Value = Redemption Value.
13. Current Market Price of a Bond is equal to its Par Value if
a) Face Value is Rs. 1000
b) Coupon is paid half yearly
c) Coupon Rate = Current Yield
d) It is a Government Bond.
14. If the coupon rate and required rate of return are equal, the value of the bond is
equal to
a) Market Value
b) Par Value
c) Redemption Value
d) None of the above.
15. An investor buys a bond today and sells after 3 months the rate of return realised is
known as
a) Yield to Maturity
b) Current yield
c) Holding Period Return
d) Required Rate of Return.
16. What's the worth to you of a Rs.1,000 face-value bond with an 8% coupon rate when
your required rate of return is 15 percent?
a) More than its face value.
b) True.
c) Rs.1,000.
d) Less than its face value.
17. The value of bond depends on ____________.
a) the coupon rate
40 | P a g e
b) years to maturity
c) expected yield to maturity
d) all the above
18. An annual interest payment divided by current price of bond is considered as
a) current yield
b) maturity yield
c) return yield
d) earning yield
19. If coupon rate is more than going rate of interest then bond will be sold
a) more than its par value
b) seasoned par value
c) at par value
d) below its par value
20. If market interest rate rises above coupon rate then bond will be sold
a) equal to return rate
b) seasoned price
c) below its par value
d) above its par value
21. Bonds that can be converted into shares of common stock are classified as
a) convertible bonds
b) stock bonds
c) shared bonds
d) common bonds
Answer1
2
B
B
6
7
A
B
11
12
B
B
16
17
21
D
3
4
B
B
8
9
A
C
13
14
C
B
18
19
A
D
5
C
10
C
15
C
20
C
A
41 | P a g e
CHAPTER 4
COST OF CAPITAL
LEARN OBJECTIVE
After studying this chapter you will be able to:

Understand the concept of "Cost of Capital” that impacts the capital investment
decisions for a business.

Understand what are the different sources of capital (Debt, Equity Shares, preference
share etc.)

Understand what is the cost of employing each of these sources of capital?

Know what is weighted average cost of capital (WACC) (Overall cost of capital) for a
business and also what is marginal cost of capital?

Summarize how cost of capital is important in financial management.
 CONCEPT 1
INTRODUCTTON
The financing decision relates to the composition of relative proportion of various sources
of finance. The sources could be:1. Shareholders Fund: - Equity Share Capital, Preference Share Capital, Accumulated
Profits.
2. Borrowing From Outside Agencies:- Debentures, Loans from Financial institutions
The financial management weighs the merits and demerits of different sources of finance
while taking the financing decision. Whether the companies choose shareholders funds or
borrowed funds or a combination of both (which is generally the case), each type of fund
carries a cost.
The cost of equity is the minimum return the shareholders would have received if they had
invested elsewhere. Borrowed funds cost involve interest payment.
42 | P a g e
Both types of funds incur cost and this is the cost of capital to the company. This means,
cost of capital is the minimum return expected by the company.
Whenever funds are to be raised to finance investments, capital structure decision is
involved. A demand for raising funds generates a new capital structure since a decision has
to be made as to the quantity and forms of financing.
 CONCEPT 2
DEFINITION OF COST OF CAPITAL
In simple terms Cost of capital refers to the discount rate that is used in determining the
present value of the estimated future cash proceeds of the business /new project and
eventually deciding whether the business/new project is worth undertaking or now.
It is also the minimum rate of return that a firm must earn on its investment which will
maintain the market value of share at its current level.
It can also be stated as the opportunity cost of an investment, i.e. the rate of return that a
company would otherwise be able to earn at the same risk level as the investment that has
been selected. For example, when an investor purchases stock in a company, he/she
expects to see a return on that investment. Since the individual expects to get back more
than his/her initial investment, the cost of capital is equal to this minimum return that the
investor expects to receive (also termed as investor opportunity cost).
The cost of each source of capital (Equity Share or Debt) is called specific cost of capital.
When these specific costs are combined for all the sources of capital for a business, then we
arrive at overall cost of capital for a business.
We will first discuss the specific cost of capital for each source of capital before discussing
and defining the overall cost of capital.
 CONCEPT 3
MEASUREMENT OF COST OF CAPITAL
In order to calculate the specific cost of each type of capital, recognition should be given to
the explicit and the implicit cost. The cost of capital can be either explicit of implicit.
The explicit cost of any source of capital may be defined as the discount rate that equals
that present value of the cash inflows that are incremental to the taking of financing
opportunity with the present value of its incremental cash outflows.
43 | P a g e
lmplicit cost is the rate of return associated with the best investment opportunity for the
firm and its shareholders that will be foregone if the project presently under consideration
by the firm was accepted. Opportunity costs are technically referred to as implicit cost o f
capital.
The distinction between explicit and implicit costs is important from the point of view d,
the computation of the cost of capital.
The first step in the measurement of the cost of the capital of the firm is the calculation of
the cost of individual sources of raising funds. From the viewpoint of capital budgeting
decisions, the long term sources of funds are relevant as they constitute the major sources
of financing the fixed assets. ln calculating the cost of capital, therefore the focus on
longterm funds and which are:i.
ii.
iii.
iv.
Long term debt (including Debentures)
Preference Shares
Equity Capital
Retained Earnings
 CONCEPT 4
COST OF DEBT
The calculation of the cost of debt is relatively easy, A debt may be in the form of Bond or
Debenture.
A bond is a long term debt instrument or security. Bonds issued by the government do not
have any risk of default. The government honour obligations on its bonds. Bonds of the
public sector companies in India are generally secured, but they are not free from the risk
of default.
The private sector companies also issue bonds, which are also called debentures in India. A
company in India can issue secured or unsecured debentures.
The chief characteristics of a bond or debenture are as follows:
Face value: Face value is called par value. A bond or debenture is generally issued at a par
value of Rs. 100 or Rs. 1,000, and interest is paid on face value.
44 | P a g e
Interest rate: interest rate is fixed and known to bondholders or debenture holders.
Interest paid on a bond or debenture is tax deductible. The interest rate is also called
coupon rate. Coupons are detachable certificates of interest.
Maturity: A bond or debenture is generally issued for a specified period of time. It is repaid
on maturity.
Redemption value: The value that a bondholder or debenture holder will get on maturity
is called redemption or maturity value. A bond or debenture may be redeemed at par or at
premium (more than par value) or at discount (less than par value).
Market value: A bond or debenture may be traded in a stock exchange. The price at which
it is currently sold or bought is called the market value of the bond or debenture. Market
value may be different from par value or redemption value.
 CONCEPT 5
COST OF DEBENTURES
The cost of debentures and long term loans is the contractual interest rate adjusted further
for the tax liability of the company. For a company, the higher the interest charges, the
lower the amount of tax payable by the company. An illustration will help you in
understanding this point.
Illustration 1:
Consider two companies X and Y:
Earnings before interest and taxes (EBIT)
Interest (l)
Profit before tax (PBT)
Tax (T)1
Profit after tax (PAT)
Company
X
100
100
35
65
Company
Y
100
40
60
21
39
Assume an effective rate of tax of 35 percent
Solution
A comparison of the two companies shows that an interest payment of 40 in company Y
results in a tax shield of 14 - that is 40 multiplied by 0.35, the corporate tax rate.
45 | P a g e
The important point to remember, while calculating the average cost of capital, is that the
post-tax cost of debt must be used and not the pre-tax cost of debt.
 CONCEPT 6
COST OF IRREDEEMABLE DEBENTURES:
Cost of debentures not redeemable during the life time of the company.
𝐾𝑑 =
Where,
Kd
I
NP
t
=
=
=
=
1
(1 − 𝑡)
𝑁𝑃
Cost of debt after tax
Annual interest payment
Net proceeds of debentures
Tax Rate
 CONCEPT 7
COST OF REDEEMABLE DEBENTURES
lf the debentures are redeemable after the expiry of a fixed period, the cost of debentures
would be:
𝐾𝑑 =
Where,
I
NP
RV
t
N
=
=
=
=
=
𝐼(𝐼 − 𝑡) + (𝑅𝑉 − 𝑁𝑃)/𝑁
𝑅𝑉 + 𝑁𝑃
2
Annual interest payment
Net proceeds of debentures
Redemption value of debentures
Tax Rate
Life of debentures.
Illustration 2:
46 | P a g e
A company issued 10,000, 10% debentures of Rs. 100 each on 1.4.2006 to be matured
on1.4.2011. If the market price of the debentures is Rs.80. Compute the cost of debt
assuming 35% tax rate.
Solution
𝑅𝑉 − 𝑁𝑃
𝐼 (𝐼 − 𝑡) +
𝑁
𝐾𝑑 =
𝑅𝑉 + 𝑁𝑃
2
𝐾𝑑 =
100 − 80
)
5
100 + 80
2
10(1 − .35) + (
=
6.5 + 4
90
= 0.1166
= 0.12
Illustration 3:
Five years ago, Sona Limited issued 12 per cent irredeemable debentures at Rs. 103, a Rs. 3
premium to their par value of Rs. 100. The current market price of these debentures is Rs.
94. If the company pays corporate tax at a rate of 35 per cent what is its current cost of
debenture capital?
Solution
Kd
=
Kd (after tax) =
12/94 = 12.8 per cent
12.8× (1-0.35) = 8.3 per cent
 CONCEPT 8
COST OF PREFERENCE SHARES
The cost of preference share capital is the dividend expected by its holders. Though
payment of dividend is not mandatory, non-payment may result in exercise of voting rights
by them.
47 | P a g e
The payment of preference dividend is not adjusted for taxes as they are paid after taxes
and is not deductible.
The cost of preference share capital is calculated by dividing the fixed dividend per share
by the price per preference share.
Illustration 5: lf Reliance Energy is issuing preferred stock at Rs.100 per share, with a
stated dividend of Rs.12, and a floatation cost of 3% then, what is the cost of preference
share?
Solution
𝑲𝒑 =
Preferred stock dividend
Market priceof preferred stock(1 – floatation cost)
=
 CONCEPT 9
𝑅𝑠. 12
= 12.4%
𝑅𝑠. 100(1 − 0.03)
COST OF IRREDEEMABLE PREFERENCE SHARES
𝑃𝐷
Cost of irredeemable preference shares = 𝑃𝑂
Where,
PD
Po
=
=
Annual preference dividend
Net proceeds in issue of preference shares.
Cost of irredeemable preference shares where Dividend Tax is paid over the actual
𝑃𝐷
dividend payment =
(1 + 𝐷𝑡 )
𝐏𝐨
Where,
PD
Po
Dt
=
=
=
Annual preference dividend
Net proceeds in issue of preference shares.
Tax on preference dividend
Illustration 6:
48 | P a g e
XYZ & Co. issues 2,000 10% preference shares of Rs. 100 each at Rs.95 each. Calculate the
cost of preference shares.
𝐊𝐩 =
𝐊𝐩 =
PD
𝑃0
(10 × 2,000)
(95 × 2,000)
=
10
95
= 0.1053
 CONCEPT 10
COST OF REDEEMABLE PREFERENCE SHARES:
lf the preference shares are redeemable after the expiry of a fixed period the cost of
preference shares would be:
Where,
PD
RV
NP
N
Kp =
=
=
=
=
PD + (RV − NP)/N
RV + NP
2
Annual preference dividend
Redemption value of preference shares
Net proceeds on issue of preference shares
Life of preference shares.
However, since dividend of preference shares is not allowed as deduction from income for
income tax purposes, there is no question of tax advantage in the case of cost of preference
shares.
The cost of redeemable preference share could also be calculated seen as the discount rate
that equates the net proceeds of the sale of preference shares with the present value of the
future dividends and principal payments.
It would, thus, be seen that both in the case of debt as well as preference shares, cost of
capital is calculated by reference to the obligations incurred and proceeds received.
Illustration 7:
49 | P a g e
Referring to the earlier question but taking into consideration that if the company proposes
to redeem the preference shares at the end of 10th year from the date of issue. Calculate
the cost of preference share?
Solution
Kp =
 CONCEPT 11
Kp =
PD + (RV − NP)/N
RV + NP
2
100 − 95
)
10
= .107 (approx)
100 + 95
)
(
2
10 + (
COST OF EQUITY
It may prima facie appear that equity capital does not carry any cost. But this is not true.
The market share price is a function of return that equity shareholders expect and get. If
the company does not meet their requirements. it will have an adverse effect on the market
share price' Also, it is relatively the highest cost of capital. Since expectations of equity
holders are high, higher cost is associated with it.
In simple words Cost of equity capital is the rate of return which equates the present va lue
of expected dividends with the market share price. In theory the management strives to
maximize the position of equity holders and the effort involves many decisions.
The calculation of equity capital cost raises a lot of problems. Different methods a re
employed to compute the cost of equity capital.
(a)
Dividend Price Approach: Here, cost of equity capital is computed by dividing the
current dividend by average market price per share. However, this method cannot be
used to calculate cost of equity of units suffering losses.
This dividend price ratio expresses the cost of equity capital in relation to what yield the
company should pay to attract investors.
𝐾𝑒 =
Where,
Ke
𝐷1
𝑃𝑜
= Cost of equity
50 | P a g e
D1
Po
= Annual dividend
= Market value of equity (ex dividend)
This model assumes that dividends are paid at a constant rate to perpetuity. It ignores
taxation.
Earnings and dividends do not remain constant and the price of equity shares is a/so directly
influenced by the growth rate in dividends. Where earnings, dividends and equity share price
all grow at the same rate, the cost of equity capital may be computed as follows:
Where,
D1
Po
G
=
=
=
K e = (D1 /Po ) + G
[Do (1+G)] i.e. next expected dividend
Current Market price per share
constant Growth Rate of Dividend.
Cost of newly issued shares, K n, is estimated with the constant dividend growth model so as
to allow for flotation costs.
K n = (D1 /Po) + G
Where,
F
=
Amount of flotation cost per share
Illustration 8:
A company has paid dividend of Rs. 1 per share (of face value of Rs. 10 each) last year and it
is expected to grow @ 10% next year. Calculate the cost of equity if the market price of
share is Rs. 55.
Solution
Ke =
Ke =
D
+G
P
1(1 + .10)
+ .10
55
51 | P a g e
= .1202 (approx)
(b)
Earning/ Price Approach: The advocates of this approach co-relate the earnings of the
company with the market price of its share.
Accordingly, the cost of ordinary share capital would be based upon the expected rate of
earnings of a company. The argument is that each investor expects a certain amount of
earnings, whether distributed or not from the company in whose shares he invests.
Thus, if an investor expects that the company in which he is going to subscribe for shares
should have at least a 20% rate of earning, the cost of ordinary share capital can be
construed on this basis. Suppose the company is expected to earn 30% the investor will be
30
prepared to pay Rs. 150 (Rs. × 100) tor each share of Rs. 100.
20
So, cost of equity will be given by.
K e = (E/P)
Where,
E
P
=
=
Current earring per share
Market share price
Since practically earning do not remain constant and the price of equity shares is also directly
influenced by the growth rate in earning, we need to modify the above calculation with an
element of growth,
So, cost of equity will be given by.
K e = (E/P)
Where,
E
P
G
=
=
=
Current earring per share
Market share price
Annual growth rate of earnings.
The calculation of 'G' (the growth rate) is an important factor in calculating cost of equity
capital. The past trend in earnings and dividends may be used as an approximation to
predict the future growth rate if the growth rate of dividend is fairly stable in the past.
52 | P a g e
G = 1.0 (1+G) n where n is the number of years
The Earning Price Approach is similar to the dividend price approach; only it seeks to
nullify the effect of changes in the dividend policy.
(c)
Realized Yield Approach: According to this approach, the average rate of return
realized in the past few years is historically regarded as 'expected return' in the future.
The yield of equity for the year is:
𝐷𝑡 + 𝑃𝑡 − 𝑃𝑡−1
𝑃𝑡−1
Where,
Y1
Dt
Pt
Pt-1
=
=
=
=
Yield for the year t,
Dividend for share for end of the year t
Price per share at the end of the year t
Price per share at the beginning and at the end of the year t
Though, this approach provides a single mechanism of calculating cost of equity, it has
unrealistic assumptions. If the earnings do not remain stable, this method is not practical.
(d)
Capital Asset Pricing Model Approach (CAPM): CAPM model describes the risk
return trade-off for securities. It describes the linear relationship between risk and
return for securities. The risks to which a security is exposed are divided into two
groups, diversifiable and non-diversifiable.
The diversifiable risk can be eliminated through a portfolio consisting of large number of
well diversified securities.
The non-diversifiable risk is attributable to factors that affect all businesses. Examples of
such risks are: Interest Rate Chances
 Inflation
 Political Changes etc.
53 | P a g e
As diversifiable risk can be eliminated by an inventor through diversification, the non'
diversifiable risk in the only element risk, therefore a business should be concerned as per
CAPM method, solely with non-diversifiable risk.
The non-diversifiable risks are assessed in terms of beta coefficient (b or p) through fitting
regression equation between return of a security and the return on a market portfolio.
Required Return
SML
Ke = Rf + (Rm - Rf) β
Rf
Risk Premium
(Rm - Rf) β
Cost of Equity under CAPM
Risk (β)
Thus, the cost of equity capital can be calculated under this approach as:
Ke = Rf + b (Rm – R1)
Where,
Ke
=
Cost of equity capital
Rf
=
Rate of return on security
b
=
Beta coefficient
Rm
=
Rate of return on market portfolio
Therefore, required rate of return = risk free rate + risk premium
54 | P a g e
The idea behind CAPM is that investors need to be compensated in two ways- time value of
money and risk.
 The time value of money is represented by the risk- free rate in the formula and
compensates the investors for placing money in any investment over a period of time.
 The other half of the formula represents risk and calculates the amount of
compensation the investor needs for taking on additional risk. This is calculated by
taking a risk measure (beta) which compares the returns of the asset to the market over
a period of time and compares it to the market premium.
The CAPM says that the expected return of a security or a portfolio equals the rate o n a risk
free security plus a risk premium. If this expected return does not meet or beat the
required return, then the investment should not be undertaken.
The shortcomings of this approach are:
a) Estimation of betas with historical data is unrealistic; and
b) Market imperfections may lead investors to unsystematic risk.
Despite these shortcomings, the capital asset pricing approach is useful in calculating cost
of equity, even when the firm is suffering losses.
The basic factor behind determining the cost of ordinary share capital is to measure the
expectation of investors from the ordinary shares of that particular company. Therefore,
the whole question of determining the cost of ordinary shares hinges upon the factors
which go into the expectations of particular group of investors in a company of a particular
risk class.
Illustration 9:
Calculate the cost of equity capital of H Ltd., whose risk free rate of return equals 10%. The
firm's beta equals 1.75 and the return on the market portfolio equals to 15 %.
Solution
Ke =Rr+b (Rm-Rr)
Ke = .10 + 1.75 (.15 -.10)
=.10 + 1.75 (.05)
=.1875
55 | P a g e
 CONCEPT 12
WEIGHTED AVERAGE COST OF CAPITAL (WACC)
WACC (weighted average cost of capital) represents the investors' opportunity cost of
taking on the risk of putting money into a company.
Since every company has a capital structure i.e. what percentage of funds comes from
retained earnings, equity shares, preference shares, debt and bonds, so by taking a
weighted average, it can be seen how much cost/interest the company has to pay for every
rupee it borrows/invest. This is the weighted average cost of capital.
The weighted average cost of capital for a firm is of use in two major areas:1. In consideration of the firm's position
2. Evaluation of proposed changes necessitating a change in the firm's capital. Thus, a
weighted average technique may be used in a quasi-marginal way to evaluate a
proposed investment project, such as the construction of a new building.
Thus, weighted average cost of capital is the weighted average after tax costs of the
individual components of firm's capital structure. That is, the after tax cost of each debt and
equity is calculated separately and added together to a single overall cost of capital.
Where,
Ko
Ki
1-t
Kp
Ke
% Dmkt
% Psmkt
% Cs
𝐊 𝐨 = %D(Mkt)(K i )(1 − t) + (% Psmkt)K p + (Cs mkt)K e
=
=
=
=
=
=
=
=
overall cost of capital
Before tax cost of debt
1- Corporate tax rate
Cost of preference capital
Cost of equity
% of debt in capital Structure
% of preference share in capital structure
% of equity share in capital structure.
The cost of weighted average method is preferred because the proportions of various
sources of funds in the capital structure are different. To be representative, therefore, cost
of capital should take into account the relative proportions of different sources of finance.
56 | P a g e
Securities analysts employ WACC all the time when valuing and selecting investments. In
discounted cash flow analysis, WACC is used as the discount rate applied to future cash
flows for deriving a business's net present value. WACC can be used as a hurdle rate against
which to assess return on investment capital performance. It also plays a key role in
economic value added (EVA) calculations.
Investors use WACC as a tool to decide whether or not to invest. The WACC represents the
minimum rate of return at which a company produces value for its investors. Let's say a
company produces a return of 20o/o and has a WACC of 110/o. By contrast, if the
company's return is less than WACC, the company is shedding value, which indicates that
investors should put their money elsewhere.
Therefore, WACC serves as a useful reality check for investors.
 CONCEPT 13
MARGINAL COST OF CAPITAL
The marginal cost of capital may be defined as the cost of raising an additional rupee of
capital.
Since the capital is raised in substantial amount in practice marginal cost is referred to as
the cost incurred in raising new funds. Marginal cost of capital is derived, when the average
cost of capital is calculated using the marginal weights.
The marginal weights represent the proportion of funds the firm intends to employ. Thus,
the problem of choosing between the book value weights and the market value weights
does not arise in the case of marginal cost of capital computation.
To calculate the marginal cost of capital, the intended financing proportion should be
applied as weights to marginal component costs. The marginal cost of capital should,
therefore, be calculated in the composite sense. When a firm raises funds in proportional
manner and the component's cost remains unchanged, there will be no difference between
average cost of capital (of the total funds) and the marginal cost of capital. The component
costs may remain constant upto certain level of funds raised and then start increasing with
amount of funds raised.
For example, the cost of debt may remain 7% (after tax) till Rs. 10 lakhs of debt is raised,
between Rs. 10 lakhs and Rs. 15 lakhs, the cost may be 8% and so on. Similarly, if the firm
has to use the external equity when the retained profits are not sufficient, the cost of equity
will be higher because of the floatation costs. When the components cost start rising, the
average cost of capital will rise and the marginal cost of capital will however, rise at a faster
rate.
57 | P a g e
PART I :- SPECIFIC COST OF CAPITAL
(A) COST OF DEBENTURE (Kd)
TYPE -1
Where,
WHEN REDEMPTION INFORMATION IS GIVEN.
𝑅 − 𝐵𝑜
𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 (1 − 𝑡) + 𝑉
𝑁
𝒌𝒅 =
× 100
𝑅𝑣 + 𝐵𝑜
(
)
2
Kd= cost of debt
Interest = coupon rate X face value
RV = Redemption value
Bo = net proceeds
N = no. of years for which debentures are issued
t = tax rate
Question 1.
ASC Ltd issued Rs 100 lakh 12% debentures of Rs 100 each redeemable after 5 years at
par. Compute cost of debt.
(i)
(ii)
(iii)
(iv)
If debentures are issued at par with no floatation cost
If debentures are issued at par with 5% floatation cost
If debentures are issued at 10% premium with 5% floatation cost
If debentures are issued at 10% discount with 5% floatation cost (Assume
Corporate
tax -40%)
Answer.
(a)
7.2% (b)
8.41% (c)
6.16% (d)
10.89%
Question 2.
A Ltd issued Rs 100 lakh 12% debentures of Rs 100 each redeemable after 5 years at
premium of 5%, if debentures are issued at par with no floatation cost (Assume corporate
tax 40%).
Answer.
8%
Question 3.
[Cost of Debt Redeemable (at par) in Lump Sum Payment]
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Tulsian Ltd. issued Rs. 100 Lakhs 12% Debentures of Rs. 100 each redeemable at par after
5 years. Calculate the cost of debt according to Approximation Method in each of the
following alternative cases. (Assume corporate tax rate being 40%)
Case (a)
Case (b)
Case (c)
Case (d)
If Debentures are issued at par with no flotation cost.
If Debentures are issued at par with 5% flotation cost.
If Debentures are issued at 10% premium with 5% flotation cost.
If Debentures are issued at 10% discount with 5% flotation cost.
Answer.
(a)7.20%
TYPE -2
(b) 8.41%
(c) 6.16%
(d) 10.89%
WHEN REDEMPTION INFORMATION IS NOT GIVEN.
𝒌𝒅 =
𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 (1 − 𝑡)
× 100
𝐵𝑜
Question 4.
(Cost of Perpetual / Irredeemable Debt)
ASC Ltd. issued Rs. 100 Lakhs 12% Debentures of Rs. 100 each. Calculate the cost of debt in
each of the following cases. (Assume corporate tax rate being 40%)
Case (a)
Case (b)
Case (c)
Case (d)
Answer.
(a)
TYPE 3
7.20%
If Debentures are issued at par with no flotation cost.
If Debentures are issued at par with 5% flotation cost.
If Debentures are issued at 10% premium with 5% flotation cost.
If Debentures are issued at 10% discount with 5% flotation cost.
(b)
7.58%
(c)
6.89%
(d)
8.42%
SHORT-CUT 𝒌𝒅 = [𝑪𝑹 (𝒊 − 𝒕)]
Question 5.
A Ltd issued 10% Debt of Rs 100 each tax rate 40%
Answer.
6%
59 | P a g e
Question 6.
A Ltd issued 10% Debt of Rs 100 each redeemable after 5 years, tax rate 40%
Answer.
6%
(B) COST OF PREFERENCE (KP)
TYPE 1
WHEN REDEMPTION INFORMATION IS GIVEN
𝑲𝒑 =
𝑷𝑫(𝟏 + 𝑪𝑫𝑻) +
𝑹𝒗 − 𝑷𝒐
𝑵
𝑹 +𝑷
( 𝒗 𝟐 𝟎)
PD = Preference dividend (CR x face value)
Rv= Redemption value
Po = Net Proceed (fv + premium - discount - brokerage)
N = years for which preference shares are issued.
CDT = Corporate dividend tax.
Question 7.
[Cost of Preference Shares Redeemable (at par) in Lump Sum Payment]
Tulsian Ltd. issued Rs. 100 Lakhs 12% Preference Shares of Rs. 100 each redeemable at par
after 5 years. Calculate the cost of Preference Share According to Approximation Method in
each of the following cases : (Assume dividend tax rate being 20%)
Case (a)
Case (b)
Case (c)
Case (d)
Answer.
If Preference shares are issued at par with no flotation cost.
If Preference shares are issued at par with 5% flotation cost.
If Preference shares are issued at 10% premium with 5% flotation
cost.
If Preference shares are issued at 10% discount with 5% flotation
cost.
(a) 14.4%
(b) 15.79% (c) 13.20%
(d) 18.65%
Question 8.
A Ltd. issued 9% preference share capital @ 100 each for Rs. 100 Lakhs redeemable after 5
years at par find cost of preference share if flotation cost 5%.
60 | P a g e
Answer.
TYPE 2
10.26%
WHEN REDEMPTION INFORMATION IS NOT GIVEN.
Question 9.
[Calculation of Cost of Irredeemable Preference Shares]
Tulsian Ltd. issued Rs. 100 Lakhs 12% Preference shares of Rs. 100 each. Calculate the cost
of Preference Share in each of the following cases : (Assume dividend tax rate being 20%)
Case (a)
Case (b)
Case (c)
Case (d)
If Preference shares are issued at par with no flotation cost.
If Preference shares are issued at par with 5% flotation cost.
If Preference shares are issued at 10% premium with 5% flotatio n
cost.
If Preference shares are issued at 10% discount with 5% flotation
cost.
Answer.
(a) 14.4%
TYPE 3
SHORT-CUT
(b) 15.16% (c) 13.78%
(d) 18.84%
Question 10.
X Ltd. issued 9% preference share Rs 100 Lakhs @ 100 each.
Answer.
9%
Question 11.
X Ltd. issued 9% preference share Rs 100 Lakhs redeemable at par after 5 years.
Answer.
9%
TYPE 1
(C)
DIVIDEND MODEL
Question 12.
COST OF EQUITY
𝑲𝒆 =
𝑫
× 𝟏𝟎𝟎
𝑷𝒐
61 | P a g e
(New firm) : X Ltd. issued equity shares Rs. 100 each at premium of 10% flotation cost Rs. 2
Dividend payable at constant rate of 5% find cost of Equity.
Answer.
4.63%
Question 13.
(Existing firm) : An equity share of the currently selling for Rs. 60. The earnings per share
is Rs. 7.50, if company’s payout ratio is 60% find cost of equity.
Answer.
7.5%
TYPE 2
DIVIDEND GROWTH MODEL  𝐊 𝐞 =
𝐃𝟏
𝐏𝐨
+𝐠
Question 14.
Calculate the cost of Equity (ke) in each fo the following alternative cases :An equity share of the company is currently selling for Rs. 50. The company expects to pay
Rs. 6 per share at the end of current year. Dividend per share is expected to grow at the
rate 8% p.a.
Answer.
20%
Question 15.
An equity share of the company is currently selling for Rs. 50. The company expects to
earn Rs. 6 per share at the end of current year. Dividend payout ratio is 60%. Dividend per
share is expected to grow at the rate of 8% p.a.
Answer.
15.2%
Question 16.
An equity share of the company is currently selling for Rs. 50. The company had paid
dividend of Rs. 6 per share at the end of last year. Dividend per share is expected to grow
at the rate of 8% p.a.
Answer.
20.96%
Question 17.
An equity share of the company is currently selling for Rs. 50. The company had earned Rs.
6 per share at the end of last year. Dividend Payout Ratio is 60%,. Dividend per share is
expected to grow at the rate of 8% p.a.
62 | P a g e
Answer.
15.78%
Question 18.
An equity share of company is currently selling for Rs. 50. The company expects to earn Rs.
6 per share at the end of current year. Dividend Payout Ratio is 60%. The company
reinvests the retained earnings at a rate of 20%.
Answer.
15.2%
Question 19.
An equity share of company is currently selling for Rs. 50. The company had earned to earn
Rs. 6 per share at the end of last year. Dividend Payout ratio is 60%. The company
reinvests the retained earnings at a rate of 20%.
Answer.
15.78%
Question 20.
The price earning ratio is 5 times. The company has an earning per share of Rs. 10 per
share. Dividend Payout Ratio is 60% Dividend per share is expected to grow at the rate of
8% p.a.
Answer.
20.96%
Question 21.
The price earning ratio is 5 times. The company has an earning per share of Rs. 10 per
share. Dividend Payout ratio is 60%
Answer.
20.96%
Question 22.
[Calculation of DPS Paid Last year if Dividends are Growing]
Mr. Dalal is planning to purchase the shares of X Ltd. His required rate of return is 20%.
Dividends are growing at a rate of 10%. What dividend had X Ltd. paid last year if he is
willing to pay Rs. 27.50 for X Ltd.’s Share ?
Answer.
2.5
63 | P a g e
Question 23.
Mr. Factor purchases and equity share of X Ltd. X Ltd. has paid dividend of Rs. 2 per share
last year. Dividends are growing at a rate of 10%. What is the required rate of return of
Mr. X on his equity investment if he purchases an equity share for Rs. 22
Answer.
20%
Question 24.
An equity share of the company is currently selling for Rs. 60. The earning per share Rs.
7.50. The company reinvests the retained earnings at a rate of 10%. Calculate the cost of
equity share if the company’s dividend payout ratio is 60%
Answer.
11.8%
TYPE 3
EARNING MODEL
𝑬
𝑲𝒆 = 𝑷 × 𝟏𝟎𝟎
𝒐
Where, E = EPS
Po = Net proceed/current M.P
Question 25.
If EPS of X limited is Rs. 10 and current market price is Rs. 100 , find out opportunity cost of
investor ?
Answer.
10%
Question 26.
X Ltd. has an annual profit of Rs 50,000 No. of shares outstanding 10,000. If current market
price of share is Rs 100 find cost of equity.
Answer.
5%
TYPE 4
REALISED YIELD APPROACH METHOD
Question 27.
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[Cost of Equity – Realised Yield Approach]
An individual wishes to purchase the Share of a Company for Rs. 500. At present the
company is expected to pay a dividend of Rs. 40 on this share at the end of the year and its
Market Price after the payment of the dividend is expected to be Rs. 520. What is the cost
of Equity in this case, using Realised Yield Approach ?
Answer.
12.00%
Question 28.
[Cost of Equity – Realised Yield Approach]
Jet Ltd. is a large Company with several thousand shareholders. An investor buys 100
shares of the Company at the beginning of the year at a Market price of Rs. 225. The Par
Value of each share is Rs. 10. During the year, the company pays a dividend at 2 5%. The
price of the share at the end of the year is Rs. 267.50. Calculate the total return on the
investment. Suppose the investor sells the shares at the end of the year, what would be the
cash inflows at the end of the year ?
Answer.
Total Return = 20% Cash Inflows = Rs. 27,000
Question 29.
[Cost of Equity – CAPM Approach)
Compute cost of Equity if interest on Government Bonds is 6%, Market Return is 18%, Beta
Factor for Company K is 1.10
Answer.
19.2%
Question 30.
[Computation of Cost of Equity using CAPM and Product wise Beta]
You are analyzing the Beta for ABC Computers Ltd. and have divided the Company into four
broad business groups, with Market Values and Betas for each group.
Business Group
Mainframes
Personal Computers
Software
Printers
Market value of Equity
Rs. 100 Billion
Rs. 100 Billion
Rs. 50 Billion
Rs. 150 Billion
Unleveraged Beta
1.10
1.50
2.00
1.00
Required :65 | P a g e
1.
If the Treasury Bond Rate is 7.5% estimate the Cost of Equity of ABC Computers Ltd.
Estimate the Cost of Equity for each division. Which cost of equity would you use to
value the Printer Division ? The average Market Risk Premium is 8.5%
Answer.
Weighted BETA = 1.275,
Ke(Group) = 18.3375
Question 31.
Calculate the Value of Beta ( ) in the following cases :Case (a)
Case (b)
Standard Deviation of Security
3
Standard Deviation of Market Portfolio
2
Correlation Coefficient of Portfolio with market
0.8
Correlation Coefficient of Portfolio with market
0.8
Variance of Market Portfolio is 4/9 th of Variance of Security
Case (c)
Case (d)
Answer.
Risk Free Rate of Interest on Govt. Treasury Bonds
5%
Average Return on Market Portfolio
17.5%
Cost of Equity (ke)
20%
Cost of Equity (ke)
20%
Average Market Risk Premium
10%
Risk Free Rate of Interest
5%
(a) 1.2
(b) 1.2
(c) 1.2
(d) 1.5
Question 32.
From the following data information, calculate the Cost of Equity (Ke)
Risk Free rate of interest
Expected return of market portfolio
Standard deviation of an asset
Market Standard deviation
Correlation coefficient of portfolio with market
8%
18%
2.8%
2.3%
0.8
66 | P a g e
Answer.
17.74%
Question 33.
The market is giving an average return of 18%. The risk free return is 11%
Required :
(i)
(ii)
Answer.
What return would be expected from an investment having a Beta factor of
0.9
Beta Factor which would be necessary for an investment to yield a return of
21.6%
Ke = 18.9%,
(D)
Kre = Ke
Beta = 1.514
COST OF RETAINED EARNING (Kre)
or
Kre = Ke (i-Pt) (1 - brokerage)
Question 34.
XYZ Ltd. has an annual profit of Rs. 50,000 and the required rate of return of the
shareholder is 10%. It is further expected that the shareholders will have to incur 3%
brokerage cost of the dividends received and invested by them for making new
investments. Find out the cost of retained earnings to the firm given that the tax rate
applicable to shareholders is 30%.
Answer.
kr = 6.79%
Question 35.
Calculate the cost of retained earnings from the following information:Current market price of a share Rs. 140
Cost of brokerage per share 3%
Growth in expected dividend 5%
Expected dividend per share on new shares Rs. 14
Shareholders marginal / personal income tax 22%
Answer.
11.35%
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(E)
COST OF TERM LOAN
KTL = CR (I – tax rate)
Question 36.
X Ltd raised Rs 100 L term Loan @ 12% P.A. if tax rate is 30% find cost of term loan.
Answer.
(A)
8.4%
OVERALL COST OF CAPITAL
WACC (Weighted Avg. Cost of capital)
WACC Kd Wd + Ke We + Kp Wp
Question 37.
[Computation of WACC]
The Capital Structure of a Company as on 31 st March is as follows :Equity Capital : 6,00,000 Equity Shares of Rs. 100
each
Rs. 6.00 Crores
Reserves and Surplus
Rs. 1.20 Crores
12% Debenture of Rs. 100 each
Rs. 1.80 Crores
For the year ended 31 st March, the company has paid Equity Dividend at 24% Dividend is
likely to grow by 5% every year. Market Price of Equity Share is Rs. 600 per Share. Income
Tax Rate applicable to the company is 30%
Required :1.
2.
Answer.
Compute the current Weighted Average Cost of Capital
The company has a plan to raise a further Rs. 3 crores by way of Long-Term
Loan at 18% interest. If the Loan is raised, the Market Price of Equity share
is expected to fall to Rs. 500 per share. What will be the new Weighted
Average Cost of Capital of the Company?
WACC: 9.04%, 10.43%
Question 38.
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The following is the capital structure of Simons Company Ltd as on 31.12.1998.
Equity shares : 10,000 shares of Rs. 100 each
10% Preference Shares (of Rs. 100 each)
12% Debentures
Rs.
10,00,000
4,00,000
6,00,000
20,00,000
The market price of the company’s share is Rs. 110 and it is expected that a dividend of Rs.
10 per share would be declared for the year 1998. The dividend growth rate is 6%.
(i)
If the company is in the 50% tax bracket, compute the weighted average cost of
capital.
(ii)
Assuming that in order to finance an expansion plan, the company intends to
borrow a fund of Rs. 10 lakh bearing 14% rate of interest, what will be the
company’s revised weighted average cost of capital ? This financing decision is
expected to increase dividends from Rs. 10 to 12 per share. However, the market
price of equity share is expected to decline from Rs. 110 to Rs. 105 per share.
Answer.
(i) W.A.C.C. 11.34
(ii) R.W.A.C.C. 10.66
Question 39.
2010 - Dec [6] (a) Sushant Ltd. has the following capital structure:
Rs.
Equity shares
50,00,000
10% Preference shares
10,00,000
14% Debentures
20,00,000
80,00,000
Equity shares of the company are sold of Rs. 25 per share in the market. It is expected that
the company will pay next year a divided of Rs. 4 per share which will grow at 8% forever,
Assume a tax- rate of 30%.
(i)
Compute weighted average cost of capital based on the existing capital structure.
(ii) Compute the new weighted average cost of capital, if the company raise an
additional Rs. 20,00,000 debt by issuing 15% debentures. This would increase the
69 | P a g e
expected dividend to Rs. 5 per share with divided growth rate unchanged, but the
price of share will fall to Rs. 20 per share
Answer. (i) WACC = 18.7% (ii) RWACC = 21.56%
Question 40.
JKL Ltd. has the following book-value capital structure as on March 31, 2003.
Rs.
Equity Share Capital (2,00,000 shares)
40,00,000
11.5% Preference Shares
10,00,000
10% debentures
30,00,000
80,00,000
The equity share of the company sells for Rs. 20. It is expected that the company will pay
next year a dividend of Rs. 2 per equity share, which is expected to grow at 5% p.a. forever.
Assume a 35% corporate tax rate.
Required :(i)
Compute weighted average cost of capital (WACC) of the company based on the
existing capital structure.
(ii)
Compute the new WACC, if the company raises an additional Rs. 20 lakhs debt by
issuing 12% debentures. This would result in increasing the expected equity
dividend to Rs. 2.40and leave the growth rate unchanged, but the price of equity
share will fall to Rs. 16 per share.
Comment on the use of weights in the computation of weighted average cost of capital.
Question 41.
[Computation of Ke using WACC – Reverse Working]
Backwork ltd. has a Debt Equity Ratio of 2:1 and a WACC of 12%, Its debentures, bear
interest of 15%, Find out the cost of Equity Capital (Assume Tax = 35%)
Answer.
(B)
Ke = 16.5%
WACC AT MV Weights)
Question 42.
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2003 - June [5] (b) Determine the weighted average cost of capital using (i) book value
weights; and (ii) market value weights based on the following information:
Book value structure:
Debentures (Rs. 100 per debenture)
Preference shares (Rs. 100 per share)
Equity shares (Rs. 10 per share)
Rs.
8,00,000
2,00,000
10,00,000
20,00,000
Resent market prices of all these securities are:
Debentures: Rs. 110 per debenture;
Preference shares: Rs. 120 per share; and
Equity shares: Rs. 22 per share.
External financing opportunity are(i)
Rs. 100 per debenture redeemable at par, 10 year maturity, 13% coupon rate,
4% flotation cost and sale price Rs. 100;
(ii) Rs. 100 per preference share redeemable at par, 10 year maturity, 14%
dividend rate, 5% flotation cost and sale price Rs. 100; and
(iii) Equity shares-Rs. 2 per share flotation costs and sale price Rs. 22.
Dividend expected on equity share at the end of the year is Rs. 2 per share; anticipated
growth rate in dividends is 7% Company pays all its earnings in the form of dividends.
Corporate tax rate is 50%.
Answer.
(C)
ke = 17%, kp = 14.87%, kd = 7.04%, ko = 12.8
Ko = 14.2066
WMCC (Weighted Marginal Cost of capital)
Question 43.
[Marginal Cost of Capital]
An entity has Rs. 50 lakhs existing funds financed Rs. 20 lakhs from equity share capital Rs.
15 lakhs from retained earnings and Rs. 15 lakhs from 12% debentures. It requires
additional funds of Rs. 20 lakhs. These can be financed Rs. 10 lakhs from 14% Debentures
and Rs. 10 lakhs from new issue of equity shares. Tax rate applicable to the company is
71 | P a g e
35%. The company is expecting to pay Rs. 4 per share at the end of the year. The company
is growth rate of dividends is expected to be 8% perpetually. Market price per equity share
is Rs. 40 per share. Issue price of the new equity shares is expected to be Rs. 35 per share.
Flotation cost to the issue is Rs. 3 per share. Compute weighted marginal cost of capital
Answer.
WMCC = 14.80%
(D) Economic Value Added
Question 44.
[Economic Value Added]
A company has 12.5% Debt Capital of Rs. 2,000 crores (redeemable in 10 years), Equity
Capital of Rs. 500 crores, Reserves and Surplus of Rs. 7,500 crores. The return on Tax Free
Government Bonds is 11%. Beta is 1.06, Market rate is 18% and corporate tax rate is 30%.
Net operating Profit After tax of the company is Rs. 2,000 crores. Compute EVA.
Answer.
Kd = 8.75%, Ko =16.486%, EVA = 351.4 crore
Question 45.
Calculate economic value added (EVA) with the help of the following information of
Hypothetical Limited
Financial Leverage
Capital Structure
:
:
Cost of Equity
Income Tax Rate
:
:
Answer.
1.4 Times
Equity Capital Rs. 170 lakhs
Reserve and Surplus Rs. 130 lakhs
10% Debentures Rs. 400 lakhs
17.5%
30%
17.5 Lakhs
MULTIPLE CHOICE QUESTIONS
1. Cost of Capital refers to:
a) Flotation Cost
b) Dividend
c) Required Rate of Return
72 | P a g e
d) None of the above.
2. Which of the following sources of funds has an Implicit Cost of Capital?
a) Equity Share Capital
b) Preference Share Capital
c) Debentures
d) Retained earnings.
3. Which of the following has the highest cost of capital?
a) Equity shares
b) Loans
c) Bonds
d) Preference shares.
4. Cost of Capital for Bonds and Debentures is calculated on:
a) Before Tax basis
b) After Tax basis
c) Risk-free Rate of Interest basis
d) None of the above.
5. Weighted Average Cost of Capital is generally denoted by:
a) kA
b) kw
c) k0
d) kc
6. Which of the following cost of capital require tax adjustment?
a) Cost of Equity Shares
b) Cost of Preference Shares
c) Cost of Debentures
d) Cost of Retained Earnings.
7. Marginal cost of capital is the cost of:
a) Additional Sales
b) Additional Funds
c) Additional Interests
d) None of the above.
8. In case the firm is all-equity financed, WACC would be equal to:
a) Cost of Debt
73 | P a g e
b) Cost of Equity
c) Neither (a) nor (b)
d) Both (a) and (b).
9. Which of the following is true?
a) Retained earnings are cost free
b) External Equity is cheaper than Internal Equity
c) Retained Earnings are cheaper than External Equity
d) Retained Earnings are costlier than External Equity.
10. Firm's Cost of Capital is the average cost of:
a) All sources
b) All borrowings
c) Share capital
d) Share Bonds & Debentures.
11. In order to calculate Weighted Average Cost of capital weights may be based on:
a) Market Values
b) Target Values
c) Book Values
d) All of the above.
12. Cost of capital may be defined as:
a) Weighted Average cost of all sources,
b) Rate of Return expected by Equity Shareholders,
c) Average IRR of the Projects of the firm,
d) Minimum Rate of Return that the firm should earn.
13. Debt Financing is a cheaper source of finance because of:
a) Time Value of Money
b) Rate of Interest,
c) Tax-deductibility of Interest
d) Dividends not Payable to lenders.
14. Minimum Rate of Return that a firm must earn in order to satisfy its investors, is
also known as:
a) Average Return on Investment
b) Weighted Average Cost of Capital
c) Net Profit Ratio
d) Average Cost of borrowing.
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15. Tax-rate is relevant and important for calculation of specific cost of capital of:
a) Equity Share Capital
b) Preference Share Capital
c) Debentures
d) (a) and (b) above.
16. Cost of retained earnings is equal to _______.
a) Cost of equity
b) Cost of debt
c) Cost of bank loan
d) Cost of term loans
17. A fixed rate of _________ is payable on debentures
a) dividend
b) Commission
c) Interest
d) Brokerage
18. Which of the following is not a generally accepted approach for Calculation of
Cost of Equity?
a) CAPM
b) Dividend Discount Model
c) Rate of Pref. Dividend Plus Risk
d) Price-Earnings Ratio.
19. Cost of Equity Share Capital is more than cost of debt because:
a) Face value of debentures is more than face value of shares
b) Equity shares have higher risk than debt,
c) Equity shares are easily saleable
d) All of the three above.
20. Advantage of Debt financing is:
a) Interest is tax-deductible
b) It reduces WACC
c) Does not dilute owners control
d) All of the above.
21. The constant growth model of equity valuation assumes that _____________.
a) the dividends paid by the company remain constant
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b) the dividends paid by the company grow at a constant rate of growth
c) the cost of equity may be less than or equal to the growth rate
d) the growth rate is less than the cost of equity.
22. Effective cost of debentures is _________ as compared to shares.
a) higher
b) lower
c) equal
d) medium
23. Which of the following is not a source of long-term finance?
a) Equity shares
b) Preference shares
c) Commercial papers
d) Reserves and surplus
24. Prices of bonds will be decreased if an yield to maturity
a) rises
b) declines
c) equals
d) none of above
25. Interest rate is 12% and tax savings (1-0.40) then after-tax component cost of
debt will be
a) 7.20%
b) 7.40%
c) 17.14%
d) 17.24%
26. Method uses for an estimation of cost of equity is classified as
a) market cash flow
b) future cash flow method
c) discounted cash flow method
d) present cash flow method
27. Stock selling price is Rs 45, an expected dividend is Rs 10 and an expected
growth rate is 8% then cost of common stock would be
a) 55.00%
b) 35.00%
c) 30.00%
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d) 30.22%
28. Dividend per share is Rs 18 and sell it for Rs 122 and floatation cost is Rs 4 then
component cost of preferred stock will be
a) 15.25%
b) 0.1525 times
c) 15.25
d) 0.15%
29. If payout ratio is 0.45 then retention ratio will be
a) 0.55
b) 1.45
c) 1.82
d) 0.45
30. Stock selling price is Rs 35, expected dividend is Rs 5 and expected growth rate is
8% then cost of common stock would be
a) 40.00%
b) 22.29%
c) 14.28%
d) 80.00%
31. Stock selling price is Rs 65, expected dividend is Rs 20 and cost of common stock
is 42% then expected growth rate will be
a) 0.1123 times
b) 11.23%
c) 11.23 times
d) Rs 11.23
32. In large expansion programs, increased riskiness and floatation cost associated
with project can cause
a) rise in marginal cost of capital
b) fall in marginal cost of capital
c) rise in transaction cost of capital
d) rise in transaction cost of capital
33. Weighted average cost of debt, preferred stock and common equity is classified
as
a) cost of salvage
b) cost of interest
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c) cost of taxation
d) cost of capital
34. In cash flow estimation, depreciation shelters company's income from
a) expansion
b) salvages
c) taxation
d) discounts
35. Which of the following model/method makes use of beta (B) in calculation of cost of
equity?
a) Risk Adjusted Discount Model
b) Capital Assets Pricing Method
c) MM Model
d) Price Earning Method
36. Marginal cost a) is the weighted average cost of new finance raised by the company.
b) is the additional cost of capital when the company goes for further raising of finance.
c) is the cost of raising an additional rupee of capital.
d) All of the above
37. Bond risk premium is added in to bond yield to calculate a) Cost of option
b) Cost of common stock
c) Cost of preferred stock
d) Cost of working capital
38. Bond risk premium is 3% and bond yield is 10.2% then cost of common stock
will be
a) 3.40%
b) 13.20%
c) 7.20%
d) 30.60%
39. The cost of equity share or debt is called specific cost of capital. When specific costs are
combined, then we arrive at - .
a) Maximum rate of return
b) Internal rate of return
c) Overall cost of capital
d) Accounting rate of return
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40. ________ is the rate that the firm pays to procure financing.
a) Average Cost of Capital
b) Combine Cost
c) Economics Cost
d) Explicit Cost
41. In weighted average cost of capital, rising in interest rate leads to a) Increase in cost of debt
b) Increase the capital structure
c) Decrease in cost of debt
d) Decrease the capital structure
42. Risk free rate is subtracted from expected market return is considered as:
a) Country risk
b) Diversifiable risk
c) Equity risk premium
d) Market Risk premium
43. CAPM describe the _____ between risk and return for securities.
a) Linear Relationship
b) Hypothetical Relationship
c) No Relationship
d) Diagonal Relationship
44. Which of the following may be defined as the cost of raising an additional rupee
of capital?
a) Average cost of capital
b) Cost of retained earnings
c) Marginal cost of capital
d) Marginal cost of reserve & surplus
45. How the economics value added (EVA) is calculated?
a) It is the difference between the market value of the firm and the book value
of equity.
b) It is the firm’s net operating profit after tax (NOPAT) less cost of capital.
c) It is the net income of the firm less cost that equals the weighted average cost
of capital multiplied by the book value of liabilities & equities.
d) None of the above is correct.
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46. The term ‘EVA’ is used for:
a) Extra Value Analysis
b) Economic Value Added
c) Expected Value Analysis
d) Engineering Value Analysis
47. ................................enhance the market value of shares and therefore equity capital is not
free of cost.
a) Face value
b) Dividends
c) Redemption value
d) Book value
48. EVA = ?
a) PAT - (Capital Employed X WACC)
b) NOPAT - (Capital Employed X Kc)
c) NOPAT - (Capital Employed X WACC)
d) NOPAT - (Total Assets XK X Kd)
49. An increase in market value of preferred stock will .................. the cost of preferred stock.
a) increase
b) not affect
c) either increase or decrease
d) decrease
50. ................................describes the relationship between non-diversifiable and return for
securities.
a) Risk Reward Model
b) CAPM Model
c) MM Model
d) Stewart Model
51. By observing the financial market, we can observe that a) Normally cost equity is more than cost of debt
b) Normally cost of debt is more than cost of equity
c) If beta factor is more than 1 then security is less risky than market
d) None of the above
52. R Ltd. has disbursed a dividend of Rs.75 on each equity share of Rs.25. The market price
of share is Rs.200. Corporate tax rate is 40%. Its cost of equity is a) 30.0%
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b) 37.5%
c) 35.7%
d) 33.5%
53. F Ltd. issued 1,00,000 equity share of Rs.100 each at a premium of Rs.20 each. Company
has incurred issue expenses of Rs.50,000. Corporate tax rate is 40%. The equity
shareholders expects the rate of dividend to 18% p.a.
Cost of equity = ?
a) 15.60%
b) 15.65%
c) 15.06%
d) 16.50%
54. The equity of X Ltd. is traded in the market at Rs.225 each. It book value per share is
Rs.100. The dividend expected at the year end per share is Rs.45. The subsequent
growth in dividends is expected at the rate of 0.06. Calculate the cost of equity capital.
a) 0.26
b) 0.22
c) 0.33
d) 0.28
55. H Ltd. Beta is 1.8025. Dividend paid by the company last year was Rs.9 per share on face
value of Rs.30. The risk free rate is .061275. Risk premium is 0.0825. Calculate cost of
equity capital.
a) 21%
b) 6.28%
c) 14.77%
d) 12%
56. X Ltd. earns profit after tax Rs.3,96,000. Corporate tax is 0.4. Its capital structure consist
of equity shares Rs.9,60,000; 15% Term loan Rs.4,80,000. Cost of equity is 0.12. Its
economic value added is a) Rs.2,66,400
b) Rs.2,80,800
c) Rs.2,08,800
d) Rs.2,80,008
57. X Ltd. has equity of 15 Million and 10% debentures of 20 Million. Cost of equity is 18%
and pre-tax cost of debt is 10%. Company estimates its EBIT for 7 Million. Applicable tax
rate is 30%. What is the Economic value added of X Ltd.
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a) 0.088 Million
b) 0.678 Million
c) 0.798 Million
d) 0.533 Million
58. Following details are submitted by Rajlakhami Ltd.
EBIT
Rs.350 lakh
Equity Capital
Rs.425 lakh
Reserves & Surplus
Rs.325 lakh
10% Debentures
Rs.1,000 lakh
Current Assets
Rs.82 lakh
Cost of Equity
17.50%
Income Tax Rate
30%
Economic Value Added is
a) Rs.43.75 lakh
b) Rs.40.75 lakh
c) Rs.43.57 lakh
d) Rs.45.37 lakh
59. Prsanna Ltd. issued 12% bonds of Rs.100 each at par. Corporate tax rate is 34%
including surcharge and education cess. Cost of Debt is
a) 12%
b) 8.42%
c) 10%
d) 12.48%
60. Parag Ltd. issued 14% bonds of Rs.100 each at 98%. Corporate tax rate is 34%. Issue
expense per bond was Rs.1.5. Cost of Debt is
a) 9.24%
b) 9.38%
c) 9.58%
d) 9.12%
61. A Company issues Rs.75,00,000 12% Debentures of Rs.100 each. Risk premium is
13.5%. Debentures are redeemable after the expiry of fixed period of 7 years at par. The
Company is in 35% tax bracket. Calculate the cost of debt after tax, if debentures are
issued at 10% discount.
a) 9.72%
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b) 7.80%
c) 9.27%
d) 8.46%
62. A Company issues Rs.48,50,000 12% Debentures of Rs.100 each. Debentures are
redeemable at par after the expiry of fixed period of 7 years. The Company is in 35% tax
bracket. Calculate the cost of debt after tax, if debentures are issued at 10% premium.
a) 6.77%
b) 6.07%
c) 7.60%
d) 6.88%
63. Following data is available for XYZ Ltd.:
No. of debentures = 5,00,000
Face value = Rs.1,000, Coupon rate = 8%
Discount on issue = 1% of face value
Issue expenses = Rs.6,25,000
Term = 12 years Corporate tax rate = 25%
These debentures are redeemable at premium of Rs.14. What is cost of debt (Kd)
a) 5.78%
b) 5.87%
c) 6.44%
d) 8.32%
64. Y Ltd. issues preference shares of face value Rs.500 each carrying 14% dividend and it
realizes Rs.480 per share. The shares are repayable after 12 years at 2% premium.
Corporate tax rate is 25%. Issue expense per share was Rs.2.5.
a) 14.65%
b) 15.82%
c) 14.73%
d) 14.92%
65. Chetna Fashions is expected to pay an annual dividend of Rs.0.80 a share next year. The
market price of the stock is Rs.22.40 and the growth rate is 5%. What is the firm’s cost of
equity?
a) 7.58 per cent
b) 7.91 percent
c) 8.24 per cent
d) 8.57 per cent
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66. X Ltd. report its NOPAT Rs.25,00,000. Its capital employed and economic value added is
Rs.60,00,000 & Rs.19,00,000 respectively. What is overall cost of capital of X Ltd.
a) 10.9%
b) 11%
c) 10%
d) 9.8%
67. Mr. X, purchases an equity share of growing company, XYY Ltd. for Rs.525. He expects
that the XYY Ltd. to pay dividend of Rs.26.25, Rs.27.83 & Rs.29.50 in year 1, 2 & 3
respectively. He expects to sell shares at the end of year 3 at Rs.607.75. What is the
required rate of return of Mr. X on his equity investment?
a) 11.50%
b) 10.50%
c) 10.05%
d) 11.05%
68. X Ltd. has furnished the following information:
Earnings Per Share (EPS)
Rs.14
Dividend Payout Ratio
25%
Market Price Per Share
Rs.140
Rate of Tax
26%
Growth rate of dividend
9%
The company wants to raise additional capital of Rs.10 lakhs including debt of Rs.4 lakhs.
Cost of debt (before tax) is 12% up to Rs. 2 lakhs and 14% beyond that. Compute the
marginal weighted average cost of additional capital
a) 11.75%
b) 10.75%
c) 11.57%
d) 12.57%
69. X Ltd. has 8% Debentures (Face value Rs.2,500) of Rs.9,00,000 which are redeemable at
5% premium, sold at 98%, 3% flotation costs with maturity of 20 years. Corporate tax
rate is 35%. After tax cost of debt is a) 8.7%
b) 7.7%
c) 5.7%
d) 6.7%
70. Compute the EVA with the help of following information:
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Rs.
Equity
10,00,000
Debt (10%)
5,00,000
Profit after tax
2,00,000
Risk-free rate of return is 7%. Beta (B) = 0.9, Market rate of return = 15%. Applicable tax
rate is 40%.
a) Rs.57,950
b) Rs.57,590
c) Rs.57,905
d) Rs.59,750
71. The following is the capital structure of a company:
Source of Capital
Book Value Rs.
Equity Shares (Rs. 100 each)
40,00,000
9% Pref. Shares (Rs. 100)
10,00,000
11% Debentures
30,00,000
Retained Earnings
20,00,000
1,00,00,000
Current market price of equity share is Rs.200. For the last year the company had paid
equity dividend at 25% and its dividend is likely to grow 5% every year. Corporate tax rate
is 30% and shareholders personal income tax rate is 20%. Compute WACC on the basis of
book value.
a) 13.36%
b) 14.50%
c) 13.96%
d) 12.32%
72. The following is the capital structure of a company:
Source of capital
Equity share (Rs. 100 each)
9% Pref. Share (Rs. 100)
11% Debentures
Retained Earnings
Rs. In Lakhs
Book Value
Market Value
80
160
20
24
60
66
40
-
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200
250
Current market price of equity share is Rs. 200. For the last year the company
had paid equity dividend at 25% and its dividend is likely to grow 5% every year.
Corporate tax rate is 30%. Shareholder’s personal tax rate 20% Compute WACC
on the basis of market value.
a) 14.5 per cent
b) 13.5 per cent
c) 12.9 per cent
d) 14.1 per cent
73. X Ltd. has Rs. 10 equity shares amounting to Rs. 15 Crore. The current market
price per equity share is Rs. 60. The prevailing default risk free interest rate on
10 year GOI treasury bonds is 5.5%. the average market risk premium is 8%. The
beta of the company is 1.1875. K e is
a) 15%
b) 11%
c) 12%
d) 13%
74. X Ltd. has a cost of equity of 12%, a pre-tax cost of debt of 7%, and a tax rate of
35%. What is the firm’s weighted average cost of capital if the debt-equity ratio
is 0.60?
a) 9.21%
b) 10.01%
c) 10.13%
d) 11.11%
75. X Enterprises just paid an annual dividend of Rs. 1.56 per share. This dividend is
expected to increase by 3 percent annually. Currently, the firm has a beta of 1.13
and a stock price of Rs. 28 a share. The risk-free rate is 3 percent and the market
rate of return is 10.5 percent.
What is your best estimate of X’s cost of equity?
a) 8.74 percent
b) 11.48 percent
c) 9.72 percent
d) 10.11 percent
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76. Compute the EVA with the help of following information:
Equity
15,00,000
Debt (10%)
7,00,000
Profit after tax
4,00,000
Risk-free rate of return is 7%. Beta (β) = 0.9, Market rate of return = 15%.
Applicable tax rate is 40%
a) Rs. 1,87,020
b) Rs. 1,78,020
c) Rs. 1,87,200
d) Rs. 1,85,200
77. X Ltd. has Rs. 1,000, 9.5% debentures amounting to Rs. 1,500 Million. The
debentures of X Ltd. are redeemable after 3 year and are quoting at Rs, 981.05
per debenture. The beta of the company is 1.1785. the applicable income rax rate
for the company is 35% Kd = ?
a) 6%
b) 6.87%
c) 7%
d) 10%
78. X Ltd. has a cost of equity of 11% and a pre-tax cost of debt of 8.5%. The firm’s
target weighted average cost of capital is 9% and its tax rate is 35%. What is the
firm’s target debt-equity ratio?
a) 0.6203
b) 0.5756
c) 0.5572
d) 0.5113
79. Gentry Motor, Inc. a producer of turbine generator, is in this situation:
EBIT = Rs.40 lakhs
Tax rate = 35%
Debt outstanding = Rs.20 lakhs
Kd = 10%
Ke = 15%
Shares outstanding = 6,00,000 shares
What is the Gentry’s earning per share (EPS) and market price per share (Po) ?
a) EPS = 3.98; Market Price = Rs.27.76
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b) EPS = 4; Market Price = Rs.26.67
c) EPS = 4.72; Market Price = Rs.30.44
d) EPS = 3; Market Price = Rs.25
80. The required rate of return is 16%. Management is anticipating 8% growth rate. The
company expects to pay dividend of Rs.5 per share at the end of coming year. On this
basis, at what price should the equity share be sold by the company?
a) Rs.60.2
b) Rs.62.5
c) Rs.64.3
d) Rs.61.7
81. A Ltd. gives following details:
Equity Capital [Rs. 10 each]
Rs.2,50,000
Market value per share
Rs.20
Dividend per share
Rs.4
Debentures [Rs. 100]
Rs.1,00,000
Market value per debenture
125
Interest rate
10%
Tax rate
50%
WACC based on market value is
a) 12.20%
b) 16.80%
c) 18.40%
d) 13.60%
82. Dividend per share is Rs.18 and sell it for Rs.122 and floatation cost is Rs.4, then
component cost of preferred stock will be:
a) 15.25%
b) 15.25 times
c) 0.01525
d) 15.52%
83. Stock selling price is Rs.65, expected dividend is Rs.20 and cost of common stock is 42%
then expected growth rate will be a) 11.23%
b) 0.01123
c) 11.23 times
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d) 11.23
84. Stock selling price is Rs.45, an expected dividend is Rs.10 per share and an expected
growth rate is 8%, then cost of common stock would be:
a) 3.02
b) 32%
c) 30.22%
d) 32.30%
85. Interest rate is 12% and tax savings (1-0.40) then after-tax component cost of debt will
be a) 0.072
b) 7.2 times
c) 17.14
d) 17.14 times
86. Cost of common stock is 14% and bond risk premium is 9% then bond yield will be a) 0.0156
b) 0.05
c) 0.23
d) 0.6428
87. If future return on common stock is 19% and rate on T-bill is 11% then current market
risk premium will be:
a) 30%
b) 8%
c) 0.8
d) None of the above
88. Dividend per share is Rs.15 and sell it for Rs.120 and floatation cost is Rs.3, then
component cost of preferred stock will be a) 12.82 times
b) 0.1282 times
c) 0.1282
d) 12.82
89. Equity dividend expected at the end of year is Rs.20 per share whereas anticipated
dividend growth rate is 5%. Corporate tax is 30%. Market price per share is Rs.200.
What is cost of equity?
a) 10.5%
b) 15%
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c) 12.9%
d) 14%
90. X Ltd. is currently financed with Rs.10,00,000, 7% bonds and Rs.20,00,000 of common
stock. The stock has a beta of 1.5, risk-free rate of return 4% and market risk premium
3.5%. The marginal tax rate for a company of this size is 35%. Compute the WACC of X
Ltd. on book value basis?
a) 6.87%
b) 8.76%
c) 9.34%
d) 7.68%
Answer:1
2
3
4
5
6
7
C
D
A
B
C
C
B
21
22
23
24
25
26
27
B
B
C
A
A
C
D
41
42
43
44
45
46
47
A
C
A
C
B
B
B
61
62
63
64
65
66
67
A
B
A
C
D
C
D
81
82
83
84
85
86
87
B
A
A
C
A
B
B
90 | P a g e
8
9
10
11
12
13
14
15
16
17
18
19
20
B
C
A
D
D
C
B
C
A
C
C
B
D
28
29
30
31
32
33
34
35
36
37
38
39
40
A
A
B
B
A
D
C
B
D
B
B
C
D
48
49
50
51
52
53
54
55
56
57
58
59
60
C
D
B
A
B
C
A
A
B
C
A
A
C
68
69
70
71
72
73
74
75
76
77
78
79
80
B
C
A
A
A
A
A
B
A
B
B
B
B
88
89
90
C
B
D
91 | P a g e
CHAPTER 5
LEVERAGE ANALYSIS
Learning Objectives
After studying this chapter you will be able to:

Define, discuss, and quantify “business risk” and “financial risk”.

Explain in detail operating and financial leverage and identify causes of both.

Understand how to calculated and interpret a firm leverage.

Calculated a firm’s operating break-even (quantity) point break-even (sales) point

Understand what is involved in determining the appropriate amount of financial
leverage for a firm.
 CONCEPT 1
INTRODUCTION
A firm can finance its operations through common and preference shares, with
retained earnings, or with debt. Usually a firm uses a combination of these financing
instruments.
Capital structure refers to a firm’s debt-to-equity ratio, which provides insight into
how risky a company is. Capital structure decisions by firms will have an effect on the
expected profitability of the firm, the risks facing debt holders and shareholders, the
probability of failure, the cost of capital and the market value of the firm.
Risk facing the common shareholders is of two types, namely business risk and
financial risk. Therefore risk facing Common Shareholders is function of these two
risks, i.e. (Business Risk, Financing Risk)
 CONCEPT 2
Business Risk and Financial Risk
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Business Risk:- It refers to the risk associated with the firm’s operations. It is the
uncertainty about the future operating income (EBIT), i.e. how well can the operating
income be predicted?
Business risk can be measured by the standard deviation of the Basic Earning Power
ratio.
Financial Risk:- It refers to the additional risk placed on the firm’s shareholders as a
result of debt use i.e. the additional risk a shareholder bears when a compa ny uses
debt in addition to equity financing. Companies that issue more debt instruments
would have higher financial risk than companies financed mostly or entirely by equity.
Leverage refers to the ability of a firm in employing long term funds having a f ixed
cost, to enhance returns to the owners. In other words, leverage is the amount of debt
that a firm uses to finance its assets. A firm with a lot of debt in its capital structure is
said to be highly levered. A firm with no debt is said to be unlevered.
 CONCEPT 3
Debt Versus Equity Financing
Financing a business through borrowing is cheaper than equity. This is because:

Lenders require a lower rate of return than ordinary shareholders. Debt financial
securities present a lower risk than shares for the finance providers because they
have prior claims on annual income and liquidation.

A profitable business effectively pays less for debt capital than equity for another
reason: the debt interest can be offset against pre -tax profits before the calculation
of the corporate tax, thus reducing the tax paid.

Issuing and transaction costs associated with raising and serving debt are
generally less than for ordinary shares.
These are some benefits from financing a firm with debt. Still firms tend to avoid very
high gearing levels.
One reason is financial distr ess risk. This could be induced by the requirement to pay
interest regardless of the cash flow of the business. If the firm goes through a rough
93 | P a g e
period in its business activities it may hav e trouble paying its bondholders, bankers
and the other creditors their entitlement.
 CONCEPT 4
RELATIONSHIP BETWEEN LEVERAGE AND RISK
Leverage can occur in either the operating or financing portions of the income
statement. The effect of leverage is to magnify the effects of changes in sales volume on
earnings.
Let’s now discuss in detail Operating, Financing and Combined Leverages.
 CONCEPT 5
TYPES OF LEVERAGE
The term Leverage in general refers to a relationship between two interrelated
variables. In financial analysis it represents the influence of one financial variable over
some other related financial variable. These financial variables may be costs, output,
sales revenue, Earnings Before interest and Tax (EBIT), Earning per share (EPS) etc.
There are three commonly measures of leverage in financial analysis. These are:
(i) Operating Leverage
(ii) Financial Leverage
(iii)Combined Leverage
 CONCEPT 6
OPERATING LEVERAGE
Operating leverage (OL) maybe defined as the employment of an asset with a fixed cost
in the hope that sufficient revenue will be generated to cover all the fixed and variable
costs.
The use of assets for which a company pays a fixed cost is called operating leverage.
With fixed costs the percentage change in profits accompanying a change in volume is
greater than the percentage change in volume. The higher the turnover operating
assets, the greater will be the revenue to the fixed charge on those assets.
Operating leverage is a function of three factors:
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(i) Rupee amount of fixed cost,
(ii) Variable contribution margin, and
(iii)Volume of sales.
Operating leverage is the ratio of net operating income before fixed charges to net
operating income after fixed charges. Degree of operating leverage is equal to the
percentage increase in the net operating income to the percentage increase in the
Sales.
OL =
(
𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
𝐸𝐵𝐼𝑇
)
Where,
OL = Operating leverage
N = Number of units sold
P = Selling price per unit
V = Variable cost per unit
F = Fixed cost
Degree of operating leverage
=
Percentage increase in net operating income
Percentage increase in sales
Operating leverage is directly proportion to business risk. More operating leverage
leads to more business risk, for then a small sales decline causes a big profit.
 CONCEPT 6
FINANCIAL LEVERAGE
Financial leverage (FL) maybe defined as ‘the use of funds with a fixed cost in order to
increase earnings per share’. In other words, it is the use of company funds on which it
pays a limited return. Financial leverage involves the use of funds obtained a t a fixed
cost in the hope of increasing the return to common stockholders.
Degree of financial leverage is the ratio of the percentage increase in earning per share
(EPS) to the percentage increase in earnings before interest and taxes (EBIT).
Degree of financial leverage =
Percentage increase in Earning per share
Percentage increase in earnings before interest and tax (EBIT)
95 | P a g e
Or,
FL =
𝐸𝐵𝐼𝑇
𝐸𝐵𝐼𝑇 −𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 −
𝑃𝐷
1−𝑡
 CONCEPT 7
DEGREE OF COMBINED LEVERAGE
Combined leverage maybe defined as the potential use of fixed costs, both operating
and financial, which magnifies the effect of sales volume change on the earning per
share of the firm.
Degree of combined leverage (DCL) is the ratio of percentage change in earning per
share to the percentage change in sales. It indicates the effect the sales changes will
have on EPS.
Degree of combined leverage
= Degree of operating leverage x Degree of financial leverage
DCL = DOL x DFL
Where,
DCL = Degree of combined leverage
DOL = Degree of operating leverage
DFL = Degree of financial leverage
Degree of combined leverage =
Percentage change in EPS
Percentage change in sale
Illustration-1
A firm’s details are as under:
Sales @ 100 per unit)
Variable Cost
Fixe Cost
Rs. 24,00,000
50%
Rs. 10,00,000
It has borrowed Rs. 10,00,000 @ 10% p.a. and its equity share capital is Rs. 10,00,000
(Rs. 100 each)
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Calculate:
a)
b)
c)
d)
e)
Operating Leverage
Financial Leverage
Combined Leverage
Return on Investment
If the sales increased by Rs. 6,00,000; what will the new EBIT?
Answer.
Rs.
24,00,000
12,00,000
12,00,000
10,00,000
2,00,000
1,00,000
1,00,000
50,000
50,000
10,000
5
Sales
Less: Variable cost
Contribution
Less: Fixed cost
EBIT
Less: Interest
EBT
Less: Tax (50%)
EAT
No. of equity share
EPS
12,00,000
(a)
Operating Leverage = 2,00,000 = 6 𝑡𝑖𝑚𝑒𝑠
(b)
Financial Leverage =
(c)
Combined Leverage = OL x FL = 6 x 2 = 12 times
(d)
R.O.I. =
(e)
Operating Leverage = 6
50 ,000
10,00 ,000
6=
2,00,000
1,00,000
= 2 𝑡𝑖𝑚𝑒𝑠
× 100 = 5%
% 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝐸𝐵𝐼𝑇
0 .25
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1.5 = % change in EBIT
Increase in EBIT = Rs. 2,00,000 x 1.5 = Rs. 3,00,000
New EBIT = 5,00,000
Illustration-2
Betatronics Ltd. has the following balance sheet and income statement information:
Balance Sheet as on March 31 st
Liabilities
(Rs.)
Equity capital (Rs. 10 per share)8,00,000
10% Debt
6,00,000
Retained earnings
3,50,000
Current liabilities
1,50,000
---------19,00,000
Assets
Net fixed assets
Current
(Rs.)
10,00,000
9,00,000
---------19,00,000
Income Statement for year ending March 31
Sales
Operating expenses (including Rs. 60,000 depreciation)
EBIT
Less: Interest
Earnings before tax
Less: Taxes
Net Earnings (EAT)
(Rs.)
3,40,000
1,20,000
2,20,000
60,000
1,60,000
56,000
1,04,000
a) Determine the degree of operating, financing and combined leverages at the
current sales level, if all operating expenses, other than depreciation, are variable
costs.
b) If total assets remain at the same level, but sales (i) increase by 20 percent and (ii)
decrease by 20 percent, what will be the earnings per share at the new sales level?
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Answer.
(a)
Calculation of Degree of Operating (DOL), Financial (DFL) and Combined leverage (DCL).
DOL = Rs. 3,40,000 - Rs. 60,000
Rs. 2,20,000
= 1.27
DFL = Rs. 2,20,000
Rs. 1,60,000
= 1.37
DCL = DOL x DFL
= 1.27 x 1.37 = 1.75
(b) Earnings per share at the new sales level
Increase by 20%
(Rs.)
Sales level
4,08,000
Less: Variable expenses
72,000
Less: Fixed cost
60,000
Earnings before interest and taxes
2,76,000
Less: Interest
60,000
Earnings before taxes
2,16,000
Less: Taxes
75,600
Earnings after taxes (EAT)
1,40,400
Number of equity shares
80,000
EPS
1.75
Decrease by 20%
(Rs.)
2,72,000
48,000
60,000
1,64,000
60,000
1,04,000
36,400
67,600
80,000
0.84
IIIustration-3
Calculate the operating leverage, financial leverage and combined leverage from the
following data under Situation I and II and Financial Plan A and B:
Installed Capacity
Actual Production and Sales
4,000 units
75% of the Capacity
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Selling Price
Variable Cost
Rs. 30 Per Unit
Rs. 15 Per Unit
Fixed Cost:
Under Situation I
Under Situation-II
Rs. 15,000
Rs. 20,000
Capital Structure:
Financial Plan
A
Rs.
10,000
10,000
20,000
B
Rs.
15,000
5,000
20,000
Situation-I
Rs.
90,000
Situation-II
Rs.
90,000
45,000
45,000
15,000
30,000
45,000
45,000
20,000
25,000
Equity
Debt (Rate of Interest at 20%)
Answer.
Operating Leverage:
Sales (s)
3000 units @ Rs. 30/- per unit
Less: Variable Cost (VC) @ Rs. 15 per unit
Contribution (c)
Less: Fixed Cost (FC)
Operating Profit (OP)
(EBIT)
(i) Operating Leverage
Contribution
𝑂𝑃
(1 ) =
45,000
30,000
= 1.5
45,000
Contribution
( 2) =
= 1.8
25,000
𝑂𝑃
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(ii) Financial Leverages
Situation 1
Operating Profit (EBIT)
Less: Interest on debt
PBT
Financial Leverage =
Financial Leverage =
A
(Rs.)
B
(Rs.)
30,000
2,000
28,000
30,000
1,000
29,000
OP
30,000
( 1) =
= 1.07
𝑃𝐵𝑇
28,000
OP
30,000
( 1) =
= 1.03
𝑃𝐵𝑇
29,000
Situation II
Operating Profit (OP)
(EBIT)
Less: Interest on debt
PBT
A
(Rs.)
B
(Rs.)
25,000
25,000
2,000
23,000
1,000
24,000
Financial Leverage =
OP
25,000
(II) =
= 1.09
23,000
𝑃𝐵𝑇
Financial Leverage =
OP
25,000
(II) =
= 1.04
PBT
24,000
(iii) Combined Leverages
(a) Situation I
(b) Situation II
A
(Rs.)
1.5 x 1.07 = 1.6
1.8 X 1.09 = 1.96
B
(Rs.)
1.5 x 1.04 = 1.56
1.8 X 1.04 = 1.87
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IIIustration 4
The data relating to two Companies are as given below:
Company A
Company B
Equity Capital
Rs. 6,00,000
Rs. 3,50,000
12% Debentures
Rs. 4,00,000
Rs. 6,50,000
Output (units) per annum
60,000
15,000
Selling price/unit
Rs. 30
Rs. 250
Fixed Costs per annum
Rs. 7,00,000
Rs. 14,00,000
Variable cost per unit
Rs. 10
Rs. 75
You are required to calculate the Operating leverage, Financial leverage and Combined
leverage of the two companies.
Answer. Computation of Degree of Operating leverage, Financial leverage and
Combined leverage of two companies
Output units per annum
Selling price/unit
Sales revenue
Less: Variable costs
Contribution (c)
Less: Fixed Costs
EBIT
Less: Interest @ 12%
On debentures
PBT
DOL =
𝐶
𝐸𝐵𝐼𝑇
Company A
60,000
(Rs.)
30
18,00,000
(60,000 units x Rs.30)
6,00,000
(60,0000 x Rs.10)
12,00,000
7,00,000
5,00,000
48,000
Company B
15,000
(Rs.)
250
37,50,000
(15,000 units x Rs. 250)
11,25,000
(15,000 units x Rs.75)
26,25,000
14,00,000
12,25,000
78,000
4,52,000
11,47,000
𝑅𝑠.12,00,000
𝑅𝑠.5,00,000
= 2.4
𝑅𝑠.26,25,000
𝑅𝑠.12,25,000
= 2.14
102 | P a g e
DFL =
(𝑅𝑠.5,00,000 )
𝐸𝐵𝐼𝑇
𝑃𝐵𝑇
(𝑅𝑠.4,52,000)
(𝑅𝑠.12,25,000)
= 1.11
(𝑅𝑠.11,47,000)
= 1.07
IIIustration-5 The net sales of Carlton Limited is Rs. 30 crores. Earnings before
interest and tax of the company as a percentage of net sales is 12%. The capital
employed comprises Rs. 10 crores of equity, Rs. 2 crores of 13% Cumulative Prefer ence
Share Capital and 15% Debentures of Rs. 6 crores. Income-tax rate is 40%.
(i)
(ii)
Calculate the Return-on-equity for the company.
Calculate the Operating Leverage of the Company given that combined leverage is
3.
Answer: (i) Net Sales : Rs. 30 crores
EBIT Rs. 3.6 crores @ 12% on sales
ROI =
𝐸𝐵𝐼𝑇
Capital Employed
3.6
× 100 = 20%
10 + 2 + 6
EBIT
Interest on Debt
EBT
Less: Tax @ 40%
EBT
Less: Preference dividend
Earnings available for Equity Shareholders
Return on Equity = 1.36/10 x 100 = 13.6%
Rs. in crores
3.6
0.9
2.7
1.08
1.62
0.26
1.36
(ii) Degree of Operating Leverage
Degree of Financing Leverage =
𝐸𝐵𝐼𝑇
𝑃𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑
EBIT − Interest −
1 − 𝑇𝑅
103 | P a g e
=
3.6
0.26
3.6 − 0.9 − 0.60
Degree of Combined Leverage =
= 1.5880
DFL x DOL
3 = 1.5880 x DOL
DOL =
Degree of Operating Leverage = 1.8892
3
1.5880
MULTIPLE CHOICE QUESTIONS
1. Operating leverage helps in analysis of:
a) Business Risk
b) Financing Risk
c) Production Risk
d) Credit Risk
2. Which of the following is studied with the help of financial leverage?
a) Marketing Risk
b) Interest Rate Risk
c) Foreign Exchange Risk
d) Financing risk
3. Combined Leverage is obtained from OL and FL by their:
a) Addition
b) Subtraction
c) Multiplication
d) Any of these
4. High degree of financial leverage means:
a) High debt proportion
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b) Lower debt proportion
c) Equal debt and equity
d) No debt
5. Operating leverage arises because of:
a) Fixed Cost of Production
b) Fixed Interest Cost
c) Variable Cost
d) None of the above
6. Financial Leverage arises because of:
a) Fixed cost of production
b) Variable Cost
c) Interest Cost
d) None of the above
7. Operating Leverage is calculated as:
a) Contribution ÷ EBIT
b) EBIT÷PBT
c) EBIT ÷Interest
d) EBIT ÷Tax
8. Financial Leverage is calculated as:
a) EBIT÷ Contribution
b) EBIT÷ PBT
c) EBIT÷ Sales
d) EBIT ÷ Variable Cost
9. Which combination is generally good for firms
a) High OL, High FL
b) Low OL, Low FL
c) High OL, Low FL
d) None of these
10. Combined leverage can be used to measure the relationship between:
a) EBIT and EPS
b) PAT and EPS
c) Sales and EPS
d) Sales and EBIT
105 | P a g e
11. FL is zero if:
a) EBIT = Interest
b) EBIT = Zero
c) EBIT = Fixed Cost
d) EBIT = Pref. Dividend
12. Business risk can be measured by:
a) Financial leverage
b) Operating leverage
c) Combined leverage
d) None of the above
13. Financial Leverage measures relationship between
a) EBIT and contribution
b) EBIT and EPS
c) Sales and PBT
d) Sales and EPS
14. Use of Preference Share Capital in Capital structure
a) Increases OL
b) Increases FL
c) Decreases OL
d) Decreases FL
15. Relationship between change in sales and change in EPS is measured by:
a) Financial leverage
b) Combined leverage
c) Operating leverage
d) None of the above
16. Operating leverage works when:
a) Sales Increases
b) Sales Decreases
c) Both (a) and (b)
d) None of (a) and (b)
17. Which of the following is correct?
a) CL= OL + FL
106 | P a g e
b) CL=OL-FL
c) CL= OL × FL
d) OL=OL÷FL
18. If the fixed cost of production is zero, which one of the following is correct?
a) OL is zero
b) FL is zero
c) CL is zero
d) None of the above
19. If a firm has no debt, which one is correct?
a) OL is one
b) FL is one
c) OL is zero
d) FL is zero
20. If a company issues new share capital to redeem debentures, then:
a) OL will increase
b) FL will increase
c) OL will decrease
d) FL will decrease
21. If a firm has a DOL of 2.8, it means:
a) If sales increase by 2.8%, the EBIT will increase by 1%
b) If EBIT increase by 2.8%, the EPS will increase by 1 %
c) If sales rise by 1%, EBIT will rise by 2.8%
d) None of the above
22. Higher OL is related to the use of higher:
a) Debt
b) Equity
c) Fixed Cost
d) Variable Cost
23. Higher FL is related the use of:
a) Higher Equity
b) Higher Debt
c) Lower Debt
d) None of the above
107 | P a g e
24. A firm's degree of operating leverage depends primarily upon its
a) Closeness to its operating break-even point.
b) Level of fixed operating costs.
c) Sales variability.
d) Debt-to-equity ratio.
25. Financial leverage measures ____________.
a) sensitivity of EBIT with respect of % change with respect to output
b) % variation in the level of production
c) sensitivity of EPS with respect to % change in level of EBIT
d) no change with EBIT and EPS
26. Operating leverage measures ____________.
a) business risk
b) financial risk
c) both risks
d) production risk
27. Financial leverage helps one to estimate ____________.
a) business risk
b) financial risk
c) both risks
d) production risk
28. Operating leverage x financial leverage= _____.
a) Combined Leverage
b) Financial Combined Leverage
c) Operating Combined Leverage
d) Fixed leverage
29. When a company uses increased fixed cost for production, this is an example of what
type of leverage.
a) operating leverage
b) financial leverage
c) variable cost leverage
d) combined leverage
30. When a company uses debt fund in its financial structure, it will lead to a change in
108 | P a g e
a) Financial leverage
b) Operating leverage
c) Money market leverage
d) Stock market leverage
31. Financial leverage is also known as.
a) Trading on equity
b) Trading on debt
c) Interest on equity
d) Interest on debt
32. A firm will have favourable leverage if its _____ are more than the debt cost
a) debt
b) interest
c) equity
d) earnings
33. Operating leverage = ______.
a) contribution / EBIT
b) contribution / EBT
c) contribution / total expenses
d) contribution / operating PBT
34. Financial risk is most associated with_______________.
a) the use of equity financing by corporations
b) the use of debt financing by corporations
c) Equity investments held by corporations
d) Debt investments held by corporations.
35. The probability of bankrupt is higher.
a) for a levered firm than an unlevered firm
b) for an unlevered firm than a levered firm
c) only levered firm
d) only unlevered firm
36. Degree of total leverage can be applied in measuring change in _________.
a) EBIT to a percentage change in quantity
b) EPS to a percentage change in EBIT
c) EPS to a percentage change in sale
109 | P a g e
d) Quantity to a percentage change in EBIT
37. The measure of business risk is __________.
a) operating leverage
b) financial leverage
c) total leverage
d) working capital leverage
38. Degree of financial leverage is a measure of relationship between ___________.
a) EPS and EBIT
b) EBIT and quantity produced
c) EPS and quantity produced
d) EPS and sales
39. Operating leverage examines.
a) The effect of the change in the quantity on EBIT
b) The effect of the change in EBIT on the EPS of the company
c) The effect of the change in output to the EPS of the company
d) The effect of change in EPS on the output of the company
40. Which of the following is the expression for operating leverage?
a) Contribution/EBIT
b) EBT/Contribution
c) Contribution/EAT
d) Contribution/Quantity
41. Operating Leverage is the response of changes in __________
a) EBIT to the changes in sales
b) EPS to the changes in EBIT
c) Production to the changes in sales
d) None of the above
42. The Degree of Financial Leverage (DFL)
a) Measures financial risk of the firm
b) Is zero at financial break-even point
c) Increases as EBIT increases
d) Both a and b
110 | P a g e
43. Operating leverage indicates the tendency of operating profits (EBIT) to vary
disproportionately with (A) Profit
(B) Fixed cost
(C) Sales
(D) EPS
44. There is no operating leverage if there is no
(A) Profit
(B) Sales
(C) Fixed cost
(D) EPS
45. Which of the following is correct formula to calculate Operating Leverage?
(A) Operating Leverage = Contribution/ EBIT
(B) Operating Leverage = Contribution/ EBT
(C) Operating Leverage = EBT/Contribution
(D) Operating Leverage = Contribution /EBT
46. Which of the following is correct formula to calculate Operating Leverage?
(A) % change in EPS / % change in Sales
(B) % change in EBIT /% change in EPS
(C) % change in EBIT /% change in Sales
(D) % change in Sales /% change in EBIT
47. If the fixed costs are high, the operating leverage will also be (A) Low
(B) High
(C) Zero
(D) Negative
48. Measure of business risk is (A) Operating leverage
(B) Financial leverage
(C) Combines leverage
(D) Working capital leverage
49. The presence of fixed costs in the total cost structure of a firm results into (A) Financial Leverage
(B) Operating Leverage
(C) Super Leverage
(D) Progressive leverage
50. A high operating leverage indicates 111 | P a g e
(A) Highly favorable situation as it consists of low fixed costs.
(B) Highly risky situation as it consists of large interest costs.
(C) Highly favorable situation as it consists of higher EPS.
(D) Highly risky situation as it consists of large fixed costs.
51. A firm has a DOL of 4.5 at Q units. What does this tell us about the firm?
(A) If sales rise by 4.5%, then EBIT will rise by 1%.
(B) If EBIT rises by 4.5%, then EPS will rise by 1%.
(C) If EBIT rises by 1%, then EPS will rise by 4.5%.
(D) If sales rise by 1%, then EBIT will rise by 4.5%
52. Operating leverage is directly .............................. to business risk.
(A) Proportional
(B) Not proportional
(C) Unrelated
(D) Not related
53. More operating leverage leads to (A) Less financial risk
(B) More financial risk
(C) More business risk
(D) Less business risk
54. Which of the following is correct formula to calculate Financial Leverage?
(A) % change in EPS/% change in EBIT
(B) % change in EBIT/ % change in EPS
(C) % change in EBT/ % change in EPS
(D) % change in Contribution / % change in EPS
55. Lower financial leverage is related to the use of additional .......................
(A) Fixed costs
(B) Variable costs
(C) Debt financing
(D) Common equity financing
56. The operating leverage indicates the impact of changes in sales on (A) Operating income
(B) Operating cost
(C) Operating profit after tax
(D) Operating sales
57. Where a company has large amount of fixed interest charges, the financial leverage
will be...................
(A) High
112 | P a g e
(B) Low
(C) Negative
(D) Unreliable
58. High financial leverage is not good as it indicates the large content of (A) Fixed cost
(B) Fixed interest charges
(C) Variable cost charges
(D) Contribution
59. If the Return on Investment (ROI) exceeds the rate of interest on debt, it is
.................financial leverage.
(A) unfavorable
(B) adverse
(C) a favorable
(D) negative
60. A firm with high operating leverage has:
(A) Low fixed costs in its production process.
(B) High variable costs in its production process.
(C) High fixed costs in its production process.
(D) High price per unit.
61. Output (units) = 3,00,000 Fixed cost = Rs.3,50,000 Unit variable cost = Rs.1.00
Interest expenses = Rs.25,000 Unit selling price = Rs.3.00 Applicable tax rate is 35%
Calculate Operating Leverage.
(A) 1.11
(B) 2.40
(C) 2.67
(D) 1.07
62. If combined leverage is 2 and financial leverage is 1.25 then operating leverage will
be (A) 0.625
(B) 2.50
(C) 1.60
(D) Data given is not sufficient
63. Operating leverage is 4. This means 10% change in sales will cause (A) 4% change in variable cost
(B) 40% change in EPS
(C) 4% change in EBIT
(D) 40% change in EBIT
64. Financial leverage is 2.5. This means 10% change in EBIT will cause 113 | P a g e
(A) 2.5% change in EBT
(B) 2.5% change in EPS
(C) 25% change in sales
(D) 25% change in EBT and EPS
65. Combined leverage is 3.125. This means 10% change in Sales will cause (A) 31.25% change in PAT
(B) 31.25% change in EPS
(C) 31.25% change in capital employed
(D) Both (A) and (B)
66. If sales increase by 6% taxable income ie. PAT and EPS will increase by 24%.
Combined leverage must be (A) 3
(B) 4
(C) 5
(D) 6
67. Contribution = Rs.7,00,000 Fixed cost = Rs.2,00,000 Interest = Rs.3,00,000 Financial
leverage =Rs.
(A) 2.0
(B) 1.5
(C) 2.5
(D) 1.0
68. EBIT = Rs.40,000
Variable cost
Sales
Rs.2,40,000
Rs.4,00,000
Operating leverage is
(A) 3.5
(B) 4.125
(C) 4.0
(D) 3.125
69. EBIT = Rs.4,00,000
Fixed cost
Interest
Rs.6,00,000
Rs.80,000
Combined leverage ?
(A) Sufficient data is not given
(B) 3.12
(C) 3.215
(D) 3.125
114 | P a g e
70. Operating leverage = 2 Combined leverage = 3.5 EBIT = Rs.2,80,000 Interest =
Rs.40,000
Tax rate = 50%.
Capital structure of the company consists of equity shares and preference shares.
Amount of Preference Dividend = ?
(A) Rs.39,967
(B) Rs.39,970
(C) Rs.39,000
(D) Rs.40,000
71. Contribution of a firm is Rs.4,000.
Fixed Cost:
Situation A
Rs.1,000
Situation B
Rs.2,000
Situation C
Rs.3,000
Compute the operating leverage for the three situations.
(A) 1.33; 1.18; 1.82
(B) 1.33; 2.36; 2.86
(C) 2.86; 2.00; 3.64
(D) 1.33; 2.00; 4.00
72. Operating leverage is 7 and financial leverage is 2.2858. How much change in sales
will be required to bring 70% change in EBIT?
(A) 10%
(B) 70%
(C) 11.429%
(D) 30%
73. Following data is available for A Ltd.
Financial Leverage
Interest
Operating Leverage
Variable cost (%to sales)
Income Tax Rate
3:1
Rs.2,000
4:1
66.67%
45%
Contribution is
(A) Rs.6,000
(B) Rs.12,000
(C) Rs.36,000
(D) Rs.18,000
115 | P a g e
74. A firm has sales of Rs.75,00,000, variable cost of Rs.42,00,000 and fixed cost of
Rs.6,00,000. It has a debt of Rs.45,00,000 at 9% and equity of Rs.55,00,000. What are
the operating, financial and combined leverages of the firm?
(A) 1.22, 1.44, 1.18
(B) 1.22, 1.12, 1.44
(C) 1.22, 1.18, 1.44
(D) 1.20,1.18,1.44
75. A firm has sales of Rs.75,00,000, variable cost of Rs.42,00,000 and fixed cost of
Rs.6,00,000. It has a debt of Rs.45,00,000 at 9% and equity of Rs.55,00,000. At what
level of sales the EBT of the firm will be equal to zero?
(A) Rs.22,84,091
(B) Rs.10,05,000
(C) Rs.22,48,910
(D) Rs.10,50,000
76. Output (units) = 3,00,000 Fixed cost = Rs.3,50,000 Unit variable cost = Rs.1.00
Interest expenses = Rs.25,000 Unit selling price = Rs.3.00 Applicable tax rate is 35%
Calculate Financial Leverage.
(A) 1.11
(B) 2.40
(C) 2.67
(D) 1.07
77. Output (units) = 3,00,000 Fixed cost = Rs.3,50,000 Unit variable cost = Rs.1.00
Interest expenses = Rs.25,000
Unit selling price = Rs.3.00 Applicable tax rate is 35%
Calculate Combined Leverage.
(A) 2.67
(B) 2.30
(C) 2.00
(D) 2.15
78. If operating leverage is 2.14 and financial leverage is 1.09 then combined leverage
will be (A) 2.3326
(B) 2.0029
(C) 0.4993
(D) Data given is not sufficient
79. If there is a 10% increase in sale, EBIT increase by 35% and if sales increase by 6%,
taxable income will increase by 24%. Operating leverage must be (A) 1.15
(B) 3.50
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(C) 4.00
(D) 2.67
80. If EBIT increases by 6%, taxable income increases by 6.9%. If sales increase by 6%,
taxable income will increase by 24%.
Financial leverage must be (A) 1.19
(B) 1.13
(C) 1.12
(D) 1.15
81. Following data is available for X Ltd.
Variable cost (% of sales)
Interest expense
DOL
DFL
Corporate tax rate
70%
Rs.20,000
5:1
3:1
30%
EBIT is
(A) Rs.30,000
(B) Rs.20,000
(C) Rs.60,000
(D) Rs.15,000
82. Following data is available for Y Ltd.
Variable cost (% of sales)
Interest expense
DOL
DFL
Corporate tax rate
75%
Rs.30,000
6:1
4:1
30%
Contribution is
(A) Rs.9,60,000
(B) Rs.2,40,000
(C) Rs.3,00,000
(D) Rs.7,80,000
83. Following data is available for X Ltd.
Financial leverage
Operating leverage
Interest charges
Corporate tax rate
Variable (% of sales)
2:1
3:1
Rs.20 lakh
40%
60%
117 | P a g e
Sales is
(A) Rs.1,00,00,000
(B) Rs.1,20,00,000
(C) Rs.2,00,00,000
(D) Rs.3,00,00,000
84. Following data is available for X Ltd.
Variable cost (% of sales)
Interest expense
DOL
DFL
Corporate tax rate
50%
Rs.1,00,000
2:1
2:1
30%
Sales is
(A) Rs.4,00,000
(B) Rs.6,00,000
(C) Rs.8,00,000
(D) Rs.9,00,000
 From the following information answer next 3 questions:
Sales
Less: Variable expenses
Contribution
Less: Fixed expenses
EBIT
Less: Interest
Taxable income
4,00,000
1,40,000
2,60,000
1,80,000
80,000
10,000
70,000
85. What percentage will EBIT increase, if there is a 10% increase in sales?
(A) 32.0%
(B) 31.14%
(C) 33.71%
(D) 32.5%
86. What percentage will taxable income increase, if EBIT increases by 6%
(A) 6.86%
(B) 6.67%
(C) 6.33%
(D) 6.22%
87. What percentage will taxable income increase, if the sales increase by 6%
(A) 22.29%
(B) 22.92%
(C) 22.78%
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(D) 22.87%
88. Calculate the degree of financial leverage (DFL) for a firm when its EBIT is
Rs.20,00,000. The firm has Rs.30,00,000 in debt that costs 10% annually. The firm
also has a 9%, Rs.10,00,000 preferred stock issue outstanding. The firm pays 40% in
taxes,
(A) 0.78
(B) 0.80
(C) 1.24
(D) 1.29
89. Total assets of X Ltd. are Rs.6,00,000. Total assets turnover ratio is 2.5 times. The
fixed operating costs are Rs.2,00,000 and variable operating cost ratio is 40%.
Income tax rate is 30%. Interest= 24000 Calculate operating, financial and combined
leverage?
(A) 1.2857; 1.0355; 1.3314
(B) 1.0355; 1.2857; 1.3314
(C) 1.3314; 1.0355; 1.2857
(D) 1.2857; 1.3314; 1.2857
90. A firm has a DFL of 3.5. What does this tell us about the firm?
(A) If sales rise by 3.5%, then EBIT will rise by 1%.
(B) If EBIT rises by 3.5%, then EPS will rise by 1%.
(C) If EBIT rises by 1%, then EPS will rise by 3.5%.
(D) If sales rise by 1% at the firm, then EBIT will rise by 3.5%
Answer:
1 A
9
C 17
C 25
C 33 A 41 A 49 B 57 A 65 D 73 B 81 A 89 A
2 D 10 C 18 D 26 A 34 B 42 A 50 D 58 B 66 B 74 C 82 B 90 C
3
C 11 B 19 B 27 B 35 C
43 C 51 D 59 C 67 C
75
A 83
D
4 A 12 B 20 D 28 A 36 C
44 C 52 A 60 C 68 C
76
A 84
C
D 77
A 85
D
5 A 13 B 21
C 29 A 37 A 45 A 53 C
6
C 30 A 38 A 46 C 54 A 62 C 70 D 78 A 86 A
C 14 B 22
61
B 69
7 A 15 B 23 B 31 A 39 A 47 B 55 D 63 D 71 D 79 B 87 A
8 B 16 C 24 B 32 D 40 A 48 A 56 A 64 D 72 A 80 D 88 A
119 | P a g e
State whether each of the following statements is True (T) or False (F)
(i)
Operating leverage analyses the relationship between sales level and EPS.
(ii)
Financial leverage depends upon the operating leverage.
(iii)
Dividend on Pref. shares is a factor of operating leverage.
(iv)
Operating leverage may be defined as Contribution ÷ EPS.
(v)
Financial leverage depends upon the fixed financial charges.
(vi)
Favourable financial leverage and trading on equity are same.
(vii)
Combined leverage establishes the relationship between operating leverage
and financial leverage.
(viii)
Financial leverage is always beneficial to the firm.
(ix)
Total risk of a firm is determined by the combined effect of oper ating and
financial leverages.
(x)
Combined leverage helps in analysing the effect of change in sales level on
the EPS of the firm.
Answers :(i) F, (ii) F, (iii) F, (iv) F, (v) T, (vi) T, (vii) F,(viii) F, (ix) T, (x) T
120 | P a g e
CHAPTER 6
CAPITAL STRUCTURE
 CONCEPT 1
MEANING OF CAPITAL STRUCTURE
Capital structure means the structure or constitution or break-up of the capital employed
by a firm. The capital employed consists of both the owners’ capital and the debt capital
provided by the lenders. Debt capital is understood here to mean the long term debt which
has been deployed to build long term assets. Apart from the elements of equity and debt in
the capital structure, a firm could have quasi equity in the form of convertible debt.
The Financing or Capital Structure decision is a significant managerial decision as it
influences the shareholder’s return and risk. Consequently the market value of the share
may be affected by the capital structure decision.
 CONCEPT 2
DESIGNING OF CAPITAL STRUCTURE
After planning the capital structure, we are faced with the issue of its design. Design takes
off from where the plan ends. Planning establishes the broad parameters of the structure. It
is left for the design to fill in the minor details. While designing a capital structure,
following points need to be kept in view:
1. Design should be functional: The design should create synergy with the long term
strategy of the firm and should not be dysfunctional. It should facilitate the day to
day working of the firm rather than create systematic bottlenecks.
2. Design should be flexible: The capital structure should be designed to incorporate a
reasonable amount of flexibility in order to allow for temporary expansion or
contraction of the share of each component.
3. Design should be conforming statutory guidelines: The design should conform to
the statutory guidelines, if any, regarding the proportion and amount of each
component. The limits imposed by lenders regarding the minimum level of owners ’
equity required in the firm should be complied with.
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 CONCEPT 3
TYPES OF CAPITAL STRUCTURE
Capital Structure of a firm is a reflection of the overall investment and financing strategy of
the firm. It shows how much reliance is being placed by the firm on external sources of
finance and how much internal accruals are being used to finance expansions etc. Capital
structure can be of various kinds as described below:
1. Horizontal Capital Structure
In a Horizontal capital structure, the firm has zero debt components in the structure mix.
The structure is quite stable. Expansion of the firm takes in a lateral manner, i.e. through
equity or retained earning only. The absence of debt results in the lack of financial leverage.
Probability of disturbance of the structure is remote.
2. Vertical Capital Structure
In a vertical capital structure, the base of the structure is formed by a small amount of
equity share capital. This base serves as the foundation on which the super structure of
preference share capital and debt is built. The incremental addition in the capital structure
is almost entirely in the form of debt. Quantum of retained earnings is low and the dividend
pay-out ratio is quite high. In such a structure, the cost of equity capital is usually higher
than the cost of debt. The high component of debt in the capital structure increases the
financial risk of the firm and renders the structure unstable. The firm, because of the
relatively lesser component of equity capital, is vulnerable to hostile takeovers.
3. Pyramid shaped Capital structure
A pyramid shaped capital structure has a large proportion consisting of equity capital and
retained earnings which have been ploughed back into the firm over a considerably large
period of time. The cost of share capital and the retained earnings of the firm is usually
lower than the cost of debt. This structure is indicative of risk averse conservative firms.
4. Inverted Pyramid shaped Capital Structure
Such a capital structure has a small component of equity capital, reasonable level of
retained earnings but an ever increasing component of debt. All the increases in the capital
structure in the recent past have been made through debt o nly. Chances are that the
retained earnings of the firm are shrinking due to accumulating losses. Such a capital
structure is highly vulnerable to collapse.
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 CONCEPT 4
SIGNIFICANCE OF CAPITAL STRUCTURE
Capital structure is significant for a firm because the long term profitability and solvency of
the firm is sustained by an optimal capital structure consisting of an appropriate mix of
debt and equity. The capital structure also is significant for the overall ranking of the firm
in the industry group. The significance of the capital structure is discussed below:
1. It reflects the firm’s strategy
The capital structure reflects the overall strategy of the firm. The strategy includes the pace
of growth of the firm. In case the firm wants to grow at a faster pace, it would be required
to incorporate debt in its capital structure to a greater extent.
2. It is an indicator of the risk profile of the firm
One can get a reasonably accurate broad idea about the risk profile of the firm from its
capital structure. If the debt component in the capital structure is predominant, the fixed
interest cost of the firm increases thereby increasing its risk. If the firm has no long term
debt in its capital structure, it means that either it is risk averse or it ha s cost of equity
capital or cost of retained earnings less than the cost of debt.
3. It acts as a tax management tool
The capital structure acts as a tax management tool also. Since the interest on borrowings
is tax deductible, a firm having healthy growth in operating profits would find it
worthwhile to incorporate debt in the capital structure in a greater measure.
 CONCEPT 5
ATTRIBUTES OF A WELL PLANNED CAPITAL STRUCTURE
A well-planned capital structure should have the following attributes:
1. Long Tenure: The plan should be for a fairly long tenure and should cover the working
of at least five to seven years of the project. Expansion of the capacity, addition of product
lines etc. should be accounted for in the plan.
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2. Consistency: The planned capital structure should be consistent with the overall
financing philosophy of the firm. If the firm has a risk averse philosophy, then the plan
should have minimum component of debt.
3. Feasibility: The planned capital structure should have feasibility, i.e. it should not be
impractical. Feasibility also means that it should be workable within the amount of share
capital, debt and retained earnings expected to be available to the firm.
 CONCEPT 6
THE FACTORS WHICH DETERMINE THE FORMATION OF THE CAPITAL STRUCTURE:
1. Minimisation of risk: The capital structure should aim at minimisation of risk of the
firm. The term risk here means financial risk. The term excludes the normal financial risk
and concentrates on the abnormal financial risk that might arise from a particular capital
structure decision. The normal risk has already been factored in the projections while
matching with the expected returns. It is the abnormal financial risk which should be
minimised.
2. Maximisation of profit: The capital structure is formulated with a view to achieve the
goal of maximization of firm’s profits. These profits are after tax profits which add to
shareholder wealth. Thus if the debt obligations of the firm entail tax breaks, it would be
advisable for the firm to enlarge the debt component of the structure.
3. Nature of the project: Formulation of the structure is also determined by the nature of
the investment project. If the project is a capital intensive, long gestation project then it
should be financed by debt of matching maturity.
4. Control of the firm: This aspect of the firm also plays a part in the determination of the
capital structure. Since the key to control of the firm is ownership of the equity capital, the
promoters would like to part with only that proportion of equity capital as is necessary for
execution of the project. Spreading of equity among the public investors exposes the firm to
risk of take over. Hence a capital structure which makes the firm vulnerable in this respect
is discouraged.
 CONCEPT 7
OPTIMAL CAPITAL STRUCTURE
By the term optimal capital structure we mean a particular arrangement of various
components of the structure which is just in tune with the both the long term and short
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term objectives of the firm. A combination less or more than the optimal combination
would be less than satisfying.
Hence a sub-optimal combination would affect the achievement of the goal of maximisation
of the shareholders’ wealth.
But can we plan and design an optimal capital structure? For designing such a structure,
one would need the following information:
–
–
–
–
The requirement of capital of the firm
Availability of different components
Cost of these components
Rate of return from investment
It has to be further kept in mind that the above information should be exact information. In
reality it is not possible to have the exact information on all the above four parameters.
Secondly whatever information is available is for a particular period. Thus we have to
design the structure in a static set-up which makes the design devoid of all flexibility.
The real world of business, however, is a dynamic world with ever changing demand and
supply of various components of the capital structure. Hence we cannot formulate the
optimal capital structure in a static framework.
We can, therefore, say that the optimal capital structure is an ideal situation which can
function as the benchmark of performance for a firm. But this benchmark is invincible and
the firm can expect to achieve moderated or toned down versions of this benchmark
depending upon dynamics of each project.
 CONCEPT 8
EBITDA ANALYSIS
AMORTIZATION),
(EARNINGS
BEFORE
INTEREST,
TAX,
DEPRECIATION,
EBITDA, an acronym for “earnings before interest, taxes, depreciation and amortization,” is
an often-used measure of the value of a business. EBITDA is calculated by taking net
income and adding interest, taxes, depreciation and amortization expenses back to it.
EBITDA is used to analyze a company’s operating profitability before non operating
expenses (such as interest and “other” non-core expenses) and non-cash charges
(depreciation and amortization).
Analysis with EBITDA
Page | 125
EBIDTA enables analysts to exclude the impacts of non-operating activities and focus on
the outcome of operating decisions. Non-operating activities include interest expenses, tax
rates, and large non-cash items such as depreciation and amortization.
By removing the non-operating effects, EBITDA gives investors the ability to focus on the
profitability of their operations. This type of analysis is particularly important when
comparing similar companies across a single industry for example.
Limitations of EBITDA
Factoring out interest, taxes, depreciation and amortization can make even completely
unprofitable firms appear to be fiscally healthy. The use of EBITDA as measure of financial
health made these firms look attractive.
EBITDA numbers are easy to manipulate. If fraudulent accounting techniques are used to
inflate revenues and interest, taxes, depreciation and amortization are factored out of the
equation, almost any company may appears to be profitable and great.
Operating cash flow is a better measure of how much cash a company is generating because
it adds non-cash charges (depreciation and amortization) back to net income and includes
the changes in working capital that also use or provide cash (such as changes in
receivables, payables and inventories). These working capital factors are the key to
determining how much cash a company is generating.
 CONCEPT 9
KEY CONCEPTS FOR DESIGNING OPTIMAL STRUCTURE
The capital structure decisions are so significant in financial management, as they influence
debt - equity mix which ultimately affects shareholders return and risk.
Since cost of debt is cheaper, firm prefers to borrow rather than to raise form equity. So
long as return on investment is more than the cost of borrowing, extra borrowing increases
the earnings per share. However, beyond a limit, it increases the risk and share price may
fall because shareholders may assume that their investment is associated with more risk.
For an appropriate debt-equity mix, lets some discuss key concepts:-
Page | 126
LEVERAGES
There are two leverages associated with the study of capital structure, namely operating
leverage and financial leverage.
Operating leverage:- Operating leverage exists when a firm has a fixed cost that must be
defrayed regardless of volume of business. If can be defined as the firms ability to use fixed
operating costs to magnify the effects of changes in sales on its earnings before interest and
taxes. In simple words, the percentage change in profits accompanying a change in volume
is greater than the percentage change in volume.
Operating leverage can also be defined in terms of Degree of Operating Leverage (DOL).
When proportionate change in EBIT as of results change in sales is more than the
proportionate change in sales, operating leverage exits. The greater the DOL, the higher is
the operating leverage.
Therefore DOL exists when Percentage change in EBIT? Percentage change is Sales is > 1
Financial leverage:- Financial leverage involves the use fixed cost of financing and refers
to mix of debt and equity in the capitalisation of a firm. Financial leverage is a
superstructure built on the operating leverage. It results from the presence of fixed
financial charges in the firm’s income stream. They are to be paid regardless of the amount
of EBIT available to pay them. After paying them, the operating profits (EBIT) belong to the
ordinary shareholders.
In simple words, financial leverage involves the use of funds obtained at a fixed cost in the
hope of increasing the return to the shareholders.
Positive Financial Leverage occurs when the firm earns more on the assets purchased with
the funds, than the fixed cost of their use. Financial Leverage is also called as “Trading on
Equity”.
The degree of financing leverage can be found out as:
Percentage change in Earnings per share (EPS)
Percentage change in Earnings before interest and tax (EBIT)
Positive Financial Leverage occurs when the when the result of above is greater than 1.
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Operating Leverage vis-à-vis Financial Leverage:- A company having higher operating
leverage should be accompanied by a low financial leverage and vice versa, otherwise it
will face problems of insolvency and inadequate liquidity. Thus a combination of both the
leverage is a challenging task.
However, the determination of optimal level of debt is a formidable task and is a major
policy decision. Determination of optimal level of debt involves equalizing between return
and risk. EBIT-EPS analysis is a widely used tool to determine level of debt in a firm.
Through this analysis, a comparison can be drawn for various methods of financing by
obtaining indifferent point. It is a point to the EBIT level at which EPS remain unchanged
irrespective of debt level equity mix. The concepts of leverages and EBIT-EPS analysis
would be dealt in detail separately for better understanding.
 CONCEPT 10
EBIT-EPS ANALYSIS
The basic objective of financial management is to design an appropriate capital structure
which can provide the highest earnings per share (EPS) over the firm’s expected range of
earnings before interest and taxes (EBIT).
EPS measures a firm’s performance for the investors. The level of EBIT varies from year to
year and represents the success of a firm’s operations. EBIT-EPS analysis is a vital tool for
designing the optimal capital structure of a firm.
The objective of this analysis is to find the EBIT level will equate EPS regardless of the
financing plan chosen.
 CONCEPT 11
FINANCING BREAK-EVEN AND INDIFFERENCE ANALYSIS
Financing break-even point is the minimum level of EBIT needed to satisfy all the fixed
financial charge i.e. interest and preference dividends. It denotes the level of EBIT for
which the firm’s EPS equals zero.
If the EBIT is less than the financing breakeven point, then EPS will be negative but if the
expected level of EBIT is more than the breakeven point, then more fixed costs financing
instruments can be taken in the capital structure, otherwise, equity would be preferred.
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EBIT-EPS breakeven analysis is used for determining the appropr iate amount of debt a
firm might carry.
Another method of considering the impact of various financing alternatives on earnings per
share is to prepare the EBIT chart or the range of Earnings Chart. This chart shows the
likely EPS at various probable EBIT levels. Thus, under one particular alternative, EPS may
be Rs. 2 at a given EBIT level. However, the EPS may go down if another alternative of
financing is chosen even though the EBIT remains at the same level. At a given EBIT,
earnings per share under various alternatives of financing may be plo tted. A straight line
representing the EPS at various levels of EBIT under the alternative of may be drawn.
Whether this line interests, it is known as break-even point. This point is a useful guide in
formulating the capital structure. This is known as EPS equivalency point or indifference
point since this shows that, between the two given alternatives of financing (i.e. regardless
of leverage in the financial plans), EPS would be the same at the given level of EBIT.
The equivalency or indifference point can also be calculated algebraically in the following
manner.
(EBIT − I1 ) (1 − T)
(EBIT − I2 ) (1 − T)
=
E1
E2
Where,
EBIT =
E1 =
E2 =
I1 =
I2 =
T =
Indifference point
Number of equity shares in Alternative 1
Number of equity shares in Alternative 2
Interest charges in Alternative 1
Interest charge in Alternative 2
Tax-rate
Alternative 1 = All equity finance
Alternative 2 = Debt-equity finance.
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The indifference point can also be depicted graphically as:
Debt
Equity
Earning per
Share (Rs.)
Indifference point
0
EBIT (Rs.)
Debt-Equity Indifference Point
Illustration 1 Best of luck Ltd., a profit making company has a paid-up capital of Rs. 100
lakhs consisting of 10 lakhs ordinary shares of Rs. 10 each. Currently, it is earning an
annual pre-tax profit of Rs. 60 lakhs. The company’s shares are listed and are quoted in the
range of Rs. 50 to Rs. 80. The management wants to diversify production and has approved
a project which will cost Rs. 50 lakhs and which is expected to yield a pre -tax income of Rs.
40 lakhs per annum. To raise this additional capital, the following options are under
consideration of the management.
a) To issue equity capital for the entire additional amount. It is expected that the new
shares (face value of Rs. 10) can be sold at a premium of Rs. 15.
b) To issue 16% non-convertible debentures of Rs. 100 each for the entire amount.
c) To issue equity capital for Rs. 25 lakhs (face value of Rs. 10) and 16% non -convertible
debentures for the balance amount. In this case, the company can issue shares at a
premium of Rs. 40 each.
You are required to advise the management as to how the additional capital can be raised,
keeping in mind that the management wants to maximize the earnings per share to
maintain its goodwill. The company is paying income tax at 50%.
Page | 130
Ans.
Calculation of Earnings per share under the three options:
Particulars
Option I
Option II
Option III
(Issue of
equity Only)
(Issue of equity &
debentures Equally)
(Rs. in lakhs)
(Issue of
debentures
only)
(Rs in lakhs)
Existing
Now issued
10
2
10
-
10
0.5
Total
12
10
10.5
16% debentures
Estimated total income:
From current operations
From new projects
Nil
Rs. 50 lakhs
Rs. 25 lakhs
60
40
60
40
60
40
100
100
100
Less: Interest on 16%
Debentures
-
8
4
Profit before tax
Tax at 50%
100
50
92
46
96
48
Profit after tax
50
46
48
EPS
Rs. 4.17
Rs. 4.60
Rs. 4.57
(Rs in lakhs)
Number of equity Shares
(Lakhs):
Advise:
Option II i.e. issue of 16% debentures is most suitable to maximize the earnings per share.
Illustration 2 Shahji Steels Limited requires Rs. 25,00,000 for a new plant. This plant is
expected to yield earnings interest and taxes of Rs. 5,00,000. While deciding about the
financial plan, the company considers the objective of maximizing earnings per share. It has
three alternatives to finance the project - by raising debt of R. 250,000 or Rs. 10,00,000 or
Rs. 15,00,000 and the balance, in each case, by issuing equity shares. The company ’s share
is currently selling at Rs. 150, but is expected to decline to Rs. 125 in case the funds are
borrowed in excess of Rs. 10,00,000. The funds can be borrowed at the rate of 10 percent
upto Rs. 2,50,000, at 15 percent over Rs. 2,50,000 and upto Rs. 10,00,000 and at 20 percent
over Rs. 10,00,000. The tax rate applicable to the company is 50 percent. Which form of
financing should the company choose?
Page | 131
Ans.
Plan I = Raising debt of Rs. 2.5 lakhs + Equity of Rs. 22.5 lakhs.
Plan II = Raising debt of Rs. 10 lakhs + Equity of Rs. 15 lakhs.
Plan III = Raising debt of Rs. 15 lakhs + Equity of Rs. 10 lakhs.
Earnings per share (EPS) under proposed financial alternatives are:
Particulars
Financing Alternatives to Raise Rs. 25 Lakhs
PLAN I
Plan II
Plan III
(Rs.)
(Rs.)
(Rs.)
Expected EBIT
5,00,000
5,00,000
5,00,000
Less: Interest (a)
25,000
1,37,500
2,37,500
Earnings before taxes
4,75,000
3,62,500
2,62,500
Less: Taxes
2,37,500
1,81,250
1,31,250
Earnings after taxes (EAT)
2,37,500
1,81,250
1,31,250
Number of shares (b)
15,000
10,000
8,000
Earnings per share (EPS)
15.83
18.13
16.41
Recommendation: Financing Option II (i.e. Raising debt of Rs. 10 lakhs and issue of equity
share capital of Rs. 15 lakhs) is the best option as it maximizes earnings per share.
Illustration 3 Venus Limited is setting up a project with a capital outlay of Rs. 60,00,000. It
has two alternatives in financing the project cost.
Alternative (I):
Alternative (II):
100% equity finance
Debt-equity ratio 2:1
The rate of interest payable on the debts is 18% p.a. The corporate tax rate is 40%.
Calculate the indifference point between the two alternative methods of financing.
Ans. Alternatives in Financing and its Financial Charges
a) By issue of 6,00,000 equity shares of Rs. 10 each amounting to Rs. 60 lakhs. No
financial charges are involved.
Page | 132
b) By raising the funds in the following way:
Debt = Rs. 40 lakhs
Equity = Rs. 20 lakhs (2,00,000 equity shares of Rs. 10 each)
Interest payable on debt =
40,00,000
100
× 18
= Rs. 7,20,000
The difference point between the two alternatives is calculated by:
(EBIT − I2 ) (1 − T)
(EBIT − I1 ) (1 − T)
=
E2
E1
Where,
EBIT
I1
I2
T
E1
E2
= Earning before interest and taxes
= Interest charges in Alternative (I)
= Interest charges in Alternative (II)
= Tax rate
= Equity shares in Alternative (I)
= Equity shares in Alternative (II)
Putting the value, the break-even point would be as follows:
(EBIT − 0)(1 − 0.40)
6,00,000
(EBIT) (0.60)
6,00,000
EBIT (0.60)
EBIT
3
=
=
=
(EBIT − 7,20,000)(1 − 0.40)
2,00,000
(EBIT − 7,20,000)(0.60)
2,00,000
0.60 (EBIT − 7,20,000)
1
= 3EBIT - 21,60,000
-2 EBIT = -21,60,000
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𝐸𝐵𝐼𝑇 =
21,60,000
2
EBIT = 10,80,000
Therefore, it can be seen that the EBIT at indifference point explains that the earnings per
share for the two alternatives is equal.
UNSOLVED QUESTION
TYPE I
OPTIMUM CAPITAL STRUCTURE IN CASE OF NEW FIRMS
Que 1.
X Ltd. is considering 3 financing plans to raise Rs. 200 Lakhs
Financial Plan
Equity
12% Debt.
9% Pref.
A
100%
-
-
B
50%
50%
-
C
50%
-
50%
 Face value of equity shares Rs. 10 each.
 Expected EBIT  80 Lakhs
 Corporate tax rate = 40%
Determine
1.
2.
EPS
Suggest which optimum financing plan.
(i)
(ii)
EPS  A = 2.4, Financial Plan B = 4.2, Financial Plan C = 3.9
Suggest which optimum financing plan  Plan B is optimum
Ans.
Page | 134
Que 2.
X Ltd. intends to raise Rs 100 lakhs to finance a project. It has 3 choices.
Plan
Equity
12% Debt.
14% Pref.
A
100%
-
-
B
50%
50%
-
C
50%
-
50%
Face value of equity share is Rs 10 each, issued at premium of Rs 10, Expected EBIT = 30,
Tax rate = 30%
Determine
(i)
(ii)
EPS
Suggest which is optimum choice.
EPS
=
Ans.
Plan A = 4.2
(ii)
Plan B is optimum
Plan B = 6.72
Plan C = 5.60
Que 3.
ASC Ltd. desires to raise Rs. 500 Lakhs to finance a new project and it
has 3 choices.
Plan
Equity
16% Debt.
7% Pref.
A
100%
-
-
B
50%
50%
-
C
50%
-
50%
Tax rate = 50%
Expected EBIT = Rs. 100 Lakhs
Face value of equity hare = Rs. 50
Find out EPS and suggest which is optimal plan.
Page | 135
TYPE II
OPTIMUM CAPITAL STRUCTURE IN CASE OF EXISTING FIRMS
Que 4.
2002 - Dec [3] (b) Govinda Entertainers Ltd. has 10,00,000 shares of Rs. 10
each with market price of Rs. 50 per share. It has also issued bonds for Rs. 4
crore @ 12% per annum. It is considering an expansion plan and needs to
mobiles Rs. 5 crore.
The alternatives being considered are(i) Issue equity at Rs. 40 per share.
(ii) Issue straight bonds at 10% per annum.
(iii)Issue preference shares @ 12% per annum.
(iv) Finance 50% with equity at Rs. 40 per share and 50% with bonds @ 10% per
annum.
The company is in tax bracket of 35%. If the company is hopeful of generation an EBIT of
Rs. 2.50 crore after expansion, which method of financing is the best form shareholders ’
view point? What more information is required if the market price of equity sh ares is the
criterion for decision making?
EPS :
Que 5
Option I = 5.835
Option III = 7.13
Option II = 9.88
Option IV = 7.08
2004 - June [2] (a) The capital structure of Asha Ltd. is as under:
Equity shares of Rs. 100 each.
Retained earnings
8% Preference shares
7% Debentures
Rs.
40,00,000
20,00,000
24,00,000
16,00,000
1,00,00,000
The company earns 12% on its capital.
The tax rate applicable is 35%. The company required a sum of Rs. 50,00,000 for which
following options are available to it:
(i) Issue of 40,000 equity shares at a premium of Rs. 25 per share.
(ii) Issue of 9% preference shares
(iii)Issue of 8% debentures
Page | 136
(iv) It is estimated that the P/E ratio in the cases of equity share, preference share and
debenture financing would be 22.5, 18.5 and 15.2 respectively. Which of the three
financing alternatives would you recommend and why?
Ans.
(254.6,210.53,245.176)
Que 6.
2004 - Dec [6] (a) A company’s structure consists of the following :
Rs.
Equity shares of Rs. 100 each
20,00,000
Retained earnings
10,00,000
9% Preference shares
12,00,000
7% Debentures
8,00,000
50,00,000
The company ears 12% on its employed capital. The tax rate is 50%. The company requires
a sum of Rs. 25 lakh to finance its expansion programme for which following alternatives
are available to it:
(i) Issue 20,000 equity shares at a premium of Rs. 25 per share, or
(ii) Issue 10% preference shares, or
(iii) Issue 8% debentures.
It is estimated that the price-earnings ratio in case of equity shares, preference shares and
debentures financing would be 21.4,17.0 and 15.7 respectively.
You are required to evaluate each proposal and recommend the best alternative.
TYPE III
Que 7.
INDIFFERENCE POINT
2009 - Dec [2] (c) Monark Ltd. is considering two alternative financial plans
to start a new project. In Plan-I, it is likely to issue equity shares of Rs. 16
lakh and 13% preference capital of Rs. 4 lakh. In Plan-II, the company will
equity shares of Rs. 8 lakh, 13% preference capital of Rs. 4 lakh, and 15%
debentures of Rs. 8 lakh. The face value of equity shares in both plans is Rs.
10. Tax rate is 30%.
You are required to determine level of EBIT at which the EPS would be same under both
the plan
Page | 137
Ans.
Rs. 314286
Que 8. X Ltd. is considering to raise Rs 10 lakhs and it has 2 choices.
Choice I
100% from equity (Rs. 100 each)
Choice II
50% from equity & 50% by issuing 9% Debt.
Find indifference point if tax rate = 40%
Ans.
Rs. 90,000
Que 9. Super Ltd. is considering 3 financial plans
Financial Plan
Equity
9% Debt.
12% Pref.
A
100%
-
-
B
50%
50%
-
C
50%
-
50%
Total funds to be raised Rs. 200 crore
Tax rate = 35%
Face value of equity share Rs. 10 each, these shares will be issued at a premium of Rs. 10
each
(i)
Find indifference point b/w A&B, B&C, A&C
Ans.
(i) A & B = 18 Cr (ii) B & C = N.A (iii) A & C = 36.923 Cr
TYPE IV
FINANCIAL BREAK-EVEN POINT
Que 10.
Given the capital structure of X Ltd. Find out financial Break-even point.
Equity share capital (Rs. 100 E)

10 Lakhs
9% Debenture

5 Lakhs
11% Preference

5 Lakhs
20 Lakhs
Tax rate = 30%
Page | 138
Que 11. Compute financial Break-Even Point given that capital structure of X Ltd. consist
of
Equity share capital (Rs. 100 E)

10 Lakhs
9% Debenture

10 Lakhs
11% Preference

5 Lakhs
25 Lakhs
Tax rate = 35%
MULTIPLE CHOICE QUESTIONS
1. ................................refers to the mix of a firm’s capitalization and includes long term
sources of funds.
a) Leverage
b) Capital structure
c) Debt mix
d) Owner’s equity
2. While designing a capital structure a finance manager should choose a pattern of capital
which a) Minimizes cost of capital
b) Maximizes the owners return.
c) Maximizes cost of capital and minimizes the owners return.
d) Both (A) and (B)
3. Optimal capital structure consists of a) Appropriate mix of fixed assets and current assets.
b) Appropriate mix of long term debts and fixed assets.
c) Appropriate mix of sales and profit.
d) Appropriate mix of debt and equity.
4. Which of the following is not included in capital structure?
a) Long term debt
b) Preferred stock
c) Current assets
d) Retained earnings
5. Financial structure is .................. concept while capital structure is .................. concept
a) inappropriate; appropriate
Page | 139
b) appropriate; inappropriate
c) narrow; broader
d) broader; narrow
6. Select which of the following statement is correct. Horizontal capital structure 1. is quite stable.
2. Is formed by a small amount of equity share capital.
3. There is absence of debt.
4. Have increasing component of debt.
Select the correct answer from the options given below.
a) 1,2 & 4
b) 2 & 3
c) 1 only
d) 1 & 4 only
7. In horizontal capital structure a) Expansion of the firm takes place by issuance of debt securities.
b) Expansion of the firm takes place by issuance of debt securities and preferred
stocks.
c) Expansion of the firm takes in a lateral manner, i.e. through equity or retained
earning only.
d) Expansion of the firm takes place by issuance of short term and marketable
securities.
8. In a .................. , the base of the structure is formed by a small amount of equity share
capital. This base serves as the foundation on which the super structure of preference
share capital and debt is built.
a) horizontal capital structure
b) vertical capital structure
c) diagonal capital structure
d) matrix capital structure
9. Which of the following is vulnerable to hostile takeovers?
a) Horizontal Capital Structure
b) Vertical Capital Structure
c) Pyramid Shaped Capital Structure
d) All of the above
10. Pyramid Shaped Capital Structure a) Have a high proportion of fixed assets and considerably a very low proportion of
current assets.
b) Have a high proportion of debts and considerably a very low proportion of equity.
c) Have a high proportion of equity and considerably a very low proportion of debt.
d) Have a high proportion of current assets and considerably a very low proportion of
liquid assets.
Page | 140
11. Inverted Pyramid Shaped Capital Structure a) Has a large component of equity capital.
b) Is highly stable and permanent.
c) Is opposite as that of pyramid shaped capital structure.
d) Has reasonable level of debt but an ever increasing component of retained earnings.
12. ................................denotes the level of EBIT for which the firm’s EPS equals zero.
a) Financial break-even point
b) Margin of safety
c) Equilibrium point
d) Min-max point
13. If the EBIT is less than the financial breakeven point, then the EPS will be a) Positive
b) Negative
c) Zero
d) Maximum
14. In order to calculate EPS, Profit after Tax less Preference Dividend is divided by:
a) MP of Equity Shares
b) Number of Equity Shares
c) Face Value of Equity Shares
d) None of the above.
15. Trading on Equity is :
a) Always beneficial
b) May be beneficial
c) Never beneficial
d) None of the above.
16. Benefit of 'Trading on Equity' is available only if:
a) Rate of Interest < Rate of Return
b) Rate of Interest > Rate of Return
c) Both (a) and (b)
d) None of (d) and (b).
17. Indifference Level of EBIT is one at which:
a) EPS is zero
b) EPS is Minimum
c) EPS is highest
d) None of these.
Page | 141
18. Financial Break-even level of EBIT is one at which:
a) EPS is one
b) EPS is zero
c) EPS is Infinite
d) EPS is Negative.
19. If a firm has no Preference share capital, Financial Breakeven level is defined as EBIT
equal toa) EBIT
b) Interest liability
c) Equity Dividend
d) Tax Liability.
20. At Indifference level of EBIT, different capital have:
a) Same EBIT
b) Same EPS
c) Same PAT
d) Same PBT.
21. Which of the following is not a relevant factor in EBIT EPS Analysis of capital structure?
a) Rate of Interest on Debt
b) Tax Rate
c) Amount of Preference Share Capital
d) Dividend paid last year.
22. Between two capital plans, if expected EBIT is more than indifference level of EBIT,
then
a) Both plans be rejected,
b) Both plans are good,
c) One is better than other
d) None of the above.
23. Which of the following appearing in the balance sheet generates tax advantage and
hence affects the capital, structure decision?
a) Reserves and Surplus
b) Loan
c) Preference Share Capital
d) Equity Share Capital.
24. Variable cost in an organization
a) be fixed according to the rate of growth
Page | 142
b) changes with the volume of production
c) does not change with volume of production
d) remains constant
25. Variable cost per unit.
a) varies with the level of output
b) remains constant irrespective of the level of output
c) changes with the growth of the firm
d) does not change with volume of production
26. Which of the following factors does not affect the capital structure of a company?
a) Cost of capital
b) Composition of the current assets
c) Size of the company
d) Expected nature of cash flows
27. Earnings Per Share (EPS) is equal to __________.
a) Profit before tax/No of outstanding shares
b) Profit after tax/No of outstanding shares
c) Profit after tax/Amount of equity share capital
d) Profit after tax less equity dividends/No of outstanding shares
28. The value of EBIT at which EPS is equal to zero is known as ____________.
a) Break-even point
b) Financial break-even point
c) Operating break-even point
d) Overall break-even point
29. EBIT means _____________.
a) Operating Income
b) Operating Profit
c) Earnings before interest and tax
d) All of the above
30. Total common equity divided by common shares outstanding which is used to calculate
a) book value of share
b) market value of shares
c) earning per share
d) dividends per share
Page | 143
31. An earning before interest, taxes, depreciation and amortization are calculated by
a) subtracting operating cost from net sales
b) subtracting cash net cash sales from operating costs
c) adding operating cost and net sales
d) adding interest and taxes
32. If expected level of EBIT is more than the breakeven point, then the EPS will be (A) Minimum
(B) Negative
(C) Positive
(D) Infinite
33. The rate of tax affects the (A) Cost of retained earning
(B) Cost of debt
(C) Cost of equity
(D) All of the above
34. A pyramid shaped capital structure has (A) Retained earnings of the firm which are usually lower than the cost of debt.
(B) Cost of A large proportion consisting of equity capital and retained earnings which
have been ploughed back into the firm over a considerably large period of time.
(C) Incremental addition in the capital structure is almost entirely in the form of debt.
(D) Both (A) and (B)
35. Business risk is influenced by (A) Revenue
(B) Variable cost
(C) Fixed cost
(D) All of the above
36. X Ltd. is considering the following two alternative financing plans:
Plan -1
Plan - II
Equity Shares (Rs. 10 each)
4,00,000
4,00,000
12% Debentures
2,00,000
Pref. Shares (Rs. 100 each)
2,00,000
The indifference point between the plans is Rs.2,40,000. Corporate tax rate is 30%.
Calculate rate of dividend on preference shares.
(A) 8.00%
(B) 8.04%
Page | 144
(C) 8.40%
(D) 8.80%
37. A company needs Rs.31,25,000 for the construction of new plant. The following two
plans are feasible:
(i) Company may issue 3,12,500 equity shares at Rs.10 per share.
(ii) Company may issue 1,56,250 ordinary equity shares at Rs.10 per share and 15,625
debentures of Rs.100 denomination bearing a 8% rate of interest.
Corporate income-tax rate is 40%.
Calculate indifference point.
(A) Rs.2,50,000
(B) Rs.2,75,000
(C) Rs.2,25,000
(D) Rs.3,00,000
Answer –
1
2
3
4
5
6
7
8
9
10
11
12
B
D
D
C
D
C
C
B
B
C
C
A
13
14
15
16
17
18
19
20
21
22
23
24
B
B
B
A
D
B
B
B
D
C
B
B
25
26
27
28
29
30
31
32
33
34
35
36
B
B
B
B
D
A
A
C
B
D
D
C
37
A
State whether each of the following statements is True (T) or False (F).
(i) EBIT is also known as operating profits.
(ii) If EBIT for two firms are same, then the EPS of these firms would also always be
same.
(iii) EPS depends upon the composition of capital structure,
(iv)
Financial breakeven level occurs when EBIT is zero.
(v)
At financial breakeven level of EBIT, EPS would be zero.
(vi)
Indifference level of EBIT is one at which EPS is zero.
Page | 145
(vii)
(viii)
(ix)
(x)
(xi)
Indifference level of EBIT is one at which EPS under two or more financial plans
would be same.
All equity plan and Debt-equity plan have no indifference level of EBIT.
Preference dividend is not a factor of indifference level of EBIT.
EBIT-EPS Analysis is an extension of financial leverage analysis.
Trading on equity is resorted to with a view to decrease EPS.
Answers : (i) T, (ii) F, (iii) T, (iv) F, (v) T, (vi) F, (vii) T, (viii) F (ix) F, (x) T, (xi) F
Which of the following statements is True (T) or False
(i)
The financing decision affects the total operating profits of the firm.
(ii)
The equity Shareholders get the residual profit of the firm.
(iii)
There is no difference of opinion on the relationship between capital structure and
value of the firm.
(iv)
The ultimate conclusions of NI approach and the NOI approach are same.
(v) The NI approach, the ke is assumed to be same and constant.
(vi)
The NI approach, the k0 falls as the degree of leverage is increased.
(vii)
In NOI approach, Kd and K0 are taken as constant.
(viii)
In NOI approach says that there is no optimal capital structure.
(ix) The traditional approach says that a firm may attain an optimal capital structure.
(x) At optimal capital structure, the k0 of the firm is highest.
(xi) MM model provides a behavioral justification of NOI approach.
(xii)
MM model is difficult to be applied in practice.
(xiii)
In the basic MM model, leverage does not affect the value of the firm.
(xiv) In the MM model, the value of the levered firm can be found by first finding out the
value of the unlevered firm.
Answers: (i) F, (ii) T, (Hi) F, (iv) F, (v) T, (vi) T, (vii) T, (viii) T, (ix) T, (x) F, (xi) T, (xii) T,
(xiii) T, (xiv) T.
Page | 146
CHAPTER 7
CAPITAL STRUCTURE THEORIES
 CONCEPT 1
LEARNING OBJECTIVES
To find relation between capital structure, value of firm and cost of capital
 CONCEPT 2
NET INCOME (NI) APPROACH
According to this approach, a firm can increase its value, i.e., it can lower its overall cost of
capital by increasing the proportion of debt in the capital structure. A higher debt content
in the capital structure will result in decline in overall or weighted average cost of capital.
This will cause increase in the value of firm. Reverse will happen in the converse situation.
The value of the firm on the basis of NI Approach can be ascertained as follows:
V=E +D
Where
V = Value of Equity
E = Market Value of equity.
D = Market Value of Debt.
Market value of equity can be ascertained as follows:
E = NI / ke
Where
E = Market Value of equity
NI = Earnings available for equity shareholders.
ke = Equity Capitalization Rate.
ASSUMPTIONS OF NI APPROACH
1. Kd < Ke - The debt capitalization rate (Kd) is less than the equity capitalization rate
(Ke).
2. No change in risk - The use of debt content does not change the risk perception of
investors. As a result, both debt capitalization rate (Kd) and equity capitalization rate
(Ke) remains constant.
Page | 147
3. No Taxes - There are no corporate taxes.
QUESTION ON NI APPROACH
Type 1
NI Approach
Que 1.
The expected EBIT of a firm is Rs.2,00,000. It has issued Equity Share
capital with ke @ 10% and 6% Debt of Rs.5,00,000. Find out the value of
the firm and the overall cost of capital, WACC.
Ans.
Vf = 22L, Ko = 9.09%
Que 2.
RST Ltd. belongs to a risk class where the appropriate equity capitalization
rate is 20%. It has annual operating profit of Rs.12,00,000 and has issued
12.5% Debentures of Rs.35,00,000. Find out the value of the firm and
overall capitalization rate. What would be the position if the debt is raised to
Rs.50,00,000?
Ans.
Vf = 73,12500, (ii)
Ko = 16.41% (ii)
Que 3.
The expected EBIT of a firm is Rs 2,50000 it has equity capitalization rate of
10% and 6% debt. Find out value of firm and overall cost of capital, (WACC)
if amount of Debt is Rs 5 Lakh or Rs 10 Lakh.
Ans.
Vf = 27L,
Ko = 9.26%
Que 4.
ABC Ltd. and PQR Ltd. belong to the risk class where the equity capitalization
of 10% is considered appropriate. ABC Ltd. has raised Rs.50,00,000 while
PQR Ltd. has raised Rs.70,00,000 by issue of 9% Debt. Find out the value of
these two firms applying the NI Approach given that both firms expect an
operating profit of Rs.12,00,000. Also find out their overall capitalization
rate.
(ii)
(ii)
7875000
15.24%
29L
Ko = 8.62%
ABC Ltd.  Vf = 12500000
PQR Ltd.  Vf = 12700,000
Ko = 9.6%
Ko = 9.45%
Page | 148
 CONCEPT 3
NET OPERATING INCOME (NOI) APPROACH
According to this approach the market value of the firm is not at all affected by the capital
structure changes. The market value of the firm is ascertained by capitalizing the net
operating income at the overall cost of capital (k)m which is considered to be constant. The
market value of equity is ascertained by deducting the market value of the debt from the
market value of the firm.
According to the NOI Approach, the value of a firm
V = EBIT / k
Where :
V = Value of firm;
K = Overall cost of capital
EBIT = Earnings before interest and tax.
The value of equity (S) is a residual value, which is determined by deducting the total value
of debt (B) from the total value of the firm (V). Thus, the value of equity (S) can be
determined by the following equation:
E=V-D
Where :
E = Value of equity;
V = Value of firm;
D = Value of debt.
ASSUMPTIONS OF NOI APPROACH
1.
Constant Kd - The debt capitalization rate (Kd) is constant.
2.
Constant Ko - The weighted average cost of capital (Ko) is constant for all degree of
debt equity mix since business risk on which (Ko) depends is assumed to remain
constant.
3.
No Split - The market capitalizes value of firm as a whole. Thus, the split between debt
and equity is not important.
4.
Neutralisation - The increase in the proportion of debt in the Capital structure would
lead to increase in the financial risk of equity shareholders. The advantage associated
Page | 149
with the use of the relatively less expensive debt in terms of explicit cost is exactly
neutralized by the implicit cost of debt represented by the increase in the cost of equity
capital.
5.
No Taxes - There are no corporate capital.
QUESTION ON NOI APPROACH
Type 2
NOI Approach
Que 5.
A firm has an EBIT of Rs.2,00,000 and belongs to a risk class of 10%. Find
cost of equity capital if it employees 6% Debt to the extent of 30%, 40% or
50% of the total capital fund of Rs.10,00,000
Ans.
Ke = 10.71%, 11% , 11.33%
Que 6.
XYZ Ltd. has issued 8% Debentures of Rs.3,00,00,000. It has operating
profits of Rs.50,00,000. It belongs to a risk class where the appropriate
capitalization rate is 10% Applying the Net Operating Income Approach.
What would happen if the firm increases the debt to Rs.4,00,00,000?
Ans.
Ke = 13%,
Ke = 18%,
 CONCEPT 4
TRADITIONAL APPROACH
The traditional approach is also called an intermediate approach as it takes a midway
between NI Approach (that the value of the firm can be increased by increasing financial
leverage) and NOI approach (that the value of firm is constant irrespective of th e degree of
financial leverage). According to this approach the firm should strive to reach the optimal
capital structure and its total valuation through a judicious use of the both debt and equity
in capital structure. At the optimal capital structure the overall cost of capital will be
minimum and the value of the firm is maximum. It further states that the value of the firm
increases with financial leverage upto a certain point. Beyond this point the increase in
financial leverage will increase its overall cost of capital and hence the value of firm will
decline. This is because the benefits of use of debt may be so large that even after off setting
the effect of increase in cost of equity, the overall cost of capital may still go down.
However, if financial leverage increases beyond a acceptable limit the risk of debt investor
may also increase, consequently cost of debt also starts increasing. The increasing cost of
Page | 150
equity owing to increased financial risk and increasing cost of debt makes the overall co st
of capital to increase.
QUESTION BASED ON TRADITIONAL
Type 3
Traditional Theory
Que 7.
ABC Ltd. having an EBIT of Rs.1,50,000 is contemplating to redeem a part of
the capital by introducing debt financing.
Presently, it is a 100% equity firm with equity capitalization rate, ke, of 16%. The firm is to
redeem the capital by introducing debt financing upto Rs.3,00,000 i.e., 30% of total funds
or up to Rs.5,00,000 i.e., 50% of total funds. It is expected that for the debt financing up to
30%, the rate of interest will be 10% and the ke will increase to 17%. However, if the firm
opts for 50% debt financing, then interest will be payable at the rate of 12% and the ke
will be 20%. Find out the value of the firm and its WACC under different levels of debt
financing.
Ans.
Present
Proposal 1
Proposal 1
EBIT
(-) Interest
150000
Nil
150000
30,000
150000
60000
EBIT
÷ ke
150,000
.16
120,000
.17
90,000
.20
VE
VD
937500
-
705882
3Lakhs
450000
5 Lakhs
VF
𝐸𝐵𝐼𝑇
𝐾𝐷 =
𝑉𝑓
937500
1005882
950,000
16%
14.91%
15.79%
Que 8.
The following estimates of the cost of debt and cost of equity capital have
been made at various level of the debt-equity mix for ABC Ltd.
% of Debt
0
10
20
30
40
Cost of Debt
5.0%
5.0%
5.0%
5.5%
6.0%
Cost of Equity
12.0%
12.0%
12.5%
13.0%
14.0%
Page | 151
50
60
6.5%
7.0%
16.0%
20.0%
Assuming no tax, determine the optimal debt equity ratio for the company on the basis of
the overall cost of capital, WACC.
Optimal debt equity ratio = 3:7
Ans.
We
1
.90
.80
.70
.60
.50
.40
Que 9.
Wd
0
.10
.20
.30
.40
.50
.60
Kd
5
5
5
5.5
6
6.5
7.0
Ke
12
12
12
13
14
16
20.
Wo
12%
10.8+.5=11.3%
10+1 = 11%
9.1 + 1.65 =10.75 %
8.4 + 2.4 = 10.8%
8+3.25 = 11.25%
8+4.2 = 12.2
XYZ Manufacturing Co., has a total capitalization of Rs.10,00,000 and
normally earns Rs.1,00,000 (before interest and taxes). The financial
manager of the firm wants to take a decision regarding the capital structure.
After a study of the capital market, he gathers the following data:
Amount of
Debt
0
1,00,000
2,00,000
3,00,000
4,00,000
5,00,000
6,00,000
7,00,000
Interest Rate
Ke %
4.0
4.0
4.5
5.0
5.5
6.0
8.0
10.00
10.50
11.00
11.60
12.40
13.50
16.50
20.00
What amount of debt should be employed by the firm if the Traditional Approach is held
valid? Assume that corporate taxes do not exist, and that the firm always maintains its
capital structure at book values.
Optimal debt equity Ratio= 4:6
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Ans.
Wd
0
.10
We
1
.90
Kd
4
Ke
10
10.50
Wo
10%
.4+9.45 = 9.85
.20
.80
4
11
.8+8.8=9.60
.30
.40
.70
.60
4.5
5.0
11.60
12.40
1.35+8.12=9.47
2+7.44=9.44
.50
.50
5.5
13.50
2.75+6.75=9.5
.60
.70
.40
.30
6.0
8.0
16.50
20.00
3.6+6.6=10.2
5.6+6=11.6
Que 10.
A Company’s current operating income is Rs.4 lacs. The firm has Rs.10 lacs
of 10% Debt outstanding. Its cost of equity capital is estimated to be 15%.
(i) Determine the current value of the firm, using Traditional valuation approach.
Ans. Vf = 30L
(ii) Calculate the firm’s overall capitalization rate.
Ans. Ko = 13.33%
(iii) The firm is considering increasing its leverage by raising an additional
Rs.5,00,000 debt and using the proceeds to reduce the amount of equity. As a
result of increased financial risk, the rate of interest is likely to go up to 12%
and ke to 18%. Would you recommend the plan?
Hint for part II
EBIT
(-) Interest
EBT
÷ Ke
Ve
VD
Vf
𝐾𝑜 = (
400000
100,000
300,000
0.15
20 Lakh
10 Lakh
30 Lakh
4 𝐿𝑘𝑎ℎ
× 100)
30𝐿𝑎𝑘ℎ
= 13.3%
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 CONCEPT 5
MODIGLIANI - MILLER APPROACH
The Modigliani - Miller (MM) approach is similar to the Net Operating Income (NOI)
approach. However, there is a basic difference between the two. The NOI approach is
purely definitional or conceptual. It does not provide operational justification for
irrelevance of the capital structure in the valuation of the firm. While MM approach
supports the NOI approach providing behavioural justification for the independence of the
total valuation and the cost of capital of the firm from its capital structure.
The following are the three basic propositions of the MM approach:
1. The overall cost of capital (k) and the value of the firm (V) are independent of the
capital structure. In other words k and V are constant for all levels of debt-equity
mix. The total market value of the firm is given by capitalizing the expected net
operating income (NOI) by the rate appropriate for that risk class.
2. The cost of equity (ke) is equal to capitalization rate of a pure equity stream plus a
premium for the financial risk. The financial risk increases with mor e debt content
in the capital structure. As a result, ke increases in a manner to off set exactly the
use of a less expensive source of funds represented by debt.
3. The cut-off rate for investment purposes is completely independent of the way in
which an investment is financed.
Assumptions
The MM approach is subject to the following assumptions:
1. Capital markets are perfect. This means(a) Investors are free to buy and sell securities;
(b) The investors can borrow without restriction on the same terms on which the firm
can borrow;
(c) The investors are well informed;
(d) The investors behave rationally; and
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(e) There are no transaction costs.
2. The firms can be classified into homogenous risk classes. All firms within the same class
will have the same degree of business risk.
3. All investors have the same expectation of a firm’s net operating income (EBIT) with
which to evaluate the value of any firm.
4. The dividend pay-out ratio is 100%. In other words, there are no retained earnings.
Type 4
Modigliani Miller Approach
Que 11.
There are 2 firms identical in all respect with only one difference the firm A is
levered & that of firm B is unlevered. If EBIT of firm B is Rs 2 Lakh &
opportunity cost of equity (Ke) is 10% (Given that firm A contain 9% debt for
10 lakh)
find out Value of firm A & B
(i)
(ii)
If there is no taxes
If tax rate = 40%
Firm A
𝑉𝑈 =
Firm A
2 𝐿𝑎𝑘ℎ
= 20 𝐿𝑎𝑘ℎ
. 10
𝑉𝑈 = 20𝐿𝑎𝑘ℎ + 10 𝐿𝑎𝑘ℎ (. 40)
= 24 Lakh
Que 12.
𝑉𝑈 = 20 𝐿𝑎𝑘ℎ
𝑉𝐿 = 20 𝐿𝑎𝑘ℎ
Two companies, X and Y, belong to the equivalent risk group. The two
companies are identical in every respect except that company Y is levered,
while X is unlevered. The outstanding amount of debt of the levered company
is Rs.6,00,000 in 10% Debentures. The information for the two companies is
as follows:
Net operating income (EBIT)
-Interest
Earnings to Equity holders
X
Rs. 1,50,000
1,50,000
Y
Rs. 1,50,000
60,000
90,000
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Equity Capitalization rate, ke
Market value of Equity
Market value of Debt
Total Value of firm, V,
Overall capitalization rate, k0 =
EBIT/V
0.15
10,00,000
10,00,000
15.0%
0.20
4,50,000
6,00,000
10,50,000
14.3%
An investor owns 5% equity shares of company Y. show the process and the amount by
which he could reduce his outlay through use of the arbitrage process. Is there any limit to
the ‘process’?
Que 13.
2005 - June [3] (b) Following is the data relation to Azad Ltd. and Bharat
Ltd. belongs to the same risk class :
No. of equity shares
Market price per share (Rs.)
6% Debentures (Rs.)
Profit before interest (Rs.)
Divided payout ratio
Azad Ltd.
90,000
15
8,00,000
2,00,000
100%
Bharat Ltd.
1,50,000
9
2,00,000
Explain how under the MM approach, an investor holding 10% shares in Azad Ltd. will be
better off in switching his holding to Bharat Ltd.
Page | 156
MULTIPLE CHOICE QUESTIONS
1. Which of the following is true for Net Income Approach?
a) Taxes to be ignored
b) Higher Debt is better
c) Debt Ratio is irrelevant
d) None of the above.
2. In case of Net Income Approach, the Cost of equity is:
a) Constant
b) Increasing
c) Decreasing
d) None of the above.
3. In case of Net Income Approach, when the debt proportion is increased, the cost of debt:
a) Increases
b) Decreases
c) Constant
d) None of the above.
4. Which of the following is true of Net Income Approach?
a) VF = VE+VD
b) VE = VF+VD
c) VD = VF+VE
d) VF = VE-Vd
5. Net Operating Income Approach, which one of the following is constant?
a) Cost of Equity
b) Cost of Debt
c) WACC & kd
d) Ke and Kd
6. NOI Approach advocates that the degree of debt financing is:
a) Relevant
b) May be relevant
c) Irrelevant
d) May be irrelevant.
7. 'Judicious use of leverage' is suggested by:
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a) Net Income Approach
b) Net Operating Income Approach
c) Traditional Approach
d) All of the above.
8. Which one is true for Net Operating Income Approach?
a) VD = VF - VE
b) VE = VF + VD
c) VE = VF - VD
d) VD = VF + VE.
9. In the Traditional Approach, which one of the following remains constant?
a) Cost of Equity
b) Cost of Debt
c) WACC
d) None of the above.
10. In MM-Model, irrelevance of capital structure is based on:
a) Cost of Debt and Equity
b) Arbitrage Process
c) Decreasing k0
d) All of the above.
11. 'That there is no corporate tax' is assumed by:
a) Net Income Approach
b) Net Operating Income Approach
c) Traditional Approach
d) All of these.
12. Which of the following argues that the value of levered firm is higher than that of the
unlevered firm?
a) Net Income Approach
b) Net Operating Income Approach
c) MM Model with taxes
d) Both (a) and (c).
13. In Traditional Approach, which one is correct?
a) ke rises constantly
b) kd decreases constantly
c) k0 decreases constantly
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d) None of the above.
14. Which of the following assumes constant k d and ke?
a) Net Income Approach
b) Net Operating Income Approach
c) Traditional Approach
d) MM Model.
15. Which of the following is true?
a) Under Traditional Approach, overall cost of capital remains same
b) Under NI Approach, overall cost of capital remains same
c) Under NOI Approach, overall cost of capital remains same
d) None of the above.
16. A firm has EBIT of Rs. 50,000. Market value of debt is Rs. 80,000 and overall
capitalization rate is 20%. Market value of equity under NOI Approach is:
a) Rs. 2,50,000
b) Rs. 1,70,000
c) Rs. 30,000
d) Rs. 1,30,000.
17. Which of the following is incorrect for NOI?
a) k0 is constant
b) kd is constant
c) ke is constant
d) kd & k0 are constant.
18. In MM Model with taxes, where 'r' is the interest rate, ‘D’ is the total debt and 't' is tax
rate, then present valued shields would be:
a) r×D×t
b) r×D
c) D×t
d) (D× r)/(l-t).
19. Traditional theorists believe that.
a) there exists an optimal capital structure
b) no optimal capital structure
c) equal optimal capital structure
d) 100% debt financial organizations
Page | 159
20. Arbitrage is the level processing technique introduced in _________.
a) Net income approach
b) MM approach
c) Operating approach
d) Traditional approach
21. Under which of the following approaches cost of equity capital is assumed to be
constant with the change in leverage?
a) Net income approach
b) Modigliani and Miller approach
c) Net operating income approach
d) Traditional approach
22. Which of the following approaches advocates that the costs of equity capital and debt
capital remain unaltered when the degree of leverage varies?
a) Net Income Approach
b) Traditional Approach
c) Modigliani-Miller Approach
d) Net operating Income
23. The overall capitalization rate and the cost of debt remain constant for all degrees of
leverage. This is pronounced by __________.
a) Traditional approach
b) Net operating income approach
c) Net income approach
d) MM approach
24. Which of the following is not an assumption in the Miller & Modigliani approach?
a) There are no transaction costs
b) Securities are infinitely divisible
c) Investors have homogeneous expectations
d) All the firms pay tax on their income at the same rate
25. According to Net Income Approach, capital structure decision a) Is relevant to the value of the firm.
b) Of the firm are irrelevant.
c) Will not lead to any change in the total value of the firm and the market price of
shares.
d) Division between debt and equity is irrelevant.
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26. According to Net Operating Income Approach a) Capital structure decisions of the firm are irrelevant.
b) Any change in the leverage will not lead to any change in the total value of the firm
and the market price of shares, as the overall cost of capital is independent of the
degree of leverage.
c) The division between debt and equity is irrelevant.
d) All of the above
27. According to .................. , the firm can increase its total value by decreasing its overall cost
of capital through increasing the degree of leverage.
a) Net Operating Income Approach
b) Net Income Approach
c) Both (A) and (B)
d) Neither (A) nor (B)
28. The overall cost of capital under Net Income Approach is a) EBIT ÷ Value of firm
b) Net Income ÷ Ke
c) Value of firm ÷ EBIT
d) EBIT ÷ Ko
29. Which formula would you use to calculate market value of equity?
a) Net Income ÷ Ke
b) Ke ÷ Net Income
c) Sales ÷ K
d) Gross Profit ÷ Ke
30. which of the followings statement regarding the net operating income approach is
incorrect?
a) the overall approach capitalization rate K0 is constant.
b) the cost of debt funds, Kd is constant
c) the required return on equity, Ke, is constant.
d) the total value of the firm is unaffected by changes in financial leverage
31. M & M proposition, without taxes, states that:
a) firms should borrow to the point where the tax benefit from debt is equal to the cost
of the increased probability of financial distress.
b) financial risk is determined by the debt-equity ratio.
c) the cost of equity rise when financial leverage rises.
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d) it is completely irrelevant how a firm arranges its finances.
32. EBIT of X Ltd. Is Rs.5,00,000. The company has 10% Rs.20,00,000 debentures. The
equity capitalization rate i.e. Ke is 16%. Calculate market value of firm as per net
income (NI) approach. Ignore taxation.
a) Rs.20,00,000
b) Rs.38,75,000
c) 38,57,000
d) Rs.20,75,000
33. take the data of above question and calculate the overall cost of capital.
a) 12.90%
b) 11.90%
c) 10.90%
d) 9.90%
34. EBIT of X Ltd. Is Rs.4,50,000.
Debt in capital structure = Rs.6,00,000
Cost of debt (Kd) = 10%
Cost of equity (Ke) = 12.5%
Ignore taxation.
Total market value of X LTD. = ?
a) Rs.37,20,000
b) Rs.34,72,222
c) Rs.32,70,000
d) Rs.34,70,000
35. EBIT is of X Ltd. Is Rs.4,50,000.
Debt in capital structure = Rs.7,50,000
Cost of debt (Kd) = 11%
Cost of equity (Ke) = 13.5%
Ignore taxation.
Total market value and overall cost of capital of X LTD. = ?
a) 34,72,222; 14.9%
b) 34,27,222;12.96%
c) 34,72,222;12.96%
d) 32,72,222;14.96%
36. EBIT is of X Ltd. Rs.4,50,000. Which of the following capital structure will you
recommend?
Page | 162
Debt
Kd
1
Rs. 4,50,000
10%
2
Rs. 6,00,000
10%
3
Rs. 7,50,000
11%
4
Rs. 9,00,000
12%
Select the correct answer from the options given below.
a) 1
b) 2
c) 3
d) 4
Ke
12%
12.5%
13.5%
15%
37. Operating income of A Ltd. is Rs.5,00,000. The firms cost of debt is 10% and currently
firm employs Rs.15,00,000 of debt. The overall cost of capital of the firm is 15%. You are
required to determine ‘total value of the firm’ and ‘market value of equity’ using Net
Operating Income Approach (NOI). Ignore taxation.
a) Rs.33,33,333; Rs.15,00,000
b) Rs.33,33,333;Rs. 18,33,333
c) Rs.18,33,333; Rs.15,00,000
d) Rs.20,22,222;Rs. 18,22,222
38. Sun Ltd. has 12% debt of Rs.30,00,000. It earns 24% before interest and tax on its total
assets of Rs.50,00,000. Tax rate is 40% and capitalization rate is 18%. Calculate the
value of the company using Net Income Approach.
a) Rs.58,00,000
b) Rs.20,00,000
c) Rs.55,00,000
d) Rs.40,00,000
39. Moon Ltd. earns 24% before interest and tax on its total assets of Rs.50,00,000. It is
unlevered company and has no debts in its capital structure. Tax rate is 40% and
capitalization rate is 18%. Calculate the value of the company using Net Income
Approach.
a) Rs.60,00,000
b) Rs.40,00,000
c) Rs.50,00,000
d) Rs.55,00,000
40. Sun Ltd. has 12% debt of Rs.30,00,000. It earns 24% before interest and tax on its total
assets of Rs.50,00,000. Tax rate is 40% and capitalization rate is 18%. Calculate the
value of the company using Net Operating Income Approach.
Page | 163
a) Rs.58,00,000
b) Rs.56,00,000
c) Rs.54,00,000
d) Rs.52,00,000
41. Moon Ltd. earns 24% before interest and tax on its total assets of Rs.50,00,000. It is
unlevered company and has no debts in its capital structure. Tax rate is 40% and
capitalization rate is 18%. Calculate the value of the company using Net Operating
Income Approach.
a) Rs.20,00,000
b) Rs.30,00,000
c) Rs.40,00,000
d) Rs.50,00,000
42. X Ltd. has EBIT of Rs.30,00,000 and 40% tax rate. It required rate of return on equity in
the absence of borrowing is 18%. In the absence of personal taxes, what is the ‘total
value of the company' and ‘value of equity’ in an MM world with Rs.70,00,000 in debt.
a) Rs.128 lakh; Rs.85 lakh
b) Rs.128 lakh; Rs.58 lakh
c) Rs.182 lakh; Rs.58 lakh
d) Rs.182 lakh; Rs.85 lakh
43. Domino is an all-equity firm with a current cost of equity of 18%. The EBIT of the firm is
Rs.2,04,000 annually forever. Currently, the firm has no debt but is in the process of
borrowing Rs.5,00,000 at 9% interest. The tax rate is 34%. What is the value of the
unlevered firm Rs.
a) Rs.7,23,150
b) Rs.6,54,900
c) Rs.7,48,000
d) Rs.6,09,900
44. There are two firms P and Q which are identical except P does not use any debt in its
capital structure while Q has Rs.8,00,000, 9% debentures in its capital structure. Both
the firms have EBIT of Rs.2,60,000 p.a. and the capitalization rate is 10%. Corporate tax
is 30%. Calculate the total market value of these firms according to MM Hypothesis.
a) Rs.20,60,000;Rs. 18,20,000
b) Rs.18,20,000;Rs. 20,60,000
c) Rs.18,20,000;Rs. 12,60,000
d) Rs.12,60,000;Rs. 20,60,000
Page | 164
45. Following data is available for P Ltd.:
Total Assets : Rs.15,00,000
10% Debt : Rs.9,00,000
EBIT : 20% of total assets
Tax rate : 50%
Capitalization rate =15%
Calculate total value of the firm using Net Operating Income (NOI) approach.
a) Rs.5,50,000
b) Rs.14,50,000
c) Rs.10,50,000
d) Rs.12,50,000
46. Following data is available for Company Y:
Total Assets : Rs.15,00,000
Debt : Nil
EBIT : 20% of total assets
Tax rate : 50%
Capitalization rate =15%
Calculate market value of equity using Net Income (NI) approach.
a) Rs.10,00,000
b) Rs.16,00,000
c) Rs.12,00,000
d) Rs.15,00,000
47. Following data is available for Company X:
Total Assets : Rs.15,00,000
10% Debt : Rs.9,00,000
EBIT : 20% of total assets
Tax rate : 50%
Capitalization rate = 15%
Calculate market value of equity using Net Income (NI) approach.
a) Rs.16,00,000
b) Rs.7,00,000
c) Rs.10,00,000
d) Rs.5,00,000
48. Following data is available for Q Ltd.:
Total Assets : Rs.15,00,000
Debt : Nil
EBIT : 20% of total assets
Page | 165
Tax rate : 50%
Capitalization rate = 15%
Calculate total value of the firm using Net Operating Income (NOI) approach.
a) Rs.8,00,000
b) Rs.9,00,000
c) Rs.12,00,000
d) Rs.10,00,000
49. Ganesha Ltd. is setting up a project with a capital outlay of Rs.60,00,000. It has two
alternatives in financing the project cost.
Alternative (a): 100% equity finance Alternative (b): Debt-equity ratio 2:1
The rate of interest payable on the debts is 18% p.a. Corporate tax rate is 40%.
Calculate the indifference point between the two alternative methods of financing.
a) Rs.10,80,000
b) Rs.18,80,000
c) Rs.18,00,000
d) Rs.10,08,000
50. IPL Ltd. has EBIT of Rs.1,00,000. The company makes use of debt and equity capital.
The firm has 10% debentures of Rs.5,00,000 and the firm’s equity capitalization rate is
15%. You are required to compute: (i) Current value of the firm; (ii) Overall cost of
capital.
a) Rs.3,33,333; 15%
b) Rs.8,33,333; 12%
c) Rs.5,33,333; 14%
d) Rs.6,33,333; 18%
Page | 166
ANSWERS -
1
B
11
D
21
A
31
D
41
B
2
A
12
D
22
A
32
B
42
B
3
C
13
D
23
B
33
A
43
C
4
A
14
A
24
D
34
A
44
B
5
C
15
C
25
A
35
C
45
B
6
C
16
B
26
D
36
A
46
A
7
C
17
C
27
B
37
B
47
B
8
C
18
C
28
A
38
B
48
D
9
D
19
A
29
A
39
B
49
A
10
B
20
B
30
C
40
D
50
B
Page | 167
CHAPTER 8
DIVIDEND POLICY
 CONCEPT 1
SIGNIFICANCE OF DIVIDEND DECISION
The dividend decision is one of the three basic decisions which a financial manager may be
required to take, the other two being the investment decisions and the financing decisions.
In each period any earning that remains after satisfying obligations to the creditors, the
Government, and the preference shareholders can either be retained, or paid out as
dividends or bifurcated between retained earnings and as dividends. The retained earnings
can then be invested in assets which will help the firm to increase or at least maintain its
present rate of growth. The dividend decision requires a financial manager to decide about
the distribution of profits as dividends. The profit may be distributed either in the form of
cash dividends to shareholders or in the form from of stock dividends (also known as
bonus shares). In dividend decision, a financial manager is concerned to decide one or
more of the following:
-
Should the profits be ploughed back to finance the investment decisions?
Whether any dividend be paid ? If yes, how much dividends be paid?
When these dividends be paid? Interim or Final?
In what form the dividends be paid? Cash dividends or Bonus Shares?
All these decisions are inter-related and have bearing on the future growth plans of the
firm. If a firm dividends, it affects flow position of the firm but earns goodwill among the
investors who therefore, may be willing to provide additional funds for th e financing of
investment plans of the firm. On the other hand, the profits which are not distributed as
dividends become an easily available source of funds at no explicit costs. However, in the
case of ploughing back of profits, the firm may lose the goo dwill and confidence of the
investors and may also defy the standards set by other firms. Therefore, in taking the
dividend decision, the financial manager has to consider and analyze various factors. Every
aspects of dividend decision is to be critically evaluated. The most important of these
considerations is to decide as to what portion of profit should be distributed. This is also
known as the dividend payout ratio.
Page | 168
 CONCEPT 2
DIVIDEND POLICY AND VALUE OF THE FIRM
Dividend policy is basically concerned with deciding whether to pay dividend in cash now,
or to pay increased dividends at a later stage or distribution of profits in the form of bonus
shares. The current dividend provides liquidity to the investors but the bonus share will
bring capital gains to the shareholders. The investor’s preferences between the current
cash dividend and the future capital gain have been viewed differently. Some are of the
opinion that the future capital gain are more risky than the current dividends while others
argue that the investors are indifferent between the current dividend and the future capital
gains.
Different models have been proposed to evaluate the dividend policy decision in relation to
value of the firm. While agreement is not found among the models as to the precise
relationship, it is still worthwhile to examine some of these models to gain insight into the
effect which the dividend policy might have on the market price of the share and hence on
the wealth of the shareholders. Two schools of thoughts have emerged on the relationship
between the dividend policy and value of the firm.
One school associated with Walter, Gordon, etc., holds that the future capital gains
(expected to result from lower current dividend payout) are more risky and the investors
have preference for current dividends. The investors do have a tilt towards those firms
which pay regular dividend. So, the dividend payment affects the market value of share and
as a result the dividend policy is relevant for the overall value of the firm. On the other
hand, the other school of thought associated with Modigliani and Miler holds that the
investors are basically indifferent between current cash dividends and future capital gains.
 CONCEPT 3
TYPES OF DIVIDEND POLICY
There are basically 4 types of dividend policy. Let us discuss them on by one:
(1) Regular dividend policy: in this type of dividend policy the investors get dividend at
usual rate. Here the investors are generally retired persons or weaker section of the society
who want to get regular income. This type of dividend payment can be maintained only if
the company has regular earning.
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Merits of Regular Dividend Policy:
-
It helps in creating confidence among the shareholders.
It stabilizes the market value of shares.
It helps in marinating the goodwill of the company.
It helps in giving regular income to the shareholders.
(2) Stable dividend policy: here the payment of certain sum of money is regularly paid to
the shareholders. It is of three types:
 Constant dividend per share: here reserve fund is created to pay fixed amount of
dividend in the year when the earning of the company is not enough. It is suitable
for the firms having stable earning.
 Constant payout ratio: it means the payment of fixed percentage of earning as
dividend every year.
 Stable rupee dividend + extra dividend: it means the payment of low dividend
per share constantly + extra dividend in the year when the company earns high
profit.
Merits of stable dividend policy:
-
It helps in creating confidence among the shareholders.
It stabilizes the market value of shares.
It helps in marinating the goodwill of the company.
It helps in giving regular income to the shareholders.
(3) Irregular dividend: as the name suggests here the company does not pay regular
dividend to the shareholders.
The company uses this practice due to following reasons:
-
Due to uncertain earning of the company.
Due to lack of liquid resources.
The company sometime afraid of giving regular dividend.
Due to not so much successful business.
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(4) No dividend: the company may use this type of dividend policy due to requirement of
funds for the growth of the company or for the working capital requir ement.
 CONCEPT 4
DETERMINANTS/CONSTRAINTS OF DIVIDEND POLICY
In the company organisation, dividend policy is determined by the Board of directors
having taken into consideration a number of factors which include legal restrictions
imposed by the Government to safeguard the interests of various parties or the
constituents of the company.
The main considerations are as follows:
1) Legal: As regards cash dividend policy several legal constraints bear upon it – a firm
may not pay a dividend which will impair capital. Dividend must be paid out of
firm’s earnings/current earnings. Contract/ Agreements for bonds/loans may
restrict dividend payments. The purpose of legal restriction is to ensure that the
payment of dividend may not cause insolvency.
2) Financial: There are financial constraints to Dividend Policy. A firm can pay
dividend only to the extent that it has cash to disburse; a firm can’t pay dividend
when its earnings are in accounts receivables or firm does not have adequate
liquidity.
3) Economic Constraints: Besides, there are economic constraints also. The question
arise, does the value of dividend affects the value of the firm. If the answer to it is
yes then there must be some optimum level of dividend, which maximises the
market price of the firm’s stock.
4) Nature of Business Conducted by a Company: A company having a business of the
nature which gives regular earnings may like to have a stable and consistent
dividend policy. Industries manufacturing consumer/consumer durable items have
a stable dividend policy.
5) Existence of the Company: The length of existence of the company affects dividend
policy. With their long standing experience, the company may have a better
dividend policy than the new companies.
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6) Type of Company Organisation: The type of company organisation whether a
private limited company or a public limited company affects dividend decisions. In a
closely held company, a view may be taken for acquiescence and conservative policy
may be followed but for a public limited company with wide spread of shareholder,
a more progressive and promising dividend policy will be the better decision.
7) Market Conditions: Business cycles, boom and depression, affects dividend
decisions. In a depressed market, higher dividend declarations are used to market
securities for creating a better image of the company. During the boom the company
may like to save more, create reserves for growth and expansion or meeting its
working capital requirements.
8) Financial Arrangement: In case of financial arrangements being entered into or
being planned like merger or amalgamation with another company, liberal policy of
dividend distribution is followed to make the share stock more attractive.
 CONCEPT 5
TYPES OF DIVIDEND/FORM OF DIVIDENDS
Dividend may be distributed among the shareholders in the form of cash or stock. Hence,
Dividends are classified into:
Dividend
Cash Dividend
Bond Dividend
Stock Dividend
Property Dividend
(1) Cash Dividend
If the dividend is paid in the form of cash to the shareholders, it is called cash dividend.
It is paid periodically out the business concerns EAIT (Earnings after interest and tax).
Cash dividends are common and popular types followed by majority of the business
concerns.
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(2) Stock Dividend
Stock dividend is paid in the form of the company stock due to raising of more finance.
Under this type, cash is retained by the business concern. Stock dividend may be bonus
issue. This issue is given only to the existing shareholders of the business concern.
(3) Bond Dividend
Bond dividend is also known as script dividend. If the company does not have sufficient
funds to pay cash dividend, the company promises to pay the shareholder at a future
specific date with the help of issue of bond or notes.
(4) Property Dividend
Property dividends are paid in the form of some assets other than cash. It will distribute
under the exceptional circumstance. This type of dividend is not published in India.
 CONCEPT 6
WALTER’S MODEL
Walter J.E. supports the view that the dividend policy has a bearing on the market price of
the share and has presented a model to explain the relevance of dividend policy for
valuation of the firm based on the following assumptions:
(i) All investment proposals of firm are to be financed through retained earnings
only and no external finance is available to the firm.
(ii) The business-risk complexion of the firm remains same even after investment
decisions are taken. In other words, the rate of return on investment i.e., ‘r’ and
the cost of capital of the firm i.e., ke’ are constant.
(iii) The firm has an infinite life.
This model considers that the investment decision and dividend decision of a firm are
inter-related. A firm should or should not pay dividends depend upon whether it has got
the suitable investment opportunities to invest the retained earnings or not. A firm pays
dividends to shareholders, they in turn, will invest this income to get future returns. This
expected return to shareholders is the opportunity cost of the firm and hence the co st of
capital, ke’ to the firm. On the other hand, if the firm does not pay dividends, and instead
retains, then these retained earnings will be reinvested by the firm to get return on these in
investment. This rate of return on the investment, r, of the firm must be at least equal to the
cost of investment, r, of the firm must be at least equal to the cost of capital, k e. If r = ke’ the
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firm is earning a return just equal to what the shareholders could have earned, had the
dividends been paid to them.
However, what happen if the rate of return, r, is more than the cost of capital, k e ? In such a
case, the firm can earn more by retaining the profits, than the shareholders can earn by
investing their dividend income. The Walter’s model, thus, says that if r > ke’ the firm should
refrain from dividends and should reinvest the retained earnings and thereby increase the
wealth of the shareholders. However, if the investment opportunity before the firm to
reinvest the retain earnings are expected to give a rate of return which is less than the
opportunity cost of the shareholders of the firms, then the firm should better distribute the
entire profits. This will give opportunity to the shareholders to reinvest this dividend
income and get higher returns.
According to Walter a firm can maximize the market value of its share and the value the
firm by adopting dividend policy as follows:
(i) If r > ke’ the payout ratio should be zero (i.e., retention of 100% profit).
(ii) If r < ke’ the payout ratio be 100% and the firm should not retain any profit, and
(iii) If r = ke’ the dividend is irrelevant and the dividend policy is not expected to affect the
market value of the share.
In order to testify the above, Walter has suggested a mathematical model i.e.,
𝑟
𝐷
𝑘𝑒 (𝐸 − 𝐷)
𝑃0 =
+ (
)
𝑘𝑒
𝑘𝑒
Where,
P = Market price of Equity share.
D = Dividend per share paid by the Firm.
r = Rate of return on Investment of the Firm.
Ke = Cost of Equity share capital, and
E = Earnings per share of the Firm.
As per the above formula, the market price of a share is the sum of two components i.e.,
(i) The present value of an infinite stream of dividends, and
(ii) The present value of an infinite stream of return from retained earnings.
Thus, the Walter’s formula shows that the market value of a share is the present value of
the expect stream of dividends and capital gains.
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TYPE 1
QUESTION BASED ON WALTER’S MODEL
Que 1.
ABC Ltd. was started a year back with a paid-up equity capital of
Rs.40,00,000. The other details are as under:
Earnings of the company
Dividend paid
Price-earnings ratio
Number of shares
Rs.4,00,000
Rs.3,20,000
12.5
40,000
You are required to find out whether the company’s dividend payout ratio is optimal, using
Walter’s formula.
Hint:𝐸𝑎𝑟𝑛𝑖𝑛𝑔 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 (𝐸 )
Ans.
=
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 (𝐷)
=
𝐼𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 ( 𝑟)
=
Present + P0 = 131.25 & optimum P0 = 156.25
Total earnings of firm
Number of shares
Amount of Dividend paid
Number of shares
Total earnings of the firm
Total equity capital of firm
Que 2.
(a) The EPS of a company is Rs.16. The market capitalization rate applicable
to the company is 12.5%. Retained earnings can be employed to yield a
return of 10%. The company is considering a payout of 25%, 50% and 75%.
Which of these, if any, would maximize the wealth of shareholders as per the
Walter’s Model?
Ans.
At 25% D/p ratio Rs.108.80; At 50% D/P ratio Rs.115.20; At 75% D/P ratio
Rs.121.60;
Que 3.
The earnings per share (EPS) of a company is Rs.10. It has an internal rate of
return of 15% and the capitalization rate of its risk class is 12.5%. If Walter’s
Model is used(i)
(ii)
What should be the optimum payout ratio of the company?
What would be the price of the share at this payout?
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(iii)
How shall the price of the share be affected, if a payout ratio is 100%
(i)
(ii)
(iii)
Po = 0%
Po = 96
Po = Rs. 80
Ans.
Que 4.
From the following information, ascertain whether the firm is following an
optional dividend policy as per Walter’s Model:
Total earnings (Rs.)
Number of equity shares of Rs.100 each
Dividend paid (Rs.)
Prices-Earnings (P/E) ratio
600,000
40,000
1,60,000
10
The firm is expected to maintain its rate of return on fresh investment. Will your decision
change if the P/E ratio is 5 instead of 10?
Ans.
Market price can be increased by following a zero payout. Under the
situation, when P/E is 5, the optimum dividend policy for the company would
be to payout 100% dividend at which the value of the firm will be maximum.
Que 5.
A closely-held toys manufacturing company has been following a dividend
policy, which can maximize the market value of the company as per Walter ’s
Model. Accordingly, each year at dividend time, the capital budget is
reviewed in conjunction with the earnings for the period and alternative
investment opportunities for the shareholders. In the current year, the
company reports net profits of Rs.10,00,000. It is estimated that the company
can earn Rs.2,50,000 if such profits are retained. The investors have
alternative investment opportunities that will yield them 12%. The company
has 1,00,000 shares outstanding. What would be the dividend payout ratio of
the company, if it wishes to maximize the wealth of the shareholders?
Ans.
DP ratio of the company should be Zero. Price = Rs.173.58.
 CONCEPT 7
GORDON’S MODEL
Myron Gordon has also proposed a model suggesting that the dividend policy is relevant
and can affect the value of the share and that of the firm. This model is also based on the
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assumptions similar to that made in Walter’s model. However, two additional assumptions
made by this model are as follows:
(i) The growth rate of the firm ‘g’, is the product of its retention ratio, b, and its rate
of return, r, i.e., g = br, and
(ii) The cost of capital besides being constant is more than the growth rate i.e., >g.
Gordon argues that the investor do have a preference for current dividends and
there is a direct relationship between the dividend policy and the market value
of the share. He has built the model on the basic premise that the investors are
basically risk averse and they evaluate the future dividends/capital gains as a
risky and uncertain proposition. Dividends are more predictable than capital
gains; management can control dividends but it cannot dictate the market price
of the share. Investors are certain of receiving incomes from dividends than
from future capital gains. The incremental risk associated with capital gains
implies a higher required rate of return for discounting the capital gains than for
discounting the current dividends. In other words, an investor values, current
dividends more highly than an expected future capital gains.
Thus, Gordon’s model is a share valuation model (like that of Walter’s). Under this model,
the market price of a share can be calculated as follows:
P−
Where,
E(I − b)
Ke − br
P = Market price of Equity share.
E = Earnings per share of the Firm.
b = Retention Ratio (1 - Payout ratio).
r = Rate of return on Investment of the Firm.
Ke = Cost of Equity share capital, and
br = g. i.e., Growth rate of the firm.
This model shows that there is a relationship between payout ratio (i.e., 1 -b), cost of
capital ke, rate of return, r, and the market value of the share.
Que 6.
2002 - June [4] (b) The MNC Ltd.’s available information is:
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Ke = 15%
E = Rs. 30
R = (i) 14%; (ii) 15% and (iii) 16%.
Your are required to calculate market price of a share of the MNC Ltd. as per Gordon Model
it(i) b = 40%;
(ii) b = 60%; and
(iii) b=80%.
Que 7.
Find out value of share according to Gorden’s Model from given information
EPS
=10
Payout ratio
=40%
Rate of return on invest
=10%
Opportunity cost of equity =12%
Ans.
P0 = 66.66
 CONCEPT 8
DIVIDEND AND UNCERTAINTY: THE BIRD-IN-HAND ARGUMENT
Gordon revised this basic model later to consider risk and uncertainty. Gordon ’s model, like
Walter’s model, contends that dividend policy is relevant. According to Walter, dividend
policy will not affect the price of the share when r = k. But Gordon goes one step ahead and
argues that dividend policy affects the value of shares even when r = k. The crux of
Gordon’s argument is based on the following two assumptions :
1. Investors are risk averse and
2. They put a premium on a certain return and discount (penalise) uncertain return.
The investors are rational. Accordingly they want to avoid risk. The term risk refers to the
possibility of not getting the return on investment. The payment of dividends now
completely removes any chance of risk. But if the firm retains the earnings the investors
can expect to get a dividend in the future. But the future dividend is uncertain both with
respect to the amount as well as the timing. The rational investors, therefore prefer current
or near dividend to future dividend. Retained earnings are considered as risky by the
investors. In case earnings are retained, therefore the price per share would be adversely
affected. This behaviour of investor is described as “Bird in Hand Argument”. A bird in hand
is worth two in bush. What is available today is more important than what may be available
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in the future. So the rational investors are willing to pay a higher price for shares on which
more current dividends are paid, all other things held constant. Therefore the discount rate
(K) increases with retention rate. Thus, distant dividends would be discounted at a higher
rate than the near dividends.
 CONCEPT 9
IRRELEVANCE OF DIVIDEND POLICY
Residuals Theory of Dividends
This theory is based on the assumption on that either the external financing is not available
to the firm or if available, cannot be used due to its excessive costs for financing the
profitable investment opportunities of the firm. Therefore, the firm fina nces its investment
decisions by retaining profits. The quantum of profits to be distributed is a balancing
opportunities. If a firm has sufficient profitable investment opportunities, then the wealth
of the shareholders will be maximized by retaining profits and reinvesting them in the
financing of investment opportunities, then the profits may be distributed among the
shareholders.
Thus, a firm does not decide as to how much dividends be paid rather it decides as to how
much profits should be retained. The profits not required to be retained may be distributed
as dividends. Therefore, dividend decision is a passive decision. The dividends are a
distribution of residual profits after retaining sufficient profits for financing the available
opportunities. Under the Residents Theory, the firm would treat the dividend decision
in three steps:
(i)
Determining the level of capital expenditures which is determined by the
investment opportunities.
(ii)
Using the optimal financing mix, find out the amount of equity financing mix,
find out the amount of equity financing needed to support the capital
expenditure in step (i) above,
(iii)
As the cost of retained, kr’ is less than the cost of new equity capital, the
retained earnings would be used to meet the equity portions financing in step
(ii) above. If the available profits are more than the this need, then the surplus
may be distributed as dividends to shareholders. As far as the required equity
financing is in excess of the amount of profits available, no dividends would be
paid to the shareholders.
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In the Residuals Theory, the dividends policy is influenced by (i) the company’s investment
opportunities, and (ii) the availability of internally generated funds, where dividends are
paid only after all acceptable investment proposals have been financed. The dividend policy
is totally passive in nature and has no direct influence on the market price of the share. So,
the Residuals Theory treats the dividend as a passive decision determined by the dividends
availability of profitable investments. Consequently, the dividends may fluctuate from one
year to an other depending upon the investment opportunity. But the shareholders do not
compensated for reduction in dividends or no dividends at all by future capital gains. The
market price of the share is still taken as the present value of all future dividends and the
pattern of these dividends does not matter.
 CONCEPT 10
MODIGLIANI AND MILLER APPROACH
The irrelevance of dividend policy for valuation of the firm has been most comprehensively
presented by Modigliani and Miller (MM). They have argued that the market price of a
share is affected by the earnings of the firm and is not influenced by the patte rn of income
distribution. The dividend policy is immaterial and is of no consequence to the value of the
firm. What matters, on the other hand, it the investment decisions which determine the
earnings of the firm and thus affect the value of the firm. They argue that subject to a
number of assumptions, the way a firm splits its earnings between dividends and retained
earnings has no effect on the value of the firm.
Assumption of the MM Approach(important)
The MM approach to irrelevance of dividend is based on the following assumption:
(i) The capital markets are perfect and the investors behave rationally.
(ii) All information are freely available to all the investors.
(iii) There is no transaction cost and no time lag.
(iv) Securities are divisible and can be split into any fraction.
(v) There are no taxes and no flotation cost.
(vi) The firm has a defined investment policy and the future profits are known with
certainly. The implication is that the investment decisions are unaffected by the
dividend decision and operating cash flows are same no matter which dividend policy
is adopted.
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𝑃𝑜 −
Where,
1 × (D1 + P1)
(1 + Ke)
P0 = Present market price of the share
Ke = Cost of equity share capital
D1 = Expected dividend at the end of year 1
P1 = Expected market price of the share at the
End of year 1
Que 8.
D Ltd. has 10 lakhs equity shares outstanding at the beginning of the accounting
year 1997. The current market price of the shares is Rs.150 each. The Board of
directors of the company has recommended Rs.8 per share as dividend. The rate
of capitalization, appropriate to the risk-class to which the company belongs, is
12%.
(i)
Based on M-M Approach, calculate the market price of the share of the company
when the recommended dividend is (a) declared; and (b) not declared.
(ii)
How many new shares are to be issued by the company at the end of the
accounting year on the assumption that the net income for the year is Rs.2 crores
and the investment budget is Rs.4 crores when (a) the above dividends are
distributed; and (b) dividends are not declared.
(iii)
Show that the market value of the shares at the end of accounting year will
remain the same whether dividends are distributed or not declared.
Ans.
Que 9.
(i) (a) Rs.160, (b) Rs.168; (ii) (a) 1.75 lakhs, (b) 1.1905 lakhs.
HPA Ltd. has a capital of Rs.10,00,000 in equity shares of Rs.100 each. The
shares are currently quoted at par. The company proposes declaration of a
dividend of Rs.10 per share. The capitalization rate for the risk class to which
the company belongs is 12%. What will be the market price of the share at
the end of the year, if- (i) no dividend is declared; and (ii) 10% dividend is
declared?
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Assuming that the company pays the dividend and has net profits of Rs.5,00,000 and makes
new investments of Rs.10,00,000 during the period, how many new shares must be issued?
Use the M.M. Model.
Ans.
Market price (i) when dividend s not declared Rs.112, (ii) when dividend is declared
Rs.102; Total number of new shares to be issued 5,882 shares.
Que 10.
Costal Chemicals Ltd. Belongs to a risk class of which the appropriate
capitalization rate is 10%. It currently has 1,00,000 shares selling at Rs 100
each. The firm is contemplating declaration of a dividend of Rs 6 per share at
the end of the current fiscal year which has begun.
Answer the following question based on Modigliani and Miller Model and
assumption of no taxes;
(i)
What will be the price of the shares at the end of the year if a dividend is not
declared?
(ii)
What will be the price if dividend is declared?
(iii)
Assuming that the firm pays dividend, has net income of Rs 10 lakhs and makes new
investments of Rs 20 lakhs during the period, how many new shares must be
issued?
Calculation market Price of share under MM- Dividend Irrelevancy Model
Que 11.
Best buy Auto Ltd. has outstanding 1,20,000 shares selling at Rs.20 per share.
The company hopes to make a net income of Rs.3,50,000 during the year
ended 31st March, 2003. The company is considering to pay a dividend of
Rs.2 per share at the end of current year. The capitalization rate for risk class
of this company has been estimated to be 15%.
Assuming no taxes, answer the questions listed below on the basis of the Modigliani Miller
Dividend Valuation Model:
(i)
What will be the price of a share at the end of 31 st March, 2003- If the dividend is paid; and
- If the dividend is not paid?
(ii)
How many new shares must the company issue if the dividend is paid and
company needs Rs.7,40,000 for an approved investment expenditure during the
year?
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Ans.
(i)
(ii)
Que 12.
P1= 21; p1 = 23
30,000
Nishi Ltd. had 1,00,000 equity shares of Rs.10 each outstanding on 1 st
January,2007. The shares are currently being quoted at par in the market. In
the wake of the removal of the dividend restraint, the company now intends
to pay a dividend of Rs.2 per share for the current financial year. It belongs to
a risk class whose appropriate capitalization rate is 15%. Using ModiglianiMiller Model and assuming no taxes, ascertain the price of the company’s
shares as it is likely to prevail at the end of the year(i)
(ii)
When dividend is declared; and
When no dividend is declared.
Also find out the number of new equity shares that company must issue to meet its
investment needs of Rs.4 lakh assuming that the dividend is paid and the earnings per
share works out @ Rs.2.20.
Ans.
(i) P1 = Rs.11.5- Rs.2 = Rs.9.5; (ii) P1 = Rs.11.50; (iii) No. of Equity Shares =
40,000 [ 3,80,000 / 9.5].
Que 13.
Leena Chemicals Ltd. has outstanding 1,20,000 shares selling at Rs.20 per
share. The company hopes to make a net income of Rs.3,50,000 during the
year ending 31st March, 2009. The company is thinking of paying a dividend
of Rs.2 per share at the end of current year. The capitalization rate for risk
class of this firm has been estimated to be 15%. Assuming no taxes, answer
the questions listed below on the basis of the Modigliani Miller dividend
valuation model:
(i)
What will be the price of share at the end of 31 st March, 2009, if- (a) the dividend is
paid; and (b) the dividend is not paid?
(ii)
How many new shares the company must issue if the dividend is paid and company
needs Rs.9,50,000 for an approved investment expenditure during the year?
Ans.
(a) P1 = 21 (b) P1 = 23,
(ii) (a) 40000
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MULTIPLE CHOICE QUESTIONS
1. Walter’s Model suggests for 100% DP Ratio when
a) ke = r
b) ke < r
c) ke > r
d) ke = 0
2. If a firm has ke > r the Walter's Model suggests for
a) 0% payout
b) 100% Payout
c) 50% Payout
d) 25% Payout
3. Walter’s Model suggests that a firm can always increase price share by
a) Increasing Dividend
b) Decreasing Dividend
c) Constant Dividend
d) None of the above
4. ‘Bird in hand' argument is given by
a) Walker's Model
b) Gordon's Model
c) MM Mode
d) Residuals Theory
5. Residuals Theory argues that dividend is a
a) Relevant Decision
b) Active Decision
c) Passive Decision
d) Irrelevant Decision
6. Dividend irrelevance argument of MM Model is based on:
a) Issue of Debentures
b) Issue of Bonus Share
c) Arbitrage
d) Hedging
7. Which of the following is not true for MM Model?
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a) Share price goes up if dividend is paid
b) Share price goes down if dividend is not paid
c) Market value is unaffected by Dividend policy
d) All of the above.
8. If ke = r, then under Walter's Model, which of the following is irrelevant?
a) Earnings per share
b) Dividend per share
c) DP Ratio
d) None of the above
9. Which of the following represents passive dividend policy?
a) that dividend is paid as a % of EPS
b) that dividend is paid as a constant amount
c) that dividend is paid after retaining profits for reinvestment
d) all of the above
10. MM Model argues that dividend is irrelevant as
a) the value of the firm depends upon earning power
b) the investors buy shares for capital gain
c) dividend is payable after deciding the retained earnings
d) dividend is a small amount
11. If 'r' = 'ke', than MP by Walter's Model and Gordon's Model for different payout
ratios would be
a) Unequal
b) Zero
c) Equal
d) Negative
12. Dividend Payout Ratio is
a) PAT÷ Capital
b) DPS ÷ EPS
c) Pref. Dividend ÷ PAT
d) Pref. Dividend ÷ Equity Dividend
13. Shares of face value of Rs. 10 are 80% paid up. The company declares a dividend of
50%. Amount of dividend per share is
a) Rs. 5
b) Rs.4
Page | 185
c) Rs. 80
d) Rs. 50
14. 'Constant Dividend Per Share' Policy is considered as:
a) Increasing Dividend Policy
b) Decreasing Dividend Policy
c) Stable Dividend Policy
d) None of the above
15. According to the _______ model, the dividend decision is irrelevant.
a) MM
b) Gorden
c) Walter
d) None of the above
16. The dividend-payout ratio is equal to __________.
a) the dividend yield plus the capital gains yield
b) dividends per share divided by earnings per share
c) dividends per share divided by par value per share
d) dividends per share divided by current price per share.
17. Dividends paid to common shareholders and divided by common shares
outstanding are equals to
a) earning per share
b) dividends per share
c) book value of share
d) market value of shares
18. Retained earnings are a) An indication of a company’s liquidity.
b) The same as cash in the bank.
c) Not important when determining dividends.
d) The cumulative earnings of the company after dividends.
19. As per Modigliani-Miller hypothesis of dividend irrelevance price of share at year
zero is a) D0 + P0/1+Ke
b) (D, + P,)X(l+Ke)
c) D,+ P1/1+Ke
d) 1 - (D0 + P0) ÷ Ke
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20. Payout ratio is subtracted from one to calculate a) Growth ratio
b) Present value ratio
c) Retention ratio
d) Future value ratio
21. Constant payout ratio means a) Declaration same bonus ratio every year.
b) The payment of fixed percentage of earning as dividend every yea r.
c) Constantly paying same dividend if EPS is same for all the year.
d) None of the above
22. How you calculate Dividend Cover Ratio?
a) PAT ÷ Dividend
b) Dividend ÷ PAT
c) EBIT ÷ Dividend
d) Dividend ÷ EBIT
23. A ............... is a payment of additional shares to shareholders in lieu of cash.
a) Stock split
b) Stock dividend
c) Extra dividend
d) Regular dividend
24. Myron Gordon believe that the required return on equity increases as the dividend
payout ratio is decreased. Their argument is based on the assumption that
a) Investors are indifferent between dividends and capital gains.
b) Investors require that the dividend yield and capital gains yield equal a constant.
c) Capital gains are taxed at a higher rate than dividends.
d) Investors view dividends as being less risky than potential future capital gains.
25. ................................ is a non-recurring dividend paid to share holders in addition to the
regular dividend.
a) A stock split
b) A stock dividend
c) An extra dividend
d) A regular dividend
26. Which of the following is correct formula to calculate dividend payout ratio?
a) DPS ÷ EPS
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b) EPS ÷DPS
c) Market Price ÷ EPS
d) EPS ÷ Market Price
27. The ............... is the proportion of earnings that are paid to common shareholders in
the form of a cash dividend.
a) Retention rate
b) 1 + Retention rate
c) Growth rate
d) Dividend payout ratio
28. The dividend payout ratio describes:
a) The proportion of earnings paid as dividends
b) The relationship of dividends per share to market price per share
c) The percentage change in dividends this year compared to fast year
d) Dividends as a percentage of the price/earnings ratio
29. Which of the following is correct formula to calculate dividend yield ratio?
a)
b)
𝐷𝑃𝑆
× 100
𝑀𝑃
(1−𝐸𝑃𝑆)
𝑀𝑃𝑆
𝐸𝑃𝑆
× 100
c) 𝑀𝑃𝑆 × 100
d)
𝑀𝑃
𝐷𝑃𝑆
× 100
30. As per Walter’s Model in case of growth firm a) Dividend policies are irrelevant
b) Optimal payout ratio is 100%
c) Payout ratio is irrelevant
d) Optimal payout ratio is nil
31. How market price will be calculated by using dividend growth model?
a) P0 = D1 ÷ (K -g)
b) P0 = (Ke-g) ÷ D1
c) P0 = (l+D1) ÷ (Ke-g)
d) P0 = (1+D,) X (K -g)
32. Market price is
a) D1 ÷ (Ke - g)
b) EPS XP/E Ratio
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c) (D1 + P1) ÷ (1 + K )
d) All of the above
33. Required return X Retention Ratio is
a) Ke (Cost of equity)
b) WACC
c) B (Beta)
d) g (Growth Rate)
34. Anurag has invested in a share whose dividend is expected to grow @15% for 5
years and thereafter @ 5% till life of the company. Find out the value of the share, if
current dividend is Rs.4 per share and investors required rate of return is 6%.
a) Near about Rs.756
b) Near about Rs.567
c) Near about Rs.657
d) Near about Rs.675
35. The cost of capital and rate of return on investment of X Ltd. is 10% and 15%
respectively. The company has 10 lakh shares of Rs.10 each. Its earnings per share is
Rs.7.5. Calculate the value of the firm per share using Walter’s Model assuming all
earnings are distributed as dividend.
a) Rs.75
b) Rs.100
c) Rs.125
d) Rs.150
36. EPS of X Ltd. is Rs.15. Its cost of capital is 16%. Internal rate of return on investment
is 20% and retention ratio is 40%. What is the market price per share of X Ltd. as
per Walter’s Model?
a) Rs.103.125
b) Rs.105.225
c) Rs.108.125
d) Rs.110.525
37. Following details are available for PQR Ltd.:
Earnings per share Rs.27.5
Cost of capital 16%
Internal rate of return on investment 20%
Retention ratio 50%
Calculate the price per share as per Walter’s Model.
a) Rs.315.40
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b) Rs.193.36
c) Rs.292.91
d) Rs.282.86
38. Following details are available for PQR Ltd.:
Earnings per share
Cost of capital
Internal rate of return on investment
Retention ratio
Rs.27.5
16%
20%
60%
Calculate the price per share as per Walter’s Model.
a) Rs.190.60
b) Rs.188.72
c) Rs.176.28
d) Rs.189.06
39. Details regarding A Ltd. are given below:
EPS = Rs.24
K = 11%
r= 12%
If retention ratio is 80%, market price as per Gordon’s Model is a) Rs.340.68
b) Rs.346.82
c) Rs.324.65
d) Rs.342.86
40. Details regarding B Ltd. are given below:
EPS = Rs.24
K = 13.20%
r = 14.40%
If retention ratio is 50%, market price as per Gordon's Model is a) Rs.200
b) Rs.300
c) Rs.400
d) Rs.600
41. ABC Ltd. was started a year back with a paid-up capital of Rs.56,00,000. The other
details are as under:
Earnings of the company
Rs.5,60,000
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dividend paid
Rs.4,48,000
price earnings ratio
12.5
number of shares
56,000
You are required to find out market price per share using Walter ’s formula.
a) Rs.138.57 per share
b) Rs.131.25 per share
c) Rs.175.83 per share
d) Rs.185.73 per share
42. The EPS of the Ganga Ltd. is Rs.16. the market capitalization rate applicable to the
company is 12.5% retained earnings can be employed to yield return of 10%. The
company is considering payout ratio of 25%, 50%, 75% and 100%. Which of these, if
any would maximize the wealth of shareholders as per Walter’s Model?
a) if payout ratio is 25%
b) if payout ratio is 50%
c) if payout ratio is 75%
d) if payout ratio is 100 percentage
43. Market price of X Ltd. is Rs.200 per share as per Gordon Model. EPS is Rs.20 per
share. Cost of capital is 11%. Rate of return on investment is 12%. What is retention
ratio?
a) 80%
b) 75%
c) 100%
d) 50%
44. following information is available in respect of X Ltd.:
No. of shares outstanding
1 lakh
Earnings per share
Rs.4
Equity capitalization rate
12%
Rate of return on investment
15%
You are required to calculate dividend payout ratio to keep share price at Rs40,
according to Walter model
Page | 191
a) 50%
b) 40%
c) 60%
d) 20%
45. A chemical company belong to a risk class for which P/E ratio is 10. It currently has
50,000 equity shares selling at Rs.200 each. The firm is contemplating the
declaration of dividend of Rs.16 per share at the current fiscal year which has just
started. Given the assumption of Modigliani-Miller, what will be the price of share at
the end of the year if dividend is declared?
a) Rs.205
b) Rs.208
c) Rs.204
d) Rs.225
46. An equity share of Rs.100 is expected to earn an annual dividend of Rs.10 and this
share can be sold at price of Rs.180 at the end of year. If the required rate of return
is 12%, calculate the value the value of equity share.
a) Rs.196.46
b) Rs.169.64
c) Rs.149.66
d) Rs.170.05
47. Net profit before tax of X Ltd. is Rs.17,50,000. The company has 1,00,000 equity
share of face value Rs.10 each, fully paid-up. Current market price of the shares is
Rs.85 per share Income –tax @ 30% applies to the company. Compute the P/E ratio
for the company.
a) 5.92
b) 8.63
c) 6.94
d) 9.46
48. Rama Ltd. had 1,00,000 equity shares of 10 each outstanding. Shares are currently
being quoted at par in the market. In the wake of the removal of the dividend
restraint, the company now intends to pay a dividend of 2 per share for the current
financial year. It belongs to a risk class whose appropriate capitalization rate is 15%.
Using MM Model and assuming no taxes, ascertain the price of the company’s shares
as it is likely to prevail at the end of the year - (i) when dividend is declared; and (it)
when no dividend is declared.
(i)
(ii)
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(A)
(B)
(C)
(D)
Rs.15.0
Rs.10.5
Rs.11.5
Rs. 9.5
Rs. 12.5
Rs. 11.5
Rs. 12.5
Rs. 11.5
49. Rosa Ltd. has outstanding 1,20,000 shares selling at 20 per share. The company
hopes to make a net income of 3,50,000 during the year. Company is thinking of
paying a dividend of 2 per share at the end of current year. Capitalization rate has
been estimated to be 15%. On the basis of MM model how many new shares the
company must issue if the dividend is paid and company needs 9,50,000 for an
approved investment expenditure?
a) 40,000 equity shares
b) 50,000 equity shares
c) 60,000 equity shares
d) 70,000 equity shares
50. Current price of share of X Ltd. is Rs.60 and just paid dividend per share is Rs.4. If
the capitalization rate is 12%, what is the dividend growth rate?
a) 3%
b) 5%
c) 4%
d) 6%
51. Small Events Incorporation has recently paid dividend of 3.50 per share. The
dividends are growing at 10% p.a. and the equity capitalization rate applicable to
the company is 12%. Find out the implicit P/E Ratio if the EPS of the company is 7.
a) 27.50
b) 28.50
c) 30.00
d) 32.50
52. Following information is available in respect of X Ltd.:
No. of shares outstanding: 3 lakh
Net profit: 18 lakh
Equity capitalization rate : 16%
Rate of return on investment : 20%
You are required to calculate Dividend payout ratio to keep share price at 42.
a) 42%
b) 46%
c) 58%
Page | 193
d) 52%
Answer:
1
2
3
4
5
6
7
8
9
10
11
12
13
C
B
D
B
C
C
C
C
C
A
C
B
B
14
15
16
17
18
19
20
21
22
23
24
25
26
C
A
B
B
D
C
C
B
A
B
D
C
A
27
28
29
30
31
32
33
34
35
36
37
38
39
D
A
A
D
A
D
D
C
A
A
B
D
D
40
41
42
43
44
45
46
47
48
49
50
51
52
A
B
D
D
D
C
B
C
D
A
B
A
D
Which of the following statements is True (T) or False
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
Dividend is a part of retained earnings.
(ii)Dividend is compulsorily payable to preference shareholders.
Effective dividend policy is an important tool to achieve the goal of wealth
maximization.
Retained earnings are an easily available source of funds at no explicit cost.
Dividend payout ratio refers to that portion of total earnings which is distributed
among shareholders.
% rate of dividend is also known as dividend payout ratio.
There is a difference of opinion on relationship between dividend payment and
value of the firm.
Walters model supports the view that dividend is relevant for value of the firm.
Gordon's model suggests that dividend payment does not affect the market price
of the share.
Page | 194
(x)
(xi)
(xii)
(xiii)
(xiv)
In the Walters model, the DP ratio should depend upon the relationship between
r and ke
Residual theory says that dividend decision is no decision.
MM model deals with irrelevance of dividend decision
MM model is a fool proof model of dividend irrelevance.
In the arbitrage process of MM model, the dividends paid by a company are
replaced by fresh investment.
MM model asserts that value of the firm is not affected whether the firm pays
dividend or not.
Answer: (i) F, (ii) F, (iii) T, (iv) T, (v) T, (vi) F, (vii) T, (viii) T, (ix) F, (x) T, (xi) T, (xii) T,
(xiii) F, (xiv)T, (xv) T.
State whether each of the following statements is True (T) or False (F).
(i)
(ii)
(iii)
(iv)
(v)
(vi)
DP ratio of a firm should be directly related to future growth plans of the firm.
Dividends are paid out of profit and therefore do not affect the liquidity position
of the firm.
Stability of dividend refers to the fact that the rate of divided must be fixed.
Cash dividend and bonus share issue affect the firm in the same way.
No company in India, can pay final dividend already paid an interim dividend.
Dividends, in India, can be paid only out of profits.
Answers: (i) T, (ii) F, (iii) F, (iv) F, (v) F, (vi) F.
Page | 195
CHAPTER 9
CAPITAL BUDGETING




CAPITAL BUDGETING – A CONCEPT
IMPORTANCE OF CAPITAL BUDGETING
RATIONALE OF CAPITAL BUDGETING DECISIONS
KINDS OF CAPITAL BUDGETING DECESIONS
 CONCEPT 1
CAPITAL BUDGETING
Capital budgeting refers to long-term planning for proposed capital outlays and their
financing. Thus, it includes both raising of long-term funds as well as their utilisation. It
may, thus, be defined as the "firm's formal process for acquisition and investment of
capital." To be more precise, capital budgeting decision may be defined as "the firms'
decision to invest its current fund more efficiently in long-term activities in anticipation of
an expected flow of future benefit over a series of years." The long-term activities are those
activities which affect firms operation beyond the one year period. The basic feature of
capital budgeting decisions are:
(1) current funds are exchanged for future benefits;
(2) there is an investment in long-term activities; and
(3) the future benefits will occur to the firm over series of years.
 CONCEPT 2
IMPORTANCE OF CAPITAL BUDGETING
Capital budgeting decisions are of paramount importance in financial decision. So it needs
special care on account of the following reasons:
(1) Long-term Implications: A Capital budgeting decision has its effect over a long time
span and inevitably affects the company’s future cost structure and growth. A wrong
decision can prove disastrous for the long-term survival of firm. It leads unwanted
expansion of assets, which results in heavy operating cost to the firm. On the other hand,
Page | 196
lack of investment in asset would influence the competitive position of the firm. So the
capital budgeting decisions determine the future destiny of the company.
(2) Involvement of large amount of funds: Capital budgeting decisions need substantial
amount of capital outlay. This underlines the need for thoughtful, wise and correct
decisions as an incorrect decision would not only result in losses but also prevent the firm
from earning profit from other investments which could not be undertaken.
(3) Irreversible decisions: Capital budgeting decisions in most of the cases are irreversible
because it is difficult to find a market for such assets. The only way out will be to scrap the
capital assets so acquired and incur heavy losses.
(4) Risk and uncertainty: Capital budgeting decision is surrounded by great number of
uncertainties. Investment is present and investment is future. The future is uncertain and
full of risks. Longer the period of project, greater may be the risk and uncertainty. The
estimates about cost, revenues and profits may not come true.
(5) Difficult to make: Capital budgeting decision making is a difficult and complicated
exercise for the management. These decisions require an overall assessme nt of future
events which are uncertain. It is really a marathon job to estimate the future benefits and
cost correctly in quantitative terms subject to the uncertainties caused by economic political social and technological factors.
 CONCEPT 3
RATIONALE OF CAPITAL BUDGETING DECISIONS
The rationale behind the capital budgeting decisions is efficiency. A firm has to
continuously invest in new plant or machinery for expansion of its operations or replace
worn out machinery for maintaining and improving efficiency. The 4 main objective of the
firm is to maximize profit either by way of increased revenue or by cost reduction. Broadly,
there are two types of capital budgeting decisions which expand revenue or reduce cost.
1) Investment decisions affecting revenue: It includes all those investment decisions
which are expected to bring an additional revenue by raising the size of firm's total
revenue. It is possible either by expansion of present operations or the development
of new product in line. In both the cases fixed assets are required.
Page | 197
2) Investment decisions reducing costs: It includes all those decisions of the firms
which reduces the total costs and leads to increase in its total earnings i.e. when an
asset is worn out or becomes outdated, the firm has to decide whether to continue
with it or replace it by new machine. For this, the firm evaluates the benefit in the
form of reduction in operating costs and outlays that would be needed to replace old
machine by new one. A firm will replace an asset only when it finds it beneficial to
do so. The above decision could be followed decisions following alternative courses:
i.e. Tactical investment decisions to strategic investment decisions, as briefly defined
below.
3) Tactical investment decisions: It includes those investment decisions which
generally involves a relatively small amount of funds and does not constitute a major
departure from what the firm has been doing in the past.
4) Strategic investment decisions: Such decisions involve large sum of money and
envisage major departure from what the company has been doing in the past.
Acceptance of strategic investment will involve significant change in the company's
expected profits and the risk to which these profits will be subject. These changes
are Hkely to lead stock-holders and creditors to revise their evaluation of the
company.
 CONCEPT 4
KINDS OF CAPITAL BUDGETING DECISIONS
Generally the business firms are confronted with three types of capital budgeting decisions
(i) the accept-reject decisions; (ii) mutually exclusive decisions; and (iii) capital rationing
decisions.
Accept-reject decisions: Business firm is confronted with alternative investment proposals.
If the proposal is accepted, the firm incur the investment and not otherwise. Broadly, all
those investment proposals which yield a rate of return greater than cost of capital are
accepted and the others are rejected. Under this criterion, all the independent prospects
are accepted.
Page | 198
Mutually exclusive decisions: It includes all those projects which compete with each other
in a way that acceptance of one precludes the acceptance of other or others. Thus, some
technique has to be used for selecting the best among all and eliminates other alternatives.
Capital rationing decisions: Capital budgeting decision is a simple process in those firms
where fund is not the constraint, but in majority of the cases, firms have fixed capital
budget. So large number of projects compete for these limited budget. So the firm ration
them in a manner so as to maximise the long run returns. Thus, capital rationing refers to
the situations where the firm have more acceptable investments requiring greater amount
of finance than is available with the firm. It is concerned with the selection of a group of
investment out of many investment proposals ranked in the descending order of the rate of
return.
PRACTICAL QUESTIONS
TYPE – I
(FORMATION PROBLEM)
Question – 1 ABC Co. is considering a proposal to replace one of its plants costing Rs.
60,000 and having a written down value of Rs. 24,000. The remaining economic life of the
plant is 4 years after which it will have no salvage value. However, if sold today, it has a
salvage value of Rs. 20,000. The new machine costing Rs. 1,30,000 is also expected to have a
life of 4 years with a scrap value of Rs. 18,000. The new machine, due to its technological
superiority, is expected to contribute additional annual benefit (before depreciation and
tax) of Rs. 60,000. Find out the cash flows associated with this decision given that the tax
rate applicable to the firm is 40%. (The capital gain or loss may be taken as not subject to
tax.)
[Ans: Initial – 1,10,000, Subsequent – 44,800 Terminal – Rs.62,800]
Question 2 ABC Instruments Ltd. is considering the purchase of a /machine to replace an
existing machine that has a book value of Rs. 24,000, and can be sold for Rs. 12,000. The
salvage value or the old machine in four years is zero, and it is depreciated on a straight-line
basis. The proposed machine will perform the same function the old machine is
performing; however improvements in technology will enable the firm to reap cash benefits
(before depreciation and taxes) of Rs. 56,000 per year in materials, labour, and overhead.
The new machine has a four year life, costs Rs. 1,12,000 and can be sold for an expected Rs.
Page | 199
16,000 at the end of the fourth year. Assuming straight-line depreciation and a 40% tax
rate, compute cash flows associated with this replacement.
[Ans: Initial Outlay : Rs. 95,200; Yearly incremental inflows are Rs. 40,800 per annum; The
terminal cost inflow is Rs. 16,000.]
Question 3 A cosmetic company is considering to introduce a new lotion. The
manufacturing equipment will cost Rs. 5,60,000. The expected life of the equipment is 8
years. The company is thinking of selling the lotion in a single standard pack of 50 grams at
Rs. 12 each pack. It is estimated that variable cost per pack would be Rs. 6 and annual fixed
cost Rs. 4,50,000. Fixed cost includes (straight-line) depreciation of Rs. 70,000 and
allocated overheads of Rs. 30,000. The company expects to sell 1,00,000 packs of the lotion
each year. Assume that tax is 45% and straight-line depreciation is allowed for tax purpose.
Calculate the cash flows.
[Ans: Annual cash inflows are Rs.1,69,000 and Initial cash outflow is Rs.5,60,000.]
Question -4 XYZ is interested in assessing the cash flows associated with the replacement
of an old machine by a new machine. The old machine bought a few years ago has a book
value of Rs. 90,000 and it can be sold for Rs. 90,000. It has a remaining life of five years after
which its salvage value is expected to be nil It is being depreciated annually at the rate of 20
per cent (written down value method.)
The new machine costs Rs. 4,00,000. It is expected to fetch Rs. 2,50,000 after five years
when it will no longer be required. It will be depreciated annually at the rate of 33 1/3 per
cent (written down value method.) The new machine is expected to bring a saving of Rs.
1,00,000 in manufacturing costs. Investment in working capital would remain unaffected.
The tax rate applicable to the firm is 50 per cent. Find out the relevant cash flow for this
replacement decision. (Tax on capital gain/loss to be ignored).
[Ans: Initial – 3,10,000, Subsequent – 1. 107.6, 2. 87.2, 3. 73.9, 4. 65.2, 5. 59.4 Terminal –
Rs.3,09,400]
 CONCEPT 5
VARIOUS TECHNIQUES OF DECISION IN CAPITAL BUDGETING
Page | 200
A wide variety of techniques are used for evaluating investment proposals. The most
commonly used techniques are as follows:
The Payback Method
The Average Rate of Return Method
Discount Cash Flow Method
Net Present Value Method (NPV)
Internal Rate of Return Method (IRR)
Profitability Index (PI) or Benefit Cost Ratio (BC).
Every method is designated with some purpose in view and as such different methods are
not equally useful to every firm and under all circumstances. However, proper
understanding of these techniques will help the management to determine the most
suitable technique to be used and thus make better investment decisions keeping in view
the business situation, particular requirements of the firm and nature of investment
proposals}
1- The Payback Method
This technique estimates the time required by the project to recover, through cash inflows,
the firms initial outlay. Beginning with the project with the shortest payout period, different
projects are arranged in order of time required to recapture their respective estimated
initial outlays. The payback period for each investment proposal is compared with the
maximum period acceptable to management and proposals are then ranked and selected in
order of those having minimum payout period.
Decision Rule:
Accept the project if the payback period calculated for it is less than the maximum set by
the management. Reject the project if it is otherwise. In case of multiple projects, the
project with shorter payback period will be selected. In essence, payback period shows
break-even point where cash inflows are equal to cash out flows. Any inflows beyond this
period are surplus inflows.
Advantages:
1. It is easy to calculate and investment proposals can be ranked quickly.
2. For a firm experiencing shortage of cash, the payback technique may be used with
Page | 201
advantage to select investments involving minimum time to recapture the original
investment.
3. The payout method permits the firm to determine the length of time required to
recapture through cash flows, the capital expenditure incurred on a given project
and thus helps it to determine the degree of risk involved in each investment
proposal.
4. This is ideal in deciding cash investment in a foreign country with volatile political
position and a long-term projection of political stability is difficult.
5. This is, likewise, more preferred in case of industries where technological
obsolescence comes within short period; say electronic industries.
Disadvantages:
1. The payback method ignores the time value of money and treats all cash flows at par.
Thus, projects A and B with the following cash flows are treated equally:
Years
1.
2.
3.
4.
Investment
Project A
5,000
Rs.
4,000
3,000
2,000
14,000
Cash Flows
Project B
2,000
Rs.
3,000
4,000
5,000
14,000
Although Pay Back period is 4 years for both the projects, project A is preferable
since it recovers larger amount of money during the initial years.
2.
3.
The pay back method, therefore, ignores the fact that amount of cash received today
is more important than the same amount received after say, 2 years.
The payback method does not consider cash flows and income that may be earned
beyond the payout period.
Moreover, it does not take into account the salvage or residual value, if any, of the longterm asset.
Page | 202
The payback technique ignores the cost of capital as the cut-off factor affecting
selection of investment proposals.
4.
Suitability:
Payback period
circumstances:
(i)
(ii)
(iii)
(iv)
method
may be successfully applied in the following
Where the firms suffers from liquidity problem and is interested in quick
recovery of fund than profitability;
high external financing cost of the project;
for projects involving very uncertain return; and
political and economic pressures.
It may, therefore, be said that payback period is defined as the measure of projects liquidity
and capital recovery rather than its profitability.
2- The Average Accounting Rate of Return Method
This method is designated to consider the relative profitability of different capital
investment proposals as the basis for ranking them - the fact neglected by the payout
period technique. Since this method uses accounting rate of return, it is sometimes
described as the financial statement method. Rate of return is calculated by dividing
earnings by capital invested. The numerator, i.e., earnings can be interpreted in a number of
ways. It might mean income after taxes and depreciation, income before taxes and
depreciation, or income after taxes but before depreciation. Since both numerator and
denominator carry different meanings. It is not surprising if one comes across a number of
variations of the average rate of return method. However, the two common variations are:
(a)
Average Rate of Return in Original Investment:
=
(b)
Net earnings after Depreciation and Taxes
= Original Investment
No. of years project will last
Average Rate of Return on Average Investment:
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=
Net earnings after Depreciated and Taxes
= Average Investment
No. of years project will last
Average investment is estimated by dividing the total of original investment and investment
in the project at the end of its economic life by 2. The approach of dividing average annual
after-tax earnings of the project by its original investment makes no attempt to incorporate
the fact of gradual recovery of investment over time, hence tends to undertake the average
rate of return. The average investment approach on the other hand, gives best result when
original investment is evenly recovered over the economic life of the project which may not
always be the case.
Decision Rule:
Normally business firm determine rate of return. So accept the proposal if
ARR > Minimum rate of return (cut off rate)
and Reject the project if
ARR < Minimum rate of return (cut off rate)
In case of more than one project, where a choice has to be made, the different projects may
be ranked in descending or ascending order of their rate of return. Project below the
minimum rate will be dropped. In case of project yielding rate of return higher than
minimum rate, it is obvious that project yielding a higher rate of return will be preferred to
all.
Advantages:
(i) Earnings over the entire life of the project are considered.
(ii) This method is easy to understand, simple to follow. Accounting concept of income
after taxes is known to every student of accountancy.
Disadvantages:
(i) Like the payback technique, the average return on investment method also ignore
the time value of funds. Consideration to distribution of earnings over time is
important. It is to be accepted that current income is more valuable than income
received at a later date.
(ii) The method ignores the shrinkage of original investment through the process of
charging depreciation allowances against earnings. Even the assumption of
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regular recovery of capital over time as implied in average investment approach is
not well founded. '
(iii) The average rate of return on original investment approach cannot be applied to a
situation where part of the investment is to be made after the beginning of the
project.
Suitability:
If the project life is not long, then the method can be used to have a rough
assessment of the internal rate of return. The present method is generally used as
supplementary tool only.
Comparison between Average Rate of Return and Payback Method:
The average rate of return method and its comparison with payback method may be
illustrated as follows:
Suppose there are two investment proposals A and B each with capital investment of Rs.
20,000 and depreciable life of 4 years. Assume that following are the estimated profit and
cash inflows when annual straight line depreciation charged is Rs. 5,000.
Period
1.
2.
3.
4.
Total
Average rate of return on
original investment
Project A
Book
Net Cash
Profits
Inflows
4,000
3,000
2,000
Rs.
1,000
10,000
12.5%
9,000
Rs.
8,000
7,000
6,000
30,000
Project B
Book Profits
Net Cash
Inflows
1,000
2,000
Rs.
3,000
4,000
10,000
12.5%
6,000
Rs.
7,000
8,000
9,000
30,000
If evaluated in terms of average rate of return method, the two projects are equally
favourable. However, project A is more favourable than project B since it provides larger
cash inflows in the initial period (i.e. Quicker Payback).
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3- Net Present Value Method
The net present value method is understood to be the best available method for evaluating
the capital investment proposals. Under this method, the cash outflows and inflows
associated with each project are ascertained first. Cash inflows are worked out by adding
depreciation to profit after tax arising to each project*. Since the cash outflows and inflows
arise at different point of time and cannot be compared, so both are reduced to the present
values at the rate of return acceptable to the management. The rate of return is either cost
of capital of the firm or the opportunity cost of capital to be invested in the project. The
assumption under this method remain that cash inflows are reinvested at the same
discount rate.
Advantages:
(i) Income over the entire life of the project is considered.
(ii) The method takes into account time value of money.
(iii) The method provides clear acceptance so interpretation is easy.
(iv) When projects involves different amount of investment, the method may not
provide satisfactory answers.
Disadvantages:
(i)
(ii)
(iii)
Suitability:
As compared with the first two methods, the present value approach is
certainly more difficult to understand and apply.
An additional difficulty in this approach is encountered when projects with
unequal lives are to be evaluated.
It is difficult to determine the firm cost of capital or appropriate rate of
discount.
Net present value is the most suitable method in those circumstances where availability of
resources is not a constraint. The management authority can accept all those projects
having Net Present Value either Zero or positive. This method shall maximise shareholders
wealth and market value of share which is the sole aim of any business enterprise.
4- Rate of Return (IRR)
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The internal rate of return refers to the rate which equates the present value of cash inflows
and present value of cash outflows. In other words, it is the rate at which net present value
of the investment is zero. If the Net Present Value is positive, a higher discount rate may be
used to bring it down to equalise the discount cash inflows and vice versa. That is why.
Internal Rate of Return is defined as the break even financing rate for the p roject.
 CONCEPT 6
COMPUTATION OF INTERNAL RATE OF RETURN:
The computation of Internal Rate of Return is relatively complicated and difficult compared
to Net Present Value. One has to follow trial and error exercise to ascertain Internal Rate of
Return (r) which equates the cash inflows and outflows of the investment proposals. Under
net present value, k is known, but under this method it is worked out.
Initially the Internal rate of return (r) may give
NPV > 0
NPV = 0
NPV < 0
Advantages:
(i)
r > k (higher rate will be tried)
r=k
r < k (lower rate will be tried)
The discounted cash flow (IRR) takes into account the time value of money.
(ii) It considers cash benefits, i.e. profitability of the project for the whole of its economic
life.
(iii) The rate of discount at which the present value of cash flows is equated to capital
outlay on a project is shown as a percentage figure. Evidently, this method provides
for uniform ranking and quick comparison of relative efficiency of different projects.
(iv) This method is considered to be a sophisticated and more reliable technique of
evaluating capital investment proposals.
(v) The objective of maximising of owner's welfare is met.
Disadvantages:
(i)
(ii)
The discounted cash flow is the most difficult of all the methods of project
evaluation discussed above.
An important assumption implied in this method is that incomes are reinvested
(compounding) over the project's economic life at the rate earned by the investment.
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This assumption is correct and justified only when the internal rate of return is very
close to the average rate of return earned by the company on its total investments.
To the extent internal rate of return departs from the typical rate of earnings of the
company, results of this method, will be misleading. Thus, when the internal rate of
return on a project is computed to be 30% while company's average rate of return is
15%, the assumption of earning income on income at the rate of 30% is highly
unrealistic. From this point of view the assumption of the net present value method
that incomes are reinvested at the rate of discount (cost of capital) seems to be more
reasonable.
(iii)
The rate may be negative or one or may be multiple rate as per calculations. When a
project has a sequence of changes in sign of cash flow, there may be more than one
internal rate of return.
5- Profitability Index (PI)
Profitability index is defined as the rate of present value of the future cash benefits at the
required rate of return to the initial cash outflow of the investment. Symbolically,
Profitability index is expressed as
𝑃𝑉. 𝑜𝑓 𝐼𝑛𝑓𝑙𝑜𝑤
𝑃𝐼 =
𝑃𝑉. 𝑜𝑓 𝐹𝑙𝑜𝑤
The above ratio is an indicator of the profitability of the project. If the ratio is equal to or
greater than one, it shows that project has an expected yield equal to or greater than the
discount rate. If the index is less than one, it indicates that project has an expected yield less
than the discount rate.
Decision Rule:
If PI > 1 Accept the Project, PI = 1 indifferent, PI < 1 Reject the project.
In the event of more than one alternatives, projects may be ranked according to their ratio the project with the highest ratio should be ranked first and vice versa.
Advantages:
1) Profitability Index method gives due consideration to the time value of money.
2) Profitability Index method satisfies almost all the requirements of a sound
investment criterion.
3) This method can be successfully employed to rank projects of varying cash and
benefits in order of their profitability.
Page | 208
Disadvantages:
1) This method is more difficult to understand and compute.
2) This method does not take into account the size of investment.
3) When cash outflows occur beyond the cement period Profitability Index Ratio
criterion is unsuitable as a selection criterion.
 CONCEPT 7
COMPARISON OF NET PRESENT VALUE AND INTERNAL RATE OF RETURN APPROACH
The net present value and internal rate of return, two widely used methods are the species
of the same genus i.e. Discount cash flow method, yet they are different from each other on
various points.
The broad points of difference between the two are as follows:
Points of Differences
1. Interest Rate: Under the net present value method rate of interest is assumed as
the known factor whereas it is unknown in case of internal rate of return method.
2. Reinvestment Axiom: Under both the methods, it is assumed that cash inflows can
be re-invested at the discount rate in the new projects. However, reinvestment of
funds, at cut-off rate is more possible than internal rate of return. So net present
value method is more reliable than internal rate of return method for ranking two or
more projects.
3. Objective: The net present value method took to ascertain the amount which can be
invested in a project so that its expected yields will exactly match to repay this
amount with interest at the market rate. On the other hand, internal rate of return
method attempts to find out the rate of interest which is maximum to repay the
invested fund out of the cash inflows.
Points of Similarities
Page | 209
IRR will give the same results as NPV in terms of acceptance or rejection of investment
proposals in the following circumstances:
1.
2.
Projects having conventional cash flows i.e. a situation where initial investment (outlay
or cash outflow) is followed by series of cash inflows.
Independent Investment Proposals: Such proposal, the acceptance of which does not
exclude the acceptance of others.
 CONCEPT 8
CHOICE OF METHODS
The business enterprise is confronted with large number of investment criteria for
selection of investment proposals. It should like to choose the best among all. Specially, it is
the choice between Net Present Value and Internal Rate of Return Method because these
are the two methods which are widely used by the firms. If a choice must be made, the Net
Present Value Method generally is considered to be superior theoretically because:
(i) It is simple to operate as compared to internal rate of return method;
(ii) It does not suffer from the limitations of multiple rates;
(iii) The reinvestment assumption of the Net Present Value Method is more realistic than
internal rate of return method.
On the other hand, some scholars have advocated for internal rate of return method on the
following grounds:
1.
2.
It is easier to visualise and to interpret as compared to Net Present Value Method.
It suggests the maximum rate of return and even in the absence of cost of capital, it
gives fairly good idea of the projects profitability. On the other hand, Net Present Value
Method may yield incorrect results if the firm's cost of capital is not calculated with
accuracy.
The internal rate of return method is preferable over Net Present Value Method in the
evaluation of risky projects.
Page | 210
SOLVED ILLUSTRATIONS
Illustration-1
Machine A costs Rs.1,00,000 payable immediately. Machine B costs Rs. 1,20,000 half
payable immediately and half payable in one year's time. The cash receipts expected are as
follows:
Year (at end)
Machine
(A)
Machine
(B)
1
2
3
4
5
20,000
60,000
40,000
30,000
20,000
-60,000
60,000
60,000
80,000
—
At 7% opportunity cost, which machine should be selected on the basis of NPV?
Solution:
1. Calculation of NPV
Year
0
1
2
3
4
5
Year
0
Machine A
Cash flows
PVF@ 7%
(1,00,000)
1
20,000
0.935
60,000
0.873
40,000
0.816
30,000
0.763
20,000
0.713
NPV
PVR (Rs)
(1,00,000)
18700
52380
32640
22890
14260
40870
Machine B
Cash flows
PVF@ 7%
(60,000)
1
PVR (Rs)
(60,000)
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1
2
3
4
5
(60,000)
60,000
60,000
80,000
-
0.935
0.873
0.816
0.763
0.713
(56100)
52380
48960
61040
0
46280
Machine B is having higher : NPV and may be selected.
Illustration-2
A company is considering a new project for which the investment data are as follows:
Capital outlay
Rs. 2,00,000
Depreciation
20% p.a.
Forecasted annual income before charging depreciation, but after all other charges are as
follows:
Year 1
2
3
4
5
Rs. 1,00,000
1,00,000
80,000
80,000
40,000
4,00,000
On the basis of the available data, set out calculations, illustrating and comparing the
following methods of evaluating the return:
(a)
(b)
Solution:
Payback method.
Rate of return on original investment.
Since there is no tax, the annual income before depreciation and after other
charges is equivalent to Cash flow (CF).
Page | 212
(a)
(b)
Capital outlay of Rs.2,00,000 is recovered in the first two years, (Rs. 1,00,000
(year 1) + Rs. 1,00,000 (year 2), therefore, the payback period is two years.
Rate of return on original investment:
Year
1
2
3
4
5
Income
(Rs.)
Depreciation
(Rs.)
1,00,000
1,00,000
80,000
80,000
40,000
40,000
40,000
40,000
40,000
40,000
Net
Income
Rs.
60,000
60,000
40,000
40,000
–
2,00,000
Average Income = Rs. 2,00,000/5 = Rs. 40,000
Rate of Return
=
=
Average income
 100
Original investment
Rs.40,000
 100  20%
Rs.2,00,000
BASED ON TECHNIQUES OF CAPITAL BUDETING
PROBLEMS
Problem.1
Machine A costs Rs.1,00,000, payable immediately. Machine B costs Rs.1,20,000, half
payable immediately and half payable in one year’s time. The cash receipts expected are as
follows:
Rs.
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Year (at the
end)
1
2
3
4
5
A
B
Rs.
20,000
—
Rs.
60,000
60,000
80,000
—
60,000
40,000
30,000
20,000
With 7% cost of capital, which machine should be selected?
[Answer : B is having higher NPV and hence acceptable.]
Problem.2
A machine costing Rs.110 lacs has a life of 10 years, at the end of which its scrap value is
likely to be Rs.10 lacs. The firm’s cut-off rate is 12%. The machine is expected to yield an
annual profit after tax of Rs.10 lacs, depreciation being r eckoned on straight line basis.
Ascertain the net present value of the project.
[Answer: the NPV of the project is Rs.6,22,000]
Problem.3
XYZ co. is considering the purchase of one of the following machines, whose relevant data
are as given below:-
Estimated life
Capital cost
Earnings (after tax):
Year 1
Year 2
Year 3
Machine
X
3 years
90,000
40,000
50,000
40,000
Rs.
Machine
Y
3 years
90,000
20,000
70,000
50,000
Page | 214
The company follows the straight-line method of deprecation; the estimated salvage value
of both the types of machines is zero. Show the most profitable investment based on (i) Pay
back period, (ii) Accounting rate of return, and (iii) Net present value assuming a 10% cost
of capital.
[Answer: The PB are 1.25 and 1.4 years; ARR are 96.3% and 103.7% and NPV are Rs.
92,280 and Rs.98,130.]
Problem 4
A firm has the following two proposals before it.
Cost.
Cash Inflows:
Years
1
2
3
4
Proposal I
Rs.
11,000
Proposal II
Rs.
10,000
Rs.
Rs.
6,000
2,000
1,000
5,000
1,000
1,000
2,000
10,000
Find out IRR of both the proposals, which proposal is acceptable if the required rate of
return of the firm is (i) 11% or (ii) 10%.
[Answer: IRR of Proposal I is 11.26% and Proposal II is 10.22%. If the required rate of
return is 11%, only Proposal I is acceptable. However, if the required rate of return is 10%,
then both proposals are acceptable.]
Problem 5
XYZ Ltd. has to replace one of its machine for which it has following options:
(a)
(b)
Installation of equipment "Best" having cost of Rs. 75,000 which is expected to
a generate a cash inflow of Rs. 20,000 per annum for next 6 years.
Installation of equipment "Better" having cost of Rs. 50,000 which is expected
to generate a cash inflow of Rs. 18,000 per annum for next 4 years.
Page | 215
Which equipment should be preferred if the company adopts method of (i)
Payback period (ii) Internal Rate of Return.
(c)
Answer:
payback period = 3.75 year, 2.78 years
IRR = 15.34%, 16.36%
Problem 6
A company has to consider the following Project
Cost
Rs. 10,000
Cash inflows:
Year 1
Rs. 1,000
3
2,000
2
1,000
4
10,000
Compute the internal rate of return and comment on the project if the opportunity cost is
14%.
Answer:
Problem 7
10.22%, company should reject project
A firm whose cost of capital is 10% is considering two mutually exclusive projects X and Y,
the details of which are:
Cost
Cash inflows
Year
0
1
2
Project X
Rs. 1,00,000
10,000
20,000
Project Y
Rs. 1,00,000
50,000
40,000
Page | 216
3
4
5
30,000
45,000
60,000
20,000
10,000
10,000
Compute the Net Present Value at 10%, Profitability Index and Internal Rate of Return for
the two projects.
Answer:
NPV (x)= 16135, NPV (y)= 6550, PI (y)= 1.065, IRR (x)= 14.71, IRR
(y)=13.56%
Problem 8
2013-Dec [3] (a) Raghu electronic wants to take a new project involving manufacture of
an electronic device which has good market prospects. Further details are given below:
(Rs in
lakh)
(i)
(ii)
Cost of the project (as estimated):
- Land (to be incurred at the beginning of the
year 1)
- Buildings (to be incurred at the end of the
year 1)
- Machinery (to be incurred at the end of the
year 2)
- Working capital (margin money)
(to be incurred at the beginning of the year 3)
2.00
3.00
10.00
5.00
20.00
The project will go into production from the beginning of year 3 and will be
operational for a period of 5 years. The annual working results are estimated as
follows:
Sales
Variable cost
Fixed cost (excluding depreciation)
(Rs in lakh)
24
8
5
Page | 217
Depreciation of assets
(iii)
(iv)
2
at the end of the operational period, it is expected that the fixed assets can be sold
for Rs 5 lakh (without any profit).
Cost of capital of the firm is 10%. Applicable tax rate is 33.33% inclusive of
surcharge and education cess etc.
You are required to evaluate the proposal using the net present value approach and advise
the firm. (10 marks)
 CONCEPT 11
EAC & EAB APPROACHES
This concept is used when life of two projects under consideration is not same.
𝐸𝐴𝐶 =
𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤
(𝑃𝑉𝐴𝐹 )𝑛 ,𝑖
𝐸𝐴𝐵 =
𝑁𝑃𝑉
(𝑃𝑉𝐴𝐹 )𝑛 ,𝑖
Decision on Basis of EAB = Project with higher EAB will be selected
Decision on Basis of EAC = Project with Lower EAC will be selected
Illustration 3:
REPLACEMENT –MAY 2000 [1] (A)
Company X is forced to choose between two machines A and B. The two machines are
designed differently, but have identical capacity and do exactly the same job. Machine A
costs Rs. 1,50,000 and will last for 3 years. It costs Rs. 40,000 per year to run. Machine B is
an economy model costing only Rs. 1,00,000, but will last only for 2 years, and costs Rs.
60,000 per year to run. These are real cash flows. The Costs are forecasted in rupees of
Page | 218
constant purchasing power. Ignore Tax. Opportunity cost of capital is 10 per cent. Which
machine should the company buy?
Solution:
Evaluation of machines (in Rs.)
The decision is to be based on Equated Annual Costs since the life is different.
Decision: Company X should purchase machine A because of its lower cost.
Illustration 4
Company ABC Ltd is forced to choose between 2 machines A & B, the two machines are
designed differently but have identical capacity & do exactly same job. The information
regarding 2 machines is given below:
Machine A
Machine B
Cost
2 lakh
1 lakh
Life
6 Years
5 Years
Revenue P.A
60,000
40,000
Saving in Exp.
10,000
5000
discount Rate
12%
12%
Tax rate  30%
Which machine should company buy
 CONCEPT 12
CAPITAL BUDGETING UNDER INFLATION
Page | 219
1) When there is inflation, cash inflows/outflows will be inflation adjusted (i.e. in
money term). The provider of fund will expects higher return for money provided &
hence cost of capital will also be inflation adjusted (money term).
2) When there is no inflation then cash flows will be in real terms and cost of capital
will also be in real terms.
a) Relationship between inflation adjusted cash flows and real cash flows.
Real cash cash flow (1 + inflation) = money cash flows
Real cash flows = money cash flow
(1+inflation)
b) Relationship between money cost of capital real cost of capital.
(1+real rate) (1+inflation rate) = (1+money rate)
Illustration 5:
INFLATION –MAY 2005
A firm has projected the following cash flows from a project under evaluation:
Year
0
1
2
3
Rs. lakhs
(70)
30
40
30
The above cash flows have been made at expected prices after
recognizing inflation. The firm s cost of capital is 10%. The expected
annual rate of inflation is 5%.
Show how the viability of the project is to be evaluated.
Solution:
Cash Flows: The cash flows have recognized inflation. Hence they are in money terms.
Discount Rate: The given discount rate of 10% is assumed to be in real terms. To compute
Money Terms we need to use the following formula
(1+MDR) =
=
(1+RDR) × (1 + IR)
1.10 × 1.05 =1.155
Page | 220
NPV calculations
Year
Money Cash flow
DF @ 15.5%
PV of cash flows
0
(70)
1.000
(70)
2
40
0.749
1
3
30
30
0.866
25.98
0.649
19.47
NPV
29.96
5.41
Decision : Since the NPV is positive the project should be accepted
QUESTIONS FOR PRACTICE
Question-1 If initial cash outflow - 500,000
Year Ended
1
2
3
inflows (Inflation adjusted)
200,000
300,000
350,000
If money discount rate = 11.3% p.a..
Inflation rate = 5% p.a.
(i)
(ii)
Find NPV with given information
Calculate real cash flow, real discount rate & NPV.
Note: Whenever question is silent, we get all cash flows inflation adjusted & use inflation
adjusted discount rate (money term).
Question-2 Initial cash out flow - 800,000 Annual inflow (Real term)
Year Ended
1
2
Inflows
300,000
450,000
Page | 221
3
250,000
Real cost of capital = 5% inflation rate 10% find NPV using money cashflow & money
discount rate.
Question-3 Initial outflow - 800,000 Annual inflows - 280,000 p.a. (Real term) Time - 4
year, money cost of cap - 9% Inflation rate = 3.2% p.a. Calculate NPV at real rate and at
money rate.
 CONCEPT 13
CAPITAL RATIONING
The firm may put a limit to the maximum amount that can be invested during a "given
period of time, such as a year. Such a firm is then said to be resorting to capital rationing. A
firm with capital rationing constraint attempts to select the combination o f investment
projects that will be within the specified limits of investments to be made during a given
period of time and at the same time provide greatest profitability.
Capital rationing may be effected through budget ceiling. A firm may resort to capital
rationing when it follows the policy of financing investment proposals only by ploughing
back its retained earnings. In that case, capital expenditure in a given period cannot exceed
the amount of retained earnings available for reinvestment. Management may also
introduce capital rationing when a department is authorised to make investments upto a
limit beyond which investment decisions will be made by higher level management.
Capital rationing may result in accepting several small investment proposals then
accepting a few large investment proposals so that there may be full utilisation of budget
ceiling. This may result in accepting relatively less profitable investment proposals if full
utilization of budget is a primary consideration. Similarly, capital rationing also means that
the firm foregoes the next most profitable investment falling after the budget ceiling even
though it is estimated to yield a rate of return much higher than the required rate of
return. Thus, capital rationing does not lead optimum results.
ILLUSTRATION-6: CAPITAL RATIONING – INDIVISIBLE PROJECTS – NOV 1998 [1] (B)
S Ltd has Rs.10,00,000 allocated for capital budgeting purposes. The following proposals
and associated profitability indexes have been determined.
Page | 222
Project
Amount Rs.
1
2
3
4
5
6
3,00,000
1,50,000
3,50,000
4,50,000
2,00,000
4,00,000
Profitability
Index
1.22
0.95
1.20
1.18
1.20
1.05
Which of the above investments should be
undertaken? Assume that projects are
indivisible and there is no alternative use of
money allocated for capital budgeting.
Solution:
Step 1: Identify projects with positive NPV
Project
(a)
1
2
3
4
5
6
Outflow
(b)
3,00,000
1,50,000
3,50,000
4,50,000
2,00,000
4,00,000
PI
(c)
1.22
0.95
1.20
1.18
1.20
1.05
Cash inflow
(d) = (b) × (c)
3,66,000
1,42,000
4,20,000
5,31,000
2,40,000
4,20,000
NPV of the
project (d + b)
66,000
(7,500)
70,000
81,000
40,000
20,000
Project 2 has negative NPV and should be dropped
Step 2: Identify that capital rationing exists
a. Demand: Rs 17 lakhs (Exclude Project 2 which has been dropped)
b. Supply: Rs. 10 lakhs
Since supply is less than demand capital rationing exists.
Step 3: Rank projects in the order of PI
Page | 223
Project
PI
Rank
1
1.22
1
3
1.20
2
4
1.18
3
5
1.20
2
6
1.05
4
Step 4: Create basic feasible solutions and compute aggregate NPV
Projects
Outlay
NPV
1
3
5
4
6
Surplus
cash
3,00,000 3,50,000 2,00,000 4,50,000 4,00,000
66,000
70,000
40,000
1



2


3


81,000
NPV
NA
20,000
0
Combination

4
1,50,000 1,76,000

50,000 1,87,000


1,00,000 1,26,000

Nil 1,91,000
It is assumed that NPV of surplus Cash is zero.
Combination 4 having projects 3, 4, 5 with NPV of Rs.1,91,000 and no surplus cash should
be undertaken.
IIUSTRATION 7:
CAPITAL RATIONING – DIVISIBLE PROJECTS – NOV 1998 [1] (B
Project
A
B
C
D
E
F
Initial outlay
50
80
60
30
25
40
Annual receipts to
perpetuity
15
20
18
10
8
10
C Ltd. is experiencing a shortage of funds for investment in the current year, when only Rs.
100,000 is available for investment. No shortages are foreseen thereafter. The cost of
investment funds is 20%. The following projects are available.
Page | 224
Advise management which projects to accept.
Solution:Step 1: Computation of NPV (Capitalize annuity at 20%) (Rs. thousands)
A
B
C
D
E
F
Perpetual inflow
15
20
18
10
8
10
Present value
75 100
90
50
40
50
Outlay
50
80
60
30
25
40
NPV
25
20
30
20
15
10
All the six are acceptable projects since they have positive NPV.
Step 2: Identify if capital rationing exists
(a) Money required
= 285 (Sum of outflows of all projects)
(b) Money available
= 100
(c) Since money available is less than money required, money is in short supply.
Step 3: Rank in the order of NPV/Outlay (Rs. thousand)
A
B
C
D
E
F
a)
NPV
25
20
30
20
15
10
b)
Outlay
50
80
60
30
25
40
c)
Index 0.5 0.25 0.50 0.67 0.60 0.25
d)
Rank
III
IV
III
I
II
IV
Step 4: A lot money to project in the order of rank and compute NPV (Rs. thousands)
Project
Available
Allotted
Money
Remaining
NPV
100
Page | 225
Money
D
30
70
20
E
25
45
15
0.9A
45
Nil
22.5
Step 5: Computing aggregate NPV
Aggregate NPV for projects D, E and A is Rs.57,500. Projects D, E and A should b e
accepted.
 CONCEPT 14
RISK ANALYSIS IN CAPITAL BUDGETING
A: RISK AND UNCERTAINTY
A decision to take up or leave out a project depends on expectations of future cash flows
from the project. Such expectations are based on information that is currently available.
The 'future' by definition, is uncertain. Therefore, cash flows when they occur are likely to
differ from what were expected. This uncertainty about a project's future cash flows gives
rise to risk. But risk is not the same as uncertainty!
Meaning of Risk
Risk is a situation where
•
•
•
•
Several outcomes (a k a range of outcomes), are possible
Within this range, any one outcome can occur
Each possible outcome has a known probability
Such probabilities are assessed by reference to past information about
relative frequencies of outcome
‘Risk' therefore refers to "the possibility that the actual outcome will differ from expected
outcome".
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Meaning of Uncertainty
Uncertainty is a situation where
•
•
•
the range of outcomes is unknown
the probability of outcomes is unknown
or, both are unknown
Let us explain with an example. You come out of an examination hall saying, "There is a
60% chance that I will get 80 marks and a 40% chance that I will score 50 marks." Your
friend, Anne comes out of the hall saying, “God only knows how I have done.” Yours is a case
of risk. Anne’s is a case of uncertainty.
 CONCEPT 15
STANDARED DEVIATION
Meaning of Standard Deviation
Project cash flows are forecasts. A forecast cannot be accurate and there can be a margin of
error. The risk associated with a project can be expressed, as the extent to which the actual
value of outcome will differ from the expected value. This risk is measured with the help of
a statistical tool known as Standard Deviation.
By definition, Standard Deviation is a standardized unit of deviation from mean. This
measure is denoted by the symbol . The square of Standard Deviation (2) is known as
variance of distribution. Higher the Standard Deviation, higher is the risk associated with a
project.
Method of computing Standard Deviation
There are three steps involved in this computation.
Step 1: Compute expected value.
Step 2: Compute deviation from expected value.
Page | 227
n
Step 3: Apply formula,  
 Pi d where ‘P’ is probability of occurrence ‘d’ is deviation
i 1
2
i
from mean, ‘n’ is number of observations.
For Example
Consider the data given in the following table. The information covers probability
distribution of five possible outcomes of a project. Compute standard deviation.
Obsvn
Likely
outcome
Probability
(Amt/Rs.)
1
25,000
0.15
3
74,000
030
2
4
5
Solution:
36,000
0.20
92,000
0.20
1,00,000
Step 1:
0.15
Step 2:
Step 3:
Obs Likely
Probability Expected Deviation
Outcome
value
=d
(Rs.)
(Rs.)
Probability
× d2
1
25,000
0.15
258,960,375
4
92,000
0.2
2
3
5
36,000
74,000
1,00,000
0.2
3,750
-41,550
18,400
25,450
7,200
-30,550
15,000
33,450
0.3
22,200
Total
66,550
0.15
186,660,500
7,450
16,650,750
Total
129,540,500
167,835,375
759,647,500
Page | 228
Step 3: Apply formula,  
n
Pi d  759,647,500  27,562
i 1
2
i
 CONCEPT 16
STANDARD DEVIATION  : A UNIT OF MEASURE
Standard Deviation is a measure of risk. It is expressed in the same units as the range of
probable outcomes is expressed. That is, if you are applying the  to evaluating % returns in
a security,  is expressed in % age terms. If it computed for outputs in tonnes,  is
expressed in tonnes, etc.
 CONCEPT 17
STANDARD DEVIATION  : WHAT IT MEANS
Probabilities of different outcomes in a project may be normally distributed or it may be
skewed consider the following two cases.
Probability Set Probability Set
I
II
0.15
0.03
0.30
0.40
0.20
0.20
0.15
1.00
0.27
If ER is 15% and SD is 2% this means
that there is 95% probability that actual
will be within 2 times SD i.e., it will
range between 11% and 19%
0.18
0.12
1.00
The first set is known as normal probability distribution, in as much as the distribution on
either side of mid-point (0.30) is even. In the second set the probability distribution is said
to be skewed.
Statistics tells us that when the density
function of probabilities which are
normally distributed, is presented
graphically, it will look like in a bellshaped curve. The expected or
estimated NPV of a project, which is the
Page | 229
mean value, will occupy the central point. The normal distribution curve will appear as:
In this normal distribution, roughly 68% of probability distribution falls within one unit of
standardised deviation and 95% falls within two units of deviation. An analysis of this
nature helps us assess the probability of actual returns being greater or less than a given
level of outcome. We shall see more about this in a later part of this Chapter.
 CONCEPT 18
STANDARD DEVIATION  - DECISION
Now that we know how Expected Value (a k a return) and how Standard Deviation (a k a
Risk) are computed, we must learn how to put them to use in decision-making. The
following decision rules will be helpful.



Between two projects, which have the same return, the one with the lower risk will
be preferred.
Between two projects, which have the same risk, the one with the higher return will
be preferred.
Between two projects, which have different levels of risk and return, the choice
would depend on the risk preferences of the investor.
The aggressive investor will prefer the one, which gives higher return, whereas the
conservative investor will prefer the one, which involves lower risk. [You will read more
about this in the chapter on Capital Asset Pricing Model]
 CONCEPT 19
WHAT STANDARD DEVIATION DOES NOT MEAN
Project NPVs are derived using the best-suited discount rate for a given level of risk. The
discount rate reflects the investor's assessment of risk-return trade off.
Standard deviation is merely a unit of measure with which we can assess the extent to
which the possible outcomes can deviate from the expected mean value of outcome. It is
true that higher the standard deviation of possible outcomes in a project, higher is the risk
associated with a project. Nevertheless, this criterion does not lead us to conclude that
greater is the standard deviation, greater should necessarily be the discount rate used for
Page | 230
evaluating the project, or that the investor should realign his perception of risk-return
trade off in that project.
Let us consider two projects each with a mean NPV of Rs. 10 lacs. The standard deviation of
possible NPVs in the first project is Rs. 8 lacs, while that in the second is Rs.9 lacs. It does
not follow that the investor should evaluate the second project once again with a higher
discount rate. The rationale lies in the fact that the NPV of Rs.10 lacs in these two projects
stands derived using a discount rate that takes care of risk-return trade off.
ILLUSTRATION 8
A Company is evaluating two projects. The probability distribution as also the likely NPVs
for each of these projects is furnished below.
Determine:
PROJECT A
NPV
Probability
4,000
0.2
8,000
0.3
11,000
0.3
14,250
0.2
PROJECT B
NPV
4,000
8,000
11,000
14,000
Probability
0.15
0.35
0.35
0.15
Expected NPV of the two projects.
(i)
(ii)
(iii)
Solution:
Risk attached to each of these projects.
Which project would you prefer and why?
Compute Expected NPV
PROJECT A
4,000
0.2
14,250
0.2
8,000
800
0.3
2,400
Expected NPV
9,350
11,000
0.3
3,300
2,850
PROJECT B
4,000
0.15
14,000
0.15
8,000
600
0.35
2,800
Expected NPV
9,350
11,000
0.35
3,850
2,100
Page | 231
Risk : Compute Standard Deviation
Risk in project B, measured in terms of  is 3,021.
Conclusion:
(i)
(ii)
(iii)
NPV in both the projects is Rs. 9,350.
Risk in Project A is Rs. 3,448; while that in Project B is Rs. 3,021.
Project A is riskier than Project B because it has a higher Standard deviation.
Page | 232
Decision: The expected NPV of both the projects is identical. However Project B has a lower
risk. Hence project B will be selected.
ILLUSTRATION 9:
PROBABILITY
Ajay and Sanjay Ltd., propose installing a new machine at a cost of Rs.400,000. Concerned
about X the uncertainty about the life of machine, enquiries were made with other units in
the same line of business, which revealed that:
(a) The total number of machines operating in all these units is 375
(b) The lives as also the NPV of machines varied from place to place
A summary of results is given below
Machine life in Corresponding Number
years
3
4
5
6
7
of machines
30
75
150
105
15
Total : 375
NPV of these
machines (Rs.)
(1,15,500)
(49,500)
43,500
1,29,000
2,05,500
Advise whether the company should acquire the machine
Solution :
Step 1 : Based on the number of machines and their lives, the probability of life is as under:
Life
3
4
5
6
7
Machine
30
75
150
105
15
Calculation
30/375
75/375
150/375
105/375
15/375
Probability
0.08
0.20
0.40
0.28
0.04
Page | 233
Step 2 : Statement showing the predicted NPV of machines
Machine Life
3
4
5
6
7
NPV (Rs.)
(1,51,500)
(49,500)
43,500
1,29,000
2,05,500
ILLUSTRATION 10:
Probability
0.08
0.20
0.40
0.28
0.04
Expected NPV (Rs.)
(12,120)
(9,900)
17,400
36,120
8,220
Predicted
NPV
39,720
PROBABILITY
Based on the data given below, estimate the NPV of the projects and recommend one for
adoption, based on your assessment of the risk involved.
Project A
Project B
NPV (Rs.)
Probability NPV (Rs.)
Probability
3,000
0.05
3,000
0.15
6,000
0.30
6,000
-12,000
0.25
16,000
0.10
5,000
12,000
Solution:
15,000
0.30
0.30
0.05
5,000
0.25
0.25
NPV of the projects, and risk involved measured in terms of Standard Deviation of the
projects are furnished in the following Table.
Page | 234
Since expected NPV of both project is same, so we should select project A with lower
standard deviation.
ILLUSTRATION 11:
PROBABILITY AND EXPECTED VALUE – MAY 1999 [1] (A)
A company is considering two mutually exclusive projects X and Y. Project X costs Rs.
30,000 and Project Y Rs. 36,000. You have been given below the net present value
probability distribution for, each project.
Project X
NPV (Rs.)
3,000
6,000
12,000
15,000
Project Y
Probability NPV Estimate(Rs.)
0.1
3,000
0.4
6,000
0.4
12,000
0.1
15,000
Probability
0.2
0.3
0.3
0.2
(a) Compute the expected net present value of projects X and Y.
Page | 235
(b) Compute the risk attached to each project i.e. Standard Deviation of each probability
distribution.
(c) Which project do you consider more risky and why?
(d) Compute the probability index of each project.
Solution :
Project X
NPV
3,000
6,000
12,000
15,000
Probability
0.1
0.4
0.4
0.1
NPV × P
300
2,400
4,800
1,500
9,000
d
6,000
3,000
(3,000)
(6,000)
Pd2
36,00,000
36,00,000
36,00,000
36,00,000
1,44,00,000
Project Y
NPV
3,000
6,000
12,000
15,000
Probability
0.2
0.3
0.3
0.2
NPV × P
600
1,800
3,600
3,000
9,000
d
6,000
3,000
(3,000)
(6,000)
Pd2
72,00,000
27,00,000
27,00,000
72,00,000
1,98,00,000
a. Expected NPV of Projects X and Y is Rs. 9,000
b. Risk attached at each project
Project X :
Project Y :
 pd
2
 pd = √144,00,000 = Rs. 3795
2
 pd
2
= √ 1,98,00,000 = Rs. 4450
c. since standard deviation of project Y is more so project Y is more riskier
d. Profitability Index of each project
Profitability Index =
Discounted Cash inf low
Discounted Cash outflow
Page | 236
Project X :
9.000  30,000
 1.30
30,000
Project Y :
9,000  36000
 1.25
36,000
ILLUSTRATION 12
PROBABILITY AND EXPECTED VALUE –MAY 2003[1](C)
A company is considering Projects X and Y with following information:
Project
Expected NPV Rs.
Standard Deviation
X
1,22,000
90,000
Y
2,25,000
1,20,000
(a) Which project will you recommend based on the above data?
(b) Explain whether your opinion will change, if you use coefficient of variation as a
measure of risk.
(c) Which measure is more appropriate in this situation and why.
Solution:
(i)
Based on the standard deviation project X can be chosen because it is less risky than
project Y.
(ii)
Coefficient of Variation =
CoVx =
S tandard deviation
Expected Net Pr esent Value
90,000
 0.738
122,000
CoVy =
120,000
 0.533
225,000
Coefficient of variation as a measure of risk indicated, project X to be more risky
than project Y.
Therefore Project Y can be selected.
(iii)
Since expected NPV is not same, hence coefficient of variation is more appropriate
Page | 237
ILLUSTRATION 13
RISK ADJUSTED DISCOUNT RATE –MAY 1999[1](B) & 2005
Determine the risk adjusted net present value of the following projects.
Net cash outlays (Rs.)
A
B
C
5 years
5 years
5 years
1,00,000
Project Life
Annual Cash inflow (Rs.)
Coefficient of variation
30,000
0.4
1,20,000
2,10,000
42,000
70,000
0.8
1.2
The company selects the risk adjusted rate of discount on the basis of the coefficient of
variation.
Coefficient of Variation
0.0
0.4
0.8
1.2
1.6
2.0
More than 2.0
Risk adjusted rate of
discount
Solution :
10%
12%
14%
16%
18%
22%
25%
Present value factor 1 to 5
at risk adjusted rate of
discount
3.791
3.605
3.433
3.274
3.127
2.864
2.689
Determine of discount factor and the present value
(i)
(ii)
(iii)
Particular
A
B
C
Coefficient of variation
0.4
0.8
1.2
Relevant risk adjusted rate of discount
Present value annuity for 5 years
12%
3.605
14%
3.433
16%
3.274
Computation of risk adjusted Net present value
Page | 238
Particular
(a)
(b)
(c)
A
Net cash outlays
B
C
1,00,000 1,20,000 2,10,000
Annual cash inflows
(d)
Present value annuity factor for 5
years (as per the above table)
(e)
Risk adjusted factor NPV (d-a)
Discounted cash inflows
30,000
42,000
3.605
3.433
70,000
3.274
1,08,150 1,44,186 2,29,180
8,150
24,186
19,180
ILLUSTRATION 14
RISK ADJUSTED DISCOUNT RATE
Fast Track Co. Ltd. is undertaking a project at a cost of Rs. 1,14,000. Estimated net cash flow
after tax, during the life of the project is as under:
Rs.
Year1
Year 2
Year 3
Year 4
Year 5
25,000
28,000
31,000
33,000
34,000
RADR = 16% can the company go ahead?
Solution :
Step 1: Compute expected cash flows. (Given)
Step 2: Compute RADR = 16%
Step 3: Compute NPV.
Year
0
1
2
3
4
5
Cash flow (Rs.)
(1,14,000)
25,000
28,000
31,000
33,000
34,000
DF (a)
16%
1.000
0.862
0.743
0.641
0.552
0.476
NPV
PV/ Rs.
(1,14,000)
21,550
20,804
19,871
18,216
16,184
(17,375)
NPV, of the project is negative. Hence, the project should be rejected.
Page | 239
ILLUSTRATION 15
CERTAINTY EQUIVALENT FACTOR – NOV 1999[1](B)
The Globe manufacturing Co. Ltd., is considering an investment in one of the two mutually
exclusive proposals, project X and project Y, which require cash outlays o/Rs. 3,40,000 and
Rs. 3,30.000 respectively. The CE approach is used in incorporating risks in capital
budgeting decisions. Risk free rate is 8%, and risk-adjusted rate is 10%. The expected net
cash flows and their certainty equivalents are as follows:
Amount / Rs.
Project X
Year end
Cash flow (Rs.) CE
Cash flow (Rs.) CE
1
1,80,000
0.8
1,80,000
0.9
3
2,00,000
0.5
2,00,000
0.7
2
Required:
Project Y
2,00,000
0.7
1,80,000
0.8
(i) Which project should be accepted under CE approach?
(ii) For which of the two projects, would you use higher RADR & why
Solution: Part (i)
Step 1: Ascertain the discount rate,
When CE approach is adopted, risk-free rate (i.e., 8% in this case) is relevant.
Step 2: Compute NPV of the project X
Year
0
1
2
3
Cash flow
(Rs.)
(3,40,000)
1,80,000
2,00,000
2,00,000
Certainty
factor
1.0
0.8
0.7
0.5
Certain cash
flows (Rs.)
(3,40,000)
1,44,000
1,40,000
1,00,000
DF @
(8%)
1.000
0.926
0.857
0.794
PV of Cash
flows (Rs.)
(3,40,000)
1,33,344
1,19,980
79,400
NPV (7,276)
Page | 240
Year
0
1
2
3
Cash flow (Rs.)
Certainty factor
(3,30,000)
1,80,000
1,80,000
2,00,000
1.0
0.9
0.8
0.7
Certain DF @ (8%)
cash flow
(Rs.)
(3,30,000)
1,62,000
1,44,000
1,40,000
1.000
0.926
0.857
0.794
PV of cash
flows (Rs.)
(3,30,000)
1,50,012
1,23,408
1,11,160
NPV 54,580
Statement showing NPV of Project Y
Step 3: Decision
Since the NPV of Project X is negative it should be rejected. Since the NPV of project Y is
positive, it should be accepted.
Part (ii): Project for which RADR will be applied
Since the CE coefficient is lower in project X, it is deemed to be riskier than project Y. Project X
should, therefore, be evaluated by using RADR of 10%.
ILLUSTRATION 16
CERTAINTY EQUIVALENT FACTOR – NOV 2003
The Textile Manufacturing Company Ltd., is considering one of two mutually exclusive
proposals, Projects M and N, which require cash outlays ofRs. 8,50,000 and Rs. 8,25,000
respectively. The certaintv-equivalent (C. E) approach is used in incorporating risk in
capital budgeting decisions. The current yield on government bonds is 6% and this is used
as the risk free rate. The expected net cash flows and their certaintv equivalents are as
follows:
Project M
Project N
Year-end
Cash Flow Rs.
C.E.
Cash Flow Rs.
C.E.
1
4,50,000
0.8
4,50,000
0.9
2
5,00,000
0.7
4,50,000
0.8
Page | 241
3
5,00,000
0.5
5,00,000
0.7
Present value factors of Re. 1 discounted at 6% at the end of year I, 2 and 3 are 0.943, 0.890
and 0.840 respectively.
Required:
Which project should be accepted?
(i)
(ii) If risk adjusted discount rate method is used, which project would be appraised with
a higher rate and why?
Solution:
Net Present Value of Project M
Year end
0
1
2
3
Cash Flow
(Rs.)
(a)
(8,50,000)
4,50,000
5,00,000
5,00,000
C.E.
(b)
Adjusted Cash
Flow (Rs.)
(c) = (a) × (b)
Present value
factor at 6%
(d)
8,50,000
3,60,000
1.000
0.943
1.0
0.8
0.7
0.5
3,50,000
2,50,000
0.890
0.840
NPV
NPV (Rs.)
(e) = (c) ×
(d)
(8,50,000)
3,39,480
3,11,500
2,10,000
10,980
Net Present Value of Project N
Year
end
0
1
2
3
Cash Flow
(Rs.)
C.E.
(a)
(b)
(8,25,000)
4,50,000
4,50,000
5,00,000
1.0
0.9
0.8
0.7
Adjusted Cash
Flow (Rs.)
Present value
factor
(c) = (a) × (b)
(d)
(8,25,000)
4,05,000
3,60,000
3,50,000
NPV
(Rs.)
(e) = (c) ×
(d)
1.000
0.943
0.890
0.840
NPV
(8,25 ,000)
3,81,915
3,20,400
2,94,000
1,71,315
Page | 242
Decision: Since the net present value of Project N is higher, so the project N should be
accepted.
ILLUSTRATION 17
JOINT PROBABILITY
Albatross Ltd., are purchasing a machine at a cost of Rs.3,000. Life is two years. The CFAT
for two years is as follows:
Year 1
Cash Flow (Rs.) Initial
Probability
1,500
0.4
2,500
(i)
0.6
Year 2
Cash flow (Rs.) Conditional
Probability
2,200
0.5
1,800
0.5
1,800
0.7
2,000
0.3
What are the various joint probabilities of occurrences of various branches?
(ii) If the risk free rate is 12%, what are the mean and Standard deviation of the
probability distribution of possible NPVs?
Solution:
Step 1: There are four branches. There will be four joint probabilities.
Probability Probability Joint Probability
Year 1
Year 1
Year 1 × Year 2
0.40
0.50
0.20
0.40
0.50
0.20
0.60
0.70
0.42
0.60
0.30
0.18
Step 2: Computation of present values of cash flows (Rs.)
Year 1
CF (Rs.)
Discount PV (Rs.)
Fact @
12%
Year 2
CF
(Rs.)
Discount PV (Rs.)
Factor @
12%
Total PV
(Rs.)
Page | 243
1,500
0.893
1,339.50
2,200
0.797
1,753.40
3,092.90
2,500
0.893
2,232.50
1,800
0.797
1,434.60
3,667.10
1,500
2,500
0.893
0.893
1,339.50
1,800
2,232.50
0.797
2,000
7,144.00
0.797
1,434.60
1,594.00
6,216.60
2,774.10
3,826.50
13,360.60
Computing mean NPV of the project
Total PV
(Rs.)
Jt. Prob
Product
3092.90
0.20
618.58
3667.10
0.42
1540.18
2774.10
3826.50
13360.60
0.20
554.82
0.18
688.77
3402.35
Less : Cost (3000.00)
NPV
402.35
Step 3: Computing standard deviation of probability distribution of possible NPVs.
Total PV
(Rs.)
Cost (Rs.)
NPV (X)
(Rs.)
d  (X – X )
3,092.90
3,000
-309.45
-225.90
-628.25
3,667.10
3,000
92.90
3,000
3,000
667.10
826.50
264.75
2,774.10
3,826.50
402.35
424.15
d2
J.P
Prod
9,5759.30
0.20
19,151.9
70,092.6
0.42
29,438.9
3,94,698.1
1,79,903
0.20
0.18
2

78,939.6
32,382.6
15,9913.0
399.891
Page | 244
Conclusion: Mean NPV is Rs.402.35. Project has a positive NPV. Project can be accepted.
The standard deviation of probability distribution of possible NPVs is Rs.399.891, or say
Rs.400.00.
 CONCEPT 20
SENSITIVITY ANALYS I S
The five important determinants of NPV, besides some others, are:
(i)
selling price
(ii)
sales quantity
(iii)
cash cost
(iv)
cost of capital, and
(v)
amount of investment.
Sensitivity analysis is a tool to measure the risk surrounding a capital expenditure
project. The analysis measures how responsive/ sensitive the project's NPV is to
change in the variables that determine NPV .
This analysis is carried on the projects reporting positive Net Present Values. It
requires the calculation of % change in value of each determinant of the NPV that may
reduce the NPV to zero. These percentages are put in an ascending order. The item
corresponding to minimum change is considered to be most sensitive/ risky. The
concept of the sensitivity suggests that management should pay maxim um attention to
this item as small adverse change in this item may result in big unfavourable results.
Sensitivity analysis therefore provides an indication of why a project might fail.
Critics of this concept opine that the management should not pay maximum
attention towards most sensitive item; rather they should pay maximum attention
towards the item where there is highest probability of adverse change.
ILLUSTRATION- 18
Vanshu Ltd. is considering a project, the details are as follows. Cost of project: Rs. 2,
00,000. Life of the project years. Scrap value is expected to be Rs. 5000. Annual
expected sale 1000 units @ Rs. 300. Unit variable costs. 200. Cost of capital 16%.
Page | 245
Ignore tax. Perform sensitivity Analysis.
ANSWER
(i) Cost of project: Let cost of project = X
- X + 1,00,000 (2.246) + 5,000 (0.641) = 0
X = 2,27,805
% sensitivity: (27805/ 2,00,000) X 100 = 13.90%
(ii) Sales volume :
Let sales volume = X
-2,00,000 + 100X(2.246) + 5000 (0,641) = 0
X= 876
% Sensitivity = (124 / 1000) X 100 = 12.40%
(iii)
Unit cost
Let unit cost = x
-2,00,000 + (300 -x)( l 000)(2.246) + 5000(0.641 )
x= 212.38
% sensitivity = (12.38 / 200) X 100 = 6.1996
(iv)
Selling price
Let selling price = x
- 2,00,000 + 1,000(x-200)(2.246) + 5,000(0.641) = 0
X = 287.62
% Sensitivity = (12.38 / 300) X 100 = 4.1296
(v) Discounting rate :
Average cash flow = (1,00,000 + 1,00,000 + 1,05,000)/ 3 = 1,01,667
Fake payback period
=2,00,000/1,01,667 =
1.97
Page | 246
Approximate IRR = 2496
NPV at 2496 = -2,00,000 + 1,00,000 X 1.981 + 5,000 X 0.524 = +720
NPV at 2596 = -2,00,000 + 1 ,00,000 X 1.952 + 5,000 X 0.512 = -2,240
𝐼𝑅𝑅 = 24 +
720
× 1 = 24.24%
720 − (−2240)
% Sensitivity = (8.24/ 16) X 100 = 51.50 96
ILLUSTRATION 19
SENSITIVITY ANALYSIS –MAY 2007
Type I
XYZ Ltd is considering a project for which the following estimates are avaibale
Initial Cost
Sales price
Cost
No. of units
Life
Discount rate
(i)
(ii)
(iii)
ANSWER.
Rs 10,00,000
Rs 60 P.U.
Rs 40 P.U.
50000 Per Year
3 Years
10%
Find out sensitivity analysis of initial outflow if initial outflow is increased upto
Rs 20 lakh
Find out sensitivity analysis of Discount rate if discount rate is increased to 15%
Find out sensitivity Analysis of life of project if life is reduced to 2 years.
OPTION I
NPV) Present  CFAT (𝑃𝑉𝐴𝐹) 𝑛=3 - Initial cost
𝑟=15%
 20 x 50000 (2.486) – 10 Lakh
 14,86000
NPV) When initial out flow = 20 Lakh
 20 x 50000 (2.486) – 20 Lakh
 486000
Page | 247
SENSITIVITY
OPTION II
1486000 − 486000
× 100 = 67.29%
1486000
NPV when discount rate increased to 15%
CFAT (𝑃𝑉𝐴𝐹) 𝑛=3 - initial outflow
𝑟 =15%
SENSITIVITY
OPTION III
 20 x 50000 (2.283) – 10 Lakh
 1283000
1486000 − 1283000
× 100 = 13.66%
1486000
NPV when project life is reduced to 2 year
CFAT (𝑃𝑉𝐴𝐹) 𝑛=3 - initial outflow
𝑟 =10%
SENSITIVITY
Type II
 20 x 50000 (1.735) – 10 Lakh
 735000
1486000 − 735000
× 100 = 50.53%
1486000
ILLUSTRATION- 20
ABC Ltd is considering a project for which the following estimates are available
Initial Cost
Sales price
Cost
No. of units
Rs 15 lakh
Rs 50 P.U.
Rs 20 P.U.
10000
Page | 248
Life
Discount rate
10 Years
10%
Find out sensitivity analysis for
Initial outflow
(i)
Discount rate
(ii)
(iii)
ANSWER
Life
NPV using Existing information
CFAT (𝑃𝑉𝐴𝐹) 𝑛=3 - initial outflow
𝑟 =10%
 30 x 10000 (6.144) – 15 Lakh
 343200
Case I : for sensitivity analysis of initial outflow let initial outflow be x
NPV = o
30 x 10000 (6.144) - x = o
x = 18,43,200
343200
Sensitivity in initial outflow = (15 𝐿𝑎𝑘ℎ × 100) = 22.88%
 If initial outflow increase by 22.88% NPV = o
Case II For sensitivity analysis of discount rate we will calculate IRR.
Trail & error method.
NPV ) r = 10 % = 343200.
NPV ) r = 15 % = 30 x 10000(𝑃𝑉𝐴𝐹) 𝑛=3
𝑟 =10%
- 15 Lakh
= 3 Lakh x 5.018 – 15 Lakh
= 5400.
Page | 249
NPV ) r = 15 % = 30 x 10000(𝑃𝑉𝐴𝐹) 𝑛=3
𝑟 =10%
- 15 Lakh
= 3 Lakh x 5.018 – 15 Lakh
= 5400.
NPV ) r = 16 % = 30 x 10000(𝑃𝑉𝐴𝐹) 𝑛=3
𝑟=10%
- 15 Lakh
= 3 Lakh x 4.833 – 15 Lakh
= - 50100
= 15.097%
𝐼𝑅𝑅 = 15% + (
5.097
1%
) × 5400
55,500
Sensitivity Analysis for discount rate = 10 × 100
= 50.97%
Case III – If Discount rate increase by 50.97% NPV =o
Life
For sensitivity analysis of life we will calculate discounted payback period.
Cash flow
Disc. Rate 10%
PV
Cum. PV
1.
3 Lakh
.909
272700
272700
3.
3 Lakh
.751
225300
745800
2.
4.
5.
6.
7.
8.
9.
10
3 Lakh
3 Lakh
3 Lakh
3 Lakh
3 Lakh
3 Lakh
3 Lakh
3 Lakh
.826
.683
.621
.564
.513
.466
.424
.385
247800
204900
186300
169200
153900
139800
127200
115500
520500
950700
1137000
1306200
1460100
1599900
1727100
1842600
Page | 250
= 7.285 year
𝑝𝑎𝑦𝑏𝑎𝑐𝑘 = 7 𝑦𝑒𝑎𝑟 + (
𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑎𝑛𝑎𝑙𝑦𝑠𝑖𝑠 = (
1 𝑌𝑒𝑎𝑟
× 39900)
139800
2.71
× 100) = 27.1%
10 𝑦𝑒𝑎𝑟
 If Life reduce by 27.1% then NPV will reduce to zero
 CONCEPT 21
SIMULATION / HERTZ MODEL
Simulation is a mathematical technique which is used to predict the expected
outcome when several outcomes are possible.
The technique is based on random number. (A set of numbers is said to be random
number when the probability of its selection is equal to the probability of selection of
any other number i.e .the set of number is said to be random when the probability of
selection of all members is equal).
For business applications, Monte Carlo simulation is which is based on probabilities.
Hertz used it for evaluation of risky investment decisions by calculating average of
various possible returns. (Hertz's capital budgeting model). Hertz suggested that
simulation can be used to estimate return on capital employed on a proposed project
facing various uncertainties.
There are three steps in his model (i) Estimate various possible factors affecting the
return on CE, also estimate the in probabilities (ii) Calculate ROCE on the basis of
various factors using random numbers. Taking the help of computer this trial may be
repeated a number of times. (iii)The average return obtained for all these trials is
considered as possible ROCE under his mode.
ILLUSTRATION 21
Frontier Bakery keeps stock of a particular brand of cake. Daily demand based on
past experience is as given below
Page | 251
Experience indicates:
Daily
0
Probability 0.01
15
25
35
45
50
0.15
0.20
0.50
0.12
.02
Consider the sequence of random number:
48, 78, 09, 51, 56, 77, 15, 14, 68, 09
Using the sequence, simulate the demand for the next 10 days.
ANSWER.
Daily
demand
Probability
Cum.
Probability
Cumulative
probability
range
Random no.
adjusted
cumulative
probability
range
0
0.01
0.01
0-0.01
0-0
15
25
0.15
0.20
0.16
0.36
0.01-0.16
0.16-0.36
35
0.50
0.86
0.36-0.86
45
50
0.12
0.02
0.98
1.00
0.86-0.98
0.98-1.00
0.01 -0.1 5
0.16-0.35
I
0.3.6-0.85
0/
86-0.97
0.98-0.99
Simulation of demand for next 10 days
1
2
3
4
5
Demand
35
35
15
35
35
Page | 252
6
7
8
9
10
A
35
15
15
15
35
15
/
ILLUSTRATION 22
A company manufactures around 200 mopeds. Depending upon the availab1hty of raw
materials and other conditions, the daily production has been varying from 196 mopeds to
204 mopeds, whose probability distribution is as given below
Production per
Probability
196
1 97
198
199
200
201
202
203
204
0.05
0.09
0.12
0.14
0.20
0.15
0.11
0.08
0.06
The finished mopeds are transported in a specially designed three storey lorry that can
accommodate only 200 mopeds. Using the following 15 random numbers 82, 89, 78, 24, 53,
61, 12, 45, 04, 23, 50, 77, 27, 54, 10, simulate the process to find out: what will be average
number of mopeds waiting in the factory?
ANSWER.
Production
per day
196
Probability
0.05
Cum.
Probabilit
y
Cumulative
probability
range
0.05
0-0.05
Random
no.
adjusted
cumulative
0 - 0.04
Page | 253
197
0.09
0.14
0.05-0.1 4
0.05-0.13
198
0.12
0.26
0.14-0.26
0.14-0.25
199
0.14
0.40
0.26-0.40
0.26-0.39
200
0.20
0.60
0.40-0.60
0.40-0.59
201
0.15
0.75
0.60-0.75
0.60-0.74
202
0.11
0.86
0.75-0.86
0.75-0.85
203
0.08
0.94
0.86-0.94
0.86-0.93
204
0.06
1.00
0.94-1.00
0.94- 0.99
Day
Production
Dispatch
Stock
1
202
200
2
2
203
200
5
3
202
200
7
4
198
200
5
5
200
200
5
6
201
200
6
7
197
200
3
8
200
200
3
9
196
199
0
10
198
198
0
11
200
200
0
12
202
200
2
13
199
200
1
14
200
200
1
15
197
198
0
Total
40
Page | 254
Average No. of moped waiting for transportation: 2.67
MULTIPLE CHOICE QUESTIONS
BASIC
1. Capital Budgeting is a part of:
a) Investment Decision
b) Working Capital Management
c) Marketing Management
d) Capital Structure.
2. Capital Budgeting deals with
a) Long-term Decisions
b) Short-term Decisions
c) Both (a) and (b)
d) Neither (a) nor (b).
3. Capital Budgeting Decisions are:
a) Reversible
b) Irreversible
c) Unimportant
d) All of the above
4. Which of the following is not a relevant cost in Capital Budgeting?
a) Sunk Cost
b) Opportunity Cost
c) Allocated Overheads
d) Both (a) and (c) above.
5. Capital Budgeting Decisions are based on:
a) Incremental Profit
Page | 255
b) Incremental Cash Flows
c) Incremental Assets
d) Incremental Capital.
6. Cash Inflows from a project include:
a) Tax Shield of Depreciation
b) After-tax Operating Profits
c) Raising of Funds
d) Both (a) and (b).
7. Depreciation is incorporated in cash flows because it:
a) Is unavoidable cost
b) Is a cash flow
c) Reduces Tax liability
d) Involves an outflow.
8. Which of the following is not true for capital budgeting?
a) Sunk costs are ignored
b) Opportunity costs are excluded,
c) Incremental cash flows are considered
d) Relevant cash flows are considered.
9. A proposal is not a Capital Budgeting proposal if it:
a) is related to Fixed Assets
b) brings long-term benefits
c) brings short-term benefits only
d) Has very large investment.
10. Savings in respect of a cost is treated in capital budgeting as:
a) An Inflow
b) An Outflow
c) Nil
d) None of the above.
11. In cash flow estimation, depreciation is considered as
a) cash charge
b) noncash charge
c) cash flow discounts
d) net salvage discount
Page | 256
12. Situation in which company replaces existing assets with new assets is classified as
a) replacement projects
b) new projects
c) existing projects
d) internal projects
13. Capital budgeting is the process a) which help to make master budget of the organization.
b) By which the firm decides how much capital to invest in business
c) by which the firm decides which long-term investments to make.
d) undertaken to analyze how make available various finance to the business.
14. ................................is a project whose cash flows are not affected by the accept/reject
decision for other projects.
a) Mutually exclusive project
b) Independent project
c) Low cost project
d) Risk free project
15. A project whose acceptance precludes the acceptance of one or more alternative
projects is referred to as ..................
a) Mutually exclusive project
b) Independent project
c) Dependent project
d) Contingent project
16. A project whose acceptance does not prevent or require the acceptance of one or more
alternative projects is referred to as ..................
a) Mutually exclusive project
b) Independent project
c) Dependent project
d) Contingent project
17. If we add depreciation and other non-cash expenses in profit after tax, the resulting
figure is a) Profit available for equity shareholder
b) CFAT
c) Net cash flow
Page | 257
d) Free cash flow
18. The term mutually exclusive investments mean:
a) Choose only the best investments
b) Selection of one investment precludes the selection of an alternative
c) The elite investment opportunities will get chosen.
d) There are no investment options available.
19. Which of the following statements is true about mutually exclusive projects?
a) They are not in direct competition with each other.
b) They are in direct competition with each other.
c) They are not evaluated based on shareholder wealth.
d) They are never evaluated.
20. A proposal is not a capital budgeting proposal if it:
a) is related to Fixed Assets
b) brings long-term benefits
c) brings short-term benefits only
d) has very large investment
Net present value
21. A project whose cash flows are more than capital invested for rate of return then net
present value will be
a) positive
b) independent
c) negative
d) zero
22. In mutually exclusive projects, project which is selected for comparison with others
must have
a) higher net present value
b) lower net present value
c) zero net present value
d) all of above
23. In capital budgeting, positive net present value results in
a) negative economic value added
b) positive economic value added
Page | 258
c) zero economic value added
d) percent economic value added
24. In capital budgeting, a negative net present value results in
a) zero economic value added
b) percent economic value added
c) negative economic value added
d) positive economic value added
25. Project whose cash flows are less than capital invested for required rate of return then
net present value will be
a) negative
b) zero
c) positive
d) independent
26. In capital budgeting, a technique which is based upon discounted cash flow is classified
as
a) net present value method
b) net future value method
c) net capital budgeting method
d) net equity budgeting method
27. If present value of cash outflow is equal to present value of cash inflow, the net present
value will be:
a) Positive
b) Negative
c) Zero
d) Infinite
28. Generally, a project is considered acceptable if its net present value is:
a) Negative or zero
b) Negative or positive
c) Positive or zero
d) Negative
29. An increase in the discount rate will:
a) Reduce the present value of future cash flows.
b) Increase the present value of future cash flows.
Page | 259
c) Have no effect on net present value.
d) Compensate for reduced risk.
30. In mutually exclusive projects, project which is selected for comparison with others
must have a) Higher net present value
b) Lower net present value
c) Zero net present value
d) All of the above
31. The difference between the present value of cash inflows and the present value of cash
outflows associated with a project is known as:
a) Net present value of the project
b) Net future value of the project
c) Net historical value of the project
d) Net salvage value of the project
32. Machine Z purchased at year zero for Rs.5,00,000 which will be depreciated @ 25% for
5 years on written down value basis and then will be sold at Rs.70,000. Capital gain tax
rate is 35% while corporate income tax rate is 40%. What is the present value of cash
flow of machine at 5th year if cost of capital is 12%?
a) Rs.68,326
b) Rs.39,690
c) Rs.49,345
d) Rs.87,028
33. Machine P purchased at year zero at Rs.10,00,000 which will be depreciated @ 25% for
5 years on written down value basis and then will be sold at Rs.1,40,000. Tax rate is
35%. Profit before depreciation at 5th year is Rs.84,000. What is the present value of
CFAT at year five if cost of capital is 12%?
a) Rs.1,45,346
b) Rs.1,54,643
c) Rs.1,43,546
d) Rs.1,54,463
Profitability Index
34. Present value of future cash flows is Rs 4150 and an initial cost is Rs 1300 then
profitability index will be
Page | 260
a) 3.00%
b) 3.19
c) 0.31 times
d) Rs 5,450.00
35. An initial cost is Rs 6000 and probability index is 5.6 then present value of cash flows
will be
a) Rs 25,000.00
b) Rs 28,000.00
c) Rs 33,600.00
d) Rs 30,000.00
36. A Profitability Index (PI) of 0.92 for a project means that ..................
a) The project’s costs (cash outlay) are (is) less than the present value of the
project’s benefits.
b) The project’s NPV is greater than zero.
c) The project’s NPV is greater than 1.
d) The project returns 92 cents in present value for each rupee invested.
37. Using profitability index, the preference rule for ranking projects is:
a) the lower the profitability index, the more desirable the project.
b) the higher the profitability index, the more desirable the project.
c) the lower the sunk cost, the more desirable the project.
d) the higher the sunk cost, the more desirable the project.
38. Accept a project if the profitability index is:
a) less than 1
b) positive
c) greater than 1
d) negative
39. Profitability index is actually a modification of the a) Payback period method
b) IRR Method
c) Net present value method
d) Risk premium method
40. Profitability index of Project X is 1.20167 when its cash flow is discounted at 12%.
Initial investment on project was Rs.1,50,000. This project generates equal cash flow
Page | 261
over the five years time. How much cash flow will be generated by the project each
year?
a) Rs.50,000
b) Rs.40,000
c) Rs.60,500
d) Rs.40,897
IRR
41. In uneven cash flow, 'IRR' is an abbreviation of an
a) internal rate of return
b) international rate of return
c) intrinsic rate of return
d) investment return rate
42. In independent projects evaluation, results of internal rate of return and net present
value lead to
a) cash flow decision
b) cost decision
c) same decisions
d) different decisions
43. To estimate an unknown number that lies between two known numbers is knows as a) Capital rationing
b) Capital budgeting
c) Interpolation
d) Amortization
44. Criterion for IRR (Internal Rate of Return)
a) Accept, if IRR > Cost of capital
b) Accept, if IRR < Cost of capital
c) Accept, if IRR = Cost of capital
d) None of the above
45. Internal Rate of Return is defined as a) The discount rate which causes the payback to equal one year.
b) The discount rate which causes the NPV to equal zero.
Page | 262
c) The ROE when the NPV equals 0.
d) The ROE associated with project maximization.
46. ABC Ltd. wishes to undertake a project requiring an investment of Rs.7,32,000 which
will generate equal annual inflows of Rs.1,46,400 in perpetuity. What is the IRR of the
project?
a) 20%
b) 25%
c) 400%
d) 500%
47. A project whose useful life is 4 years has IRR of 15% and will save cost of Rs.1,60,000
annually. What is the project cost that is initial investment?
a) Rs.10,66,667
b) Rs.4,60,000
c) Rs.5,32,800
d) Rs.4,56,800
Payback period
48. The return after the pay off period is not considered in case of __________.
a) Payback period method
b) Interest rate method
c) Present value method
d) Discounted cash flow method
49. Which of the following techniques of project appraisal does not consider the time value
of money?
a) Benefit cost ratio
b) Net present value
c) Internal rate of return
d) payback period
50. An uncovered cost at start of year is Rs 200, full cash flow during recovery year is Rs
400 and prior years to full recovery is 3 then payback would be
a) 5 years
b) 3.5 years
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c) 4 years
d) 4.5 years
51. An uncovered cost at start of year is divided by full cash flow during recovery year then
added in prior years to full recovery for calculating
a) original period
b) investment period
c) payback period
d) forecasted period
52. Number of years forecasted to recover an original investment is classified as
a) payback period
b) forecasted period
c) original period
d) investment period
53. Which of the following represents the amount of time that it takes for a capital
budgeting project to recover its initial cost?
a) Maturity period
b) Payback period
c) Redemption period
d) Investment period
54. The shorter the payback period a) the more risky is the project.
b) the less risky is the project.
c) less will the NPV of the project.
d) more will the NPV of the project
55. Ranking projects according to their ability to repay quickly may be useful to firms:
a) when experiencing liquidity constraints.
b) when careful control over cash is required.
c) to indicate the prospective investors specifying when their funds are likely to be
repaid.
d) All of the above
56. Which of the following is demerit of payback period?
a) It is difficult to calculate as well as understand it as compared to accounting rate
of return method.
Page | 264
b) This method disregards the initial investment involved.
c) It fails to take into account the timing of returns and the cost of capital.
d) None of the above
57. What are the two drawbacks associated with the payback period?
a) The time value of money is ignored. It ignores cash flows beyond the payback
period.
b) The time value of money is considered. It ignores cash flows beyond the payback
period.
c) The time value of money is considered. It includes cash flows beyond the
payback period.
d) The time value of money is ignored. It includes cash flows beyond the payback
period.
58. Calculate payback period for following two machines.
X
Original investment
4,000
Life of machine
4 years
Saving in scrap
500
Saving in wages
6,000
Cost of running
800
Cost of supervision
1,200
Select the correct answer from the options given below
(A)
(B)
(C)
(D)
Machine X
0.88 year
0.67 year
0.92 year
0.67 year
Y
18,000
5 years
800
8,000
1,000
1,800
Machine Y
3 year
2 year
2 year
3 year
59. X Ltd. is providing the following information:
Annual cost of saving Rs.96,000
Useful life 5 years
Salvage value Zero
Internal rate of return 15%
Profitability index 1.05
What is cost of capital of X Ltd.Rs.
Page | 265
a) 12%
b) 13%
c) 14%
d) 15%
60. Using the data of above question calculate NPV.
a) Rs.16,940
b) Rs.16,409
c) Rs.16,094
d) Rs.16,904
61. LMN Corporation is considering an investment that will cost Rs.80,000 and have a
useful life of 4 years. During the first 2 years, the net incremental after -tax cash flows
are Rs.25,000 per year and for the last 2 years they are Rs.20,000 per year. W hat is the
payback period for this investment?
a) 3.2 year
b) 3.5 year
c) 4.0 year
d) Cannot be determined with this information.
62. A project requires initial investment of Rs.2,00,000 and estimated to generate cash flow
after tax of Rs.1,00,000, Rs.80,000, Rs.40,000, Rs.20,000 & Rs.10,000 in next 5 years.
What is the payback period of the project?
a) 3 years and 4 months
b) 2 years and 6 months
c) 4 years and 2 months
d) 2 years and 8 months
Discounted payback period
63. Payback period in which an expected cash flows are discounted with help of project
cost of capital is classified as
a) discounted payback period
b) discounted rate of return
c) discounted cash flows
d) discounted project cost
64. Net present value, profitability index, payback and discounted payback are methods to
Page | 266
a) evaluate cash flow
b) evaluate projects
c) evaluate budgeting
d) evaluate equity
65. A project is accepted when:
a) Net present value is greater than zero
b) Internal Rate of Return will be greater than cost of capital
c) Profitability index will be greater than unity
d) Any of the above
66. Which of the following statements is incorrect regarding a normal project?
a) If the NPV of a project is greater than 0, then its PI will exceed 1.
b) If the IRR of a project is 8%, its NPV, using a discount rate, K0, greater than 8%,
will be less than0.
c) If the PI of a project equals 0, then the project’s initial cash outflow equals the PV
of its cash flows.
d) If the IRR of a project is greater than the discount rate, then its PI will be greater
than 1.
67. Which of the following method of capital budgeting ignores the time value of money?
a) Discounted payback period
b) Net present value
c) Internal rate of return
d) None of the above
68. As per discounted payback period method, a project with a) more discounted payback period will be selected.
b) higher NPV will be preferred.
c) low NPV will be preferred.
d) less discounted payback period will be selected.
69. Which of the following capital budgeting techniques takes into account the incremental
accounting income rather than cash flows?
a) Net present value
b) Internal rate of return
c) Accounting/simple rate of return
d) Cash payback period
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70. Which of the following techniques does not take into account the time value of money?
a) Internal rate of return method
b) Simple cash payback method
c) Net present value method
d) Discounted cash payback method
71. Y Ltd. is considering a project which requires initial investment of Rs.6,75,000. Its cost
of capital is 10%. Estimated cash flow after tax are as follows:
Year 1
Year 2
1,50,000
Year 3
6,60,000
Year 4
4,20,000
Year 5
4,20,000
What is projects discounted payback period?
a) 3 years & 7.58 months
b) 4 years & 4.12 months
c) 3 years & 2.32 months
d) 4 years & 8.11 months
72. A Machine requires initial investment of Rs.40,000 and expected to generate cash flow
of Rs.8,400,Rs. 14,300 & Rs.32,800 in next 3 years. Applicable tax rate is 30%
Machine A
Machine B
Cost
(Rs. )
(?)
17,50,000
17,50,000
and WACC of the company is 12%. The company will select machine because a) It has positive NPV of Rs.2,522
b) It profitability index is 1.653 which is more than 1.
c) Its IRR is between 14% to 15% which is more than WACC of the company.
d) All of the above
CE Approach
73. In Certainty-equivalent approach, adjusted cash flows are discounted at:
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a) Accounting Rate of Return
b) Internal Rate of Return
c) Hurdle Rate
d) Risk-free Rate
74. In CE Approach, the CE Factors for different years are:
a) Generally increasing
b) Generally decreasing
c) Generally same
d) None of the above
75. ................................is the ratio of assured cash flows to uncertain cash flows.
a) Beta Factor (BF)
b) Contingency Equivalent Factor (CEF)
c) Risk Premium Factor (RPF)
d) Certainty Equivalent Factor (CEF)
RADR
76. In Risk-Adjusted Discount Rate method, the normal rate of discount is:
a) Increased
b) Decreased
c) Unchanged
d) None of the above
77. In Risk-Adjusted Discount Rate method, which one is adjusted?
a) Cash flows
b) Life of the proposal
c) Rate of discount
d) Salvage value
78. NPV of a proposal, as calculated by RADR and CE Approach will be:
a) Same
b) Unequal
c) Both (a) and (b)
d) None of (a) and (b)
79. Which of the following is correct for RADR?
a) Accept a project if NPV at RADR is negative
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b) Reject a project if IRR is more than RADR
c) RADR is overall cost of capital plus risk-premium
d) All of the above.
80. Following data is available for Project A:
Net cash outlay Rs.1,00,000
Project life 5 Years
Annual cash inflow Rs.30,000
Coefficient of variation 0.4
Company selects the risk adjusted rate of discount on the basis of coefficient of
variation.
Coefficient of
Risk Adjusted
Variation
Rate of Discount
0.0
10%
0.4
12%
0.8
14%
1.2
16%
1.6
18%
2.0
22%
More than 2.0
25%
Determine the risk adjusted net present value of the Project A.
a) 6,550
b) 7,940
c) 8,150
d) 9,340
Capital Ratio
81. In capital budgeting, the term Capital Rationing implies:
a) That no retained earnings available
b) That limited funds are available for investment
c) That no external funds can be raised
d) That no fresh investment is required in current year
82. In case of divisible projects, which of the following can be used to attain maximum NPV?
a) Feasibility Set Approach
b) Internal Rate of Return
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c) Profitability Index Approach
d) Any of the above
83. In case of the indivisible projects, which of the following may not give the optimum
result?
a) Internal Rate of Return
b) Profitability Index
c) Feasibility Set Approach
d) All of the above
84. The available capital funds are to be carefully allocated among competing projects by
careful prioritization. This is called ____________.
a) capital positioning
b) capital structuring
c) capital rationing
d) capital budgeting
85. In a capital rationing situation (investment limit Rs.25 lakhs), suggest the most
desirable feasible combination on the basis of the following data:
Project
Initial outlay
(Rs. in lakhs) NPV
A
15
6.00
B
10
4.50
C
7.5
3.60
D
6
3.00
Suggest which combination of project should be selected.
a) A&C
b) B&D
c) C&D
d) A & B
Inflation
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86. If there is no inflation during a period, then the Money Cashflow would be equal to:
a) Present Value
b) Real Cashflow
c) Real Cashflow + Present Value
d) Real Cashflow - Present Value
87. The Real Cashflows must be discounted to get the present value at a rate equal to:
a) Money Discount Rate
b) Inflation Rate
c) Real Discount Rate
d) Risk free rate of interest
88. Real rate of return is equal to:
a) Nominal Rate × Inflation Rate
b) Nominal Rate ÷ Inflation Rate
c) Nominal Rate - Inflation Rate
d) Nominal Rate + Inflation Rate
89. If the Real rate of return is 10% and Inflation rate is 4% then Money Discount Rate is:
a) 14.4%
b) 2.5%
c) 25%
d) 14%
90. If the Money Discount Rate is 19% and Inflation Rate is 12%, then the Real Discount
Rate is:
a) 7%
b) 5%
c) 5.70%
d) 6.25%
91. Money Discount Rate if equal to:
a) (1 + Inflation Rate) (1 + Real Rate)-1
b) (1 + Inflation Rate) ÷ (1 + Real Rate)-1
c) (1 + Real Rate) ÷(1 + Inflation Rate)-1
d) (1 + Real Rate) + (1 + Inflation Rate)-1
92. Real Discount Rate is equal to:
a) (1 + Inf. Rate) (1 + Money D Rate)-1
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b) (1 + Money D Rate) + (1 + Inf. Rate)-1
c) (1 + Money D Rate) ÷ (1 + Inf. Rate)-1
d) (1 + Money D Rate) - (1 + Inf. Rate)-1
93. Which of the following cannot be true?
a) Inflation Rate > Money Dis. Rate
b) Real Dis. Rate < Money Dis. Rate
c) Inflation Rate < Real Dis. Rate
d) Inflation Rate = Real Dis. Rate
94. Money Cash flows should be adjusted for:
a) Only Inflation Effect
b) Only Time Value of Money
c) None of (a) and (b)
d) Both of (a) and (b)
95. A major difference between real and nominal returns is that_______________.
a) real returns adjust for inflation and nominal returns do not
b) real returns use actual cash flows and nominal returns use expected cash flows
c) real returns adjust for commissions and nominal returns do not
d) real returns show the highest possible return and nominal returns show the
lowest possible return
96. In capital budgeting, positive net present value results in
a) negative economic value added
b) positive economic value added
c) zero economic value added
d) percent economic value added
97. Real interest rate and real cash flows do not include
a) equity effects
b) debt effects
c) inflation effects
d) opportunity effects
98. In cash flow estimation and risk analysis, real rate will be equal to nominal rate if there
is
a) no inflation
b) high inflation
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c) no transactions
d) no acceleration
99. Nominal interest rates and nominal cash flows are usually reflected the
a) inflation effects
b) opportunity effects
c) equity effects
d) debt effects
100. Real interest rate and real cash flows do not include a) Equity effects
b) Debt effects
c) Inflation effects
d) Opportunity effects
101. The one year rate of inflation is expected to be 3%. The one year money discount
rate is 6.3%. The one year real rate of discount is:
a) 3.30%
b) 3.20%
c) 9.30%
d) 9.49%
102. The one year rate of inflation is expected to be 5%. The one year real discount rate is
10%. The one year money rate of discount is:
a) 1096
b) 1396
c) 13.396
d) 15.596
Sensitivity
103. In Sensitivity Analysis, the emphasis is on assessment of sensitivity of
a) Net Economic Life
b) Net Present Value
c) Both (a) and (b),
d) None of (a) and (b)
104. Most Sensitive variable as given by the Sensitivity Analysis should be:
a) Ignored
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b) Given Least important
c) Given the maximum importance
d) None of the above
105. Rani & Co. desires to take a project whose cost is Rs.12,000 and useful life is 4 years.
Expected annual cash flows are Rs.4,500 p.a. Cost of capital is 1496. Calculate the
sensitivity of the 'cost of capital’ in percentage given that:
PVAF (14%, 4) 2.9137
PVAF (18%. 4) 2.6900
a) 29%
b) 22%
c) 22.22%
d) 24.64%
106. X Ltd. is considering a project with following cash flow:
Cost of the plant: 70,000
Year
Running cost
Savings
1
20,000
60,000
2
25,000
70,000
The cost of capital is 8%. Measure the sensitivity of the project to the change in level of
plant cost.
a) 8.9296
b) 7.5096
c) 9.1696
d) 8.0096
EAV/EAC
107. EAV should be used in case of:
a) Divisible Projects
b) Projects with different life
c) One-off Investments
d) Indivisible Projects
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108. EAV is Equal to:
a) NPV × PVAF (r,n)
b) NPV + PVAF (r,n)
c) NPV ÷ PVAF (r,n)
d) NPV-PVAF (r,n)
109. If a project has positive NPV, its EAV is
a) Equal to NPV
b) More than NPV
c) Less than NPV
d) Any of the above
110. Two mutually exclusive projects with different economic lives can be compared on
the basis of
a) Internal Rate of Return
b) Profitability Index
c) Net Present Value
d) Equivalent Annuity Value
111. Xpert Engineering Ltd. is considering buying one of the following two mutually
exclusive investment projects:
Project A: Buy a machine that requires an initial investment outlay of Rs.1,00,000 and
will generate CFAT of Rs.30,000 per year for 5 years.
Project B: Buy a machine that requires an initial investment outlay of Rs.1,25,000 and
will generate CFAT of Rs.27,000 per year for 8 years.
The company uses 10% cost of capital to evaluate the projects.
The company will select a) Project B as its NPV is high than Project A.
b) Project B as its equivalent NPV is high than Project A.
c) Project A as its equivalent NPV is high than Project B.
d) Project A as its NPV is high than Project B.
Risk
112. Risk in Capital budgeting implies that the decision-maker knows ___________of the
cash flows.
a) Variability
b) Probability
c) Certainty
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d) None of the above
113. Risk in Capital budgeting is same as:
a) Uncertainty of Cash flows
b) Probability of Cash flows
c) Certainty of Cash flows
d) Variability of Cash flows
114. Which of the following is a risk factor in capital budgeting?
a) Industry specific risk factors
b) Competition risk factors
c) Project specific risk factors
d) All of the above
115. Risk of a Capital budgeting can be incorporated
a) Adjusting the Cash flows
b) Adjusting the Discount Rate
c) Adjusting the life
d) All of the above
116. Lower standard deviation indicates a) lower risk
b) higher risk
c) no risk at all
d) highly favorable situation
117. A company is considering Projects X and Y with following information:
Project
Expected NPV(Rs.)
Standard-deviation
X
9,000
3,250
Y
11,000
3,600
Which project will you recommend and why?
a) Project Y as its higher expected NPV.
b) Project X as its co-efficient of variation is high.
c) Project Y as its co-efficient of variation is less.
d) Project X as its risk ie. standard deviation is less.
Page | 277
118. X Ltd. is considering to start a new project for which it has gathered following data:
NPV ( in lakh)
Probability
32
0.4
44
0.4
57
0.2
Compute the risk associated with the project.
a) 89.88
b) 9.30
c) 11.62
d) 8.97
119. X Ltd. is considering to start a new project for which it has gathered following data:
Cash Flow
Probability y
1,08,000
0.1
2,16,000
0.4
4,32,000
0.4
5,40,000
0.1
Calculate the expected cash flow.
a) Rs.3,42,000
b) Rs.3,18,000
c) Rs.3,24,000
d) Rs.3,32,000
120. A project has expected NPV of 1,22,000. Its coefficient of variation is 0.7377. Risk
free rate is 896 and cost of capital is 1096. What is the standard deviation of project?
a) 1,00,000
b) 80,000
c) 90,000
d) 88,889
Page | 278
Decision tree
121. Concept of joint probability is used in case of:
a) Independent Cashflows
b) Uncertain Cashflows
c) Dependent Cashflows
d) Certain Cashflows
122. Probability-tree analysis is best used when cash flows are expected to be:
a) Independent over time.
b) Risk-free.
c) Related to the cash flows in previous periods.
d) Known with certainty.
123. The probability in subsequent periods that is conditioned on what has occurred
earlier is referred to as the a) Initial probability
b) Conditional probability
c) Joint probability
d) None of the above
124. Which of the following is correct formula to calculate coefficient of variation?
a) Standard deviation ÷ Expected NPV
b) Standard deviation × Expected NPV,
c) Correlation × SD ÷Expected NP
d) None of the above
Answers1
A
21
A
41
A
61
B
81
B
101
B
121
B
2
A
22
A
42
C
62
B
82
C
102
D
122
C
3
B
23
B
43
C
63
A
83
C
103
B
123
B
4
D
24
C
44
A
64
B
84
C
104
C
124
A
5
B
25
A
45
B
65
D
85
D
105
A
6
D
26
A
46
A
66
C
86
B
106
D
7
C
27
C
47
D
67
D
87
C
107
B
Page | 279
8
B
28
C
48
A
68
D
88
B
108
C
9
C
29
A
49
D
69
C
89
A
109
C
10
A
30
A
50
B
70
B
90
D
110
D
11
B
31
A
51
C
71
C
91
A
111
C
12
A
32
C
52
A
72
C
92
C
112
A
13
C
33
A
53
B
73
D
93
A
113
D
14
B
34
B
54
B
74
B
94
C
114
D
15
A
35
C
55
D
75
D
95
A
115
D
16
B
36
D
56
C
76
A
96
B
116
A
17
B
37
B
57
A
77
C
97
C
117
C
18
B
38
C
58
A
78
B
98
A
118
B
19
B
39
C
59
B
79
C
99
A
119
C
20
C
40
A
60
C
80
C
100
C
120
C
State whether each of the following statements is True (T) or False (F):
1.
2.
3.
4.
5.
6.
7.
8.
9.
Investment decisions and capital budgeting are same.
Capital budgeting decisions are long term decisions.
Capital budgeting decisions are reversible in nature.
Capital budgeting decisions do not affect the future Stability of the firm.
There is a time element involved in capital budgeting.
An expansion decision is not a capital budgeting decision
In mutually exclusive decision situation, the firm can accept all feasible proposals.
Capital budgeting and capital rationing are alternative to each other.
Correct capital budgeting decisions can be taken by comparing the cost with future
benefits.
10. Capital Rationing as a situation when the Government has imposed a ceiling on
investment by a firm.
11. Cash flows are the appropriate measure of costs and benefits from an investment
proposal.
12. Sunk cost is a relevant cost in capital budgeting.
13. A risky situation is one in which the probability for the occurrence or non occurrence of an event cannot be assigned.
14. Allocated overhead costs are not relevant for capital budgeting.
Page | 280
15. Cash flows and accounting profits are different.
16. Cash flows are same as profit before tax.
17. Net cash flow is on after tax basis.
18. Money cash flows should be discounted at nominal discount rate.
19. Real cash flows should be discounted at normal discount rate.
20. EAB is, in a way, an extension of NPV method.
21. Feasibility Set Approach is based on the NPV method of capital budgeting.
22. Selection based on PI method gives optimum decision making in case of indivisible
projects.
23. Inflation affects not only the cash flows but also the discount rate.
24. In capital budgeting proposals, risk may arise due to different factors.
25. In risky capital budgeting proposals, the discount rate is not known with certainty.
26. In Payback Period method, the risk of the proposal is incorporated by lessening the
target payback period.
27. In Certainty Equivalents method, both the cashflows and the discount rate are
adjusted.
28. In Sensitivity Analysis, one variable is adjusted at a time to see its effect on the NPV.
29. Sensitivity Analysis helps in calculation of NPV of the proposal.
30. Expected value of cash flows is equal to the arithmetic average of the cash flows.
31. In case of capital budgeting, higher the standard deviation better the project is.
32. In case of dependent cash flows, the risk is measured with reference to joint
probabilities.
33. Coefficient of variation is as good a measure of risk as the standard deviation.
34. Decision Tree Approach is suitable to analyse a multistage decision situation.
ANSWERS FOR TRUE & FALSE1
2
T
T
8
9
F
F
15
16
T
F
22
23
F
T
29
30
F
F
3
4
5
F
F
T
10
11
12
F
T
F
17
18
19
T
T
T
24
25
26
T
F
T
31
32
33
F
T
F
6
7
F
F
13
14
F
T
20
21
T
T
27
28
F
T
34
T
Page | 281
Page | 282
CHAPTER 10
LEASE OR BUY DECISION
Learning objective
After studying this chapter, you should be able to understand:
 Basic terms relating to lease
 Classification of lease
 Debt financing vs. lease financing decision
BASIC TERMS RELATING TO LEASE
 CONCEPT 1
WHAT IS MEANT BY TERM ‘LEASE’
A Lease is an agreement whereby the owner of an asset grants to the user the right to use
an asset for payment of periodic rents over agreed period of time
 CONCEPT 2
WHO IS A ‘LESSOR’ IN THE LEASE AGREEMENT
A Lessor is a person or entity who owns the asset and who grants the right to use the asset
for payment of periodic rentals over agreed period of time.
 CONCEPT 3
WHAT ARE ‘LESSOR’ RENTALS
A series of periodic payments over agreed period of time by the user of the asset to the
owner of the asset for acquiring the right to use the asset, are called ‘Lease Rentals’
 CONCEPT 4
What is ‘Lessor Term
It is non-cancellable period for which the lessee has agreed to take on lease the asset
together with any further period for which the lessee has the option to continue the lease of
asset, with or without further payment, and at the inception of the lease it is reasonable
certain that this option will be exercised by the lessee.
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 CONCEPT 5
WHAT IS MEANT BY THE TERM ‘INCEPTION OF THE LEASE’
Inception of the lease is earlier or:
a. Date of the lease agreement and
b. The date of commitment by the parties to the principal provision of the lease.
 CONCEPT 6
WHAT IS A ‘NON-CANCELLABLE LEASE’
A non- cancellable lease is a leas that is cancellable only
a. Upon the occurrence of some remote contingency: or
b. With the permission of the lessor: or
c. If the lessee enter into a new lease for the same or an equipment asset with the
same lessor: or
d. Upon payment by the lessee of an additional amount such that at inception
continuation of lease is reasonably certain.
Classification of lease
 CONCEPT 7
WHAT IS THE BASIC PRINCIPAL REGARDING CLASSIFICATION OF LEASES
The classification of lease is based on the extent to which risks and rewards incidental to
ownership of a leased assets lie with the lessor or lessee. Risks include the possibilities of
losses from idle capacity or technological obsolescence and of variations in return due to
changing economic conditions. Rewards may be represented by the expectation of
profitable operation over the economic life of the asset and of gain appreciation in value or
realization of residential value.
 CONCEPT 8
WHEN IS THE LEASE CLASSIFIED AS A FINANCE LEASE
A lease is classified as a finance lease if it transfers substantially all the risks and rewards
incident to ownership of an asset.
Examples of situations, which would normally lead to a lease being classified as finance
lease:
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a) The lease transfer the ownership of the asset to the lessee by the end of the lease
terms.
b) The lessee has the option to purchase the asset at a price which is expected to be
sufficiently lower than the fair value at the date when option become exercisable
such that, at the inception of lease. It is reasonable certain that the option will be
exercised.
c) The lease term is for major part of the economic life of the assets even if title is not
transferred.
d) At the inception of lease present value of the minimum lease payments amounts to
at substantially all of the fair value of the leased asset.
e) The leased asset is of specialized nature such that only the lessee can use it without
major modification being made.
Indicators of situations, which individually or in combination could also lead to a
lease being classified as a finance lease are:
I.
If the lessee can cancel the lease, the lessor’s associated with the cancellation are
borne by the lessee.
II.
Gains or losses from the fluctuation in the fair value of residual fall to the lessee (for
example in the form of a rent rebate equaling most of the sale proceeds at the ends
of the lease)
III.
When the lessee can continue the lease for a secondary period at a rent which is
substantially lower then market rent
Thus, financial lease are long-term non-cancellable leases where all risks as to the
asset are borne by the lessee and all returns of the asset are enjoyed by the lessee.
 CONCEPT 9
WHEN IS THE LEASE CLASSIFIED AS OPERATING LEASE
An operating lease is a lease other than a finance lease. In other words, operating lease are
short terms, cancellable lease where the risk of obsolescence is borne by the lessor and
annual maintenance cost is also borne by the lessor unless contract provides otherwise.
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 CONCEPT 10
DISTINCTION BETWEEN FINANCE LEASE AND OPERATING LEASE (M. IMPORTANT)
A finance lease differ from an operating lease in the following respects:
Basis of
Difference
Finance Lease
(i) Lease Term
Lease term is for the major part of the
economic life of the assets
Under Finance lease, the Lessor Transfer
(ii) Are Risk and Substantially all the risks and rewards
incident to ownership of an assets to the
Rewards
lessee.
Transferred?
(iii) Who Bears
The risk of obsolescence falls on the
Risk of
Lessee.
obsolescence?
(iv) Is
Continuation of
Lease certain?
Continuation of lease is reasonably certain
(v) Is the Lease
cancellable?
(vi) Who Bears
Annual
Maintenance
Cost?
Finance Leases are generally noncancellable otherwise
Annual Maintenance cost is generally
borne by the lessee unless contract
provides otherwise
Operating Lease
Lease term is significantly
less than the economic
life of the assets
Under Operating Lease the
Lessor, does not transfer
substantially all the risks
and rewards incident
ownership of an asset to
the lessee.
The risk of obsolescence
falls on the Lessor.
Continuation of lease is not
reasonably certain
Operating lease are
generally cancellable
unless contract provides
otherwise.
Annual Maintenance cost is
borne by the lessor unless
contract provides
otherwise
DEBT FINANCING VS. LEASE FINANCING DECISION
 CONCEPT 11
MEANING OF DEBT FINANCING
Debt Financing is an arrangement under which an asset is acquired out of loan which is
payable in periodic installments over the loan period as per loan agreement.
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 CONCEPT 12
MEANING OF LEASE FINANCING
Lease Financing is an arrangement under which right to use an asset is acquired for
payment of periodic rentals over the agreed period as per lease agreement.
 CONCEPT 13
DEBT VS. LEASE FINANCING DECISION
Debt vs. Lease Financing decision basically is a financing decision which involves making
choice out of Debt or Lease Financing. The choice be made by comparing the present Value
of Net Cash outflow under Debt Financing with by comparing the Present Value of Net Cash
outflow under lease financing. Debt financing is should be used if the present value of net
cash out flow under debt financing is less than the Present Value of net cash outflow under
lease financing. Lease financing should be used if the Present Value of net cash outflow
under lease financing is less than the Present value of Net Cash outflow under debt
financing.
 CONCEPT 14
TRIPLE NET LEASE
A triple net lease (triple-Net or NNN) is a lease agreement on a property where the
tenant or lessee agrees to pay all real estate taxes, building insurance, and maintenance
(the three "nets") on the property in addition to any normal fees that are expected under
the agreement (rent, utilities, etc.).
 CONCEPT 15
DIFFERENT TYPES OF LEASE
a) Sale and Lease back Leasing: Under this arrangement an asset which exists and in
use by the lessee is first sold to the lessor for consideration in cash. The same asset is
then acquired for use under financial lease agreement from lessor. This is a method of
raising funds immediately required by lessee for working capital or other purposes. The
lessee continues to make economic use of assets against payment of lease rentals while
ownership vests with the lessor.
b) Sales aid lease: When the lessor enters into an arrangement with the seller, usually
manufacture of equipment, to market the latter’s product through its own leasing
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operation, it is called a ‘sales aid lease’. The leasing company usually gets a commission
on such sales from the manufactures & doubles its profits.
c) Leverage lease: Sometimes assets are so costly that a single lessor may not be able to
provide the assets on lease, then many lessors may group together and get to finance
the assets from a financial institution. To provide the assets on lease, such a lease is
called ‘Leverage lease’.
UNSOLVED QUESTION
Ques.1 ABC Ltd. is considering a proposal to acquire an equipment costing Rs.5,00,000.
The expected effective life of the equipment is 5 years. The company has two options either to acquire in by obtaining a loan of Rs.5 lakhs at 12% interest p.a. or by lease. The
following additional information are available:
(i)
The principal amount of loan will be repaid in 5 equal yearly instalments.
(ii)
The full cost of the equipment will be written off over a period of 5 years on
straight line basis and it is to be assumed that such depreciation charge will be
allowed for tax purpose.
(iii)
The effective tax rate for the company is 40% and the after tax cost of capital is
10%.
(iv)
The interest charge, repayment of principal and the lease rentals are to be paid
on the last day of each year.
You are required to work out the amount of lease rental to be paid annually, which will
match the loan option. The discount factor at 10% are as follows:
Year
Discount
factor
1
0.909
2
0.826
3
0.751
4
0.683
5
0.621
Ques.2 Diligend Ltd. is considering the lease of an equipment which has a purchase price of
Rs.3,50,000. The equipment has an estimated economic life of 5 years with a salvage value
zero. For the purpose of taxation it is to be assumed that the asset will be written off over a
period of 5 years on a straight line basis. The lease rentals per year are Rs.1,20,000.
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Assume that the company’s corporate tax rate is 50%. If the before-tax rate of borrowing
for the company is 16%, should the company lease the equipment?
Note: Present value of Re.1 for 5 years are:
Year
P.V. @ 8%
P.V. @ 16%
1
0.9259
0.8621
2
0.8573
0.7432
3
0.7938
0.6407
4
0.7350
0.5523
5
0.6806
0.4761
MULTIPLE CHOICE QUESTIONS
1. In lease system, interest is calculated on
a) Cash down payment
b) Cash price outstanding
c) Hire purchase price
d) None of the above
2. A short-term lease which is often cancellable is known as
a) Finance Lease
b) Net Lease
c) Operating Lease
d) Leverage Lease
3. Which of the following is not a usual type of lease arrangement?
a) Sale & leaseback
b) Goods on Approval
c) Leverage Lease
d) Triple net lease
4. Under income-tax provisions, depreciation on lease asset is allowed to
a) Lessor
b) Lessee
c) Any of the two
d) None of the two
5. A lease which is generally not cancellable and covers full economic life of the asset is
known as
a) Sale and leaseback
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b) Operating Lease
c) Finance Lease
d) Economic Lease
6. Lease which includes a third party (a lender) is known as
a) Sale and leaseback
b) Direct Lease
c) Inverse Lease
d) Leveraged Lease
7. From the point of view of the lessee, a lease is a:
a) Working capital decision
b) Financing decision
c) Buy or make decision
d) Investment decision
8. For a lessor, a lease is a
a) Investment decision
b) Financing decision
c) Dividend decision
d) None of the above.
9. Type of financial security in which firms do not borrow money rather lease their assets
is classified as
a) leases
b) preferred stocks
c) common stocks
d) corporate stocks
10. A company is faced with decision to purchase or acquire on lease a machine. Cos t of the
machine is Rs.2,53,930. The asset can be financed by taking loan on which interest is
payable @ 1596 and loan will be paid in 5 equal instalments inclusive of interest. Tax
rate is 4096. Assume loan instalment is payable at the end of each year. W hat will be the
loan instalment amount for each year?
a) Rs.75,800
b) Rs.65,278
c) Rs.67,800
d) Rs.66,824
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11. X Ltd. faced with decision to purchase or acquire on lease a machine. Cost of the
machine is Rs.5,07,860. The asset can be financed by taking loan on which interest is
payable @15% and loan will be paid in 5 equal instalments inclusive of interest. Tax
rate is 40%. Assume loan instalment is payable at the beginning of the year. What will
be the loan instalment amount for each year?
a) Rs.1,19,778
b) Rs.1,29,580
c) Rs.1,31,570
d) Rs.1,45,452
12. A company can obtain an asset on lease by paying 5 equal lease rentals annually. Such
lease rentals are payable at the end of the year. The leasing company desires a return of
10% on the gross value of the asset. Tax rate is 40%. Cost of capital is 9%. The cost of
the asset is Rs.7,61,790. Calculate the lease rental payable by the company each year.
a) Rs.2,01,000
b) Rs.1,95,833
c) Rs.1,98,563
d) Rs.2,10,000
13. Z Ltd. can acquire a machine by taking 15% loan or on lease basis from leasing
company. Cost of machine is X1,26,965. Tax rate is 40%. The leasing company desires a
return of 10% on the gross value of the asset. The present value of cash flow under
buying option is Rs.87,528. What should be the annual lease rental to be charged by the
leasing company to match the loan option?
a) Rs.37,900
b) Rs.37,805
c) Rs.37,424
d) Rs.37,501
14. Agrani Ltd. is in the business of manufacturing bearings. Some more product lines are
being planned to be added to the existing system. The cost of machine is Rs.40,00,000
having a useful life of 5 years with the salvage value of Rs.8,00,000. The full purchase
value of machine can be financed by 20% loan repayable in 5 equal instalments falling
due at the end of each year.
Calculate the figure of interest payable at the end of 5th year.
a) Rs.4,08,831
b) Rs.2,08,138
c) Rs.2,21,813
d) Rs.3,12,318
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Answers1
2
B
C
3
4
B
A
5
6
C
D
7
8
B
A
9
10
A
A
11
12
C
A
13
14
D
C
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CHAPTER 11
INTRODUCTION OF WORKING
CAPITAL
 CONCEPT 1
MEANING OF WORKING CAPITAL
The capital which is required to finance current assets is called working capital. It is the capital of a
business which is used to carry out day-to-day business operations of a firm.
Current Assets: An asset is classified as current when:
(i)
It is expected to be realised or intends to be sold or consumed in normal operating cycle
of the entity;
(ii)
The asset is held primarily for the purpose of trading;
(iii)
It is expected to be realised within twelve months after the reporting period;
(iv)
It is non- restricted cash or cash equivalent.
Generally current assets of an entity, for the purpose of working capital management can be
grouped into the following main heads:
a) Inventory (raw material, work in process and finished goods)
b) Receivables (trade receivables and bills receivables)
c) Cash or cash equivalents (short-term marketable securities)
d) Prepaid expenses.
 CONCEPT 2
SIGNIFICANCE OF WORKING CAPITAL MANAGEMENT
 Importance of Adequate Working Capital
Management of working capital is an essential task of the finance manager. He has to ensure that
the amount of working capital available with his concern is neither too large nor too small for its
requirements. A large amount of working capital would mean that the company has idle funds.
Since funds have a cost, the company has to pay huge amount as interest on such funds. If the firm
has inadequate working capital, such firm runs the risk of insolvency. Paucity of working capital
may lead to a situation where the firm may not be able to meet its liabilities.
The various studies conducted by the Bureau of Public Enterprises have shown that one of the
reasons for the poor performance of public sector undertakings in our country has been the large
amount of funds locked up in working capital. This results in over capitalization. Over
capitalization implies that a company has too large funds for its requirements, resulting in a low rate
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of return, a situation which implies a less than optimal use of resources. A firm, therefore, has to be
very careful in estimating its working capital requirements. Maintaining adequate working capital is
not just important in the short-term. Sufficient liquidity must be maintained in order to ensure the
survival of the business in the long- term as well. When businesses make investment decisions they
must not only consider the financial outlay involved with acquiring the new machine or the new
building, etc., but must also take account of the additional current assets that are usually required
with any expansion of activity.
For e.g.:-Increased production leads to holding of additional stocks of raw materials and work-inprogress. An increased sale usually means that the level of debtors will increase. A general increase
in the firm’s scale of operations tends to imply a need for greater levels of working capital. A
question then arises what is an optimum amount of working capital for a firm? We can say that a
firm should neither have too high an amount of working capital nor should the same be too low. It is
the job of the finance manager to estimate the requirements of working capital carefully and
determine the optimum level of investment in working capital.
 CONCEPT 3
OPTIMUM WORKING CAPITAL
If a company’s current assets do not exceed its current liabilities, then it may run into trouble with
creditors that want their money quickly. Current ratio along with acid test ratio has traditionally
been considered the best indicator of the working capital situation. It is understood that a current
ratio of 2 (two) for a manufacturing firm implies that the firm has an optimum amount of working
capital. This is supplemented by Acid Test Ratio which should be at least 1 (one). Thus, it is
considered that there is a comfortable liquidity position if liquid current assets are equal to current
liabilities. Bankers, financial institutions, financial analysts, investors and other people interested in
financial statements have, for years, considered the current ratio at ‘two’ and the acid test ratio at
‘one’ as indicators of a good working capital situation. As a thumb rule, this may be quite adequate.
However, it should be remembered that optimum working capital can be determined only with
reference to the particular circumstances of a specific situation. Thus, in a company where the
inventories are easily saleable and the sundry debtors are as good as liquid cash, the current ratio
may be lower than 2 and yet firm may be sound. In nutshell, a firm should have adequate working
capital to run its business operations. Both excessive as well as inadequate working capital positions
are dangerous.
 CONCEPT 4
NATURE AND TYPES OF WORKING CAPITAL
In the working capital management, a financial manager is faced with a decision involving some of
the consideration as follows:
1. What should be the total investment in working capital of the firm?
2. What should be the level of individual current assets?
3. What should be the relative proportion of different sources to finance the working capital
requirements?
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The term working capital may be used in different ways:
(i)
Gross Working Capital (or Total Working Capital): The gross working capital refers to
the firm’s investment in all the current assets taken together. The total of investments in
all the individual current assets is the gross working capital. For example, if a firm has a
cash balance of Rs.50,000, debtors of Rs.70,000 and inventory of raw material and
finished goods has been assessed at Rs.1,00,000, then the gross working capital of the
firm is Rs.2,20,000 (i.e., Rs.50,000 + Rs.70,000 + Rs.1,00,000).
(ii)
Net Working Capital: The term ‘net working capital’ may be defined as the excess of
total current assets over total current liabilities. It may be noted that the current liabilities
refer to those liabilities which are payable within a period of 1 year. The extent, to which
the payments to these current liabilities are delayed, the firm gets the availability of
funds for that period. So, a part of the funds required to maintain current assets is
provided by the current liabilities and the firm will be required to invest the funds in
only those current assets which are not financed by the current liabilities.
(iii)
Initial working capital: The capital, which is required at the time of the commencement
of business, is called initial working capital. These are the promotion expenses incurred
at the earliest stage of formation of the enterprise which include the incorporation fees,
attorney’s fees, office expenses and other preliminary expenses.
 CONCEPT 5
FACTORS DETERMINING WORKING CAPITAL REQUIREMENT
The working capital needs of a firm are determined and influenced by various factors. A wide
variety of considerations may affect the quantum of working capital required and these
considerations may vary from time to time. The working capital needed at one point of time may
not be good enough for some other situation. The determination of working capital requirement is a
continuous process and must be undertaken on a regular basis in the light of the changing situations.
Following are some of the factors which are relevant in determining the working capital needs of
the firm:
1. Basic Nature of Business: The working capital requirement is closely related to the nature
of the business of the firm. In case of a retail shop or a trading firm, the amount of working
capital required is small enough. Most of the transactions are undertaken in cash and the
length of the operating cycle is generally small. The trading concerns usually have smaller
needs of working capital, however, in certain cases, large inventories of goods may be
required and consequently the working capital may be large.
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2. Business Cycle Fluctuations: Different phases of business cycle, i.e., boom, recession,
recovery, etc. also affect the working capital requirement. In case of boom conditions,
inflationary pressure appears and business activities expand. As a result, the overall need for
cash, inventories, etc., increases resulting in more and more funds blocked in these current
assets. In case of recession period however, there is usually dullness in business activities
and there will be an opposite effect on the level of working capital requirement. There will
be a fall in inventories and cash requirement, etc.
3. Seasonal Operations: If a firm is operating in goods and services having seasonal
fluctuations in demand, then the working capital requirement will also fluctuate with every
change. In a cold drink factory, the demand will certainly be higher during summer season
and, therefore, more working capital is required to maintain higher production, in the form
of larger inventories and bigger receivable. On the other hand, if the operations are smooth
and evenly scattered throughout the year, then the working capital requirement will be
constant and will not be affected by the seasonal factors.
4. Market Competitiveness: The market competitiveness has an important bearing on the
working capital needs of a firm. In view of the competitive conditions prevailing in the
market, the firm may have to offer liberal credit terms to the customers resulting in higher
debtors. Even larger inventories may be maintained to serve an order as and when received;
otherwise the customer may go to some other supplier. Thus, the working capital tends to be
high as a result of greater investment in inventories and receivable. On the other hand, a
monopolistic firm may not require larger working capital. It may ask the customers to pay in
advance or to wait for some time after placing the order.
5. Credit Policy: The credit policy means the totality of terms and conditions on which goods
are sold and purchased. A firm has to interact with two types of credit policies at a time.
One, the credit policy of the supplier of raw materials, goods, etc., and two, the credit policy
relating to credit which it extends to its customers. In both the cases, however, the firm
while deciding its credit policy, has to take care of the credit policy of the market. For
example, a firm might be purchasing goods and services on credit terms but selling goods
only for cash. The working capital requirement of this firm will be lower than that of a firm
which is purchasing cash but has to sell on credit basis.
6. Supply Conditions: The time taken by a supplier of raw materials, goods, etc., after placing
an order, also determines the working capital requirement. If goods are received as soon as
or in a short period after placing an order, then the purchaser will not like to maintain a high
level of inventory of that good. Otherwise, larger inventories should be kept, e.g., in case of
imported goods. It is often seen that the shopkeepers may not be keeping stock of all items,
but whenever there is a demand, they procure from the wholesale / producer and supply it to
their customers.
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Thus, the working capital requirement of a firm is determined by a host of factors. Every
consideration is to be weighed relatively to determine the working capital requirement.
Further, the determination of working capital requirement is not once a while exercise, rather a
continuous review must be made in order to assess the working capital requirement in the changing
situation. There are various reasons which may requirement review of the working capital
requirement, e.g., change in credit policy, change in sales volume, etc.
 CONCEPT 6
OPERATING CYCLE AND WORKING CAPITAL NEEDS
The operating cycle of firm consists of the time required for the completion of the chronological
sequences of some or all of the following:
(i)
(ii)
(iii)
(iv)
(v)
Procurement of raw materials and services.
Conversion of raw materials into work-in-progress.
Conversion of work-in-progress into finished goods.
Sale of finished goods (cash or credit).
Conversion of receivable into cash.
Operating cycle period- The length or time duration of the operating cycle of any firm can be
defined as the sum of its inventory conversion period and the receivable conversion period.
Inventory Conversion Period (ICP): It is the time required for the conversion of raw materials
into saleable finished goods. In a manufacturing firm the ICP is consisting of Raw Material
Conversion Period (RMCP), Work-in-Progress Conversion Period (WPCP), and the Finished Goods
Conversion Period (FGCP). RMCP refers to the period for which the raw materials is generally kept
in stores before it is issued to the production department. The WPCP refers to the period for which
the raw material remains in the production process before it is taken out as a finished unit. The
FGCP refers to the period for which finished units remain in stores before being sold to a customer.
(i)
Receivable Conversion Period (RCP): It is the time required to convert the credit sales into
cash realisation. It refers to the period between the occurrence of credit sales and collection
from debtors.
The total of ICP and RCP is also known as Total Operating Cycle Period (TOCP). The firm might
be getting some credit facilities from the supplier of raw materials, wage earners, etc. This period
for which the payments to these parties are deferred or delayed is known as Deferral Period (DP).
The Net Operating Cycle (NOC) of the firm is arrived at by deducting the DP from the TOCP.
Thus,
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NOC = TOCP - DP
= ICP + RCP - DP
The operating cycle of a firm has been as shown in below:
Receivable Conversion
Period
RMCP
WPCP
FGCP
Inventory Conversion Period
-------------------------Gross Operating Cycle--------------------Net Operating Cycle
Deferral Period
For calculation of TOCP and NOC, various conversion periods may be calculated as follows:
RMCP =
Average Raw Materials Stock
Total Raw Materials Consumption
X 365
WPCP =
Average Work-in-progress
Total Cost of production
X 365
FGCP =
Average Finished Goods
Total Cost of Goods Sold
X 365
RCP =
Average Receivable
Total Credit Sales
X 365
DP =
Average Creditors
Total Credit Purchase
X 365
In respect of these formulations, the following points are worth noting:
1. The ‘Average’ value in the numerator is the average of opening balance and closing balance
of the respective item. However, if only the closing balance is available, then even the
closing balance may be taken as the ‘Average’.
2. The figure ‘365’ represents number of days in a year. However, there is no hard and fast rule
and sometimes even 360 days are considered.
3. The ‘Total’ figure in the denominator refers to the total value of the item in a particular year.
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4. In the calculation of RMCP, WPCP, and FGCP, the denominator is calculated at cost-basis
and the profit margin has been excluded. The reason being that there is no investment of
funds in profit as such.
On the basis of above conversion periods, the TOCP and NOC may be ascertained as follows:
Particulars
RMCP
+ WPCP
+ FGCP
+ RCP
TOCP
-DP
NOC
Number of Days
----- Days
----- Days
----- Days
----- Days
----- Days
----- Days
----- Days
The TOCP and NOC do not measure the absolute amount of funds invested in working capital.
However, a longer NOC indicates a requirement for more working capital. The operating cycle for
an individual component keeps on changing from time to time, particularly the RCP and the DP.
Therefore, a regular attention and review is required. It would be extremely difficult to determine an
optimum operating cycle for a particular firm. The comparison of firm’s operating cycle for a
period with that of the previous period and with that of the operating cycle of other firms may help
in maintaining and controlling the length of the operating cycle.
 CONCEPT 7
IMPORTANCE OF WORKING CAPITAL MANAGEMENT
The importance of working capital management can be expressed in terms of the following points:
(i)
The level of current assets changes constantly and regularly depending upon the level of
actual and forecasted sales. This requires that the decisions to bring a level of current assets
to the desired levels of current assets should be made at the earliest opportunity and as
frequently as required.
(ii)
The changing levels of current assets may also require review of the financing pattern. How
mush working capital needs to be financed by different sources of financing must be
periodically reviewed.
(iii)
Inefficient working capital management may result in loss of sales and consequently decline
in profits of the firm.
(iv)
Inefficient working capital management may also lead to insolvency of the firm if it is not in
a position to meet its liabilities and commitments.
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(v)
Current assets usually represent a substantial portion of the total assets of the firm, resulting
in investment of a larger chunk of funds in the current assets.
(vi)
There is an obvious and inevitable relationship between the sales growth and the level of
current assets. The target sales level can be achieved only if supported by adequate working
capital. The increase in sales level requires increase in working capital and thus the financial
manager must be able to respond quickly in providing and arranging additional working
capital.
Thus, the efficient working capital management is important from the point of view of both the
liquidity and the profitability. Keeping in view the importance of working capital management, the
financial manager should look into the framing of a suitable working capital policy for the firm.
Following are some of the important aspects of a working capital policy:
 CONCEPT 8
DETERMINING THE RATIO OF CURRENT ASSETS TO SALES:
There is a relationship between the sales and the current assets. The actual and the forecasted sales
have a major impact on the amount of current assets which the firm must maintain. So, depending
upon the sale forecast, the financial manager should also estimate the requirement of current assets.
However, as the sales forecast cannot be certain, so is the case with the forecast of current assets
also. This uncertainty may result in spontaneous increase in current assets in line with the increase
in sales level, and may bring the firm to face tight working capital position. In order to overcome
this uncertainty, the financial manager may establish a minimum level as well as a safety
component for each of the current assets for different levels of sales. There are three types of
working capital policies which a firm may adopt, i.e., Moderate working capital policy,
Conservative working capital policy, and Aggressive working capital policy. These policies
describe the relationship between sales level and the level of current assets and have been shown
below:
Current Assets
Conservative
Moderate
Aggressive
Sales Level
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Above figure shows that in case of Moderate working capital policy, the increase in sales level will
be coupled with proportionate increase in level of current assets also, e.g., if the sales increase or are
expected to increase by 10%, then the level of current assets will also be increased by 10%. In case
of Conservative working capital policy, the firm does not like to take risk. For every increase in
sales, the level of current assets will be increased more than proportionately. Such a policy tends to
reduce the risk of shortage of working capital by increasing the safety component of current assets.
The conservative working capital policy also reduces the risk of non-payment to liabilities.
On the other hand, a firm is said to have adopted an Aggressive working capital policy if the
increase in sales does not result in proportionate increase in current assets. For example, for 10%
increase in sales the level of current assets is increased by 7% only. This type of aggressive policy
has many implications. First, the risk of insolvency of the firm increases as the firm maintains
lower liquidity. Second, the firm is exposed to greater risk as it may not be able to face unexpected
change in market, and third, reduced investment in current assets will result in increase in
profitability of the firm.
 CONCEPT 9
LIQUIDITY VERSUS PROFITABILITY - A RISK-RETURN TRADE-OFF
Another important aspect of a working capital policy is to maintain and provide sufficient liquidity
to the firm. A firm must maintain enough cash balance or other liquid assets so that it never faces
problems of payment to liabilities. Does it mean that a firm should maintain unnecessarily large
liquidity to pay the creditors? Can a firm adopt such a policy? Certainly not. There is also another
side of the coin. Greater liquidity makes the firm meeting easily its payment commitments, but
simultaneously greater liquidity involves cost also.
The risk-return trade-off involved in managing the firm’s working capital is a trade-off between the
firm’s liquidity and its profitability. By maintaining a large investment in current assets like cash,
inventory, etc., the firm reduces the chances of (i) production stoppages and the lost sales from the
inventory shortages, and (ii) the inability to pay the creditors on time. However, as the firm
increases its investment in working capital, there is not a corresponding increase in its expected
returns. This means that the firm’s return on investment drops because the profits are unchanged
while the investment in current assets increases.
In addition to the above, the firm’s use of current liability versus long-term debt also involves a
risk-return trade-off. Other things being equal, the greater the firm’s reliance on the short-term debts
or current liabilities in financing its current assets, the greater the risk of illiquidity. On the other
hand, the use of current liability can be advantageous as it is less costly and flexible means of
financing. A firm can reduce its risk of illiquidity and the profitability.
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The effect of changing levels of current assets on the risk-return trade-off can be demonstrated as
follows:
For a given firm, if the level of current assets is increased (it impliedly means that the fixed assets
will reduce by the same amount) then the liquidity position of the firm will also increase and it will
be easily meeting its payment commitments. But simultaneously its profit will decrease as the level
of fixed assets has gone down. In other words, when the level of current assets is increased, the
liquidity of the firm increases but there is always a cost associated with the increased liquidity.
More and more funds will be blocked in current assets which are less profitable and, therefore, the
profitability of the firm will suffer.
Now, in order to increase the profitability, the firm reduces the current assets (and thereby
increasing the fixed assets). Consequently, the profitability of the firm will increase but the liquidity
will be reduced. The firm is now exposed to a greater risk of insolvency. The risk-return syndrome
can be summed up as follows: When liquidity increases, the risk of insolvency is reduced but the
profitability is also reduced. However, when the liquidity is reduced, the profitability increases but
the risk of insolvency also increases. So, the profitability and risk move in the same direction. What
is required on the part of the financial manager is to maintain a balance between risk and
profitability.
 CONCEPT 10
TYPES OF WORKING CAPITAL NEEDS
Another important aspect of working capital management is to segregate the total working capital
needs of the firm into permanent and temporary needs.
1. Permanent Working Capital: PWC is the minimum level of working capital which is
continuously required by a firm in order to maintain its activities. Every firm must have a
minimum of cash, stock and other current assets in order to meet its business requirements
irrespective of the level of operations. Even during slack season, every firm maintains some
current assets. This minimum level of current assets which must be maintained by any firm
all the times, is known as permanent working capital for that firm. This amount of working
capital is constantly and regularly required in the same way as fixed assets are required. So,
it may also be called fixed working capital.
2. Temporary Working Capital: Over and above the permanent working capital, the firm may
also require additional working capital in order to meet the requirements arising out of
fluctuations in sales volume. This extra working capital needed to support the increased
volume of sales is known as temporary or fluctuating working capital for example, in case of
spurt in sales, more stock must be maintained in order to meet the demand. This additional
inventory may become excess when the normal sales level reappears after some time.
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Above figure shows that the permanent working capital may either be constant over a period of time
or may be increasing over a period of time. Further, that the permanent working capital is constant
or increasing regularly while the temporary working capital is fluctuating from time to time. The
bifurcation of total working capital into permanent and temporary components is relevant for the
working capital policy decisions relating to financing of working capital needs.
 CONCEPT 11
FINANCING OF CURRENT ASSETS
Another important aspect of working capital management is to decide the pattern of financing the
current assets and one of the major problem in working capital management is the decision whether
to finance the working capital with one source or the other. The firm has to decide about the sources
of funds which can be availed to make investment in current assets.
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It has been noted earlier that the net working capital is the excess of total current assets over total
current liabilities. A part of total current assets is funded by current liabilities and only the
remaining portion of current assets, known as net working capital, is to be arranged for. Therefore,
the financial manager has to arrange funds for making investment in net working capital only.
Different long-term and short-term sources of funds are available to a firm and all these sources are
different from one another with respect to their nature and characteristics. The working capital
requirements of a firm can be financed by all or any combination of these sources.
1. Hedging Approach (also known as Matching Approach): The hedging principle states that the
financing maturity should follow the cash flow characteristics of the assets being financed. For
example, an asset that is expected to provide cash flows over a period of say, 5 years, then it
should be financed with a debt having similar pattern of cash flow requirements. The hedging
approach involves matching the cash flows generating characteristics of an asset with the
maturity of the sources of financing used to finance it.
The Hedging Approach to working capital financing is based upon the concept of bifurcation of
total working capital needs into permanent working capital and temporary working capital. As
the name itself suggests, the life duration of current assets and the maturity period of the sources
of funds are matched. The general rule is that the length of the finance should match with the
life duration of the assets. That is why the fixed assets are always financed by long-term sources
only. So, the permanent working capital needs are financed by long-term sources. On the other
hand, the temporary working capital needs are financed by short-term sources only. In other
words, the core or fixed working capital is financed by long-term sources of funds while the
additional or fluctuating working capital needs are financed by the short-term sources.
The hedging approach to working capital financing has been shown below:
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2. Conservative Approach: The working capital policy of a firm is called a conservative policy
when all or most of the working capital needs are met by the long-term sources and thus the
firm avoids the risk of insolvency. The conservative approach to financing of working capital
has been shown in the figure A and figure B.
So, under the conservative approach, the working capital is primarily financed by long-term
sources. The larger the portion of long-term sources used for financing the working capital, the
more conservative is said to be working capital policy of the firm. In case, the firm has no
temporary working capital need then the idle long-term funds can be invested in marketable
securities. This will help the firm to earn some income. The Figure B shows that the firm uses a
small amount of short-term sources to meet its peak level working capital needs. It also stores
liquidity in the form of marketable securities in slack season. The light shaded area in Figure B
shows the use of short-term financing for meeting the short-term needs while the dark shaded area
shows the investment of excess funds in marketable securities.
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3. Aggressive Approach: A working capital policy is called an aggressive policy if the firm
decides to finance a part of the permanent working capital by short-term sources. So, the shortterm financing under aggressive policy is more than the short-term financing under the hedging
approach. The aggressive policy seeks to minimize excess liquidity while meeting the shortterm requirements. The firm may accept even greater risk of insolvency in order to save cost of
long-term financing and thus in order to earn greater return. Neither the Hedging approach nor
the Conservative approach can be used by any firm in the strict sense. Therefore, the financial
manager should try to have a trade-off between the hedging and conservative approach.
 CONCEPT 12
SOURCES OF FINANCE IN WORKING CAPITAL
Sources of financing of working capital differ as per the classification of working capital into
permanent working capital and variable working capital.
1. Sources of permanent working capital are the following:
(a) Owner’s funds are the main source. Sale of equity stock or preference stock could provide a
permanent working capital to the business with no burden of repayment particularly during
short period. These funds can be retained in the business permanently. Permanent working
capital provides more strength to the business.
(b) Another source of permanent working capital is bond financing but it has a fixed maturity
period and ultimately repayment has to be made. For repayment of this source, company
provides sinking funds for retirement of bonds issued for permanent working capital.
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(c) Term loan from banks or financial institutions has the same characteristics as the bond
financing of permanent working capital.
(d) Short-term borrowing is also a source of working capital finance on permanent basis.
2. Source of variable working capital
Working capital required for limited period of time may be secured from temporary sources as
discussed below:
(a) Trade Creditors: Trade credit provide a quite effective source of financing variable
working capital for the period falling between the point goods are purchased and the point
when payment is made. The longer this period, the more advantageous it becomes for the
firm to avoid efforts of seeking finance for holding inventories or receivables.
(b) Bank loan: Bank loan is used for variable or temporary working capital. Such loans run
from 30 days to several months with renewals being very common. These loans are granted
by bank on the goodwill and credit worthiness of the borrower, and collateral may include
goods, accounts/notes receivable or Government obligations or other marketable securities,
commodities and equipments.
(c) Commercial Paper: It can be defined as a short term money market instrument, issued in
the form of promissory notes for a fixed maturity. It will be totally unsecured and will have
a maturity period ranging from 90 days to 180 days. It will meet the short term finance
requirements of the companies and will be good short term investment for parking
temporary surpluses by corporate bodies.
(d) Depreciation as a source of working capital: Increase in working capital results form the
difference in the amount of depreciation allowance deducted from earnings and new
investment made in fixed assets.
Usually, the entire amount deducted towards depreciation on fixed assets is not invested in the
acquisition of fixed assets and is saved and utilised in business as working capital. This is also a
temporary source of working capital so long as the acquisition of fixed asset is deferred.
(e) Tax liabilities: Deferred payment of taxes is also a source of working capital. Taxes are not
paid from day-to-day, but estimated liability for taxes is indicated in Balance Sheet. Besides,
business organisations collect taxes by way of income tax payable on salaries of staff
deducted at source, old age retirement benefits, excise taxes, sales taxes, etc. and retain them
for some period in business to be used as working capital.
(f) Other miscellaneous sources are Dealer Deposits, Customer advances etc.
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 CONCEPT 13
NEGATIVE WORKING CAPITAL
Net working capital is the term used to denote the difference of current assets and current liabilities.
Traditionally it has been assumed that the current assets of a firm should be more than adequate to
meet the current liabilities.
In other words, the current ratio, i.e. the ratio of current assets to current liabilities should be more
than one. The rationale behind this assumption is that the firm should at all times be in a position to
maintain liquidity. By definition, current assets are treated as those assets which are capable of
quick conversion into cash and secondly, the time period for conversion into cash is usually small
but not more than one year in any case.
Carrying the argument further, one can postulate that the older the current asset gets, the lesser are
its chances of easy conversion into cash. So, in order to maintain the quality of its current assets, the
firm seeks to reduce their holding period. Simultaneously, the firm tries to prolong the time period
available for payment of its current liabilities by building up the level of inventory through trade
finance and using bank borrowing against inventory and debtors. The result of this exercise is that
the net working capital of the firm turns negative and its current ratio becomes less than one.
On the face of, it the concept of negative net working capital appears to be thought with unfavorable
consequences for the firm. In such a situation, if the firm is required to meet its current obligations
all at once, it might not have adequate liquidity available and as a result, it could default on its
obligations. This could happen in a situation where the cash has moved out of the operating cycle to
long term uses like creation of fixed assets or towards non-productive investments in other firms.
But if the firm has, as part of its conscious working capital management policy, kept the level of
current assets to the minimum and deployed the surplus cash in non-working capital, yet liquid
investments, then it can afford to function with a net working capital that is negative.
Hence so long as a firm does not default on payment of its current liabilities, the fact that it has a
negative net working capital need not be a cause for concern. This may not always be true as most
of the organisatons may like to see current assets more than current liabilities. Example of such
organisations could be banks who provide short-term credit or suppliers of raw material who sell on
credit to firms.
 CONCEPT 14
WORKING CAPITAL: MONITORING AND CONTROL
It goes without saying that the working capital quantum as well as its financing pattern are subject
to constant monitoring and review by the financial manager. There are different analytical tools
which can help a financial manager in monitoring, reviewing and controlling the working capital,
some of which are as follows:
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1. Monitoring the Operating Cycle: It is already noted that the total working capital need
depends upon the length of the operating cycle. The longer the operating cycle, the greater
would be the working capital need. The operating cycle of a firm is consisting of different
cycles for different elements of working capital. Therefore, the financial manager must
monitor the duration of all these individual operating cycles for different elements in order
to effectively control the working capital. The following points are worth noting here:
(a) The actual operating cycle period should be ascertained for each element, i.e., the raw
materials, the work-in-progress, the finished goods, the receivables, etc., over a period of
time and should be compared with the standard operating cycle period set for the same
firm or for the industry as a whole. Efforts should also be made to point out the reasons
for differences in the actual operating cycle period and the standard operating cycle
period.
(b) There should always be an attempt to reduce the length of the operating cycle, total as
well as for each element. The standard operating cycle period need not be lowered but
the actual operating cycle period must be kept as low as possible. This makes the firm to
have comfortable liquidity.
(c) Efforts, in particular, are needed to control the Receivable Conversion Period. If the firm
relaxes in collection, the customers will always like to take liberty.
2. Working Capital Ratios: Another analytical tool that can be used to monitor the working
capital is the accounting ratios, particularly the working capital ratios. For this purpose, the
following working capital ratios may be noted:
(i)
(ii)
(iii)
(iv)
Current ratio, i.e., Current assets to Current liabilities ratio.
Liquid ratio, i.e., Quick assets to Current liabilities ratio.
Current assets to Total assets ratio.
Current assets to Total sales ratio.
These ratios may be ascertained for a number of year to find out the emerging working capital
position of the firm. It may be noted that the Current Ratio is the most important one and it indicates
the position of net working capital also. If the Current Ratio is more than 1, then the net working
capital is positive. If the Current Ratio is 1, then the current assets are just equal to current liability
and there is no net working capital.
The Current Ratio as well as the Quick Ratio, both indicate the liquidity position of the firm vis-àvis the current liabilities. However, the Quick Ratio is supposed to give a better indication of the
liquidity since it excludes the stock which may not be immediately realizable. The standard form of
Current Ratio and Quick Ratio is taken as 2 :1 and 1 : 1 respectively.
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3. Monitoring the Liquidity: It is the liquidity which ensures the short-term survival of the
firm. Sufficient liquidity can be obtained by efficient management of different elements of
working capital. If a firm faces liquidity problems, then it must be realised that this liquidity
problem arises from lack of finance. The liquidity problem can be overcome by raising
additional funds from different sources. But this may not always be possible for the firm.
 CONCEPT 15
WORKING CAPITAL LEVERAGE
Working capital leverage may refer to the way in which a company’s profitability is affected in part
by its working capital management. Profitability of a business enterprise is affected when working
capital is varied relative to sales but not in the same proportion. If the flow of funds created by the
movements of working capital through the various business processes is interrupted, the turnover of
working capital is decreased as is the rate of return on investment. Working capital management
should enhance the productivity of the current assets deployed in business. This correlates the
working capital with Return-on-Investment (ROI). ROI is product of two factors
–
assets turnover and profits margin. If either of these ratios can be increased, ROI will be
increased to a great degree. DU Pont Chart illustrates this position as under:
If profit margins is 6% and By increasing profit margin
By increasing assets turnover
Asset
Turnover is 3 times then ROI by 1%, ROI increases by 3% by 1, ROI increases by 6%
would be 18%
i.e. 6 + 1 = 7 x 3 = 21%
6% x 4 = 24
Assets turnover side of ROI computation may also reflect the working capital management.
Current assets reflect the funds position of a company and is known as Gross Working Capital.
Working Capital leverage is nothing but current assets leverage which refers to the asset turnover
aspect of ROI. This reflects company’s degree of efficiency in employing current assets. In other
words, the ability of the company to guarantee large volume of sales with small current asset base is
a measure of company’s operating efficiency. This phenomenon is asset turnover which is a real
tool in the hands of finance manager in a company to monitor the employment of fund on a
cumulative basis to result into high degree of working capital leverage.
 CONCEPT 16
THE MYTH OF ADEQUATE CURRENT ASSETS
Aligned to the first issue is the myth of adequate current asset. Traditionally, it has been believed
that liquidity is proportional to the level of current assets. A firm having a high current ratio is
treated as favorably placed as regards payment of its current liabilities. This is myth since the
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holding of current assets is always in proportion to the turnover. If level of current assets is rising
disproportionately to the turnover, then notwithstanding the high current ratio, the situation has the
following implications:
–
The age of current assets is increasing which tells upon their quality. As the current assets,
particularly inventory and receivables, get older the chances of their easy and complete
conversion into cash recede.
Once this happens, there is every possibility of the operating cycle cracking.
–
The firm is paying a huge cost for the higher build up of current assets. This cost consists of
a) The amount spent towards raw materials and intermediate inputs
b) The cost incurred towards storing and maintaining the inventory.
c) The interest cost for obtaining finance against these current assets
d) The cost of obsolescence associated with holding inventory for longer periods and
e) The cost of expected default on receivables as reflected in charge to Profit and loss account
towards bad debts.
 CONCEPT 17
DOES THE BALANCE SHEET GIVE A TRUE PICTURE OF CURRENT ASSETS?
We have restricted the discussion of current assets to the position obtained as on a particular date.
This position may not be representative of the state of affairs prevailing on a day to day basis
throughout the year. In order to even out the effects of daily variation in the level of current assets,
it is advisable to take average of weekly, monthly or quarterly holding depending upon the nature of
the industry and turnover of the assets.
The position at the end of a day is a static position which is not representative of the entire year. By
taking period averages some amount of dynamism is brought into the picture.
The second point to be noted is that an industry might have seasonal peaks or troughs of working
capital requirement. For example agro based industry like fruit processing unit would need to stock
more raw material during the peak season when the crop has been harvested than during the lean
season. In such cases different norms have to be applied for peak season and non peak season for
holding of current assets for judging the reasonability of their holding.
We find, therefore that the high level of current assets is nothing but a fiction when we seek to
realize the current assets. It may happen that the inventory carried by the firm may consist of
obsolete items, packing materials, finished goods which have been rejected by buyers and items like
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dies and tools which are more fixed than current in character. Prudence would advise that the firm
should get rid of these current assets as early as possible.
On the other hand, the current liabilities are more ascertainable and less fictions. The payment of
these liabilities, if not possible from the operating cycle, has to be arranged from long term sources
of funds which results in a mismatch that is not conducive to financial health of the firm.
ILLUSTRATIONS FOR PRACTICE
Illustration.1 From the following information of XYZ Ltd. Calculate:
(i) Net operating cycle period.
(ii) Number of operating cycle in a year.
1. Row material inventory consumed during the year
2. Average stock of raw material
3. Work-in-progress inventory
4. Average work- in-progress inventory
5. Finished goods inventory
6. Average finished goods stock held
7. Average collect period from debtors
8. Average credit period availed
9. No of days in a year
6,00,000
50,000
5,00,000
30,000
8,00,000
40,000
45 days
30 days
360 days
Ans. (i) Statement Showing Computation of Net Operation Cycle Period
I. Raw Material conversion period
[
50,000
× 360]
6,00,000
II. Work-in-Progress conversion period
[
30,000
5,00,000
40,000
8,00,000
22
× 360]
III. Finished goods conversion period
[
Days
30
× 360]
IV. Average collection period from debtors
18
45
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V. Less: Average credit period awaited
(30)
Operating Cycle
85
(ii) No. of operating cycles in a year
=
360
85
= 4.24 cycle in a year
Illustration. 2 XYZ Ltd. has obtained the following data concerning the average working capital
cycle for other companies in the same industry:
Raw material stock turnover
20 Days
Credit received
- 45 Days
Work-in-progress turnover
15 Days
Finished goods stock turnover
40 Days
Debtor’s collection period
60 Days
95 Days
Using the following data, calculate the current working capital cycle for XYZ Ltd. and briefly
comment on it.
(Rs. in ‘000)
Sales
3,000
Cost of sales
2,100
Purchases
600
Average raw material stock
80
Average work- in-progress
85
Average finished goods stock
180
Average creditors
90
Average debtors
350
Ans. Statement showing operating cycle
Raw Material conversion period (80/600 x 360)
WIP Conversion period (85/2100 x 360)
Finished goods conversion period (180/2100 x 360)
Avg. collection period from Debtors (350/3000 x 360)
Average a period availed (900/600 x 360)
Operating cycle period
= 48 days
= 15 days
= 31 days
= 42 days
= 54 days
= 82 days
Comment: XYZ Ltd. has an operating cycle better than that of industry. Though the raw material of
XYZ Ltd. takes more than double time to be converted in consumption in comparison to the
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industry, however, the WIP takes the same period to be completed into finished product as the
industry. Finished goods of XYZ Ltd. is converted into goods sold earlier than the industry. Further
the credit period allowed to customers is less than the industry and credit period allowed by
suppliers is more than the industry.
Illustration. 3 From the following information extracted from the books of a manufacturing concern,
compute operating cycle in days.
Period Covered
Average period of credit allowed by supplier
365 days
16 days
(Rs. ‘000)
480
4,400
10,000
10,500
16,000
Average total of debtors outstanding
Raw material consumption
Total production cost
Total cost of sales
Sales for the year
Value of average stock maintained
Raw materials
Work-in-progress
Finished goods
Ans.
320
350
260
Computation of Operating Cycle
(a) Length of Raw Material Inventory
Period
(b) Length of Conversion Period
(c) Length of Finished Stock Period
=
=
=
Average Stock of Raw material
Raw Material Consumption Per Day
320
× 365 = 27 Days
4400
Average Stock of Work−in−Progress
Total Cost of Production Per Day
=
350
10000
× 365 = 13 Days
=
Average Stock of Finished Goods
=
260
× 365 = 9 Days
10,500
Total Cost of Sales Per Day
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(d) Period of Credit Allowed to Debtors
(e)
=
Average Total of Debtors Outstanding
=
480
× 365 = 11 Days
16,000
Sales Per Day
Gross Total Period of Operating Cycle (a+b+c+d)
Less: Average Period of Credit Allowed by Suppliers
Net Total Period of Operating Cycle
60 days
16 days
44 days
Illustration. 4 Calculate the Operating cycle from the following figures related to company ‘X’:
Particulars
Raw Material inventory
Work-in-progress inventory
Finished goods inventory
Debtors
Creditors
Purchase of Raw Material
Cost of Sales
Sales
Ans.
Average amount
Outstanding
(Rs.)
1,80,000
96,000
1,20,000
1,50,000
1,00,000
Average value per day (340
days assumed)
(Rs.)
2,500
4,000
5,000
Calculation of operating cycle
Days
1. Period of Raw Material Stock
Less: Credit granted by supplier
2. Period of Production
3. Turnover of Finished Goods
4. Credit taken by customers
Operating Cycle Period
1,80,000
2500
1,00,000
2500
96,000
4000
1,20,000
4000
1,50,000
5000
72
40
32
24
30
30
116
Comments: Operating cycle is long and a number of steps could be taken to shorten this operating
cycle. Debtors could be cut by a quicker collection of accounts.
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Finished goods could be turned over more rapidly, the level of raw material inventory could be
reduced or the production period shortened.
Illustration. 5 The following information is available for Swati Ltd.
Rs.
Average stock of raw materials and stores
2,00,000
Average work-in-progress inventory
3,00,000
Average finished goods inventory
1,80,000
Average accounts receivable
3,00,000
Average accounts payable
1,80,000
Average raw materials and stores purchased on credit and consumed per day
10,000
Average work-in-progress value of raw materials committed per day
12,500
Average cost of goods sold per day
18,000
Average sales per day
20,000
Calculate the duration of operating cycle.
Ans.
Calculation of operating cycle
Days
Period of Raw Material Stock
Period of work-in-progress stage
Period of finished goods stage
Period of Accounts receivable stage
Period of Accounts payable stage
2,00,000
10,000
3,00,000
12,500
1,80,000
18,000
3,00,000
20,000
1,80,000
10,000
20
24
10
15
18
Duration of operating cycle = (20 + 24 + 10 + 15) – 18 =51 days
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MULTIPLE CHOICE QUESTIONS
1. Working capital = ..............
a) Core current assets less current liabilities
b) Core current assets less core current liabilities
c) Liquid assets less current liabilities
d) Current assets less current liabilities
2. A positive working capital means that a) The company is able to pay-off its long-term liabilities.
b) The company is able to select profitable projects.
c) The company is unable to meet its short-term liabilities.
d) The company is able to pay-off its short-term liabilities.
3. While calculating working capital based on cash cost a) Depreciation is ignored '
b) Non-cash items are not considered
c) Debtors are calculated on the basis of cost of goods sold and not on sale price
d) All of the above
4. Which of the following analyzes the accounts receivable, inventory and accounts payable cycles
in terms of number of days?
a) Operation cycle
b) Current asset cycle
c) Operating cycle
d) Business cycle
5. Which of the following is correct formula to calculate WIP Conversion Period?
a) Annual Cost of Production x 355 days Average Stock of WIP
b) Average Stock of WIP x 365 days Annual Cost of Sales
c) Average Stock of WIP x 365 days Annual Cost of Production
d) Annual Cost of Sales x365days Average Stock of WIP
6. Which of the following is determinant of working capital?
a) Nature and size of business
b) Manufacturing cycle
c) Credit policy
d) Production policy
Select the correct answer from the options given below.
a) only
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b) and (2) only
c) (1), (2) and (3) only
d) (1), (2), (3) and (4)
7. Which of the following is correct formula to calculate working capital leverage?
a) % Change in ROCE/ % Change in Current Assets
b) EBIT / Δ Current Assets
c) Current Assets/Total Assets - Δ Current Assets
d) (A)or(C)
8. Fluctuating Working Capital is also called as a) Reserve Margin Working Capital
b) Temporary Working Capital
c) Permanent Working Capital
d) Variable working capital
9. A conservative policy implies –
a) Greater liquidity and lower risk
b) Greater risk lower liquidity
c) Negligible risk
d) No risk at all with low liquidity
10. Gross working capital refers to a) The amount utilized at the time of contingencies.
b) The firm’s investment in current assets.
c) The capital which is required at the time of the commencement of business.
d) The working capital which is necessary on a continuous and uninterrupted basis.
11. Aggressive approach covers those policies a) Where the firm relies heavily on short term bank finance.
b) Seeks to increase dependence on long term financing.
c) Both (A) and (B)
d) Neither (A) nor (B)
12. A higher current assets/fixed assets ratio indicates a) Hedging Approach
b) Conservative Approach
c) Matching/hedging Approach
d) Aggressive Approach
13. Permanent Working Capital is also known as a) Fixed working capital
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b) Temporary working capital
c) Long term funds
d) Gross margin working capital
14. An aggressive policy indicates a) higher liquidity and poor risk
b) higher risk and poor liquidity
c) higher risk and higher liquidity
d) lower risk with lower liquidity
15. Permanent working capital a) Varies with seasonal needs.
b) Includes fixed assets.
c) Is the amount of current assets required to meet a firm’s long-term minimum needs.
d) Includes accounts payable.
16. Any amount over and above the permanent level of working capital is known as
.............................. working capital.
a) Temporary
b) Fluctuating
c) Variable
d) All of the above
17. ................................ Varies inversely with profitability.
a) Liquidity
b) Risk
c) Gross profit
d) None of the above
18. ................ ................refers to the difference between current asset and current liabilities.
a) Differential working capital
b) Net working capital
c) Operation working capital
d) None of the above
19. Net working capital refers to a) Total assets minus fixed assets.
b) Current assets minus current liabilities.
c) Current assets minus inventories.
d) Current assets.
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20. Which of the following is correct formula to calculate debtor’s collection period?
a) Average book debts/Average Total Sales per day
b) Average Credit Sales per day/ Average book debts
c) Average book debts /Average Credit Sales per day
d) Average Total Sales per day /Average book debts
21. Which of the following working capital strategies is the most aggressive?
a) Making greater use of short term finance and maximizing net short term asset.
b) Making greater use of long term finance and minimizing net short term asset.
c) Making greater use of short term finance and minimizing net short term asset.
d) Making greater use of long term finance and maximizing net short term asset.
22. A conservative policy means a) Lower return and risk.
b) Higher return and risk.
c) Lower return but very high risk.
d) Higher return and higher risk.
23. An aggressive policy produces a) higher return and risk
b) lower return and risk
c) lower return and very low risk
d) none of the above
24. Working Capital Turnover measures the relationship of Working Capital with:
a) Fixed Assets
b) Sales
c) Purchases
d) Stock
25. Working capital is also known as a) Current capital or circulating capital
b) Work-in-progress capital
c) Day-to-day capital
d) Trading capital
26. Which of the following is correct formula to calculate credit period availed?
a) Average credit purchases per day /Average trade creditors
b) Average trade creditors/Average credit purchases per day
c) Average trade creditors /Average total purchases per day
d) Average Total Sales per day /Average book debts
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27. Decrease in current assets means a) Increase in working capital
b) Decrease in inventories
c) Decrease in working capital
d) Increase in accounts payable days.
28. Which of the following is not considered while calculating accounts receivable period?
a) Bills receivable
b) Cash sales
c) Debtors
d) Credit sales
29. ................................ Is also known as working capital ratio.
a) Current ratio
b) Quick ratio
c) Liquid ratio
d) Working capital turnover ratio
30. If annual sales figure is not available then which of the following figure will be taken as base for
calculation of debtors?
a) Factory Cost
b) Cost of Production
c) Cost of Goods Sold
d) Cost of Sales
31. Operating cycles period equals:
a) Collection period + Inventory holding period - Creditor Payment Period
b) Collection period - Inventory holding period + Creditor Payment Period
c) Creditor Payment Period + Inventory holding period - Collection period
d) Any of the above
32. ................................refers to the length of time allowed by a firm for its customers to make
payment for their purchases.
a) Holding period
b) Pay-back period
c) Average collection period
d) Credit period
33. In Current Ratio, Current Assets are compared with:
a) Current Profit
b) Current Liabilities
c) Fixed Assets
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d) Equity Share Capital
34. If raw material consumed is Rs.8,42,000; cost of production is Rs.14,25,000; Stock of raw
material & WIP is Rs.1,24,000 and Rs.72,000 respectively then Raw Material Conversion
period will be Note: 1 Year = 365 days
a) 54 days
b) 18 days
c) 29 days
d) 49 days
35.
Annual credit sales
Cash sales
Debtors
=
=
=
Rs.19,50,000
Rs.1,50,000
Rs.1,60,000
Bills receivable
Finished goods
Collection Period
=
=
=
Rs.1,00,000
Rs.1,22,000
?
Note: 1 Year = 360 days
a) 29 days
b) 30 days
c) 49 days
d) Data given is not sufficient
36. Calculate the working capital from the following data:
Particulars
%
Raw Material Stock
11,70,000
WIP Stock
9,58,750
Finished Goods Stock
26,65,000
Debtors
55,12,000
Cash & Bank
6,00,000
Creditors
17,55,000
Outstanding expenses
a) 76,75,550
b) 76,55,750
c) 75,65,750
d) 77,55,650
14,95,000
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37. Total sales of X Ltd. are Rs.31,248 out of which 25%f are cash sales. Closing balance of debtors
are Rs.9,468 Debtors collection period = ?.
Note: 1 Year = 365 days
a) months
b) 157 days
c) 148 days
d) Month
38. X Ltd. opening stock was Rs.2,50,000 and closing stock was Rs.3,75,000. Sales during the year
was Rs.13,00,000 and gross profit ratio was 25% on sales. Average accounts payable are
Rs.80,000. Creditors Turnover Ratio = ?.
a) 13.75
b) 14.33
c) 13.33
d) 14.44
39. Raw material consumption = Rs.6,48,000 Raw material purchase = Rs.8,42,000 Annual cost of
production = Rs.14,42,000 Creditors = Rs.75,000
Bills payable = Rs.25,000 Creditors Payment Period = ?.
Note: 1 Year = 360 days
a) 34 days
b) 43 days
c) 40 days
d) 39 days
40. If credit sales for the year is Rs.5,40,000 and Debtors at the end of year is Rs.90,000 the
Average Collection Period will be?
Note: 1 year — 365 days
a) 30 days
b) 61 days
c) 90 days
d) 120 days
41. Total wages for the year of Rakshit Ltd., a listed company areRs. 64,80,000 out of which Rs.
2,40,000 are paid in cash immediately after they became due.
Lag in payment of wages - 1 month. If you are appointed to prepare working capital statement
for the company, then how much outstanding wages you will take while preparing working
capital statement?
a) Rs. 5,40,000
b) Rs. 5,50,000
c) Not enough data
d) Rs. 5,20,000
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42. Permanent working capital means
a) Is the amount of current assets required to meet a firm's long-term minimum needs?
b) Includes accounts payable.
c) Includes fixed assets.
d) Varies with seasonal needs.
43. Net working capital refers to
a) Current assets.
b) Total assets minus fixed assets.
c) Current assets minus current liabilities.
d) Current assets minus inventories.
44. Net working capital is the excess of current asset over ____________.
a) Current liability
b) Net liability
c) Total payable
d) Total liability
45. Working capital management is managing ____________.
a) short term assets and liabilities
b) long term assets
c) long terms liabilities
d) only short term assets
46. Which of the following is a basic principle of finance as it relates to the management of working
capital?
a) Profitability varies inversely with risk
b) Liquidity moves together with risk
c) Profitability moves together with risk
d) Profitability moves together with liquidity
47. Greater the size of a business unit ________ will be the requirements of working capital.
a) larger
b) lower
c) no change
d) fixed
48. The amount of the temporary working capital __________.
a) keeps on fluctuating from time to time
b) remains constant for all times
c) financed through long term services
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d) None of the above.
49. The amount of current assets that varies with seasonal requirements is referred to as
__________ working capital.
a) Permanent
b) Net
c) Temporary
d) Gross
50. The fixed proportion of working capital should be generally financed from the ____ capital
sources.
a) fixed
b) variable
c) semi-variable
d) Long term
Answers1
D
11
A
21
C
31
A
41
D
2
D
12
B
22
A
32
D
42
A
3
D
13
A
23
A
33
B
43
C
4
C
14
B
24
B
34
A
44
A
5
C
15
C
25
C
35
C
45
A
6
D
16
D
26
B
36
B
46
C
7
D
17
A
27
C
37
C
47
A
8
D
18
B
28
B
38
A
48
A
9
A
19
B
29
A
39
B
49
C
10
B
20
C
30
B
40
B
50
D
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CHAPTER 12
ESTIMATION & CALCULATIONS
 CONCEPT 1
ASSESSMENT OF WORKING CAPITAL
Requirement of working capital over the operating cycle period could be guessed for shortterm, medium term as well as long-term. For short term, working capital is required to support
a given level of turnover to pay for the goods and services before the cash is received from sales
to customers.
Effort is made that there remains no idle cash and no shortage of money to erase liquidity
within the company’s working process. For this purpose sales budget could be linked to the
expected operating cycle to know working capital requirement for any given period of time or
for each month. Medium term working capital include profit and depreciation provisions. These
funds are retained in business and reduced by expenditure on capital replacements and
dividend and tax payment.
By preparing budget the minimum amount required for medium term working capital can be
estimated. The company can work out its working capital needs for different periods through
cash budget which is key part of working capital planning. To prepare such a budget operating
cycle parameters are of great use as estimation of future sales level, time and amount of funds
flowing into business, future expenditure and costs all can be made with least difficulty to help
the main target.
Then, operating cycle help in assessing the needs of working capital accurately by determining
the relationship between debtors and sales, creditors and sales and inventory and sa les. Even
requirement of extra working capital can be guessed from such estimate.
 CONCEPT 2
WORKING CAPITAL REQUIREMENT ASSESSMENT
Working capital requirement assessment requires :
1. Calculation of average value of Raw Material Inventory, Work in Progress inventory and
Finished Goods inventory
2. Calculation of Trade receivables
3. Calculation of Cash and Cash Convertibles required for normal running of business,
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4. Calculation of trade payables.
The formula which is used for assessing the working capital requirement is listed below:
A. Current Assets `
Value of Raw Material Stock
XXXX
Value of Work in Progress
XXXX
Value of Finished Goods Stock
XXXX
Value of Trade Receivables
XXXX
Value of Cash Required
XXXX
Total of A
XXXXX
B. Current Liabilities
Value of Trade Payable
XXXX
Value of Bank Overdraft
XXXX
Value of Outstanding expenses
XXXX
Total of B
XXXXX
Working Capital Total of (A)-Total of (B)
XXXX
 CONCEPT 3
TANDON COMMITTEE (MPBF)
Bank lending: The Committee introduced the concept of working capital gap. This gap arised
due to the no coverage of the current assets by the current liabilities other than bank
borrowings. A certain portion of this gap will be filled up by the borrower ’s own funds and
long-term borrowings. The Committee developed three alternatives for working out the
maximum permissible level of bank borrowings:
1.
75% of the working capital gap will be financed by the bank i.e.
Total Current assets
Less: Current Liabilities other than Bank Borrowings
= Working Capital Gap.
Less: 25% of Working Capital gap from long-term sources.
2.
Alternatively, the borrower has to provide for a minimum of 25% of the total current
assets out of long-term funds and the bank will provide the balance. The total current
liabilities inclusive of bank borrowings will not exceed 75% of the current assets:
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Total Current Assets
Less: 25% of current assets from long-term sources.
Less: Current liabilities other than Bank borrowings
= Maximum Bank Borrowing permissible.
3. The third alternative is also the same as the second one noted above except that it excludes
the permanent portion of current assets from the total current assets to be financed out of the
long-term funds, viz.
Total Current assets
Less: Permanent portion of current assets
Real Current Assets
Less: 25% of Real Current Assets
Less: Current liabilities other than Bank Borrowings
= Maximum Bank borrowing permissible.
Thus, by following the above measures, the excessive borrowings from banks will be gradually
eliminated and the funds could be put to more productive purposes.
ILLUSTRATIONS
Illustration 1
Astle Garments Ltd. is a famous manufacturer and exporter of garments to the European
countries. The Finance manager of the company is preparing its working capital forecast for the
next year. After carefully screening all the documents, following information is collected:
Production during the previous year was 15,00,000 units. The same level of activity is intended
to be maintained during the current year. The expected ratios of cost to selling price are:
Raw material
Direct wages
Overheads
40%
20%
20%
The raw materials ordinarily remain in stores for 3 months before production. Every units of
production remains in the process for 2 months and is assumed to be consisting of 100% raw
material, wages and overheads. Finished goods remain in the warehouse for 3 months. Credit
allowed by the creditors is 4 months from the date of the delivery of raw material and credit
given to debtors is 3 months from the date of dispatch.
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Lag in payment of overhead expenses
Rs.
2,00,000
½ month
Lag in payment of direct wages expenses
½ month
Estimated balance of cash to be held
Selling price is Rs. 10 per units. Both production and sales are in regular cycle. You are required
to make provision of 10% for contingency (except cash). Relevant assumption may be made.
As the Finance Manager of the Company you are required to prepare the forecast statement of
estimated working capital required.
Solution
Calculation of Profit Margin
Particulars
Raw material
Direct wages
Overheads
Total cost
Add: Profit
Selling price
%
40
20
20
80
20
100
Rs. (per unit)
4
2
2
8
2
10
Estimation of Working Capital
Current Assets
Raw materials stock
(15,00,000 units × Rs. 4 × 3/12)
15,00,000
Work-in-progress
(15,00,000 units × Rs. 8 × 2/12)
20,00,000
Finished goods stock
Debtors
(15,00,000 units × Rs. 8 × 3/12) 30,00,000
(15,00,000 units × Rs. 10 × 3/12) 37,50,000
(a)
1,02,50,000
(15,00,000 units × Rs. 4 × 4/12)
(15,00,000 units × Rs. 2 ×
0.5/12)
(15,00,000 units × Rs. 2 ×
0.5/12)
(b)
20,00,000
Current Liabilities
Creditors for raw material
Wages outstanding
Outstanding expenses
Current assets less
current liabilities
(a) – (b)
1,25,000
1,25,000
22,50,000
80,00,000
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Add: Contingency
(10% of Rs. 80,00,000)
8,00,000
Add: desired cash balance
2,00,000
Estimated Working capital
90,00,000
Illustration 2
Total Current Assets required: Rs. 40,000
Current liabilities other than bank borrowings: Rs. 10,000
Core current assets: Rs. 5,000
Compute maximum permissible bank finance under all the three methods of lending
norms as suggested by the Tandon Committee.
Solution
Rs.
1st Method
Total current assets required
Less: current liabilities
Working capital gap
Less 25% permissible bank borrowings
Maximum permissible bank borrowings
40,000
(10,000)
30,000
(7,500)
22,500
2nd Method
Current assets required
Less: 25% to be provided
Long term funds
Less: Current Liabilities
Maximum permissible bank borrowings
40,000
(10,000)
30,000
(10,000)
20,000
3rd Method
Current assets
Less: Core current assets required
Less: 25% to be provided for
Long term funds
Less: Current Liabilities
Maximum permissible bank borrowings
40,000
(5,000)
(8,750)
26,250
(10,000)
16,250
UNSOLVED QUESTION
Ques.1 PQR Ltd. is engaged in sale and purchase of durables. It expects to attain a turnover of
Rs.60,00,000 next year. Past experience shows that the operating cycle of the firm is 90 days. It
requires a cash balance of Rs.1,00,000. Find out the expected working capital requirement
given that the year consists of 360 days.
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Ans. 1600,000.
Ques.2 Calculate the amount of working capital requirement for SRCC Ltd. from the following
information:
Rs. (Per Unit)
Raw Material
160
Direct Labour
60
Overheads
120
Total Cost
340
Profit
60
Selling Price
400
Raw materials are held in stock on an average for one month. Materials are in process on an
average for half-a-month. Finished goods are in stock on an average for one month.
Credit allowed by suppliers is one month and credit allowed to debtors is two months. Time lag
in payment of wages is 1 ½ weeks. Time lag in payment of overhead expenses is one month.
One-fourth of the sales are made on cash basis.
Cash in hand and at the bank is expected to be Rs.50,000: and expected level of production
amounts to 1,04,000 units for a year of 52 weeks.
You may assumed that production is carried on evenly throughout the year and a time period of
four weeks is equivalent to a month.
Ans. 67,10,000.
Ques.3 Prepare an estimate of net working capital requirement of Nuro Ltd. from the data
given below:
Cost per Unit (Rs.)
Raw Materials
100
Direct Labour
40
Overheads
80
220
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The following is the additional information:
Selling price per unit
Level of activity
Raw Materials in stock
Work-in-progress [Assume 100% stage of
Completion of materials and 50% for labour & overheads]
Finished Goods in stock
Credit allowed by Suppliers
Credit allowed to Debtors
Lag in payment of Wages
Rs.240
1,04,000 units per annum
average 4 weeks
average 2 weeks
average 4 weeks
average 4 weeks
average 8 weeks
average 1 ½ weeks
Cash at Bank is expected to be Rs.25,000. Assume that production is sustained during 52 weeks
of the year.
Ans. 58,25,000.
Ques.4 The cost sheet of PQR Ltd. provides the following data:
Raw material
Direct Labour
Overheads (including depreciation of Rs.10)
Total cost
Profits
Selling price
Cost per unit (Rs.)
50
20
40
110
20
130
Average raw material in stock is for one month. Average material in work-in-progress is for half
month. Credit allowed by suppliers: one month; credit allowed to debtors: one month. Average
time lag in payment of wages: 10 days; average time lag in payment of overheads 30 days. 25%
of the sales are on cash basis. Cash balance expected to be Rs.1,00,000. Finished goods lie in the
warehouse for one month.
You are required to prepare a statement of the working capital needed to finance a level of the
activity of 54,000 units of output. Production is carried on evenly throughout the year and
wages and overheads accrue similarly. State your assumption, if any, clearly.
Ans. 8,91,250
Ques.5 The management of Royal Industries has called for a statement showing the working
capital to finance a level of activity of 1,80,000 units of output for the year. The cost structure
for the company’s product for the above mentioned activity level is detailed below:
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Raw material
Direct labour
Overheads (including depreciation of Rs.5 per unit)
Profit
Selling price
Cost per unit (Rs.)
20
5
15
40
10
50
Additional information:
(a) Minimum desired cash balance is Rs.20,000.
(b) Raw materials are held in stock, on an average, for two months.
(c) Work-in-progress (assume 50% completion stage for all components) will approximate
to half-a-month’s production.
(d) Finished goods remain in warehouse, on an average, for a month.
(e) Suppliers of materials extend a month’s credit and debtors are provided two month’s
credit; cash sales are 25% of total sales.
(f) There is a time-lag in payment of wages of a month; and half-a-month in the case of
overheads.
From the above facts, you are required to prepare a statement showing working capital
requirement.
Ans. 16,13,750
Ques.6 RTS Ltd. expects to sell 30,000 units in a year. The expected cost of production is as
follows:
Rs(Per Unit)
Raw Material
100
Manufacturing Expenses
30
Selling, Administration and Financial Expenses
20
Selling Price
200
The duration at various stages of the operating cycles is expected to be as follows:
Raw Material Stage
2 months
Work-in-progress stage
1 month
Finished Goods stage
½ month
Debtors stage
1 month
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Assuming the monthly sales level of 2,500 units, estimate the Gross Working Capital
requirement if the desired cash balance is 5% of the gross working capital requirement, and
work-in-progress is 25% complete with respect to manufacturing expenses.
Ans. 13,75,000
Ques.7 Prepare a working capital forecast from the following information:
Production during the previous year was 10,00,000 units. The same level of activity is intended
to be maintained during the current year:
The expected ratios of cost to selling price are:
Raw materials
Direct wages
Overheads
40%
20%
20%
The raw materials ordinarily remain in stores for 3 months before production. Every unit of
production remains in the process for 2 months and is assumed to be consisting of 100% raw
materials, wages and overheads. Finished goods remain in the warehouse for 3 months. Credit
allowed by creditors is 4 months from the date of the delivery of raw materials and credit given
to debtors is 3 months from the date of dispatch.
The estimated balance of cash to be held Rs.2,00,000.
Lag in payment of wages ½ month.
Lag in payment of expenses ½ month.
Selling price is Rs.8 per unit. Both production and sales are in a regular cycle. You are required
to make a provision of 10% for contingency (except cash). Relevant assumptions may be made.
Ans. 44,53,334
Page | 333
MULTIPLE CHOICE QUESTIONS
1. Raw material conversion period is 36 days. Raw material consumed and cost of goods sold
in the year is Rs.1,80,000 & Rs.2,16,000 respectively. How much raw material stock will
appear in working capital statement?
Note: 1 Year = 360 days
a) Rs.18,000
b) Rs.20,000
c) Rs.21,600
d) Rs.19,800
2. The following information is available for your calculation.
Level of activity = 1, 56,000 units
(Rs. per unit)
Raw Materials
90
Direct Labour
40
Overheads
75
205
Profit
60
Selling Price
265
Raw materials are in stock on average two month and Materials are in process, on average
half month.
Calculate value of ‘Raw Material Stock’ for working capital purpose.
a) Rs.26,65,000
b) Rs.23,40,000
c) Rs.6,45,250
d) Rs.9,58,750
3. Creditors payment period = 60 days Material consumed = Rs.1,20,000 Material purchased in
cash = Rs.10,000 Material purchased on credit = Rs.90,000
Creditors that will appear in balance sheet and working capital statement = ?.
Note: 1 Year = 360 days
a) Rs.16,667
b) Rs.15,000
c) Rs.20,000
d) Rs.36,667
4. Operating cycle days of X Ltd. is 167 days. Other details are as follows:
Raw material stock velocity
79 days
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Debtors collection period
WIP conversion period
Finished goods conversion period
70 days
36 days
29 days
Creditors payment period = ?
a) 47 days
b) 94 days
c) 52 days
d) 59 days
5. Total ‘cost of sales’ and ‘sales’ of Gama Ltd. is Rs.3,19,80,000 and Rs.4,13,40,000
respectively. It makes 20% sales on cash basis. Debtors are allowed 2 months credit period.
If company calculates working capital on cash cost basis then debtors are a) Rs.55,12,000
b) Rs.42,12,000
c) Rs.42,64,000
d) Rs.55,64,000
6. The following cost information per unit has been ascertained for annual production of
36,000 units :
Variable manufacturing overheads
Fixed manufacturing overheads
Lag in payment of overheads
Rs.2
Rs.1
one month
Expected production and sales are 48,000 units and
35,000 units respectively.
Outstanding overheads will be shown in working capital statement at a) Rs.11,000
b) Rs.11,667
c) Rs.12,000
d) Rs.12,500
7. Management of Royal Ltd. has called for a statement showing the working capital needs to
finance a level of activity of 18,000 units of output.
Cost structure per unit:
Particulars
(Rs. )
Raw materials
20
Direct labour
5
Overheads (including depreciation of Rs.5 per unit)
15
Total cost
40
Page | 335
Profit
10
Selling price
50
Work-in-progress (full for material, 70% & 40% completion in respect of wages &
overheads) will approximate to 15 days of production. 1 year = 360 days. (on total basis)
Calculate closing stock of WIP
a) Rs.22,125
b) Rs.20,652
c) Rs.20,562
d) Rs.20,875
8. Management of X Ltd. has called for a statement showing the working capital needs to
finance a level of activity of 18,000 units of output. Cost structure per unit:
Particulars
(Rs. )
Raw materials
20
Direct labour
5
Overheads (including depreciation of Rs.5 per unit)
15
Total cost
40
Profit
10
Selling price
50
Work-in-progress (full for material, 70% & 40% completion in respect of wages & overheads)
will approximate to 15 days of production. 1 year = 360 days.
Calculate closing stock of WIP on cash cost basis.
a) Rs.22,125
b) Rs.19,250
c) Rs.19,215
d) Rs.20,625
9. Opening and closing stock of X Ltd. is Rs.1,20,000 & Rs.1,80,000 respectively. Material
consumed in income statement is shown at Rs.3,60,000. Suppliers of material extend 4 week
credit. How much of creditors will be shown in preparation of working capital statement if
cash purchase is Rs.50,000?
a) Rs.28,246
b) Rs.28,642
c) Rs.28,426
d) Rs.28,462
10. Opening and closing stock of X Ltd. is Rs.1,20,000 & Rs.1,80,000 respectively. Material
consumed in income statement is shown at Rs.3,60,000. Suppliers of material
Page | 336
extend 4 week credit. How much of creditors will be shown in preparation of working
capital statement?
a) Rs.32,380
b) Rs.32,830
c) Rs.32,308
d) Rs.32,803
11. From the following information calculate working capital:
Equity share capital
18,00,000
Stock
3,15,000
Income tax payable
56,250
Outstanding expenses
1,40,000
Prepaid expenses
37,500
Debtors
4,00,000
Creditors
1,50,000
The management is of the opinion to make 20% margin for contingencies on computed figure.
a) Rs.4,81,250
b) Rs.4,59,370
c) Rs.4,87,500
d) Rs.4,51,370
12. X Ltd. is engaged in large scale customer retailing. From the following information, you are
required to forecast its working capital requirement:
Projected annual sales
Rs.65 lakhs
Net profit on cost of sales
20%
Credit allowed to debtors
10 weeks
Credit allowed by creditors
4 weeks
FGCP
8 weeks
Add 10% to allow for contingencies. (hints: debtors on sales)
a) Rs.14,33,333
b) Rs.15,66,667
c) Rs.16,33,333
d) Rs.16,66,667
13. A company has prepared its annual budget, relevant details of which are reproduced below:
Sales Rs.46.80 lakh (25% cash sales and balance on credit:)
No. of units - 78,000 units
Labour cost: Rs.6 per unit Wages are paid as follows:
For 1st & 2nd week: in the 3rd week For 3rd & 4th week: in the next week.
Assume 1 year = 52 weeks.
How much outstanding wages will appear in working capital statement?
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a) Rs.18,000
b) Rs.20,000
c) Rs.16,000
d) Rs.22,000
14. Selling price is Rs.50 per unit and production and sales for the year are 69,000 units and
75,000 units respectively. Direct wages are 10% of selling price. There is regular production
and sales cycle, and wages and overheads accrue evenly. Wages & overheads are paid in the
next month of accrual. One production process cycle is completed in two month.
How much outstanding wages will be shown in working capital statement?
a) Rs.28,750
b) Rs.57,500
c) Rs.31,250
d) Rs.28,250
15. What relationship exists between the average collection period and accounts receivable
turnover?
a) As average collection period increases (decreases) the accounts receivable turnover
decreases (increases)
b) There is a direct and proportional relationship
c) Both ratios are expressed in number of days
d) Both ratios are expressed in number of times receivables are collected per year
16. Maximum permissible bank finance as per first method of Tandon Committee norms was
Rs.57,41,813 while current liabilities are reported at 32,50,000. Current assets = ?
a) Rs.1,09,05,750
b) Rs.81,79,313
c) Rs.1,09,07,550
d) Rs.1,05,09,750
17. If current assets are Rs. 1,09,05,750 and current liabilities are Rs. 32,50,000 then maximum
permissible bank finance as per first method of Tandon Committee norms is a) Rs.57,41,813
b) Rs. 49,29,313
c) Rs.52,29,813
d) Rs. 49,41,813
18. If current assets are Rs. 1,09,05,750 and current liabilities are Rs. 32,50,000 then maximum
permissible bank finance as per second method of Tandon Committee norms is a) Rs. 57,41,813
b) Rs. 49,29,313
Page | 338
c) Rs. 52,29,813
d) Rs. 49,41,813
19. A company plans to manufacture and sell 400 units of domestic appliances per month at a
price of Rs.600 each. The ratios of cost to selling price are {% of selling price)
Raw materials
30%
Packing material
10%
Direct labour
15%
Direct expenses
5%
Fixed overhead are Rs.4,32,000 p.a.
Finished goods stock = 200 units
Working days in year are taken as 300 days for budget year. Norms maintained for work-inprogress is 7 days. Finished goods stock and WIP stock will appear in balance sheet and
working capital of the company at a) Rs.31,920;Rs. 80,000
b) Rs.80,000;Rs. 31,920
c) Rs.90,000; Rs.67,200
d) Rs.90,000;Rs. 31,920
20. Following is the balance sheet of X Ltd. Calculate maximum permissible bank finance by
Third Method of Tandon Committee norms. Assume the level of Core Current Assets to be
Rs.60 lakhs.
LIABILITIES
Rs. Lakhs
Equity Shares of Rs.10 each
400
Retained Earnings
1,000
Public Deposits
200
Trade Creditors
160
Bills Payable
200
1,960
ASSETS
Fixed Assets
Current Assets:
Rs. Lakhs
1,000
Raw Material
Work-in-progress
Finished Goods
Debtors
Cash at Bank
200
300
150
200
110
1,960
a) Rs.450 lakhs
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b) Rs.360 lakhs
c) Rs.315 lakhs
d) Rs.425 lakhs
21. Current assets & current liabilities of X Ltd. are
9,60,000 and 3,60,000respectively. Maximum permissible bank finance as per Tandon
Committee norms is 3,15,000. What are the core current assets of X Ltd?
a) Rs.60,000
b) Rs.45,000
c) Rs.30,000
d) Rs.90,000
22. Maximum permissible bank finance as per 1st method of Tandon committe e norms is
Rs.3,18,75,000. Long terms loans are Rs.5,58,80,450. Current liabilities are Rs.70,00,000.
Current assets of the company are a) Rs.4,25,00,000
b) Rs.4,95,00,000
c) Rs.3,55,00,000
d) Rs.1,10,00,726
23. X Ltd. submit following figures:
Current Assets = Rs.232.5 lakh Core current assets = Rs.30 lakh
Maximum permissible bank finance as third method of Tandon Committee norms =
Rs.55.625 lakh
Working capital in this case is a) Rs.136.25
b) Rs.106.05
c) Rs.163.25
d) Rs.160.05
ANSWERS 1
2
3
4
5
6
7
8
9
10
A
B
B
A
C
A
A
D
D
C
11
12
13
14
15
16
17
18
19
20
C
D
A
A
A
A
A
B
D
C
21
22
23
A
B
A
Page | 340
CHAPTER 13
RECEIVABLES MANAGEMENT
 CONCEPT 1
WHAT IS RECEIVABLE MANAGEMENT
Receivable Management means planning, organizing, directing and controlling of Receivables.
It provides an answer to the following basic questions:
It involves as identification of customers,
1. To whom credit should be allowed to whom the goods can be sold on credit
after carrying out credit analysis.
It involves the determination of Credit
2. How much credit period should be
Period within which the customers are
allowed?
required to pay.
It involves the determination of amount
3. How much amount of credit should
upto which the credit can be granted to
be allowed?
the customers.
 CONCEPT 2
WHAT IS THE OBJECTIVE OF RECEIVABLE MANAGEMENT
The objective of Receivable Management is to avoid the situation of excessive and inadequate
receivables and to determine and maintain optimum level of receivables after achieving a
trade off between the profitability and liquidity so as to maximize the wealth of shareholders
as a whole. Whenever the situation of excessive and inadequate receivables arises, prompt
and timely action should be taken by management to correct imbalances. Then optimum level
of receivables will lie between the two danger points of excessive and inadequate r eceivables.
The consequences of excessive and inadequate receivables are:
Consequences of Excessive Receivables
1. High Opportunity Cost of investment in
Receivables
2. High Risk of Bad debts
3. High Credit Administration Cost
4. 4. High Risk of Liquidity
Consequences of Inadequate
Receivables
1. Decrease in Sales
2. Risk of loosing Market Share
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 CONCEPT 3
WHAT ARE RECEIVABLES
Receivables (also known as Book Debts) represent the amount to be collected from the
customers to whom the goods or services have been sold on credit.
Customers from whom receivables or book debts have to be collected in near future are called
trade debtors. Investment in Debtors represents the funds blocked for the period beginning
from the date of sale and ending with the date of payment.
 CONCEPT 4
WHY DO FIRMS GRANT CREDIT
The firms credit to retain old customers and the create new customers. In other words, the
firms grant credit to maintain the exiting market share and to increase their market share,
which may pass to their competitors otherwise.
 CONCEPT 5
WHAT IS CREDIT POLICY
Credit Policy refers to the combination of following three decision variables:
CREDIT Policy
Credit Standards
Credit Terms
Collection Efforts
 CREDIT STANDARDS
Credit standards are criteria to decide to whom credit sales can be made and to what extent.
The firm may have soft standards or tight standards.
Type
of Effect
Standard
Sales
on Effect on Bad Effect
on
Credit
Debt
Administration Cost
Soft
Standards
in Increase
bad debt
Increase
Sales
in Increase
in
Credit
administration Cost
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Tight
Standards
Decrease in Decrease
Sales
bad debt
in Decrease
in
Credit
administration Cost
To prepare the various categories of customers, credit analysis should be carried out. Under
credit analysis, the following two factors should be considered:
(a) Average Collection Period, which means the time taken by customers to repay the
credit obligation.
(b) Default Risk, which is the likelihood that a custoit obligation. Default risk is usually
measured in terms of bad debt losses ratio. To determine the default risk, the credit
manager should consider the following three factors:
(i) Character, which refers to the customer’s willingness to pay.
(ii) Capacity, which refers to the customer’s ability to pay.
(iii) Condition, which refers to economic conditions, which may affect the
customer’s ability to pay.
After credit analysis, the customers may be classified in various categories such as follows:
Category of Customers
Good
Marginal
Bad
Average Collection Period
Within credit period
Moderate Collection Period
Very Large Collection Period
Default Risk
0
Moderate
High
 CREDIT TERMS
Credit terms refer to the stipulations under which the firm sells goods on credit to the
customers. These include (a) credit period and (b) cash discount.
a)
Credit Period refers to the length of time for which credit is granted to the customers.
It is usually stated in terms of net days. For example, if credit terms are “net 60”, it
means customers required to pay within 60 days.
b)
A Cash Discount is a reduction in payment offered to customers to include them to pat
within a specified period of time, which will be less than the discount terms specify the
rate of discount and the period for which it is available. If a customer wants to avail
cash discount, he must make the payment in specific credit period otherwise he may
make the payment within cash discount if payment is made 20 days and so cash
discount, if payment is made within normal credit period. For example: Credit terms of
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“2/20 net 60” implies 2 % cash discount if payment is made within 20 days no cash
discount, if payment is made within days.
Credit Terms may be soft or tight.
Types of
Terms
Effect on
Sales
Soft Terms
Increase in
Tight
Terms
Decrease in
Effect on
Investment in
Accounts
Receivables
Increase in
Investment
Decrease in
Investment in
Accounts
receivable.
Effect on Bad
Debt
Effect on Credit
Administration Cost
Increase in bad
debt
Decrease in Bad
debt
Increase in Credit
Decrease in Credit
Administration Cost
 COLLECTION EFFORTS
Collection efforts are needed to accelerate collection from slow payers and to reduce bad debt
losses. The collection policy should specify the collection procedures clearly. The following
procedure is suggested when the customers has not made the payment within the credit
period allowed.
a)
b)
c)
d)
Send first reminder in polite wordings.
If customers still does not respond, send second reminder in some strong wordings.
If the customer still does not respond, send third reminder in strong wordings and
follows up by e-mail, fax telephone, personal visit etc.
If the customer still fails to make the payment and his financial position appears to be
weak, a personal visit should be made with intention to settles the payment with
compromise. On the other hand, if the financial position appears to be strong, initiate a
legal action.
However individual cases should be dealt with on the merits of each individual case.
 CONCEPT 6
WHAT IS THE GOOD OF CREDIT POLICY
The goal of credit policy is to maximize shareholders’ wealth. I is neither the maximisation of
sales nor minimisation of bad debt losses. If sales maximisation would have been the goal of
firm’s credit policy, the firm would follow a very lenient credit policy and would sell on credit
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to everyone. If ministration of debt losses would have been the goal of firm’s credit policy, the
firm would follows tight credit policy and would not sell on credit to anyone.
 CONCEPT 7
WHAT IS OPTIMUM CREDIT POLICY
Optimum Credit Policy refers to the policy, which maximizes the value of the firm. The value
of the firm is maximized when the incremental rate of return (also called the marginal rate of
rerun) is equal to the incremental rate of return required by suppliers of funds (also called the
marginal cost of capital) used to finance the investment. The evaluation of investment in
accounts receivable may be done by following either the total approach or incremental
approach.
 What are the major factors on which the firm’s investment in accounts receivables
depends?
Following may be expressed in terms of sales revenue or cost.
Example: Average Credit Sales is Rs. 10 lacs per day, Average collection Period is 60 days and
Cost of Sales is 80%.
Thus, firm’s investment in Accounts receivable (in terms of sales revenue)
= Daily Credit Sales x Average Collection Period (in days)
= 10 Lacs x 60 = Rs. 600 lacs
Thus, firm’s investment in Accounts receivables (in terms cost)
= Cost of Daily Credit Sales x Average Collection Period (in days)
= 10 Lacs x 80% x 60 = Rs. 480 Lacs
 CONCEPT 8
DISTINCTION BETWEEN CREDIT PERIOD AND AVERAGE COLLECTION PERIOD
Credit Period- Credit period refers to the period for which credit is granted to the customers
as per firm’s credit policy. It is the period within which customers are required to make the
payment. It is usually stated in terms of days. Depending upon the availability o f Cash
Discount, the credit period may be stated as follows:
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Case
Credit Period
1. Where no Cash Discount is allowed 1. ‘net 30’ means customers are
required to pay within 30 days.
2. Where Cash Discount is allowed
2. “2/10, net 30” means with 2% Cash
Discount, make payment within 10 days
and without Cash Discount make
payments 30 days.
 CONCEPT 9
OPPORTUNITY COST OF INVESTMENT IN RECEIVABLES
Meaning - Opportunity Cost of Investment in Receivables is the return forgone on funds
blocked in receivables, which could have been earned if such funds would have been invested
elsewhere.
Usefulness - It is useful in evaluating various debtors policies and in determining the optimal
debtors policy.
How to Calculate - It is calculated as follows :
Opportunity Cost = Cost of Credit Sales x Collection Period (days) x Required Rate of Retu rn
365 days
 CONCEPT 10
MEANING OF FACTORING
Factoring is a financial service, which involves managing, financing and collecting receivables.
It is both a financial as well as management support to supplier of goods/services . It is
method of converting non-productive assets (receivables) into productive assets (Cash). A
factor makes the conversion of receivables into cash possible. Factoring may be defined as a
contract between the supplier of goods/services and the factor under which the factor agrees
to perform atleast two of the following functions:
a)
b)
c)
d)
e)
To finance the assigned book debts (receivables).
To maintain accounts relating to receivables.
To collect book debts.
To provide protection against default in payment by debtors.
To provide credit administration services to the clients to decide whether or not
and how much credit should be extended to the customers.
Page | 346
Some of the major factoring firms in India are SBI Factors and Commercial Services Ltd.,
Canara Bank Factors Ltd. (1991), Fair Growth Factors Ltd. (1992) Services Ltd., Canara Bank
Factors Ltd. (1991), Fair Growth Factors Ltd. (1992)
 CONCEPT 11
FACTORING COMMISSION
The commission charged by the factor for providing factoring services is known as factoring
commission. It is usually expressed as a percentage of face value of receivables factored. In
India, it ranges between 2.5 to 3 per cent. The commission is expected to be lower for
recourse factoring since the factor does not assume the risk of bad debts. The commission is
expected to be higher for non-recourse factoring since the factor assumes the risk of bad
debts.
 CONCEPT 12
TYPES OF FACTORING
The factoring services may be classified under following categories :
1.
Non-recourse Factoring (Old Line Factoring) - Under Non-recourse factoring factor
assumes the risk of bad debts and charges higher commission for and advances cash
upto 80/90% of book debts immediately.
2.
Recourse Factoring - Under recourse factoring, factor does not assume the risk of bad
debts and charges lower commission for and advances cash upto 70/80% of book
debts.
3.
Advance Factoring - Under advance factoring, factor advances cash against the book
debts due to client immediately.
4.
Maturity Factoring - Under maturity factoring, the factor makes the payment on
maturity (i.e. in case of non-recourse factoring on collection of book debts or on
insolvency of customers, in case of recourse factoring on collection of book debts from
customers).
5.
Financial Factoring (Bulk/Agency Factoring) - Under finance factoring, the factor
simply finances the book debts against bulk either on recourse or without recourse and
the client continues to administer and operate sales ledger.
Page | 347
6.
Non-Notification Factoring - Under non-notification factoring, the notice of
assignment of receivables is not given to the debtors. But the factor performs all his
functions without a disclosure to the customers that he owns the book debts.
 CONCEPT 13
PARTIES TO FACTORING CONTRACT
There are three parties involved generally in a factoring contract as follows:
1.
Buyers of goods who has to pay for goods bought on credit terms.
2.
Sellers of goods who has to realize credit sales from buyer.
3.
Factor who acts as agent in realizing credit sales from buyer and passes on the
realized sum to seller after deducting his commission.
 CONCEPT 14
ADVANTAGES OF FACTORING
The advantages resulting from the factoring are as follows :
1. Eliminating of trade discounts.
2. Prompt payments and credits.
3. Improves scope for operating leverage.
4. Reduction of administrative cost and burden.
5. Increase in return to the client.
6. Improvement in liquidity.
7. Provides insurance against bad debts.
8. It is neither a loan nor a deposit but facilities liquidity.
9. It avoids increased debts.
10. Current assets are efficiently managed thus reducing working capital requirements.
11. Better credit discipline amongst customers by regular realization of dues, effective
control of sales journal, reduced credit risk, better working capital management etc.
Page | 348
 CONCEPT 15
HOW TO DECIDE WHETHER OR NOT TO ENGAGE A FACTOR
To decide whether or not to engage a factor, the cost and benefits of factoring should be
evaluated.
The cost of factoring includes:
(a) Factoring commission;
(b) Interest Charged by Factor on advance granted;
The benefits of factoring includes:
(a) Saving in costs of in House Credit Collection Department.
(b) Saving in Bad Debt losses;
(c) Saving in Cost of Funds invested in receivables due to reduction n Average Collection
Period.
Que What is Mechanics of factors?
Ans: - The dynamics of factoring comprises of sequence of events outlined in figure:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
Seller negotiates with factor for establishing factoring relationship.
Seller requests credit check on buyer (client)
Factor check credit credentials & approves buyer for each approved buyer a
credit limit & period of credit is fixed.
Seller sell goods to buyer
Seller send invoices to factor & these are accounted in buyer’s account in
factor’s sales ledger.
Factor sends copy of invoice to buyer.
Factor advances the amount to which seller is entitled after retaining a margin.
On expiry of agreed credit period, buyer makes payment to factor.
Factor pays residual amount to seller
Page | 349
 CONCEPT 16
AGING SCHEDULE
Another technique available for monitoring the receivable is known as aging schedule. The
quality of the receivables of a firm can be measured by looking at the age of receivables. The
older the receivable, the lower is the quality and greater the likeliho od of a default. In the
aging schedule, the lower is the total outstanding receivables on a particular day (at the end of
a month or year) are classified into different age groups (age being the number of days since
becoming outstanding) together with percentage of total receivables that fall in each age
group. For example, the receivables of a firm, having credit period of 30 days, may be
classified as follows:
When compared with the past aging schedule done by the same firm or done by other
comparable firms, this may provide an indication of whether the firm should start worrying
about its collection procedure.
By comparing the aging schedule for different periods, the financial manager can get an idea
of any required change in the collection procedure and can also point out those customers
which require special attention.
Page | 350
Age Group
(Number of Days)
Less than 30 days
31 - 45 days
46 - 60 days
61 days and above
% of Total outstanding
Receivables
60%
20%
10%
10%
IIIustration-1. A company has a 15% required rate of return. The credit sales of the company
are Rs. 160 crore a year and the cost of sales is 75%. The company’s collection period
currently is 60 days. company offered a discount policy with terms of 2/20, net 70, 60 per cent
of its customers will take the discount and the collection period will be reduced to 40 days.
Should the terms be changed? (Assume 360 days in a year)
Ans.
Statement showing the Evaluation of Debtors Policies
Particulars
Present Policy
Proposed
Rs. in crores
Policy
Rs. in crore
A. Expected Profit:
a) Credit Sales
160.00
160.00
b) Total Cost other than Cash
120.00
120.00
Discount
c) Cash Discount
1.92
d) Expected Profit [(a) - (b) 40.00
38.08
(c)]
3.00
2.00
B. Opportunity Cost of Investment in
Receivables
37.00
36.08
C. Net Benefits (A -B)
Recommendation: The Present Policy should be continued since the net benefits under this
policy are higher than those under the proposed policy.
IIIustration-2. MP Ltd. is considering to change its credit terms and provides you the
following information.
Particulars
Present Policy
Proposed Policy I
Credit Terms
Net 30
1/10, Net 30
Sales
14,40,000
Increase in sales by Rs.40,000
Average Collection Period 30 days
Decline in Period by 1/3 rd
Bad Debts
2%
2%
Page | 351
It is expected that 50% of the customers will customers will take discount and pay on 10 th day.
The Variable cost ratio is 70%. And the opportunity cost of investment in receivables is 10%
(Pre-tax). The tax rate is 50% should the company change its credit terms? (Assume 360 day
in a year)
Ans.
Statement showing the Evaluation of Debtors Policies
Particular
Present Policy Proposed Policy
Rs.
Rs.
A. Expected Profit:
a) Credit Sales
14,40,000
14,80,000
b) Total Cost other than Bad Debts & Cash
10,08,000
10,36,000
Discount
28,800
29,600
c) Bad Debts
7,400
d) Profit Before Tax [(a) - (b) - (c) - (d)]
4,03,200
4,07,000
e) Less: Tax
2,01,200
2,03,500
f) Profit after tax
2,01,600
2,03,500
B. Opportunity Cost of investment in
4,200
2,878
Receivables
1,97,400
2,00,622
C. Net Benefits [A -B]
Recommendation: The Proposed Policy should be adopted since the net benefits under this
policy are higher than those under the present policy.
IIIustration-3 PM Ltd. is considering of introducing a cash discount and provides you the
following information.
Particular
Credit Firms
Sales
Average Collection Period
Present Policy
Net 40
120 lakhs
60 days
Proposed Policy
1/10, Net 50
120 lakhs
30 days
It is expected that 50% of the customers will take advantage of the changed credit terms. The
Cost of Sales Ratio is 80%. The required rate of return (pre-tax) in 15% and tax rate is 50%.
Required : Should the company change its credit terms ? (Assume 30 days)
Page | 352
Solution
Statement showing the Evaluation of Debtors Policies
Particulars
Present Policy
Proposed Policy
(Rs. in lakhs)
(Rs. in lakhs)
A. Expected Profit :
(a) Credit Sales
120
120
(b) Variable Costs of Sales
96
96
(c) Cash discount
0.6
(d) Expected Profit before tax [(a)-(b)24
23.4
(c)
12.00
11.7
(e) Less : Tax @ 50%
12.00
11.7
(f) Expected Profit after tax
B. Opportunity Cost of Investment in
1.2
0.60
Receivables
10.8
11.1
C. Net Benefits [A-B]
Recommendation : The Proposed Policy should be adopted since the benefits under this
policy are higher than under the present policy.
IIIustration-4 X Ltd. has credit sales of Rs. 360 lakhs and its average collection period is 30
days. The financial controller estimates that bad debt losses are around 2% of credit sales. The
firm spends Rs. 1,40,000 annually on debtors administration. This cost comprises of
telephonic and fax bills along with salaries of staff members. These are the avodable costs. A
Factoring firm has offered to buy the firm’s receivables. The factor will charge 1% commission
and will pay an advance against receivables on an interest @ 15% p.a. after withholding 10%
as reserve.
Required : Should the company engage factor ? (Assume 360 days in a year).
Solution
Calculation of Factoring Commission, Interest Charge and Advance Granted by
Factor
Particulars
Rs.
A.
Average Level of Receivables [Rs. 360 lakh x 30 days/360 days]
30,00,000
B.
Less : Factoring Commission [1% of Rs. 30 lakhs]
30,000
C.
Less : Factoring Reserve [10% of Rs. 30 lakhs]
3,00,000
D.
Eligible Amount of Advance [A-B-C]
26,70,000
E.
Less : Interest Charges [Rs. 26.7 lakhs x 15% 30 days/360 days]
33,375
F.
Actual Advance granted [D-E]
26,36,625
Page | 353
State showing the Evaluation of Factoring Arrangement
Particulars
A.
Annual Benefits of Factoring to the Firm :
Credit Debts avoided [2% of 360 lakhs]
Bad Debts avoided [2% of 360 lakhs]
Total
B.
Annual Cost of Factoring to the Firm :
Factoring Commission [1% Rs. 360 lakh]
Interest Charged by Factor on advance [Rs. 33,375 x 360
days/30 days
Total
C.
Net Annual Benefits of Factoring to the Firm :
Rs.
1,40,000
7,20,000
8,60,000
3,60,000
4,00,500
7,60,500
99,500
Recommendation: The company should adopt the Non-recourse Factoring alternative since it
results in Net Annual Benefits of Rs. 99,500.
UNSOLVED QUESTION
Ques.1 The company has prepared the following projections for a year:
Sales
Selling Price per unit
Variable Costs per unit
Total Costs per unit
Credit period allowed
21,000 units
Rs.40
Rs.25
Rs.35
One month
The Company proposes to increase the credit period allowed to its customers from one month
to two months. It is envisaged that the change in the policy as above will increase the sales by
8%. The company desires a return of 25% on its investment. You are required to examine and
advise whether the proposed Credit Policy should be implemented or not.
[Answer. Yes, proposed policy should be accepted ]
Ques.2 ABC & Company is making sales of Rs.16,00,000 and it extends a credit of 90 days to
its customers. However, in order to overcome the financial difficulties, it is considering to
change the credit policy. The proposed terms of credit and expected sales are given
hereunder:
Page | 354
Policy
I
II
III
IV
V
Terms
75 days
60 days
45 days
30 days
15 days
Sales
Rs.15,00,000
Rs.14,50,000
Rs.14,25,000
Rs.13,50,000
Rs.13,00,000
The firm has a variable cost of 80% and a fixed cost of Rs.1,00,000. The cost of capital is 15%.
Evaluate different proposed policies and which policy should be adopted? (Year may be taken
as 360 days).
[Answer. Net Profit = 168250, 159375, 158500, 161750, 155250, 152875]
Ques.3 XYZ & Company is making sales of Rs.50,00,000 by extending a credit to its customers
resulting in Average Debtors of Rs.4,29,604. It has a variable cost of 70%. It is believed that
sales can be increased by liberalizing the credit terms from present position upto 90 days. The
sales manager has given following estimates of sales under different credit period.
Policy
I
II
III
IV
Terms
45 days
60 days
75 days
90 days
Sales
Rs.56,00,000
Rs.60,00,000
Rs.65,00,000
Rs.72,00,000
Which policy is best for the firm given that the cost of capital of the firm is 20% (Year = 360
days)
[Answer. Incremental Profit = 142144, 220144, 320561, 468144.]
Ques.4 A trader whose current sales are Rs.15 lacs per annum and average collection period
is 30 days, wants to pursue a more liberal credit policy to improve sales. A study made by a
consultant firm reveals the following information:
Credit Policy
A
B
C
D
E
Increase in Collection
Period
15 days
30 days
45 days
60 days
90 days
Increase in Sales
Rs.60,000
Rs.90,000
Rs.1,50,000
Rs.1,80,000
Rs.2,00,000
Page | 355
The selling price per unit is Rs.5. Average cost per unit is Rs.4 and variable cost per unit is
Rs.2.75 paise per unit. The required rate of return on additional investments is 20 per cent.
Assume 360 days a year and also assume that there are no bad debts. Which of the above
policies would you recommend for adoption?
[Answer. Net Profit(A -B) 2,80,000; 2,96,175; 2,98,850; 3,14,063; 3,16,050; 3,02,667]
Ques.5 ABC Ltd. is examining the question of relaxing its credit policy. It sells at present
20,000 units at a price of Rs.100 per unit, the variable cost per unit is Rs.88 and average cost
per unit at the current sales volume is Rs.92. All the sales are on credit, the average collection
period being 36 days. A relaxed credit policy is expected to increase sales by 10% and the
average age of receivables to 60 days. Assuming 15% return, should the firm relax its credit
policy?
[Answer. 1,32,400; 1,33,600]
Ques.6 H. Ltd. has an annual sales level of 10,000 units at Rs.300/- per unit. The variable cost
per unit is Rs.200 per unit and the fixed costs amount to Rs.3,00,000 per annum. The present
credit allowed by the company is one month. The company is considering a proposal to
increase the credit period to two months and three months and has made the following
estimates:
Credit Policy
Increase in Sales
% of Bad debts
Existing
One Month
1%
Proposed
2 Months
15%
3%
3 Months
30%
5%
There will be increase in fixed cost by Rs.50,000 on account of increase in sales beyond 15%
of present level. The company plans a pre tax-return of 20% on investment in receivables. You
are required to compute the most paying credit policy for the company.
[Answer. Incremental Profit 28,167; -24,167]
Ques.7 A company sells a product @ Rs.30 per unit with a variable cost of Rs.20 per unit. The
fixed costs amount to Rs.6,25,000 per annum and the total annual sales to Rs.75 lacs. It is
estimated that if the present credit facility of one month is doubled, sales could be increased
by Rs.6,00,000 per annum, the company expects a return on investment of at least 20% prior
to taxation. Justify by calculation that this course can be adopted.
[Answer: The credit period may be doubled as it will result in net increase in profit by
Rs.92,917]
Page | 356
Ques.8 ABC Ltd. has currently an annual credit sales of Rs.8,00,000. Its average age of
accounts receivables is 60 days. It is contemplating a change in its credit policy that is
expected to increase sales to Rs.10,00,000 and increase the average age of accounts
receivables to 72 days. The firm’s sale price is Rs.25 per unit, the Variable cost per unit is
Rs.12 and the average cost per unit at Rs.8,00,000 sales volume is Rs.17. Assume a 360 days
year, and calculate the following:
(i)
(ii)
What is the average accounts receivable with both the present and the proposed
plans?
What is the cost of marginal investment, if the assumed rate of return is 15%?
[Answer: Average investment in debtors in existing and proposed plan is Rs.90,667 and
Rs.1,28,000 respectively. So, the marginal increase is (1,28,000 - 90,667) = Rs.37,333
and its cost @ 15% is Rs.5,600.]
Ques.9 PQR Ltd. is considering relaxing its credit policy and evaluating two proposed policies.
Currently, the firm has annual credit sales of Rs.50 lacs and Accounts receivables of
Rs.12,50,000. The current level of loss due to bad debts is Rs.1,50,000. The firm is to give a
return of 20% on investment in the new (additional) accounts receivables. The company ’s
variable costs are 70% of the selling price. The following further information is furnished:
Annual Credit sales
Accounts Receivables
Bad debt losses
Present Policy
Rs.50,00,000
Rs.12,50,000
Rs. 1,50,000
Policy option I
Rs.60,00,000
Rs.20,00,000
Rs. 3,00,000
Policy option II
Rs.67,50,000
Rs.28,12,500
Rs. 4,50,000
You are the management accountant of the firm. Advise the MD which option should be
adopted.
[Answer: Policy Option I may be adopted as it is expected to increase profit by
Rs.45,000.]
Ques.10 ABC Company’s present annual sales amount to Rs.30 lacs at Rs.12 per unit. Variable
costs are Rs.8 per unit and fixed costs amount to Rs.2.50 lacs per annum. Its present credit
period of one month is proposed to be extended to either 2 or 3 months, whichever appears to
be more profitable.
Page | 357
The following estimates are made for the purpose:
Credit Policy
Increase in Sales (%)
% of Bad debt to Sales
1 month
1
2 months
8
3
3 months
30
6
Fixed cost will increase by Rs.50,000 annually after any increase in sales above 25% over the
present level. The company requires a pre tax return on investment of at least 20% for the
level of risk involved. What will be the most rewarding credit policy in case of ABC company
under the above circumstances? Present your answer in a tabular form.
[Answer: Contribution is 1/3 of sales. The present policy is the best. The proposals of 2
months and 3 months credit are not justified as the return on additional investment in
not 20%.]
MULTIPLE CHOICE QUESTIONS
1. Receivables arise a) If the goods are sold on credit.
b) If the goods are sold on cash
c) If the services are rendered on credit
d) If the services are rendered on cash.
Select correct answer from the options given below:
a) 1 only
b) 1 & 2
c) 1 & 3
d) All 1 to 4
2. The goal of receivables management is to maximize the value of the firm by achieving a
trade-off between —
a) Risk & Profitability
b) Liquidity & Profitability
c) Return & Profitability
d) Return & Liquidity
3. The payment terms 2/10, Net 30 tell us that:
a) 2% discount will be awarded if the payment is made within 10 days of invoice date;
otherwise, the full amount is payable within next 10 days of invoice date.
b) 10% discount will be awarded if the payment is made within 20 days of invoice
date; otherwise, the full amount is payable within 30 days of invoice date.
Page | 358
c) 2% discount will be awarded if the payment is made within 30 days of invoice date;
otherwise, the full amount is payable within next 10 days of invoice date.
d) 2% discount will be awarded if the payment is made within 10 days of invoice date;
otherwise, the full amount is payable within 30 days of invo ice date.
4. The cash discount is given to customers for:
a) Early payments
b) Good business relations
c) Bulk purchase
d) Frequent purchases
5. ................................may also be offered for the early payment of dues.
a) Trade discounts
b) Special discounts
c) Both (A) and (B)
d) Cash discounts
6. If you are proposing to introduce relaxed credit policy, you will adopt it if a) There is increase in profit
b) There is reduction in loss
c) Both (A) and (B)
d) Neither (A) nor (B)
7. Which of the following is not an element of credit policy?
a) Credit Terms
b) Collection Policy
c) Cash Discount Terms
d) Sales Price.
8. Ageing schedule incorporates the relationship between
a) Creditors and Days Outstanding,
b) Debtors and Days Outstanding
c) Average Age of Directors
d) Average Age of All Employees.
9. Bad debt cost is not borne by factor in case of
a) Pure Factoring
b) Without Recourse Factoring
c) With Recourse Factoring
d) None of the above.
Page | 359
10. Which is not a service of a factor?
a) Administrating Sales Ledger
b) Advancing against Credit Sales
c) Assuming bad debt losses
d) None of the above.
11. Credit Policy of a firm should involve a trade-off between increased
a) Sales and Increased Profit
b) Profit and Increased Costs of Receivables
c) Sales and Cost of goods sold
d) None of the above.
12. Out of the following, what is not true in respect of factoring?
a) Continuous Arrangement between Factor and Seller
b) Sale of Receivables to the factor
c) Factor provides cost free finance to seller
d) None of the above.
13. 80% of sales of Rs. 10,00,000 of a firm are on credit. It has a Receivable Turnover of 8.
What is the Average collection period (360 days a year) and Average Debtors of the firm?
a) 45 days and Rs. 1,00,000
b) 360 days and Rs. 1,00,000
c) 45 days and Rs. 8,00,000
d) 360 days and Rs. 1,25,000.
14. In response to market expectations, the credit period has been increased fr om 45 days to
60 days. This would result in
a) Decrease in Sales
b) Decrease in Debtors
c) Increase in Bad Debts
d) Increase in Average Collection Period.
15. Cash Discount term 3/15, net 40 means
a) 3% Discount if payment in 15 days, otherwise full payment in 40 days
b) 15% Discount if payment in 3 days, otherwise full payment 40 days
c) 3% Interest if payment made in 40 days and 15%,(d)interest thereafter,
d) None of the above.
16. If the sales of the firm are Rs. 60,00,000 and the average debtors are Rs. 15,00,000 then
the receivables turnover is
Page | 360
a) 4 times,
b) 25%
c) 400%
d) 0.25 times
17. Offering cash discount to customers result in _______.
a) reducing the average collection period
b) increasing the average collection period
c) increasing sales
d) decreasing sales
18. Which of the following is related to Receivables Management?
a) Cash Budget
b) Economic Order Quantity
c) Ageing schedule
d) All of the above.
19. ................................ is an arrangement to have debts collected by a third party entity for a fee.
a) Factoring
b) Aging
c) Forming
d) Crediting
20. In ................. type of factoring the bank/factor takes all the risk and bear all the loss in case
of debts becoming bad debts.
a) Non-Recourse Factoring
b) Invoice Discounting
c) Maturity Factoring
d) Recourse Factoring
21. In factoring arrangement the debts as and when fall due are collected by the a) Debtor
b) Seller
c) Factor
d) Agent
22. The factoring transaction involves
a) Three parties Creditor, Buyer & Factor
b) Four parties Seller, Buyer, Creditor & Factor
c) Three parties Seller, Buyer & Factor
d) Four parties Debtor, Seller, Buyer, & Factor
Page | 361
23. Under which of the following factoring arrangement the bank/factor purchases the
receivables on the condition that any loss arising out or bad debts will be borne by the
company which has taken factoring?
a) Resource Factoring
b) Recourse Factoring
c) Non-Recourse Factoring
d) Maturity Factoring
24. Which of the following is transferred in factoring arrangement?
a) Receivable
b) Payable
c) Outstanding liabilities
d) Prepaid assets
25. Which of the following correctly describes ‘maturity factoring’ arrangement?
a) A factoring arrangement which involves special purpose vehicle.
b) A process which is governed by private contract' between company and factoring firm.
c) Under this type of factoring the bank provide an advance to the company against the
account receivables and in turn charges interest rate from the company for the
payment which bank has given to the company.
d) In this type of factoring bank/factor does not give any advance to the company rather
bank/ factor collects it from customers and pays to the company either on the date of
collection from the customers or on a guaranteed payment date.
26. In which type of factoring, the customer is not informed of the factoring arrangement?
a) Private Factoring
b) Secrete Factoring
c) Undisclosed Factoring
d) Untold Factoring
27. ................................is a means of financing used by exporters that enables them to receive cash
immediately by selling their medium-term receivables (the amount an importer owes the
exporter) at a discount, and eliminate risk by making the sale without recourse, meaning
the exporter has no liability regarding possible default by the importer on paying the
receivables.
a) Forfaiting
b) Factoring
c) Securitization
d) Reconstruction Factoring
28. A forfeiter purchase of the receivables, the sum of which is typically guaranteed by the Page | 362
a) exporter’s bank
b) importer's bank
c) buyer’s bank
d) financer’s bank
29. Forfaiting eliminates a) Risk of the exporter not receiving payment
b) Credit risk and transfer risk
c) Risks posed by foreign exchange rate or interest rate changes.
d) All of the above
30. Forfaiting is a) either with recourse or without recourse
b) always without recourse
c) pure financing agreement
d) (B)and(C)
31. ................................ is an arrangement to have export debts collected by a third party entity for
a fee.
a) Export factoring
b) Forfaiting
c) Striding
d) Countertrade
32. The term credit policy is used to refer
a) Credit standards
b) Credit terms
c) Collection efforts
d) All of the above
33. When net sales for the year are Rs.2,50,000 and debtors Rs.50,000, the average collection
period is:
a) 60 days
b) 45 days
c) 42 days
d) 73 days
34. X Ltd. had sales last year of Rs.26,50,000, including cash sales of Rs.2,50,000. If its average
collection period was 36 days, it’s ending accounts receivable balance is closest to
(Assume a 365 day year.)
a) Rs.2,63,127
b) Rs.2,40,000
Page | 363
c) Rs.2,36,712
d) Rs.2,40,721
35. A Company has prepared the following projections for a year:
Sales
21,000 units
Selling price per unit
Rs.40
Variable costs per unit
Rs.25
Total costs per unit
Rs.35
Credit period allowed
1 month
The company proposes to increase the credit period to 2 months. Tlie change in the policy
will increase the sale by 8%. The company desires a return of 25% on it investment.
Debtors are calculated on cost. The company may decide to shift to proposed policy
because a) Total profit in proposed policy will be Rs.1,30,200 whereas it is Rs.1,05,000 for present
policy.
b) Incremental profit is Rs.25,200
c) Incremental return is 36.92%
d) All of the above
36. Analysis of debtor’s collection history of X Ltd. shows the following facts.
42% debtors pays the amount due within 4 days of sales; 18% debtors pays within 20
days and 40% debtors pays within 40 days of sales. What is the average collection period
of X Ltd.
a) 23 days
b) 28 days
c) 21 days
d) 18 days
37. A firm has current sales of Rs.25,48,000. The firm has unutilized capacity. In order to boost
its sales, it is considering the relaxation in its credit policy. The proposed terms of credit
will be 60 days credit against the present policy of 45 days. As a result, debtors (calculated
on sales) will be a) increased by 1,06,735
b) decreased by 1,04,712
c) increased by 1,06,167
d) increased by 1,04,635
38. XYZ Ltd. has credit sales amounting to Rs.32,00,000. Sale price per unit is Rs.40, the
variable cost is Rs.25 while the average cost is Rs.32. Average age of receivables of the firm
is 72 days. Firm is considering to tighten the credit standards. It will r esult in a fall in sales
Page | 364
to Rs.28,00,000, and the average age of receivables to 45 days. Assume 20% of return.
Proposed policy will yield 1 Year — 360 days and debtors are calculated on cost.
a) Incremental profit of Rs.1,05,350
b) Incremental loss of Rs.1,05,350
c) Incremental profit of Rs.1,05,530
d) Incremental loss of Rs.1,05,530
39. X Ltd. has current sales of Rs.20,00,000. It is planning to introduce a discount policy of
2/10, Net 30. As a result, the Company expects the average collection period to go down by
10 days and 80% of the sales opt for cash discount facility. Required return on investment
is 20%, should it introduce the new discount policy? (compute: debtor on sales)
a) Yes, as profit is increasing by Rs.20,888.
b) No, as profit is decreasing by Rs.20,889.
c) Make no policy change.
d) No, as profit is decreasing by Rs.20,837.
40. Present credit terms of X Ltd. are 1/10 Net 30. Its annual sales are Rs.80 lakhs, its average
collection period is 20 days. Its variable and average total costs to sales are 0.85 & 0.95
and its Ko is 10%. Proportion of sales on which customers currently take discount is 0.5.
Company is relaxing its discount terms to 2/10 Net 30 which will increase sales by Rs.5
lakh, reduce average collection period to 14 days and increase the propo rtion of discount
to sales to 0.8. What will be the effect of on company’s profit? Take year as 360 days.
Debtors are calculated on cost.
a) Profit will increase by Rs.9,900
b) Profit will increase by Rs.9,986
c) Profit will increase by Rs.8,986
d) Profit will decrease by Rs.9,986
41. X Ltd. currently has sales of Rs.30,00,000 with an average collection period of 2 months. At
present, no discounts are offered. Management of the company is thinking to allow a
discount of 2% on sales which will result as under:
(i) The average collection period would reduce to one month.
(it) 50% of customers would take advantage of 2% discount.
Company would normally require a 25% return on its investment. Advise whether to
extend the discount on sales.
Debtors are calculated on sales.
a) Yes, as profit will increase by Rs.32,500
b) Yes, as profit will increase by Rs.30,500
c) Yes, as profit will increase by Rs.31,500
d) Yes, as profit will increase by Rs.32,000
Page | 365
42. A manufacturing firm has credit sales of Rs.360 lakh and its average collection period is 30
days. Firm estimates bad debt losses at around 2% of credit sales. Firm spends Rs.1,40,000
annually on debtors’ administration.
A factoring firm has offered to buy the firm’s receivables. The factor will charge 1%
commission and will pay an advance against receivables on an interest @ 15% p.a. after
withholding 10% as reserve. How much net amount will be paid by the Factor to the Firm?
Assume 360 days in a year.
a) Rs.26,36,625
b) Rs.26,63,625
c) Rs.26,36,526
d) Rs.26,63,265
43. A manufacturing firm has credit sales of Rs.360 lakh and its average collection period is 30
days. Firm estimates bad debt losses at around 2% of credit sales. Firm spends Rs.1,40,000
annually on debtors' administration.
A factoring firm has offered to buy the firm’s receivables. The factor will charge 1%
commission and will pay an advance against receivables on an interest @ 15% p.a. after
withholding 10% as reserve. Net saving/loss to the Firm due to factoring arrangement = ?
a) (99,500)
b) (8,60,000)
c) 99,500
d) 7,60,500
44. X Ltd. expects annual sales of Rs.2.45 million next year. They have a strict credit policy of
2/10, net 20. Based on a 365-day year, 1% of their customers pay in 1 day, 41% pay in 10
days, 56% pay in 23 days and 2% pay in 60 days. What is the expected value of their
accounts receivable for next year?
a) Rs.1,22,097
b) Rs.1,26,583
c) Rs.4,09,639
d) Rs.4,55,699
45. Ninety-per cent of X company’s total sales of Rs.6,00,000 is on credit. If its year-end
receivables turnover is 5, the average collection period (based on a 365 d ay year) and the
year-end receivables are, respectively:
a) 365 days and Rs.1,08,000
b) 73 days and Rs.1,20,000
c) 73 days and Rs.1,08,000
d) 81 days and Rs.1,08,000
State whether each of the following statements is True (T) or False (F).
Page | 366
(i)
(ii)
(iii)
(iv)
Receivables management deals only with the collection of cash from the debtors.
Receivables management involves a trade off between costs and benefits of receivable.
The objective of a credit policy is to curtail the credit period allowed to customers.
Credit period allowed to customers must be equal to credit period allowed by the
supplier to the firm.
Liberalizing the discount rate means increasing the discount rate for the same period.
Ageing schedule of receivables is one way or monitoring the receivables.
Services of a factor are always beneficial.
(v)
(vi)
(vii)
Answers: (i) F, (ii) T, (iii) F, (iv) F, (v) T, (vi) T, (vii) F
Answers –
1
C
11
B
21
C
31
A
41
A
2
A
12
C
22
C
32
D
42
A
3
D
13
A
23
B
33
D
43
C
4
A
14
D
24
A
34
C
44
A
5
D
15
A
25
D
35
D
45
C
6
C
16
A
26
C
36
C
7
D
17
A
27
A
37
C
8
B
18
C
28
B
38
B
9
C
19
A
29
D
39
B
10
D
20
A
30
D
40
D
Page | 367
CHAPTER 14
INVENTORY MANAGEMENT




Inventory Management - A Concept
Objective of Inventory Management
Assumptions of EOQ Technique
Limitations of EOQ Technique
 CONCEPT 1
WHAT IS INVENTORY MANAGEMENT
Inventory Management means planning, organizing, directing and controlling of inventory.
It provides an answer to the following two basic questions:
How much to order - It means what should be the size of an order. How much to order will
depend upon the annual consumption, carrying cost per unit per annum, ordering cost per
order and stock out cost. It involves the determination of E.O.Q.
When to place an order - It means when the fresh order should be placed with supplier to
procure additional inventory. It involves the determination of Re-order level/point.
 CONCEPT 2
WHAT IS THE OBJECTIVE OF INVENTORY MANAGEMENT
The objective of Inventory Management is to avoid the situation of excessive and
inadequate inventory and to determine and maintain optimum level of inventory after
achieving a trade off between the profitability and liquidity so as to maximize the wealth of
shareholders as a whole. Whenever the situation of excessive and inadequate inventory
arises, prompt and timely action should be taken by management to correct imbalances.
The optimum level of inventory will lie between the two danger points of excessive and
inadequate inventory. The consequences of excessive and inadequate to inventory are:
Consequences of Excessive inventory
Consequences
Inventory
of
Inadequate
1. Opportunity Costs of funds tied up in 1. Interruption in Production
inventory
2. Excessive stock out costs
2. Excessive Carrying Costs such as
Page | 368
storage costs, handling cost, insurance
etc.
3. Risk of Liquidity
Thus, an effective management should ensure the procurement of inventory
 Of right quality,
 In the right quantity,
 At right time,
 At right place,
 Form right source.
 CONCEPT 3
NEED FOR HOLDING INVENTORY
Following are the three principle motives for holding inventory:
Transaction Motive - It is need to hold inventories to facilities smooth production and
sales.
1.
2.
3.
Stock of raw material is to be held to facilities continous supply of material to
production department for uninterrupted production.
Stock of W.I.P. is to be held because of production cycle, which is the time span
between introduction of raw material into production and emergence of finished
product.
Stock of finished goods is to be held to facilities continous supply of product to
customers.
Precautionary Motive - It is need to hold inventory to meet contingencies in future.
Speculative Motive - It is the need to hold inventory in order to take advantage of profitable
opportunities as and when they arise.
 Re-Oder quantity or Economic order quantity (EOQ)
1.
Meaning of Economic order quantity (EOQ):- Re-order quantity is the quantity for
which order is placed when the stock reaches re-order level. It is known as economic
order quantity when it is the quantity which is most economical to order.
EOQ refers to the quantity of inventory, at which total of ordering costs and the
carrying costs is minimum. At EOQ the ordering costs are equal to carrying costs.
Page | 369
2.
Objective of Economic Order Quantity (EOQ):- The objective of EOQ is to determine
that order size which is most economical to order.
3.
Importance of EOQ:- The EOQ technique also solves one of the major problems of the
inventory management i.e. the order quantity problem by answering to the question:
‘How much inventory should be ordered at a particular point of time?’
 Assumptions of EOQ Technique
Following are the assumptions of EOQ:
1. Annual Usage (consumption) of inventory is known.
2. Rate of usage is known and constant.
3. Ordering Costs are known and constant.
4. Carrying Costs are known and constant.
5. Zero lead-time/delivery period. (i.e., Inputs are supplied as and when ordered)
Tutorial Notes
(i) Annual total cost of ordering and carrying is minimum at EOQ order size.
(ii) Carrying cost and ordering cost are equal at EOW order size.
Y
Minimum
Total Cost
Total Cost
Costs (Rs.)
Carrying Cost
Ordering Cost
X
0
EOQ
Order Size (Q)
 CONCEPT 4
LIMITATION OF EOQ TECHNIQUE
1) Expected annual usage may not be same as the actual due to unusual and
unexpected demand for inventory.
Page | 370
2) Rate of usage may not be constant due to unusual and expected demand for
inventory.
3) Ordering and carrying costs may not be constant due to fluctuations in the costs of
various components comprising costs.
4) Lead-time may not be constant due to reason beyond supplier’s control.
 CONCEPT 5
ABC ANALYSIS
This system is based on the assumption that in view of the scarcity of managerial time and
efforts, more attention should be paid to those items which account for a larger chunk of
the value of consumption rather than the quantity of consumption. Let us take an example
of a firm having three major components of raw material:
Component Units Consumed % to total Value per unit Total Value (Lacs)
%
A
5000
45.45
1000
50
22.93
B
4000
36.36
1200
48
22
C
2000
18.18
6000
120
55.05
11000
100
218
100
Thus, the cost of raw material C which accounts for 55% of the total consumption value
should be given priority over item A although the number of units consumed of the latter is
much more than former.
Illustration.1
A publishing house purchases 72,000 rims of a special type paper per
annum at cost Rs. 90 per rim. Ordering cost per order is Rs. 500 and the carrying cost is 5
per cent per year of the inventory cost. Normal lead time is 20 days and safety stock is NIL.
Assume 300 working days in a year:
You are required:
(i)
(ii)
(iii)
Calculate the Economic Order Quantity (E.O.Q).
Calculate the Reorder Inventory Level.
If a 1 per cent quantity discount is offered by the supplier for purchases in lots of
18,000 rims or more, should the publishing house accept the proposal?
Answer
Page | 371
EOQ = √
Where,
A
O
C
2 AO
𝑪
= Annual consumption
= Ordering cost per order
= Stock carrying cost per unit per annum
2 × 72,000 × 500
=√
5% of Rs. 90
= √1,60,00,000
= 4,000 Rims.
(ii) Re-order Level = Normal Lead Time ´ Normal Usage
= 20 × 240
= 4,800 Rims.
Note:
Normal Usage =
=
72,000
300
Annual usage
Normal working days in a year
= 240 𝑅𝑖𝑚𝑠
EOQ
Size of order
No. of orders in a year
Average inventory (
Order size
Cost:
2
)
Ordering Cost @ Rs. 500 per order
Discount Offer
4,000 Rims
18,000 Rims
18
4
2,000 Rims
9,000 Rims
Rs.
Rs.
9,000
2,000
9,000
-
-
40,095
Inventory carrying cost
At EOQ – (4,000/2) x Rs. 4.5
At Discount offer – (18,000/2) x Rs. 4.455
Page | 372
Purchases Cost
At EOQ – 72,000 x Rs. 90
64,80,000
-
Total Cost
64,98,000
64,57,295
At discount offer – 72,000 x Rs. 89.10
The total cost is less in case of quantity discount offer. Hence, quantity discount offer
should be accepted.
Illustration.2 (a) Priyanka Ltd. requires 2,000 units of an item annually. The cost of the
item per unit is Rs 20 and ordering cost is Rs 50 per order. If the carrying cost is 25% of the
cost of item find the optimum lot size. If the company purchases in lots of 1,000 or more
units of the item, it gets a rebate of 3%. Should the company accept the offer?
Answer.
The following information of Priyanka Ltd is given:
A = total annual requirement for the item – 2,000 units
B = Ordering cost per order of that item – Rs 50
C = Carrying cost per unit per annum – Rs 20 x .25 = Rs 5
2𝐴𝐵
𝐸𝑂𝑄 = √
𝐶
=√
2 × 2,000 × 𝑅𝑠 50
= 200 𝑢𝑛𝑖𝑡𝑠
𝑅𝑠 5
Company opts for EOQ
Total cost = Purchase cost + Ordering cost + Carrying cost
= 2,000 x Rs 20 + 2,000/200 x Rs 50 + 200/2 x Rs 5
= Rs 40,000 + Rs 500 + Rs 500 = Rs 41,000
When the company purchases in lot of 1,000 units
Total cost = Rs 2,000 x Rs 20 x .97 + 2,000/1,000 x Rs 50 + 1000/2 x Rs 5 x .97
= Rs 38,800 + Rs 100 + Rs 2,245 = Rs 41,325
Since the total cost in second case is higher than the cost when company purchases
in economic lot size, the company should not accept the offer.
Page | 373
Illustration 3
A company buys in lot of 125 boxes which is a three months supply. The cost per box is Rs
125 and the ordering cost is Rs 250 per order. The inventory carrying cost is estimated at
20% of unit value per annum.
You are required per annum.
(i) What is the total annual cost of the existing inventory policy?
(ii) How much money would be saves by employing the economic order quantity
(EOQ)?
Answer Economic Ordering Quantity (EOQ)= √2𝐴𝐵/𝐶
Where,
A = Annual usage = 125 x 4 = 500 units
B = Buying cost or ordering cost = Rs 250
C= Carrying cost per unit per annum = 20% of Rs 125 =Rs 25
EOQ= √2 × 𝐴𝐵/𝐶 = √2 × 500 × 250/25 = √ 10000 = 100 𝑢𝑛𝑖𝑡𝑠
Annual Cost = buying cost + carrying cost per unit
= (250 x 5) + 50 x 25 = 1250 + 12,50 = Rs 2500
(ii) Money saved to be incurred if EOQ is not followed
(i)
Actual cost to be incurred if EOQ is not followed
Illustration.4
Laxmi Ltd. produces an auto part with a monthly demand of 4,000 units. The product
requires Component- X which is purchased at Rs 20. For every finished product, one unit of
Component-X is required. The ordering cost is Rs 120 per order and the holding cost is
10% per annum.
You are required to calculate(i) Economic order quantity (EOQ)
(ii) If the minimum lot size to be supplied is 4,000 units, what is the extra cost, the
company has to incur?
(iii) What is the minimum carrying cost, the company has to incur?
Answer
Page | 374
2𝐴 𝑂
𝐸𝑂𝑄 = √
𝐶
(i)
Where,
EOQ = Economic Order Quantity
A = Annual Consumption = 12 months x 4,000 = 48,000 units
O = fixed cost per order = Rs 120
C = carrying cost per unit = 10% of Rs 20 = Rs 2 per unit
2 × 48.000 × 120
𝐸𝑂𝑄 = √
= 2,400 𝑢𝑛𝑖𝑡𝑠
2
(ii) Extra Cost to be incurred if lot size is 4,000 units
If Lot Size is 2,400
units
If Lot Size is
4,000 units
inventory Ordering Cost
Formula:
𝐴𝑛𝑛𝑢𝑎𝑙 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑛𝑒𝑛𝑡 ×𝑜𝑟𝑑𝑒𝑟𝑖𝑛𝑔 𝑐𝑜𝑠𝑡
𝑜𝑟𝑑𝑒𝑟 𝑆𝑖𝑧𝑒
48,000 × 120
2400
= 2400
Inventory carrying Cost
5,76,0000
2400
𝑖𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦 𝑆𝑖𝑧𝑒 ×𝑐𝑎𝑟𝑟𝑦𝑖𝑛𝑔 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡
24,00 × 2
2
= 24,000
total inventory holding cost
Rs 2,400 + Rs 2,400
Formula
2
= Rs 4,800
Extra cost incurred if minimum lot size is 4,000
units
48,000 × 120
4000
5,76,0000
2400
=1440
4,000 × 2
2
=4,000
Rs 1,440+ Rs
4,000
= Rs 5,440
Rs 5,440 - Rs 4,800
= Rs 640
(iii) The carrying cost will be least at the lowest level of inventory. Since the company’s
monthly demand is 4,000 units, it may order at least in size of 4,000 units
Inventory carrying cost at the order level of 4,000 units =
Formula:
4000 ×2
2
Page | 375
𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦 𝑆𝑖𝑧𝑒 × 𝑐𝑎𝑟𝑟𝑖𝑛𝑔 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡𝑠
= 4,000
2
Illustration.5 EXE Limited has received an offer of quantity discounts on its order of
materials as under :
Price per tonne (Rs.)
Tonnes (Nos.)
1,200
Less than 500
1,180
500 and less than 1,000
1,160
1,000 and less than 2,000
1,140
2,000 and less than 3,000
1,120
3,000 and above
The annual requirement for the material is 5,000 tonnes. The ordering cost per order is Rs.
1,200 and the stock holding cost is estimated at 20% of material cost per annum.
Required : (a) Compute the most economical purchase level.
(b) What will be your answer to the question which precedes this if there are no discounts
offered and the price per tonne is Rs. 1,500?
Ans.
(a) Statement Showing the Total Cost at Various Order Sizes
Total
Order
No. of
Price
Total
Ordering Carrying Cost
p.u
Annual
Size
Orders
Per
Purchasing
Cost
1
Require- (Tonnes)
Tonnes
Price of
P.a.2 x B x
20% of
ments
Inventory
Price per
tonne
A
B
C=
D
E=AxD
F=Cx
G
A/B
Rs.
1200
Rs.
Rs.
Rs.
Rs.
Rs.
5,000
250
20
1,200
60,00,000
24,000
30,000
(125 x Rs. 240)
5,000
500
10
1,180
59,00,000
12,000
59,000
(250 x Rs. 236)
5,000
1,000
5
1,160
58,00,000
6,000
1,16,000
Total
H= E+F+G
Rs.
60,54,000
59,71,000
59,22,000
Page | 376
5,000
2,000
2.5
1,140
57,00,000
3,000
5,000
3,000
1.666
1,120
56,00,000
2,000
(500 x Rs. 232)
2,28,000
(1000 x Rs.
228)
3,36,000
(1500 x Rs.
224)
59,31,000
59,38,000
The most economical purchase level is 1000 tonnes because total cost is minimum (Rs.
59,22,000) at this order size.
2AO
(𝐛)EOQ = √
C
Where, A = Annual Usage, O = Ordering Cost per order
C = Carrying Cost per unit per annum.
=√
2 x 5000 x Rs. 1200
= 200 𝑇𝑜𝑛𝑛𝑒𝑠.
20% Rs. 1500
MULTIPLE CHOICE QUESTIONS
1. EOQ is the quantity that minimizes
a) Total Ordering Cost
b) Total Inventory Cost
c) Total Interest Cost
d) Safety Stock Level.
2. ABC Analysis is used in
a) Inventory Management
b) Receivables Management
c) Accounting Policies
d) Corporate Governance.
3. If no information is available, the General Rule for valuation of stock for balance sheet is
a) Replacement Cost
b) Realizable Value
c) Historical Cost
d) Standard Cost.
Page | 377
4. In ABC inventory management system, class A items may require
a) Higher proportion in terms of value
b) Frequent Deliveries
c) Periodic Inventory system
d) Updating of inventory records.
5. Use of safety stock by a firm would
a) Increase Inventory Cost
b) Decrease Inventory Cost
c) No effect on cost
d) None of the above.
6. In the EOQ Model
a) EOQ will increase if order cost increases
b) EOQ will decrease if holding cost decreases
c) EOQ will decrease if annual usage increases
d) None of the above.
7. EOQ determines the order size when
a) Total Order cost is Minimum
b) Total Number of order is least
c) Total inventory costs are minimum
d) None of the above.
8. If A = Annual Requirement, O = Order Cost and C = Carrying Cost per unit per annum,
then EOQ
a) (2AO/C) 2
b) 2AO/C
c) 2A÷OC
d) 2AOC.
9. Inventory is generally valued as lower of
a) Market Price and Replacement Cost
b) Cost and Net Realizable Value
c) Cost and Sales Value
d) Sales Value and Profit.
10. System of procuring goods when required, is known as,
a) Free on Board (FOB)
b) always Butter Control (ABC)
c) just in Time (JIT)
d) Economic Order Quantity.
11. What is Economic Order Quantity?
a) Cost of an Order
Page | 378
b) Cost of Stock
c) Reorder level
d) Optimum order size.
12. Cost of not carrying sufficient inventory is known as
a) Carrying Cost
b) Holding Cost
c) Total Cost
d) Stock-out Cost
13. Re-order level is ____________than safety level.
a) higher
b) lower
c) medium
d) fixed
14. Raw materials are directly identifiable as part of the final product and are classified as
.................
a) Period costs
b) Fixed costs
c) Direct materials
d) Any of the above
15. Inventory consists of .................
a) Intangible property
b) Tangible property
c) (A)or(B)
d) (A) & (B)
16. Inventory held for sale in the ordinary course of business is known as .................
a) Finished Goods
b) Raw Material
c) Work-in-progress
d) Miscellaneous inventory
17. Wood used in production of tables and chairs, steel bars used in steel factory etc. are
the examples of .................
a) Indirect material
b) Direct material
c) Fixed material
d) All of the above
18. ................. are those cost, which can be identified and traceable to particular product or
costing unit or cost center.
a) Indirect material costs
b) Period costs
Page | 379
c) Direct material costs
d) Fixed costs
19. In which of the following posting is done before the transaction takes place?
a) Bill of Material
b) Bin card
c) Purchase requisition
d) General ledger
20. Which of the following technique can be used for inventory control?
a) Standard Costing
b) ABC Analysis
c) Integrated Accounting System
d) Any of the above
21. ................................ records the quantity details, rates and values of stock movements.
a) Stores ledger
b) Sales ledger
c) Material Transfer Note
d) Delivery Note
22. Which of the following statement is true in relation to ABC Analysis of inventory
control?
a) Category A: It contains a relatively large number of inexpensive items.
Category B: It contains inventory items, which are neither very expensive nor very
cheap.
Category C: It contains inventory items, which are in massive quantities.
b) Category A: It contains inventory items, which are neither very expensive nor very
cheap. Moreover, they are used in moderate quantities.
Category B: It contains a relatively large number of items. But they are either very
inexpensive items or used in very small quantities so that they do not constitute
small percentage of the total value of inventories.
Category C: It contains inventory items, which are expensive or used in massive
quantities. Thus, they low in quantity but high in value.
c) Category A: It contains inventory items, which are low in quantity but high in value.
Category B: It contains inventory items, which are neither very expensive nor very
cheap. They are used in moderate quantities.
Category C: It contains inventory items, which are in massive quantities, but they
are very inexpensive
d) Any of the above
23. Reorder Level = Safety Stock + .................
a) Maximum re-order period
b) Maximum usage
c) Minimum consumption
Page | 380
d) Normal lead time consumption
24. Which of the following formula is used to calculate Re-order Level?
a) (Maximum usage X Maximum re-order period)
b) Safety Stock + Normal lead time consumption
c) (Average usage X Average re-order period)
d) (A) or (B)
25. Which of the following formula is used to calculate Maximum Level?
a) (Re-order level + Re-order qty) - (Maximum consumption X Maximum re-order
period)
b) (Re-order level + Re-order qty) - (Minimum consumption X Minimum re-order
period)
c) (Re-order level + EOQ) - (Minimum consumption X Minimum re-order period)
d) (B)or(C)
26. Re-order Level is also known as .................
a) Re-order Quantity
b) Economic order quantity
c) Reorder point
d) (A)or(C)
27. ................. purchase means the purchase of goods or material such that delivery
immediately precedes their use.
a) Economic order quantity
b) Reorder point
c) Re-order Quantity
d) Just in time (JIT)
28. (Maximum usage - Average Usage) X Lead Time is.
a) Re-order Point
b) Danger Level
c) Safety Stock Level
d) Reorder Level
29. Economic order quantity is that quantity at which cost of holding and carrying
inventory is.................
a) Maximum and equal
b) Minimum and equal
c) It can be maximum or minimum depending upon case to case.
d) Minimum and unequal
30. ABC analysis is an inventory control technique in which: .................
a) Inventory levels are maintained
b) Inventory is classified into A, B and C category with A being the highest quantity,
lowest value.
Page | 381
c) Inventory is classified into A, B and C Category with A being the lowest quantity,
highest value
d) Either (B) or (C)
31. Annual consumption of material - 4,000 units Ordering Cost - Rs.5
Cost per unit - Rs.2
Storage & carrying cost - 8% p.a.
Economic Order Quantity for the item is:
a) 500 units
b) 800 units
c) 300 units
d) 400 units
32. The annual demand of a certain component bought from the market is 1,000 units. The
cost of placing an order is Rs.60 and the carrying cost per unit is Rs.3 p.a. The Economic
Order Quantity for the item is .................
a) 200 units
b) 400 units
c) 600 units
d) 500 units
33. For a particular item of store, the following information are available:
Re-order quantity =12 units Maximum consumption per week = 300 units Normal
consumption per week = 200 units Re-order period = 2 to 4 weeks The Re-order level is
a) 600 units
b) 400 units
c) 1,200 units
d) None of the above
34. A manufacturer requires 9,600 units of a certain component annually. This is currently
purchased from a regular supplier at Rs.50 per unit. The cost of placing an order is
Rs.60 per order and the annual carrying cost is Rs.5 per price. Annual o rdering plus
carrying cost is
a) 2,400
b) 480
c) 4,800
d) 240
35. A publishing house purchases 2,000 units of a particular item per year at a unit cost of
Rs.20. The ordering cost per order is Rs.50 and the inventory carrying cost is 25%. How
will be the total cost if company decides to buy in EOQ?
a) 41,325 b) 41,000
c) 41,500
d) 41,525
Page | 382
36. In a Company the weekly minimum and maximum consumption of Material-A are 25
and 75 units respectively. The re-order quantity as fixed by the company is 300 units.
Material-A is received within 4 to 6 weeks from the date of supply order.
Minimum Level =
a) 450 units
b) 200 units
c) 650 units
d) 800 units
37. The average annual consumption of material is 20,000 kg at a price of Rs.2 per kg. The
storage cost is 16% on average inventory and the cost of placing one order is Rs.50.
What is the time gap between two orders?
a) 7 orders in year
b) 8 orders in year
c) 9 orders in year
d) 6 orders in year
38. Raw material price = Rs.60 per kg., Handling cost = Rs.360, Freight = Rs.390 per order,
Incremental carrying cost of inventory of raw material = Rs.0.50 per kg per month, Cost
of working capital finance on the investment in inventory = Rs.9 per kg p.a. Annual
production = 1,00,000 units.
2.5 units are obtained from one kg of raw material. EOQ is
a) 2,000 kg
b) 3,000 kg
c) 4,000 kg
d) 5,000 kg
39. If the minimum stock level and average stock level of raw material A are 4,000 and
9,000 units respectively, find out its "Re-order quantity”.
a) 10,000 units
b) 5,000 units
c) 2,500 units
d) 26,000 units
40. Re-order quantity of material X is 5,000 kg.; Maximum level 8,000 kg.; Minimum usage
50 kg. per hour; minimum re-order period 4 days; daily working hours in the factory is
8 hours. You are required to calculate the re-order level of material X.
a) 4,600 kg
b) 400 kg
c) 4,200 kg
d) 11,400 kg
41. Normally delivery takes place in 6 days. 1 day stock will be safety stock. Average
consumption per day 150 units.
Re-order Point ?
a) 1,050 units
Page | 383
b) 1,350 units
c) 900 units
d) None of the above
Answer next 5 question on the basis of following data
Monthly demand (units):
2,000
Cost of placing an order (Rs.):
200
Annual carrying cost (Rs. Per unit):
30
Normal usage (units per month):
100
Maximum usage (units per month):
150
Minimum usage (units per month):
50
Re-order period (weeks):
4 to 6
42. Re-order quantity ?
a) 1,200 units
b) 126.49 units
c) 149.26 units
d) 163.29 units
43. Re-order level ?
a) 189.5 units
b) 207 units
c) 92 units
d) 287 units
44. Minimum level ?
a) 189.5 units
b) 207 units
c) 92 units
d) 287 units
45. Maximum level ?
a) 92 units
b) 189.5 units
c) 207 units
d) 287 units
46. Average stock level ?
a) 287 units
b) 92 units
c) 189.5 units
d) 207 units
47. A Company manufactures 5,000 units of a product per month. The cost of placing an
order is Rs.100. The purchase price of the raw material is Rs.10 per kg . The reorder
Page | 384
period is 4 to 8 weeks. The consumption of raw material varies from 100 kg. to 450 kg
per week, the average consumption being 275 kg. The carrying cost of inventory is 20%
p.a. EOQ ?
a) 14,300 kg
b) 1,196 kg
c) 4,396 kg
d) 3,173 kg
48. Re-order Level = 3,750 units. Minimum Level — 1,750 units, Average Delivery Period =
2 weeks, Average Consumption ?
a) 1,750 units
b) 1,250 units
c) 1,500 units
d) 1,000 units
49. Normally delivery takes place in 6 days. 3 day stock will be safety stock. Average
consumption per day 150 units. Minimum consumption per day is 75 units. Reorder
Point- ?
a) 1,125 units
b) 675 units
c) 900 units
d) 1,350 units
50. Safety Stock = 30 days consumption, Annual consumption (360 days) = 12,000 units,
Normal lead time =15 days. Re-order Level ?
a) 1,096 units
b) 1,500 units
c) 1,000 units
d) 500 units
51. Minimum Level = 2,750 units, EOQ = 2,082 units, Average Level ?
a) 4,832 units
b) 3,457 units
c) 3,791 units
d) 4,791 units
52. EOQ =100 units, Annual consumption - 2,000 units, Carrying cost per unit per annum =
Rs.480, Ordering
cost =?
a) Rs.1,400
b) Rs.1,200
c) Rs.1,600
d) Rs.2,000
53. Calculate re-order level from the following: Safety stock: 1,000 units
Consumption per week: 500 units
Page | 385
It takes 12 weeks to reach material from the date of ordering.
a) 1,000 units
b) 6,000 units
c) 3,000 units
d) 7,000 units
54. From the following information, calculate the extra cost of material by following EOQ:
Annual consumption = 45,000 units Ordering cost per order = Rs.10 Carrying cost per
unit p. a. = Rs.10 Purchase price per unit = Rs.50 Re-order quantity at present = 45,000
units
There is discount of 10% per unit in case of purchase of 45,000 units in bulk.
a) No saving
b) Rs.2,00,000
c) X2,22,010
d) Rs.2,990
55. Total cost = 24,30,000, No. of orders = 4 orders, Ordering cost = Rs.750, Ordering qty =
10,000 units, Carrying cost per unit per annum = Rs.15. Material price per unit =
a) 58.80
b) 60.20
c) 60.80
d) 60.00
56. Opening Stock = 25,000 units, Closing Stock = 15,000 units. Purchases = 1,90,000 units.
(Take 1 year = 360 days). Stock Velocity = ?
a) 30 days
b) 90 days
c) 60 days
d) 36 days
57. Inventory turnover ratio = 2.5 times, Opening Stock = 90,000 units, Closing Stock =
1,10,000 units. Purchases = ?
a) 2,30,000 units
b) 2,70,000 units
c) 2,50,000 units
d) 2,40,000 units
58. Stock Velocity = 180 days, Material consumed = 1,50,000, Closing Stock = 6 2,500 units.
Opening stock = ?
a) 2,12,500 units
b) 3,00,000 units
c) 87,500 units
d) 1,62,500 units
59. X Ltd. uses about 75,000 valves per year and the usage is fairly constant at 6,250 valves
per month. The valve costs Rs.1.50 per unit when bought in large quantities; and the
Page | 386
carrying cost is estimated to be 20% of average inventory investment on an annual
basis. The cost to place an order and process the delivery is Rs.18. Frequency of order =
?
a) 25 orders per year
b) 52 orders per year
c) 20 orders per year
d) 50 orders per year
60. About 50 items are required every day for a machine. A fixed cost of Rs.50 per order is
incurred for placing an order. The inventory carrying cost per item amount to Rs.0.02
per day. The lead period is 32 days. Re-order Level -?
a) 500 units
b) 1,600 units
c) 1,100 units
d) 600 units
61. June 2016: EOQ is 200 units, ordering cost Rs.20 per order and total purchases 4,000
units. The carrying cost per unit will be —
a) Rs.2
b) Rs.6
c) Rs.4
d) None of the above
62. June 2016: Following information is given for Component ‘A’:
Normal usage 50 units per week, maximum usage 75 units per week, re-order period 4
to 6 weeks. The minimum level of stock will be —
a) 250 Units
b) 150 Units
c) 450 Units
d) 200 Units
63. June 2016:
Re-order quantity : 300 kg
Minimum usage : 20 kg per day
Minimum lead time : 5 days
Maximum stock level : 400 kg Re-order level will be —
a) 350 kg
b) 200 kg
c) 375 kg
d) 150 kg
64. Dec 2016: A company produces a single product for which following data is available:
Average production per week: 200 units
Usage per unit:
10 kg
Page | 387
Re-order level:
Delivery time required:
8,000 kg
2 weeks
The minimum level of stock required will be —
a) 3,000 kg
b) 5,000 kg
c) 4,000 kg
d) 2,500 kg
65. Dec 2016: The maximum and minimum lead time is 4 weeks and 3 weeks respectively.
If the maximum and minimum weekly consumption is 25 units and 20 units
respectively, the re-ordering level will be —
a) 100 Units
b) 110 Units
c) 120 Units
d) 140 Units
66. Dec 2018: The monthly requirement of a component is 4,000 units. The cost per order
is Rs.1,000 and the carrying cost per unit per annum is Rs.24. The Economic Ordering
Quantity is:
a) 2,000 units
b) 4,000 units
c) 577.35 units
d) 1,825.74 units
67. June 2019: The following information is given:
10,000 units of material are consumed per year; per unit cost is Rs.20; cost of
processing an order is Rs.50; Annual interest rate is 5%; Annual carrying cost of
material per unit is 15% (other than interest). What would be the Economic Order
Quantity (EOQ)
a) 200 units
b) 500 units
c) 400 units
d) 100 units
68. Dec 2018: If annual total carrying cost, per unit carrying cost and cost per order are
Rs.15,000, Rs.10 & Rs.150 respectively, then Economic Order Quantity will be:
a) 1,500 units
b) 3,000 units
c) 100 units
d) 200 units
69. Dec 2018: If the Minimum Stock Level is 2,500 units, Normal Consumption is 150 units,
Maximum Reorder Period is 10 days and Normal Re-order Period is 8 days, then Reorder Level will be:
Page | 388
a) 1,500 units
b) 4,000 units
c) 1,200 units
d) 3,700 units
70. June 2018: If EOQ is 200 units, ordering cost is Rs.20 per order and total purchases is
4,000 units. The carrying cost per unit will be:
a) Rs.4
b) Rs.6
c) Rs.8
d) Rs.2
Answer:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
B
A
B
A
A
A
C
B
B
C
D
D
A
C
B
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
A
B
C
B
B
A
C
D
D
D
D
D
C
B
C
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
A
A
C
A
B
B
B
A
A
A
A
B
B
C
D
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
C
B
D
D
B
C
B
D
D
A
D
B
C
A
B
61
62
63
64
65
66
67
68
69
70
C
D
B
C
A
A
B
D
D
A
Whether each of the following statements is True (T) or False (F)
(i)
(ii)
(iii)
(iv)
Stock of finished goods should be as high as possible so that no customer is
denied the sale.
There is no explicit benefit of keeping inventory, hence no stock be
maintained.
Carrying cost and ordering cost are opposite forces in inventory
management.
Cost of stock out occurs whenever the firm has no stock of a particular item.
Page | 389
(v)
(vi)
(vii)
(viii)
ABC analysis helps to ascertain the minimum level of stock of raw material.
The EOQ model attempts to minimizing the total cost of holding inventory.
EOQ model assumes a constant usage rate for a particular item.
Average inventory in EOQ model is 1/2 of EOQ.
Answers (i) F, (ii) F, (iii) T, (iv) T, (v) F, (vi) T, (vii) T, (ix) T
Page | 390
CHAPTER 15
MANAGEMENT OF CASH
 CONCEPT 1
MEANING OF CASH MANAGEMENT
Cash Management means planning, organizing, directing and controlling of cash. It
provides an answer to the following basic questions:
(a) How much to maintain cash balance?
It means what should be level of cash in the organisation. How much to maintain cash
balance will depend upon the cash operating cycle. Larger the operating cycle, larger
the cash balance required.
(b) How to finance deficit (i.e., excess of estimated cash outflows over estimated cash
inflows)?
(c) How to invest surplus (i.e., excess of estimated cash inflows over estimated cash
outflows)?
 CONCEPT 2
OBJECTIVE OF CASH MANAGEMENT
The objective of cash management is to avoid the situation of excessive and inadequate
cash and to determine and maintain the optimum level of cash after achieving a trade off
between the profitability and liquidity so as to maximize the wealth of shareholders as a
whole.
Whenever the situation of surplus or deficit cash arises, prompt and timely action should
be taken by the management to correct the imbalances.
 CONCEPT 3
NEED FOR CASH/ MOTIVE OF HOLDING CASH/
The following are the three principal motives for holding cash :
a)
Transactional Motive
Page | 391
This is the most essential motive for holding cash because cash is the medium
through which all the transactions of the firm are carried out. Some examples of
transactions of a manufacturing firm are given below:
–
–
–
–
–
Purchase of Capital Goods like plant and machinery
Purchase of raw material and components
Payment of rent and wages
Payment for utilities like water, power and telephone
Payment for service like freight and courier
These transactions are paid for from the cash pool or cash reservoir which is all the time
being supplemented by inflows. These inflows are of the following kinds:
–
–
–
Capital inflows from promoters’ capital and borrowed funds
Sales proceeds of finished goods
Capital gains from investments
The size of the cash pool depends upon the overall operations of the firm. Ideally, for
transaction purposes, the working capital inflows should be more than the working capital
outflows at any point of time.
b)
Speculative Motive
Since cash is the most liquid current asset, it has the maximum potential of value
addition to a firm’s business. The value addition can come in two forms. First, as the
originating and terminal point of the operating cycle, cash is invaluable. But cash has
an opportunity cost also and if cash is kept idle, it becomes a liability rather than an
asset. Therefore, efficient firms seek to deploy surplus cash in short term
investments to get better returns. It is here that the second form of value addition
from cash can be had. Since this deployment of cash needs to be done skillfully, not
all the firms hold cash for speculative motive. Further the amount of cash held for
speculative motive should not cause any strain upon the operating cycle.
c)
Contingency Motive
This motive of holding cash takes into account the element of uncertainty associated
with any form of business. The uncertainty can result in prolongation of the working
capital operating cycle or even its disruption. It is possible that cost of raw materials
or components might go up or the time taken for conversion of raw materials into
finished goods might increase. For such contingencies, some amount of cash is kept
by every firm
Page | 392
 CONCEPT 4
WHAT IS FLOAT & ITS KIND?
Float - The term float is used to refer to the periods that effect cash as it moves through the
different stages of the collection process, it represents time gap for receiving cash after
sales.
Kind of Float - Different kinds of float with reference to management of cash are as
follows.
1.
Billing Float - Billing float refers to the time between the sale and mailing the invoice
to the customer.
2.
Mail Float - Mail float refers to the gap between the time a customer sends the cheque
and the time the cheque is received by the firm.
3.
Cheque Processing Float - Cheque Processing float refers to the gap between the time
the cheques is received by the firm and the time the cheque is deposited into the bank.
4.
Banking Processing Float - Banking Processing float refers to the gap between the
time the cheque is deposited into the bank and the time the cheque is credited to firm’s
bank account.
 CONCEPT 5
HOW TO ACCELERATE CASH COLLECTION
Cash collection can be accelerated:
(a) By reducing processing time in raising the invoice to the customer.
(b) By reducing the time gap between the time a customer sends the cheque and the
time the cheque is received by the firm.
(c) By reducing the processing time between the time the cheque is received by the firm
and the time the cheque is deposited into bank.
(d) By reducing the collection time between the time the cheque is deposited in bank
and the time the cheque is credited to firm’s bank account.
The amount of cheques sent by customers, which are not yet collected is called collection
or deposit float.
Page | 393
 CONCEPT 6
METHODS OF ACCELERATING CASH COLLECTION
 Lock Box System
Purpose - The purpose of lock box system is to eliminate the time gap between the receipt
of cheque and its deposits into the bank.
Working - The working of lock box system is as follows:
(a) The firm establishes a number of collection centres considering customer ’s location
and volume of remittances.
(b) The firm hires a local post office box at each center.
(c) The firm instructs its customers to mail their remittances to the lock boxes.
(d) The firm authorities its local bank at each center to pick up their remittance from local
box.
(e) The bank picks up the mail several times a day and deposits the cheques in firm’s bank
account.
Decision - Whether a lock box system should be used or not should be decided on the basis
of its costs and benefits. If its benefits exceed its costs, the system should be introduced,
otherwise not.
Example
Lockers Pvt. Ltd. is considering the use of a lockbox system to handle its daily collections.
The company’s credit sales are Rs.160 crore per year, and it currently processes 1,300
cheques per day. The cost of the lockbox system is Rs.95,000 per year. The system allows
for up to 1,000 cheques per day. Any additional cheques are processed at an additional
charge of Rs.1.50 per cheque. The company estimates that the system will reduce its float
by 3 days. The firm’s discount rate for equally risky projects is 15 per cent, its tax rate is 40
per cent, and its cost of short-term capital is 12 per cent. (Assume a 360-day year).
(a) How much cash will be released for other uses if the lockbox system is used ?
(b) What net benefit will Lockers Ltd. gain from using lockbox system ?
(c) Should Lockers Ltd. adopt the proposed lockbox system ?
Page | 394
(d) Assume now that the institution that offers the lockbox system requires a
Rs.7,00,000 compensating balance to be held for the complete year in a non interest-bearing account. Should Lockers Ltd. adopt the system ?
1) Credit sales per day = 160 croe / 360 days = 44,44,444
2) Cost if lock box system is adopted
Cost of lock box = Rs.95,000
Additional cost for cheques = 300 cheque x Rs.1.5 x 360 = Rs. 1,62,000
Opportunity cost = 2,57,000 x 12% = 30,840
Total cost = 257,000 + 30,840 = 2,87,840.
3) Cost of Funds = 7,00,000 x 12% = 84,000.
4) Reduction in float days = 3
(a) Cash that will be released for other use = 44,44,444 x 3 days = 1,33,33,332.
(b) Cost of locker = 2,87,840.
Gain on release of fund = 1,33,33,332 x 15% = 20,00,000 Apprx.
Hence net benefit from use of lock box = 20,00,000 - 287,840 =17,12,160.
(c) Lockers Ltd. should adopt the lock box system.
(d) Total cost if Rs. 7,00,000 to be deposited = 84,000 + 2,87,840 = 3,71,840.
Net gain = 20,00,000 - 371,840 = 16,28,160. Still Lockers Ltd. should adopt the lock box
system.
Page | 395
 CONCEPT 7
BAUMOL’S MODEL
Application- The Baumol’s Model helps in determining the optimum cash balance when
the demand for cash is certain.
Optimum Cash Balance - According to Baumol’s model, optimum cash balance is that level
of cash where the total of carrying costs (or holding costs) and transactions costs is the
minimum.
Meaning of Economic Lot Size - The Economic Lot Size refers to the size of lot, at which
total of transaction costs and the holding costs is minimum. At Economic Lot Size, total
transaction costs are equal to total holding costs.
Factors to be Considered - Economic Lot Size is determined after considering the
following factors.
(a) Transaction Costs: The transaction costs refer to the costs involved in converting the
marketable securities into cash. This happen when the firm falls short of cash and has
to sell the securities resulting in clerical, brokerage, registration and other costs. The
transaction cost per transaction is assumed to be constant. Total transaction cost is
calculated as follows:
Total Transaction Cost = Total No. of Transaction × Per Transaction
Total No. of Transaction =
Annual cash requirment (A)
Economic lot size (C)
There is an Inverse relationship between lot size and transaction cost.
Larger the lot size
Smaller the lot size
Lower the transaction costs because of fewer lots
Higher the transaction costs because of more lots
(b) Holding Costs : The holding cost or opportunity cost refers to the return foregone on
marketable securities or the cost incurred in maintaining an Average Cash Balance. It
varies with the Average Cash Balance.
Page | 396
There is positive relationship between lot size and holding cost.
Large the lot size
Smaller the lot size
Higher the holding costs because of high average cash
balance.
Lower the holding costs because of low average cash
balance
The total holding cost is calculated as follows
Total Holding Cost = Average Cash Balance × Holding Cost p.a.
=
=
Economic Lot Size (C)
× Holding Cost p. a. (H)
2
C
× H
2
(c) Annual Requirement of Cash.
Importance of Economic Lot Size - The Economic Lot Size technique solves one of the
major problems of the cash management i.e., the lot size problem by answering to the
question : ‘How much marketable securities should be sold at a particular point of time ? ’
Assumptions of Economic Lot Size Technique
Following are the assumptions of Economic Lot Size:
1. Constant Annual Requirement of Cash
2. Constant Rate of Demand for Cash
3. Constant Transaction Costs
4. Constant Holding Costs, and
5. Zero Conversion Period
Tutorial Notes:
(i) Annual total cost of transaction and holding is minimum at Economics Lot Size.
(ii) Holding cost and transaction cost are equal at Economics Lot Size.
Page | 397
Y
Minimum
Total Cost
Total Cost
Holding Cost
Costs (Rs.)
Transaction Cost
O
X
Lot Size
Control Limits - In the Miller-Orr’s model, control limits are set for cash balances. These
limits consist of upper limit (h), the return point (z) & the lower limit (o).
1. Upper Limit It is level of cash balance at which the marketable securities are
(h)
purchased to bring down the cash balance back to the normal level.
2. Lower Limit It is that level of cash balance at which the marketable securities are
(o)
sold to bring up cash balance back to the normal level.
3. Return Point It is normal level of cash balance which lies between the upper limit
(z)
and lower limit and which is to be attained after purchase/sale of
marketable securities.
ILLUSTRATION
Illustration-1 The annual cash requirement of A Ltd. is Rs. 10 lakhs. The company has
marketable securities in lot sizes of Rs. 50,000, Rs. 1,00,000, Rs. 2,00,000, Rs. 2,50,000 and
Rs. 5,00,000. Cost of conversion of marketable securities per lot is Rs. 1,000. The company
can earn 5% annual yield on its securities.
You required to prepare a table indicating which lot size will have to be sold by the
company. Also show that the economic lot size can be obtained by the Baumol Model.
Ans.
Table Indicating Total Cost at different lot sizes of securities
Page | 398
Total Annual Cash Requirement (A) 10,00,000 10,00,000 10,00,000 10,00,000 10,00,000
Lot Size (Rs.) (S)
50,000
1,00,000
2,00,000
2,50,000
50,00,000
Number of Lots
20
10
5
4
2
Transaction Cost (Rs.)
20,000
10,000
5,000
4,000
2,000
Hold Cost (Rs.) [S/2 × 5%]
1,250
2,500
5,000
6,250
12,500
Total Cost (Rs.)
21,250
12,500
10,000
10,250
14,500
[A/S x Rs. 1,000]
Economic lot size is Rs. 2,00,000 at which total costs are minimum.
Illustration-2 X Ltd. is to start production on 1 st January. The prime cost of a unit is
expected to Rs. 40 out of which Rs. 16 is for material and Rs. 24 for labour. In addition
variable expenses per unit are expected to be Rs. 8 and fixed expenses per month Rs.
30,000. Payment for materials is to be made in the month following the purchases. One
third of sale will be for cash and the rest on credit for settlement in the following the
month. Expenses are payable in the which they are incurred. The selling price is fixed at Rs.
80 per unit. The number of units manufacture and sold are expected to be as under:
January
February
March
900
1,200
1,800
April
May
June
2,100
2,100
2,400
Required : Draw up a statement showing requirements of cash from month to month,
ignoring the question of stock.
Ans.
Statement showing requirements of Cash for 6 months from January to June
Particular
January February March
April
May
Rs.
Rs.
Rs.
Rs.
Rs.
A. Total Cash Available:
Cash Sales
24,000
32,000
48,000
56,000
56,000
Collection from Debtors
48,000
64,000
96,000
1,12,000
B.
June
Rs.
64,000
1,12,000
Total Cash Payments:
24,000
80,000
1,12,000 1,52,000 1,68,000 1,76,000
Payment to Creditors
Labour
Variable Expenses
21,600
7,200
14,400
28,800
9,600
19,200
43,200
14,400
28,800
50,400
16,800
33,600
50,400
16,800
33,600
57,600
19,200
Page | 399
Fixed Expenditure
30,000
58,800
30,000
82,800
30,000
30,000
30,000
30,000
1,06,800 1,26,000 1,30,800 1,40,400
C.
Surplus (Deficit) [A -B]
-34,800
D.
Cumulative Surplus
-34,800
(Deficit)
-2,800
5,200
26,000
37,200
35,600
-37,600
-32,400
-6,400
30,800
66,400
Illustration-3 X & Co. has furnished the following information. Based on this, prepare a
cash budget for three months i.e., June, July and August :
Month
Sales
Materials
Wages
Production
Office
&
Purchases
Overheads
Selling
Rs.
Rs.
Rs.
Rs.
Expenses
Rs.
June
July
Aug.
72,000
97,000
86,000
25,000
31,000
25,500
10,000
12,100
10,600
6,000
6,300
6,000
5,500
6,700
7,500
a) Cash balance in as hand as on 1 st June : Rs. 72,500.
b) 50% of sales are Cash sales.
c) A fixed assets has to be purchased for Rs. 8,000 in July 2008.
d) Debtors are allowed one month’s credit.
e) Creditors for materials grant one month’s credit.
f) Sales commission at 3% on sales is paid to the salesman each month.
Ans.
Cash Budget for Three Months for June to Aug.
Particulars
June
July
Rs.
Rs.
A. Total Cash Available:
Opening Balance
72,500
84,840
Cash Sales
36,000
48,500
Collection from Debtors
36,000
1,08,500
1,69,340
B.
Total Cash Payments:
Creditors
Sales Commission 3%
Wages
Production Overheads
2,160
10,000
6,000
25,000
2,910
12,100
6,300
August
Rs.
1,08,330
43,000
48,500
1,99,830
31,000
2,580
10,600
6,000
Page | 400
Office & Selling Expenses
Fixed Assets
C. Closing Balance [A-B]
5,500
23,660
84,840
6,700
8,000
61,010
108,330
7,500
57,680
1,42,150
REVISIONARY PROBLEMS
Ques.1 Based on the following information prepare a cash budget for ABC Ltd.
1st Quarter
Opening cash balance
Rs.10,000
Collection
from
1,25,000
customers
Payment:
20,000
Purchase of Materials
25,000
Other Expenses
90,000
Salary and Wages
5,000
Income Tax
Purchase of Machinery
2nd Quarter
3rd Quarter
4th Quarter
Rs.1,50,000
Rs.1,60,000
Rs.2,21,000
35,000
20,000
95,000
-
35,000
20,000
95,000
-
54,200
17,000
1,09,200
20,000
The company desires to maintain a cash balance of Rs.15,000 at the end of the each
quarter. Principal can be borrowed or repaid in multiples of Rs.500 at an interest of
10% per annum.
Management does not want to borrow cash more than what is necessary and wants to
repay as early as possible. In any event, loans cannot be extended beyond four quarters.
Interest is computed and paid when repayment is made at the end of the quarter &
borrowing are made at beginning of every quarter.
[Answer: Interest payable in 3rd and 4th quarter is Rs.675 and Rs.1,100. Cash balance
at the end of 4th quarter is Rs.23,825.]
Ques.2 The following data is collected by SRG Iron and Steel Co. for first four months of the
next financial year:
Month 1
Sales
Rs.15,000
Purchase of assets 1,200
Month 2
Rs.24,000
2,000
Month 3
Rs.36,000
4,000
Month 4
Rs.24,000
Page | 401
Raw materials
Expenses
14,000
2,000
15,000
4,000
16,000
4,000
17,000
8,600
Additional Information:
(i) The opening cash balance in the beginning is expected at Rs.12,000 and the
firm wants to maintain a minimum cash balance of Rs.5,000 at the end of each
month.
(ii) Opening debtors for the Month 1 are Rs.5,000.
(iii) On an average, 2/3 of monthly sales are on credit basis and collected next
month.
(iv) Borrowing, if any, may be made in the beginning of a month in the multiple of
Rs.1,000. Repayment can be made at the end of a month together with
interest @ 2% per month.
Prepare Cash Budget for four months.
[Answer: Borrowing in Month I and II are of Rs.1,000 and Rs.3,000. Repayment in
Month III Rs.4,180 (4,000 + 180). Balance at the end of Month IV is Rs.12,020.]
Page | 402
MULTIPLE CHOICE QUESTIONS
1. Which of the following will NOT appear in a Cash Budget?
a) Machinery bought on hire purchase
b) Depreciation of machinery
c) Sales revenue
d) Wages
2. Of the four costs shown below, which would not be included in the cash budget of an
insurance firm?
a) Depreciation of fixed asset
b) Commission paid to agents
c) Office salaries
d) Capital cost of a new computer
3. Non-cash transactions .................
a) Form part of cash budget
b) Do not form part of cash budget
c) May or may not form part of cash budget
d) I cannot say whether they are part of cash budget
4. Which of the following will not affect preparation of cash budget?
a) Loan taken by firm
b) Proceeds from asset disposal
c) Reduction in provision for doubtful debts
d) Cash sales
5. Which of the following would be found in a cash budget?
a) Capital expenditure
b) Provision for doubtful debts
c) Depreciation
d) Accrued expenditure
6. A cash budget is like an income statement.
a) I agree
b) I disagree
c) I cannot say
d) The statement is ambiguous
Page | 403
7. Cash Budget statement shows the position of business as on ................. of the business
period.
a) Opening date
b) Closing date
c) Between opening and closing date
d) None of the above
8. The statement of cash flows tells us a) The financial position of the business at a point in time.
b) The forecast cash movements over a period of time.
c) How much cash has been received and paid during an accounting period.
d) How much profit the business has made during an accounting period.
9. The term cash includes
a) Cash and Bank Balances
b) All the Current Assets
c) All the Current Liabilities
d) None of the above
10. Which of the following is/are motive(s) for holding cash?
1. Transactional Motive
2. Speculative Motive
3. Derivative Motive
4. Contingency Motive
Select the correct answer from the options given below
a) 1,2,3
b) 2,4,5
c) 1,2,4
d) 1,3,5
11. Which of the following is not a motive to hold cash?
a) Transactionary Motive
b) Pre-cautionary Motive
c) Capital Investment
d) None of the above.
12. The Transaction Motive for holding cash is for
a) Safety Cushion
b) Daily Operations
c) Purchase of Assets
Page | 404
d) Payment of Dividends.
13. Float management is related to
a) Cash Management
b) Inventory Management
c) Receivables Management
d) Raw Materials Management.
14. Baumol's Model of Cash Management attempts to:
a) Minimise the holding cost
b) Minimization of transaction cost
c) Minimization of total cost
d) Minimization of cash balance
15. Basic characteristic of short-term security
a) High Return
b) High Risk
c) High Marketability
d) High Safety
16. Marketable securities are primarily
a) Equity shares
b) Preference shares
c) Fixed deposits with companies
d) Short-term debt investments.
17. The cash management refers to management of ___________.
a) cash only
b) cash and bank balances
c) cash and near cash assets
d) fixed assets
18. Which of the following transactions would not create a cash flow?
a) A company purchased some of its own shares from a shareholder.
b) Amortization of a patent
c) Payment of a cash dividend.
d) Sale of equipment at book value.
Page | 405
19. A Ltd. has observed its receivable collection pattern to be as follows: 40% in the month
of the sale, 45% in the month following the sale, and 13% in the second month
following the sale. Sales for the last 3 months of the year were as follows:
October? 3,00,000; November, Rs. 4,50,000 and December, Rs.6,25,000. Sales for
January are budgeted to be Rs.3,75,000.
What are the budgeted cash collections for January?
a) Rs.3,75,000
b) Rs.4,89,750
c) Rs.4,95,750
d) Rs.6,25,000
20. Use the following information to calculate net cash flow:
Cash sales Rs.1,00,000; cash from account receivable payments Rs.2,00,000; cash
dividends received Rs.3,000; dividends paid Rs.4,000; rent paid Rs.5,000 and
amortization expense Rs.6,000.
a) Rs.2,98,000
b) Rs.2,94,000
c) Rs.3,04,000
d) Rs.2,90,000
21. The annual cash requirement of A Ltd. is Rs.10,00,000. The company has marketable
securities in lot size of Rs.50,000. Cost of conversion of marketable securities per lot is
Rs.1,000. The company can earn 5% annual yield on its securities. Calculate total cost.
a) Rs.21,000
b) Rs.21,250
c) Rs.18,750
d) Rs.12,500
22. In a firm, the forecast of wages for month of December, January, February and March
are Rs.4,800, Rs.6,000, Rs.6,400 and Rs.6,800. The time-lag in payment of wages is 1/8
month.
Determine the amount of wages payable in each month January to March.
a) Rs.6,750, Rs.6,350 and Rs.5,850
b) Rs.5,850, Rs.6,350 and Rs.6,750
c) Rs.5,850, Rs.6,750 and Rs.6,350
d) None of the above
23. The annual cash requirement of A Ltd. is Rs.10,00,000. The company has marketable
securities in lot size of Rs.1,00,000. Cost of conversion of marketable securities per lot is
Rs.1,000. The company can earn 5% annual yield on its securities. Calculate total co st.
Page | 406
a) Rs.10,500
b) Rs.10,450
c) Rs.12,500
d) Rs.14,500
24. The annual cash requirement of A Ltd. is Rs.10,00,000 Cost of conversion of marketable
securities per lot is Rs.1,000. The company can earn 5% annual yield or its securities.
Optimal cash balance = Rs. and No. of transactions = Rs.
a) 1,00,000; 5
b) 4,00,000; 10
c) 2,00,000; 5
d) 2,00,000; 10
25. Dec 2014: The following information is available: Wages for January: Rs.20,000
Wages for February: Rs.22,000
Delay in payment of wages: 1/2 month
The amount of wages paid during the month of February is —
a) Rs.11,000
b) Rs.22,000
c) Rs.20,000
d) Rs.21,000
26. Dec 2016: While preparing cash budget, which of the following items would not be
included —
a) Interest paid to debenture holders
b) Salaries and wages
c) Bonus shares issued
d) Income-tax paid
27. June 2019: The following information extracted from the records of P Ltd.
Sales for October, November and December, 2018 are Rs.90,000, Rs.1,10,000 and
Rs.80,000 respectively. 40% of its sales are expected to be for cash. Of its credit sales
70% are expected to pay in the month after sales and take 2% discount on it. Balance is
expected to pay in second month after sales and 3% of it is expected to bad debts.
What are the sales receipts to be shown in cash budget for the month of December?
a) Rs.92,990
b) Rs.1,23,174
c) Rs.95,609
d) Rs.1,25,793
Note: MCQ is wrongly drafted; for further clarification please see the hints.
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28. June 2019: The following information is given:
Depreciation provided during the year: Furniture Rs.15,000, Building Rs.14,000. The
statement of P&L for the year: Opening balance Rs.38,500 Add Profit for the year
Rs.40,300, Less: Goodwill written off Rs.15,000, Closing balance Rs.63,800.
What will be the amount of cash from operations?
a) Rs.69,300
b) Rs.54,300
c) Rs.78,800
d) Rs.25,300
29. June 2015: Estimated wages for January is Rs.4,000 and for February Rs.4,400. If the
delay in payment of wages is 1/2 month, the amount of wages to be considered in cash
budget for the month of February will bea) Rs.4,000
b) Rs.4,400
c) Rs.4,600
d) Rs.4,200
30. June 2015: In Rise Ltd., cash sales is 25% and credit sales 75%. Sales for November,
2014 is Rs.15,00,000, December, 2014 Rs.14,00,000, January, 2015 Rs.16,00,000,
February, 2015 Rs.10,00,000 & March, 2015 Rs.9,00,000. 60% of the credit sales are
collected in the next month after sales, 30% in the second month and 10% in the third
month. No bad debts are anticipated. The cash collected in the month of March, 2015
from debtors is —
a) Rs. 14,60,000
b) Rs. 14,20,000
c) Rs. 12,20,000
d) Rs. 9,15,000
ANSWERS 1
2
3
4
5
6
7
8
9
10
B
A
B
C
C
B
C
C
A
C
11
12
13
14
15
16
17
18
19
20
C
B
A
C
C
D
C
B
B
B
21
22
23
24
25
26
27
28
29
30
B
B
C
C
D
C
A
D
D
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State whether each of the following statements is True (T) or False (F)
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
(xi)
(xii)
Management of cash means management of cash in flows.
Cash is the most important but least earning current asset.
Cash management always attempts at optimize cash flow.
Cash cycle is equal to operating cycle for a firm.
Receipts and disbursement method of preparation of cash budget is the most
widely used method.
Concentration banking is a method of controlling cash outflows.
Baumol's model of cash management assumes a constant rate of use of cash.
Baumol's model attempts at optimization of cash balance.
In cash management, expected surplus cash, if any, is not considered at all.
Capital expenditures are not considered in cash budget.
Issue of share capital or debentures are taken as inflows in cash budget.
Conversion of debentures into share capital is equal to issue of share capital and
hence it is a type of cash inflow.
Answers (i) F, (ii) T, (iii) T, (iv) F, (v) T, (vi) F, (vii) T, (viii) T,(ix) F, (x) F, (xi) T, (xii) F.
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CHAPTER 16
SECURITY ANALYSIS & PORTFOLIOS
 CONCEPT 1
WHAT ARE SECURITIES
Securities may be defined as instruments issued by seekers of funds in the inv estment
market to the providers of funds in lieu of funds.
These instruments prima facie provide evidence of ownership to the holder of the
instrument. The owner is entitled to receive all the benefits due on the instrument and to
retrieve his investment at the time of redemption.
Securities can broadly be divided into two categories – Debt Securities and Equity
Securities. However, Section 2(h) of Securities Contract (Regulation) Act, 1956, defines
securities as under:
Securities include –
(i)
shares, scrips, stocks, bonds, debentures, debenture stock or other marketable
securities of a like nature in or of any incorporated company or other body
corporate.
(a) derivative.
(b) units or any other instrument issued by any collective investment scheme to
the Investors in such schemes.
(c) units or any other such instrument issued to the investors under any mutual
fund scheme.
(ii)
Government securities.
(iii)
Such other instruments as may be declared by the Central Government to be
securities and,
 CONCEPT 2
INVESTMENT
Investment is the employment of funds on assets with the aim of earning income or capital
appreciation. Investment has two attributes namely time and risk. Present consumption is
sacrificed to get a return in the future. The sacrifice that has to be borne is certain but the
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return in the future may be uncertain. This attribute of investment indicates the risk factor.
The risk is undertaken with a view to reap some return from the investment.
The investor makes a comparison of the returns available from each avenue of investment,
the element of risk involved in it and then makes the investment decision that he perceives
to be the best having regard to the time frame of the investment and his own risk profile.
 CONCEPT 3
INVESTMENT VS. SPECULATION
BASIS FOR
COMPARISON
INVESTMENT
SPECULATION
The purchase of an asset with
the hope of getting returns is
called investment.
Fundamental factors, i.e.
performance of the company.
Speculation is an act of conducting a
risky financial transaction, in the
hope of substantial profit.
Hearsay, technical charts and
market psychology.
Time horizon
Long term
Short term
Risk involved
Moderate risk
High risk
Intent to profit
Changes in value
Changes in prices
Expected rate of
return
Modest rate of return
High rate of return
Funds
An investor uses his own
funds
A speculator uses borrowed funds.
Income
Stable
Uncertain and Erratic
Behavior of
participants
Conservative and Cautious
Daring and Careless
Meaning
Basis for decision
 CONCEPT 4
INVESTMENT VS. GAMBLING
BASIS FOR COMPARISON
Planning Horizon
Basis for Decisions
Nature
INVESTMENT
Longer Planning Horizon
Scientific Analysis of Intrinsic
worth of the security
Planned activity
GAMBLING
Short Planning Horizon
Based on tips and rumors
Unplanned activity
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Risk
Return Expectation
Motive
Commercial Risk
Risk-return trade-off
determines return
Safety of principal and
stability of returns
Artificial Risk
Negative returns are
expected
Entertainment while
earning
 CONCEPT 5
RISK AND ITS TYPES
Risk in security analysis is generally associated with the possibility that the realized
returns will be less than the returns that were expected. In finance, different types of risk
can be classified under two main groups, viz., systematic risk and unsystematic risk.
 CONCEPT 6
DIFFERENCE BETWEEN SYSTEMATIC AND UNSYSTEMATIC RISK
Systematic Risk
Unsystematic Risk
(1) Systematic risk refers to the risk
which affects the whole stock market
(1) unsystematic Risk refers to the risk
which affect price of a particular
security
(2) Systematic Risk is market specific
(2) unsystematic Risk is based on factory
which are unique to CL company
(3) This type of risk is called as nondiversifiable risk, as no amount of
diversification can reduce this risk.
(3) this type of risk is called as
diversifiable risk as risk can be
diversified away by investing in more
than one company.
(4) Example of systematic risk are global
turmoil change in interest rate etc.
(5) Examples of unsystematic risk are
poor management strike of worker,
excess debt etc.
 CONCEPT 7
APPROACHES TO VALUATION OF SECURITY
Security analysis begins with assessing the intrinsic value of security. There are three main
schools of thought on the matter of security price evaluation. Advocates of different schools
can be classified as (1) Fundamentalists; (2) Technicians; and (3) efficient market
advocates.
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(1) The Fundamental Approach: The Fundamental approach suggests that every stock
has an intrinsic value. Estimate of intrinsic worth of a stock is made by considering the
earnings potential of firm which depends upon investment environment and factors
relating to specific industry, competitiveness, quality of management, operational
efficiency, profitability, capital structure and dividend policy. The earning potential is
converted into the present value of the future stream of income from that stock discounted
at an appropriate risk related rate of interest. Security analysis is done to compare the
current market value of particular security with the intrinsic or theoretical value. Decisions
about buying and selling an individual security depends upon the comparison. If the
intrinsic value is more than the market value, the fundamentalists recommend buying of
the security and vice versa.
(2) Technical Approach: The technical analyst endeavours to predict future price levels of
stocks by examining one or many series of past data from the market itself. The basic
assumption of this approach is that history tends to repeat itself and the price of a stock
depends on supply and demand in the market place and has little relationship with its
intrinsic value. All financial data and market information of a given security is reflected in
the market price of a security. Therefore, an attempt is made through charts to identify
price movement patterns which predict future movement of the security. The main tools
used by technical analysis are: (1) The Dow Jones theory which asserts that stock prices
demonstrate a pattern over four to five years and these patterns are mirrored by indices of
stock prices.
(3) Efficient Capital Market Theory : The theory is popularly known as “Efficient Capital
Market Hypothesis: (ECMH). The advocates of this theory contend that securities markets
are perfect, or at least not too imperfect.
It is based on the assumption that in efficient capital markets prices of traded securities
always fully reflect all publicly available information concerning those securities. For
market efficiency, there are three essential conditions; (i) all available information is cost
free to all market participants; (ii) no transaction costs; (iii) all investors similarly view the
implications of available information on current prices and distribution of future prices of
each security.
It has been empirically proved that stock prices behave randomly under the above
conditions. These conditions have been rendered unrealistic in the light of the actual
experience because there is not only transaction cost involved but traders have their own
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information base. Moreover, information is not costless and all investors do not take
similar data and interpretation with them.
Efficient Market Hypothesis has put to challenge the fundamental and technical analysts to
the extent that random walk model is valid description of reality and the work of chartists
is of no real significance in stock price analysis. In practice, it has been observed that
markets are not fully efficient in the semi-strong or strong sense. Inefficiencies and
imperfections of certain kinds have been observed in the studies conducted so far to test
the efficiency of the market.
In short, if these theories are taken in their strongest forms, fundamentalists say that a
security is worth the present value (discounted) of a stream of future income to be received
from the security; technicians assert that the price trend data should be studied regardless
of the underlying data; efficient market theorists contend that a share of stock is generally
worth whatever it is selling for.
 CONCEPT 8
DOW JONES THEORY
It is one of the earliest theories of technical analysis. The theory was formulated by Charles
H. Dow of Dow Jones & Co. who was the first editor of Wall street Journal of USA. According
to this theory, share prices demonstrate a pattern over four to five years.
These patterns can be divided into three distinct cyclical trends- primary, secondary and
minor trends.
The primary trend lasts from one to three years. Over this period, the markets exhibit
definite upward or downward movement which is punctuated by shorter spans of trend
reversal in the opposite directions. The trend reversal is called the secondary trend.
Primary trend is indicative of the overall pattern of movement.
If the primary trend is upward, it is called a bullish phase of the market. If the primary
trend is downwards, it is called a bearish phase. Illustrations of bullish phase and bearish
phase are given below:
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Graph of Bullish Phase
PEAK
PRICE
TIME
In a bullish phase, after each peak, there is a fall but the subsequent rise is higher than the
previous one. The prices reach higher level with each rise. After the peak has been reached,
the primary trend now turns to a bearish phase.
Graph of Bearish Phase
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In a bearish phase, the overall trend is that of decline in share values. After each fall, there
is slight rise but the subsequent fall is even sharper. The secondary trend reversals last for
one to three months.
Minor trends are changes occurring every day within a narrow range. These trends are not
decisive of any major movement.
 CONCEPT 9
RANDOM WALK THEORY
In the Fundamental Analysis, factors such as economic influences, industry factors and
particular company information are considered to form a judgement on share value. On the
other hand, price and volume information is analysed in Technical Analysis to predict the
future course of share values. There is another approach which negates both Fundamental
and Technical analysis. This approach has been based upon the research aimed at testing
whether successive price changes are independent in different forms of market efficiency.
According to the theory, share prices will rise and fall on the whims and fancies of
manipulative individuals. As such, the movement in share values is absolutely random and
there is no need to study the trends and movements prior to making investment decisions.
No sure prediction can be made for further movement or trend of share prices based on the
given prices as at a particular moment. The Random Walk Theory is inconsistent with
technical analysis. Whereas, it states that successive price changes are independent, the
technicians claim that they are dependent. But believing in random walk does not mean
that one should not believe in analyzing stocks. The random walk hypothesis is entirely
consistent with an upward and downward movement in price, as the hypothesis supports
fundamental analysis and certainly does not attack it.
One of the advantages of this theory is that one is not bothered about good or bad
judgement as shares are picked up without preference or evaluation. It is easier for
believers in this theory to invest with confidence. The second advantage is that there is no
risk of being ill informed while making a choice as no information is sought or concealed.
Random walk theory implies that short term price changes i.e day to day or week to week
changes are random but it does not say anything about trends in the long run or how price
levels are determined.
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 CONCEPT 10
EFFICIENT – MARKET THEORY
Efficient Market Hypothesis accords supremacy to market forces. A market is treated as
efficient when all known information is immediately discounted by all investors and
reflected in share prices. In such a situation, the only price changes that occur are those
resulting from new information. Since new information is generated on a random basis, the
subsequent price changes also happen on a random basis. Major requirements for an
efficient securities market are:
– Prices must be efficient so that new inventions and better products will cause a
firms’ securities prices to rise and motivate investors to buy the stocks.
– Information must be discussed freely and quickly across the nations so that all
investors can react to the new information.
– Transaction costs such as brokerage on sale and purchase of securities are ignored.
– Taxes are assumed to have no noticeable effect on investment policy.
– Every investor has similar access to investible funds at the same terms and
conditions.
– Investors are rational and make investments in the securities providing maximum
yield.
Research studies devoted to test the random walk theory on Efficient Capital Market
Hypothesis (ECMH) are put into three categories i.e.
(a) the strong form,
(b) the semi-strong form, and
(c) the weak form theory.
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Only
(a) The Strong Form of Efficiency: This test is concerned with whether two sets of
individuals – one having inside information about the company and the other
uninformed could generate random effect in price movement. The strong form holds
that the prices reflect all information that is known. It contemplates that even the
corporate officials cannot benefit from the inside information of the company. The
market is not only efficient but also perfect. The findings are that very few and
negligible people are in such a privileged position to have inside information and may
make above-average gains but they do not affect the normal functioning of the market.
(b) Semi-strong form of Efficiency: This hypothesis holds that security prices adjust
rapidly to all publicly available information such as functional statements and reports
and investment advisory reports, etc. All publicly available information, whether good
or bad is fully reflected in security prices. The buyers and sellers will raise the price as
soon as a favourable piece of information is made available to the public; opposite will
happen in case of unfavourable piece of information. The reaction is almost
instantaneous, thus, printing to the greater efficiency of securities market.
(c) The Weak Form theory: This theory is an extension of the random walk theory.
According to it, the current stock values fully reflect all the historical information. If this
form is assumed to be correct, then both Fundamental and Technical Analysis lose their
relevance. Study of the historical sequence of prices, can neither assist the investment
analysts or investors to abnormally enhance their investment return nor improve their
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ability to select stocks. It means that knowledge of past patterns of stock prices does not
aid investors to make a better choice. The theory states that stock prices exhibit a
random behaviour.
 CONCEPT 11
CAPITAL ASSET PRICING MODEL
CAPM is defined as an economic theory that describes relationship between risk and
expected return and serves as a model for the pricing of risky securities. The CAPM asserts
that the only risk that is priced by rational investors is systematic risk, becau se that risk
cannot be eliminated. The CAPM sys that expected return of a security or a portfolio is
equal to rate on a risk free security plus a risk premium multiplied by asset’s systematic
risk. The CAPM is calculated according to the following formula
Desired return= Risk free+ β(R m - Rf)
The General idea behind CAPM is that investors need to be compensated for investing their
cash in two ways (i)Time value of Money (ii) Risk
The time value of money is represented by risk free rate (R f) & it compensates investors for
placing money in any investment over period of time. Risk calculates the amount of
compensation the investor needs for taking additional Risk. This is calculated by taking a
risk measure (beta) that compares return of the asset to the market over a period of time &
to the market premium (R m--Rf).
 CONCEPT 12
ARBITRAGE PRICING THEORY
The capital asset pricing model (CAPM) asserts that only a single number – a security’s beta
against the market – is required to measure risk. At the core of arbitrage pricing theory
(APT) is the recognition that several systematic factors affect security return.
The returns on an individual stock will depend upon a variety of anticipated and
unanticipated events. Anticipated events will be incorporated by investors into their
expectations of returns on individual stocks and thus will be incorporated into market
prices. Generally, most of the return ultimately realized will result from unanticipated
events. But even though we realize that some unforeseen events will occur, we do not know
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their direction or their magnitude. What we can know is the sensitivity of returns to these
events.
Systematic factors are the major sources of risk in portfolio returns. Actual portfolio
returns depend upon the same set of common factors, but this does not mean that all
portfolios perform identically. Different portfolios have different sensitivities to these
factors.
Because the systematic factors are primary sources of risk, it follows that they are the
principal determinants of the expected, as well as the actual, returns on portfolios. It is
possible to see that the actual return, R, on any security or portfolio may be broken down
into three constituent parts, as follows:
Z = E + bf + e
where:
E = expected return on the security
b = security’s sensitivity to change in the systematic factor
f = the actual return on the systematic factor
e = returns on the unsystematic, idiosyncratic factors
Equation Z merely states that the actual return equals the expected return, plus factor
sensitivity times factor movement, plus residual risk.
Empirical work suggests that a three-or-four-factor model adequately captures the
influence of systematic factors on stock-market returns. Equation Z may thus be expanded
to:
R = E + (b1) (f1) + (b2) (f2) + (b3) (f3)
+ (b4) (f4) + e
Each of the four middle terms in this equation is the product of the returns on a particular
economic factor and the given stock’s sensitivity to that factor. Suppose f3 is associated
with labor productivity. As labor productivity unexpectedly increases, f3 is positive, and
firms with high b3 would find their returns very high.
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What are these factors? They are the underlying economic forces that are the primary
influences on the stock market. Research suggests that the most important factors are
unanticipated inflation, changes in the expected level of industrial production,
unanticipated shifts in risk premiums, and unanticipated movements in the shape of the
term structure of interest rates.
The biggest problems in APT are factor identification and separating unanticipated from
anticipated factor movements in the measurement of sensitivities. Any one stock is so
influenced by idiosyncratic forces that it is very difficult to determine the precise
relationship between its return and a given factor. Far more critical is the measurement of
the b’s. The b’s measure the sensitivity of returns to unanticipated movements in the
factors.
 CONCEPT 13
SINGLE INDEX MODEL
The major assumption of Sharpe's single-index model is that all the covariation of security
returns can be explained by a single factor. This factor is called the index, hence the name
"single-index model."
According to the Sharpe single index model the return for each security can be given by the
following equation:
R = α +βI + E
Where R = Expected return on a security
α= Alpha Coefficient
β= Beta Coefficient
I = Expected Return an index
E = Error term with a mean of zero and a constant standard deviation.
Alpha Coefficient refers to the value of Y in the equation Y = ? + ? x when X = 0. Beta
Coefficient is the slope of the regression line and is a measure of the changes in value of the
security relative to changes in values of the index.
A beta of +1.0 means that a 10% change in index value would result in a 10% change in the
same direction in the security value. A beta of 0.5 means that a 10% change in index value
would result in 5% change in the security value. A beta of -1 means that the returns on the
security are inversely related.
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The equation given above can also be rearranged as shown below:
R = βI +α + e
Here the component I is the market related or systematic component of the return. The
other component represents the unsystematic component. As is assumed to be near zero
the unsystematic return is given by alpha only.
 CONCEPT 14
MULTI INDEX MODELS
The multi-index model assumes a return-generating process that is a linear function of
many factors. In this approach, each factor is a source of systematic risk. Since investors
cannot diversify systematic risk, they are assumed to be compensated for bearing this risk.
𝑅 = 𝐴 + 𝛽𝐹1 + 𝛽𝐹2 + ⋯ 𝐶
As a result, a security's sensitivity to each factor affects the assumed return -generating
process for the security. This sensitivity is captured by a "factor beta," and the returngenerating process is assumed to take the form
The last term is the source of idiosyncratic or diversifiable risk which is assumed to be
equal to zero Except for the fact that multiple factors make this a richer model than the
single index model, the use of a multi-factor model is similar to the single-index model.
A broad generalization of these models is the Arbitrage Pricing Theory.
 CONCEPT 15
USING SHARPE- INDEX RATIO
The Sharpe ratio is a risk-adjusted measure of return that is often used to evaluate the
performance of a portfolio. The ratio helps to make the performance of one portfolio
comparable to that of another portfolio by making an adjustment for risk.
For example, if manager A generates a return of 15% while manager B generates a return
of 12%, it would appear that manager A is a better performer. However, if manager A, who
produced the 15% return, took much larger risks than manager B, it may actually be th e
case that manager B has a better risk-adjusted return.
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To continue with the example, say that the risk free-rate is 5%, and manager A's portfolio
has a standard deviation of 8%, while manager B's portfolio has a standard deviation of
5%. The Sharpe ratio for manager A would be 1.25 while manager B's ratio would be 1.4,
which is better than manager A. Based on these calculations, manager B was able to
generate a higher return on a risk-adjusted basis.
To give you some insight, a ratio of 1 or better is considered good, 2 and better is very
good, and 3 and better is considered excellent.
The Sharpe ratio is quite simple, which lends to its popularity. It's broken down into just
three components: asset return, risk-free return and standard deviation of return. After
calculating the excess return, it's divided by the standard deviation of the risky asset to get
its Sharpe ratio. The idea of the ratio is to see how much additional return you are receiving
for the additional volatility of holding the risky asset over a risk-free asset - the higher the
better.
 CONCEPT 16
DIFFERENCE BETWEEN CML (CAPITAL MARKET LINE,) AND SML (SECURITY MARKET
LINE)
CML stands for Capital Market Line, and SML stands for Security Market Line.
1) The CML is a line that is used to show the rates of return, which depends on riskfree rates of return and levels of risk for a specific portfolio. SML, which is also
called a Characteristic Line, is a graphical representation of the market’s risk and
return at a given time.
2) While standard deviation is the measure of risk in CML, Beta coefficient determines
the risk factors of the SML.
3) While the Capital Market Line graphs define efficient portfolios, the Security Market
Line graphs define both efficient and non-efficient portfolios.
4) The Capital Market Line is considered to be superior when measuring the risk
factors.
5) Where the market portfolio and risk free assets are determined by the CML, all
security factors are determined by the SML.
 CONCEPT 17
“BETA”
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In Finance the beta (β) of an investment is a measure of the risk arising from exposure to
general market movements as opposed to idiosyncratic factors. The market portfolio of all
investable assets has a beta of exactly 1. A beta below 1 can indicate either an investment
with lower volatility than the market, or a volatile investment whose price movements are
not highly correlated with the market. An example of the first is a treasury bill: the price
does not go up or down a lot, so it has a low beta. An example of the second is gold. The
price of gold does go up and down a lot, but not in the same direction or at the same time as
the market.
A beta above one generally means that the asset both is volatile and tends to move up and
down with the market. An example is a stock in a big technology company. Negative betas
are possible for investments that tend to go down when the market goes up, and vice versa.
There are few fundamental investments with consistent and significant negative betas, but
some derivatives like equity put options can have large negative betas.
Beta is important because it measures the risk of an investment that cannot
be diversified away. It does not measure the risk of an investment held on a stand-alone
basis, but the amount of risk the investment adds to an already-diversified portfolio. In
the capital asset pricing model, beta risk is the only kind of risk for which investors should
receive an expected return higher than the risk-free rate of interest.
 CONCEPT 18
ECONOMIC VALUE ADDED
In corporate finance, Economic Value Added (EVA), is an estimate of a firm' s economic
profit being the value created in excess of the required return of the
company's INVESTORS (being shareholders and debt holders). Quite simply, EVA is the
profit earned by the firm less the cost of financing the firm's capital. The idea is that value is
created when the return on the firm's economic capital employed is greater than the cost of
that capital.
The formula for EVA is NOPAT-COST OF CAPITAL
WHERE NOPAT =EBIT-TAXES
 CONCEPT 19
MARKOWITZ MODEL
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Dr. Harry M. Markowitz is credited with developing the first modern portfolio analysis
model. It provides a theoretical framework for analysis of risk-return choices. The concept
of efficient portfolios has been enunciated in this model A portfolio is efficient when it
yields highest return for a particular level of risk or minimizes risk for a specified level of
expected return.
The Markowitz model makes the following assumptions regarding investor behaviour:
– Investors consider each investment alternative as being represented by a
probability distribution of expected returns over some holding period.
– Investors maximize one period expected utility and possess utility curve, which
demonstrates diminishing marginal utility of wealth.
– Individuals estimate risk on the basis of variability of expected returns.
– Investors base decisions solely on expected return and variance of returns only.
– At a given risk level, higher returns are preferred to lower returns. Similarly for a
given level of expected returns, investors prefer less risk to more risk.
 CONCEPT 20
EFFICIENT FRONTIER
An effient frontier represents a set of optimal portfolios that offers the highest expected
return for a defined level of risk or the lowest risk for a given level of expected return.
Portfolios that lie below the efficient frontier are sub-optimal, because they do not provide
enough return for the level of risk. Portfolios that cluster to the right of the efficient frontier
are also sub-optimal, because they have a higher level of risk for the defined rate of return.
Since the efficient frontier is curved, rather than linear, a key finding of the concept was the
benefit of diversification. Optimal portfolios that comprise the efficient frontier tend to
have a higher degree of diversification than the sub-optimal ones, which are typically less
diversified.
The efficient frontier concept was introduced by Harry Markowitz in 1952 and is a
cornerstone of modern portfolio theory.
 CONCEPT 21
OPTIMAL PORTFOLIO
The optimal portfolio concept falls under the modern portfolio theory. The theory assumes
(among other things) that INVESTORS fanatically try to minimize risk while striving for the
highest return possible. The theory states that INVESTORS will act rationally, always
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making decisions aimed at maximizing their return for their acceptable level of risk.
The optimal portfolio was used in 1952 by Harry Markowitz, and it shows us that it is
possible for different portfolios to have varying levels of risk and return.
Each INVESTOR must decide how much risk they can handle and than allocate (or
diversify) their portfolio according to this decision.
The chart below illustrates how the optimal portfolio works. The optimal-risk portfolio is
usually determined to be somewhere in the middle of the curve because as you go higher
up the curve, you take on proportionately more risk for a lower incremental return. On the
other end, low risk/low return portfolios are pointless because you can achieve a similar
return by INVESTING in risk-free assets, like government securities.
You can choose how much volatility you are willing to bear in your portfolio by picking any
other point that falls on the efficient frontier. This will give you the maximum return for the
amount of risk you wish to accept. Optimizing your portfolio is not something you can
calculate in your head. There are computer programs that are dedicated to determining
optimal portfolios by estimating hundreds (and sometimes thousands) o f different
expected returns for each given amount of risk.
 CONCEPT 22
STANDARD DEVIATION VS BETA
Page | 426
Standard deviation of return from an investment measures the total risk associated with
that investment.
Beta indicates only towards the systematic risk. Suppose the beta of a security is 1.2, SD of
returns from the market is 5. It means that the systematic risk of the security is 6.
If we have a choice between Beta and SD, we should prefer SB as a measure of risk as it will
take case of both systematic and unsystematic risk (while the Bet takes case of only
systematic risk.)
Some investment advisors have different views. They hold that investors with long -term
time horizon should consider SD while the investors with short-term time horizon may
base their decision on the basis of Beta.
Investors with long-term time horizon (investing from long term point of view) should
view SD as the proper measure of Security’s risk. SD is a measure of total risk and if the
investment if from long term point of view total risk should be considered. Longer the
period, larger the risk- as in long run fundamentals of the economy as well as company may
change. All these changes are reflected in SD of past return of security (the implied
assumption is that the history repeats itself).
Investors with short run time horizon should view beta as the proper measure of risk. Beta
measure systematic risk of the security. Any bad news (say no -trust motion against
government, slightest possibility of war, death or serious illness of some ke y person of the
economy) may upset the market and result is adverse impact on the price of the security. If
beta of the security is high, even slight adverse factor resulting in slight adverse impact on
the market may have substantial adverse impact on price of the security.
 CONCEPT 23
DISTINGUISH BETWEEN EFFICIENT AND OPTIMAL PORTFOLIO.
Efficient Portfolio
1. efficient portfolio is the one which
provides us maximum return at
minimum risk level
2. it reflects us maximum as
represented by Capital market line
(CML)
Optimal Portfolio
optimal portfolio is the efficient portfolio which
suits the requirement of an individual investor
It is a subset selected from those combinations
by an individual according to his risk-return
expectations.
 CONCEPT 24
Page | 427
DISTINGUISH BETWEEN THE FOLLOWING ‘SEMI-STRONG FORM’ & ‘STRONG FORM’
OF EFFICIENT MARKET HYPOTHESIS
Semi strong form of efficient market
hypothesis
1. According to this hypothesis, prices of
security are directly affected by financial
information publicly made available in
form of report etc.
2. If publicly available information about
securities is positive it will have a
favourable impact on prices of securities
and vice-versa.
Strong form of efficient market hypothesis
1. According to this hypothesis, market forces
have a supreme role. Information of any form
whether publicly available or otherwise
proves out to be useless
2. No information can be used to earn better
return than the market.
UNSOLVED QUESTION
TYPE 1
EXPECTED RETURN AND RISK OF GIVEN SECURITY
IS GIVEN)
Que 1.
A company is considering two securities X and Y.
Security X
(WHEN RETURN
Security Y
Return
(%)
Probability
Return
(%)
Probability
30
0.1
30
0.2
60
0.4
60
0.3
120
0.4
120
0.3
150
0.1
150
0.2
Compute the return and risk attached to each security i.e., Standard Deviation of each
probability distribution. Which security do you consider more risky and why?
Ans.
Que 2.
Rx = 90; Ry = 90; s.dx= 37.94; Sdy = 44.49
You have estimated the probability distribution of expected future return for
Stocks.
Page | 428
Stock X
Stock Y
Probability
Return
Probability
Return
0.1
-10%
0.2
2%
0.2
10
0.2
7
0.4
15
0.3
12
0.2
20
0.2
15
0.1
40
0.1
16
(a) What are the expected rate of return for Stock X and Stock Y?
(b) What is the standard deviation of expected returns for Stock X and Stock Y?
(c) Which stock would you consider to be riskier?
Ans.
(a) .15, 10 (b) 11.61 & 4.93
Que 3.
An investor estimates that return on shares in two different companies
under three different scenarious is likely to be as follows:
Scenario Chance
1
2
3
0.25
0.5
0.25
Return (%)
X Ltd. Y Ltd.
36
22
26
16
12
14
What will be the expected rate of return if he invests all his funds in Security X alone, or in
Y alone which is the preferred security?
Ans.
25%, 17%
Que 4.
Compute the expected return and risk of an investment in the following
security.
Economic
Condition
Boom
Stagnation
Probability (P)
0.275
0.45
Return on
investment %
(ROI)
(+) 40%
(+) 20%
Page | 429
Depression
0.275
(-) 10%
Ans.
Return 17.25%, Risk 18.70
Que 5.
The following information is available in respect of the return from security X
under different economic conditions:
Economic
Condition
Return
Probability
Good
20%
.1
Average
16%
.4
Bad
10%
.3
Poor
3%
.2
Find out the expected return of the security and the risk associated with that.
Ans.
12,5.49
TYPE 2
EXPECTED RETURN AND RISK OF GIVEN SECURITY
RETURN IS NOT GIVEN)
Que 6.
A Ltd. never pays dividend. Its equity share is currently selling at Rs.25. Using
the following data, find the expected return and standard deviation of
expected returns of share of A Ltd.
Price of equity share after 1 year
(Rs.)
Profitability of the
price
20
.10
30
.20
40
.40
50
.20
60
.10
(WHEN
Page | 430
Ans.
A = R = 60 S.D = 43.81
Que 7.
(Nov. 09) A stock costing Rs.120 pays no dividends. The possible prices that
the stock might sell for at the end of the year with the respective
probabilities are:
Price
Profitability
115
0.1
120
0.1
125
0.2
130
0.3
135
0.2
140
0.1
Required:
(i)
(ii)
Ans.
Que 8.
Calculate the expected return.
Calculate the Standard deviation of returns.
(i) 7.081 (ii) 5.90
(Nov. 05) Following information is respect of dividend, market price and market
condition after one year.
Market
Probability
Market
Dividend per
condition
Price
share
Rs.
Rs.
Good
0.25
115
9
Normal
0.50
107
5
Bad
0.25
97
3
The existing market price of an equity share is Rs.106 (F.V. Re.1), which is cum. 10% bonus
debenture of Rs.6 each, per share. M/s X Finance Company Ltd. will buy-back of debentures
at face value.
Page | 431
Find out the expected return and risk.
Ans.
R = 12 & S.D = 8.48
TYPE 3
RULE OF DOMINANCE / EFFICIENT FRONTIER BY MARKOWITZ
Que 9.
Following is data regarding six securities:
A
B
C
D
E
F
Return (%)
10
10
15
5
11
8
Risk (%)
5
6
13
5
6
7
(standard
Deviation)
(i)
(ii)
Assuming three will have to be selected, state which ones will be picked.
Assuming perfect negative correlation, show whether it is preferable to
invest 80% in security A and 20% in security C or to invest 100% in E.
Ans.
(i) A, E & C (ii) R = 11.11 & S.D = 1.4 (iii) Invest E  R = 11% , SD = 6%
Que 10.
Following is data regarding six securities:
A
B
C
D
E
F
Return (%)
8
8
12
4
9
8
Risk (%)
4
5
12
4
5
7
(standard
Deviation)
(i)
Assuming three will have to be selected, state which ones will be
picked.
Page | 432
(ii)
Ans.
Que 11.
Assuming perfect positive correlation, show whether it is preferable
to invest 75% in security A and 25% in security C or to invest 100% in
E.
(i) A, E & C (ii) A & C R = 9% σ = 0 (iii) Invest E  R = 9 , SD = 5%
Portfolio
A
B
C
D
E
F
G
H
Expected return (r)
%
10
12.5
15
16
17
18
14
20
Risk
23
21
25
29
29
32
35
45
(i)
(ii)
(iii)
(iv)
Five of these portfolios are efficient, and three are not. Which are
inefficient ones?
Suppose you can also borrow and lend at an interest rate of 12%.
Which of the above Portfolio’s is best?
Suppose you are prepared to tolerate a standard deviation of 25%.
What is the maximum expected return that you can achieve if you
cannot borrow or lend?
What is your optimal strategy if you can borrow or lend at 12% and
are prepared to tolerate a standard deviation of 25%? What is the
maximum expected return that you can achieve?
Ans.
(i) B ,C,E, F & H (ii) F with 18% Return (iii) C
(iv) invest in Risk free (WRF = .21875)Invest in port. F (WF = .78125)
TYPE 4
COMPUTATION OF RISK OF PORTFOLIO
Que 12.
An investor holds two equity shares X and Y in equal proportion with the
following risk and return characteristics:
X
Y
Expected Return (%)
24
19
Standard deviation (%)
28
23
The returns of these securities have a positive correlation of 0.6. You are required to
calculate the portfolio return and risk. Further, suppose that the investor wants to reduce
Page | 433
the portfolio risk to 15%. How much should the correlation coefficient be to bring the
portfolio risk to the desired level?
Ans.
(i) Combined Return = 21.5% (ii) Combined Risk =22.835% (iii) r = -.32
Que 13
A portfolio consists of three securities P, Q and R with the parameters.
P
Q
R
Correlation
Coefficient
Expected return (%)
25
22
20
Standard deviation (%)
30
26
24
Correlation Coefficient
PQ
-0.5
QR
+0.4
PR
+0.6
If the securities are equally weighted, how much is the risk and return of the portfolio of
these three securities?
Que 14.
A portfolio consist of 3 securities, 1, 2 and 3, the proportions of these
securities are w1 = 0.3, w2 = 0.5 and w3 = 0.2. The standard deviation of
returns on these securities (in percentage terms) are SD1 = 6, SD2 = 9 and
SD3 = 10, the correlation coefficients among security returns are r12 = 0.4,
r13 = 0.6, r23 = 0.7. What is the standard deviation of portfolio return?
Ans.
Combined Risk = 7.58
TYPE 5
COMPUTATION OF COMBINED RISK AND COMBINED RETURN OF
PORTFOLIO
Que 15.
Mr. X is to invest his funds in two securities, P and Q. The relevant
information is as follows:
Expected Return
P
Q
12%
20%
Page | 434
Standard deviation of
return
10%
18%
Coefficient of correlation, r, between P and Q = .15
He has decided to consider only five portfolios of P and Q as follows:
(i)
(ii)
(iii)
(iv)
(v)
All funds invested in P
50% of funds in each of P and Q
75% funds in P and 25% in Q
25% funds in P and 75% in Q
All funds invested in Q
Find out:
(a) Return & risk in all above cases.
(b) Which portfolio is best from risk point of view
(c) Which portfolio is best from return point of view
Hint Ans. A)
Return
12
16
14
18
20
Risk
10
10.93
9.307
14.09
18
Ans. B)
Portfolio (iii)
Ans. C)
Portfolio (v)
Page | 435
Que 16.
Mr. X is presently concerned with the investment of Rs.1,00,000. He has two
securities, S1 and S2 for this purpose. The relevant information in respect of
these two securities is as follows:
S1
S2
Expected return
12%
20%
σ of return
10%
18%
Coefficient of correlation, r, between S1 and S2 = .15
He has decided to consider only five portfolio of S1 and S2 as follows:
(i)
(ii)
(iii)
(iv)
(v)
All funds invested in S1
50% of funds in each of S1 and S2
75% of funds in S1 and 25% in S2
25% of funds in S1 and 75% in S2
All funds invested in S2
Find out
1. Expected return under different portfolios.
2. Risk factor associated with these portfolios.
3. Which portfolio is best for him from the point of risk, and,
4. Which portfolio is best for him from the point of view of return.
Que 17.
The following are the different state of economy, the probability of
occurrence of that state and the expected rate of return from security A and B
in these different states.
State
Probability
Rate of return
Security - A
Security - B
Page | 436
Recession
.20
-.15
.20
Normal
.50
.20
.30
Boom
.30
.60
.40
Find out the expected returns and the standard deviations for these two securities.
Suppose, an investor has Rs.20,000 to invest. He invests Rs.15,000 in security A and
balance in security B, what will be the expected return and the standard deviation of
the portfolio?
Ans.
r = 1, Rp = 25.25, σp = 21.595
TYPE 6
COMPUTATION OF COEFFICIENT OF CORRELATION COMBINED RETURN
OF PORTFOLIO
Que 18.
Calculate expected return, standard deviation, covariance and correlation of
the following two investments A and B. The economic predictions are:
Economic Climate Probability Returns from A% Return from B%
Recession
0.2
10
06
Stable
0.5
14
15
Expansion
0.3
20
11
1.0
Compute return and risk of all the following portfolio base on correlation covariance.
Investment
A
B
(i)
(ii)
(iii)
Proportion
Proportion
Proportion
0.5
0.5
0.7
0.3
0.2
0.8
Ans. R A = 15, RB = 12 & S.DA = 3.60 & S.DB = 3.46
Que 19.
Returns on shares of X Ltd. and Y Ltd. for the past three years are as under:
Page | 437
(i)
(ii)
X
Y
Year 1
9%
6%
Year 2
12%
30%
Year 3
18%
18%
Find expected return & standard deviation of securities X and Y.
Find the covariance and coefficient of correlation between X and Y.
Ans. Rx = 13%.
Ry = 18
r = .3274
Que 20.
σx = 3.74
σy = 9.7979
Returns on shares of P Ltd. and Q Ltd. for the past two years are as under:
P
Q
Years 2000
11%
20%
Years 2001
17%
8%
Calculate the following:
(i)
Find out standard deviation of each stock.(3,6)
(ii)
Find the covariance and coefficient of correlation between P and Q.(-18)
(iii) If P and Q stock is invested in the ratio of 2:1, what is the portfolio risk.(0)
Que 21.
Europium Ltd. has been specially formed to undertake two investment
opportunities. The risk and return characteristics of the two projects are
shown below:
A
B
Expected return
12%
20%
Risk
3%
7%
Page | 438
Europium plans to invest 80% of its available funds in Project A and 20% in B. The
directors believe that the correlation co-efficient between the returns of the projects is +
1.0
(i)
(ii)
Calculate the return and risk from the proposed portfolio of Projects A and B;
Suppose the correlation co-efficient between A and B was -1. How should the
company invest its funds in order to obtain zero risk portfolio.
Ans.
(i) C.R = 13.6, C.Risk = 3.8 (ii) Risk = 0, W𝛼 = 0.70, W𝛽 = 0.30
TYPE 7
COMBINATION WITH RISK –FREE
Que 22.
If the risk-free return is 10% and the expected return on BSE index 18% (and
risk measurement by standard deviation is 5%), how would you construct an
efficient portfolio to produce a 16% expected return and what would be its
risk?
How would you construct a portfolio giving expected return of 20% and what
would be its risk?
Ans.
(.25,.75) 3.75; (1.25,.25) 6.25
Que 23.
You are able to both borrow and lend at the risk- free rate of 9%. The market
portfolio of securities has an expected return of 15% and a standard
deviation of 21%. Determine the expected return and standard deviation of
the following portfolios:
(a) All wealth is invested in the risk-free asset.(9,0)
(b) All wealth is invested in the market portfolio (15,21)
(c) One third is invested in the risk-free asset and two thirds in the market
portfolio.(13,14)
(d) All wealth is invested in the market portfolio. Furthermore, you borrow
an additional one third of your wealth to invest in the market portfolio.
Ans.
(d) R = 17% Risk = 28%
TYPE 8
WEIGHTS OF SECURITIES TO REDUCE RISK TO ZERO
Que 24.
L Ltd. and M Ltd. have the following risk and return estimates.
RL = 20%
RM = 22%
Page | 439
σL = 15%
σM = 18%
(Correlation Coefficient) = RLM = -1
Calculate the proportion of investment in L Ltd. and M Ltd. to minimize the risk of portfolio
and compute the risk and return.
Ans.
WL = 18 WM = 15 ( Risk = Zero)
33
33
Combines Risk
Combines Return
Que 25.
=
=
0
20.909
Return and risk on shares P and Q are as under:
Expected Return Standard deviation
Stock P
16%
25%
Stock Q
18%
30%
What is the expected return if a portfolio is constructed to drive the standard deviation of
portfolio return to zero, given that r = -1
30
25
Ans. Return = 16.90, w1 = 55 , w2 = 55
Que 26.
Europium Ltd. has been specially formed to undertake two investment
opportunities. The risk and return characteristics of the two projects are
shown below:
A
B
Expected return 12% 20%
Risk
3%
7%
Europium plans to invest 80% of its available funds in Project A and 20% in B. The
directors believe that the correlation co-efficient between the returns of the projects is +
1.0
(i)
(ii)
Calculate the return and risk from the proposed portfolio of Projects A and B;
Suppose the correlation co-efficient between A and B was- 1. How should the
company invest its funds in order to obtain zero risk portfolio.
Page | 440
Ans.
(i) C.R = 13.6, C.Risk = 3.8 (ii) Risk = 0, W𝛼 = 0.70, W𝛽 = 0.30
TYPE 9
CAPM (CAPITAL ASSET PRICING MODEL)
Que 27.
The following data relating to two securities, A and B.
Assume:
A
B
Expected return
22%
17%
Beta Factor
1.5
0.7
IRF =10, and RM = 18%
Find out whether the securities, A and B are correctly priced?
Ans.
(A) Correctly Price (as DR =ER), (B) Not correctly Priced (DR  ER)
Que 28.
The following information is available in respect of security X and Y.
Security
Beta
Expected Returns
X
1.8
22.00%
Y
1.6
20.40%
If the risk free rate is 7%&Rm12% are these securities correctly priced? What would the
risk free rate has to be if they are correctly priced?
Que 29.
An investor is seeking the price for a security, whose standard deviation is
4%. The correlation coefficient for the security with the market is 0.9 and the
market standard deviation is 3.2%. The return from government securities is
6.2% and from the market portfolio is 10.8%. The investor knows that, by
calculating the required return, he can then determine the price to pay for
the security. What is the required return on the security?
Ans.
D.R = 11. 375; 𝛽 = 1.125
Que 30.
Assume: IRF = 9%
RM = 18%
Page | 441
If a security has a beta factor of (a) 1.4, (b) 1.0 or (c) 2.3, find out the expected return of the
security.
Ans.
(a) = 21.6%, (b) = 18, (c) 29.7
Que 31.
An investor is seeking the price to pay for a security, whose standard
deviation is 3.00 per cent. The correlation coefficient for the security with the
market is 0.8 and the market standard deviation is 2.2 percent. The return
from Government Securities is 5.2 percent and from the market portfolio is
9.8 percent. The investor knows that, by calculating the required return, he
can then determine the price to pay for the security. What is the required
return on the security?
Ans.
Required Return = 10.218%
Que 32.
Calculate the market sensitivity index and the expected return on the
investment from the following data.
Standard deviation of an asset (security)
2.5%
Market standard deviation
2.0%
Risk-free rate of return
13.0%
Expected return on market portfolio
15.0%
Correlation coefficient of portfolio with
market
0.8%
What will be the expected return on the portfolio beta is 0.5 and the risk-free return is
10%?
Ans.
Que 33.
Market sensitivity index (Beta) = 1& E (R) = 15%
Expected Return (Beta = .5) = 14%
The following information is given:
The risk free rate, IRF
= 8%
Expected return on market portfolio = 16%
Βeta of security
= .7
i)
Find out the expected return of the security.
Page | 442
ii)
Ans.
If the other security has an expected return of 20%, what must be its beta?
(i) 1.36
(ii) 1.5
Que 34.
The Risk free rate IRF, is 4% and the market risk premium (R m-Rf) is 8.6%
and β of the security is 1.3. What is the expected return of the security under
CAPM? What would be the expected return if the β were to
double?(15.18,26.36)
Que 35.
The following data relate to two securities, A and B.
A
B
Expected Return
22%
17%
Beta Factor (β)
1.5
0.7
Assume: IRF = 10% and RM = 18%.
Find out whether the securities, A and B are correctly priced? Also show the graphic
presentation of the above situation.
Ans.
(Hint: Draw security market line (SML)
Que 36.
The following information is available is respect of security X and Y.
Security
β
Expected return
X
1.8
22.00%
Y
1.6
20.40%
If risk free-rate is 7%,Rm-15% are these securities correctly priced? What
would the risk free rate has to be if they are correctly priced?
Ans.
DRA = 21.4% (Sec A Not correctly priced)
DRB = 19.8% (Sec B Not correctly priced)
Risk free rate = 7.6%
Page | 443
Que 37.
Calculate the beta factor of the following investments. Is acceptance of the
investment worthwhile, based upon its level of risk? The risk-free rate, IRF,
may be taken at 6%.
Probability
Returns on
Market (M)
Investment (S)
1/3
9%
6%
1/3
12%
30%
1/3
18%
18%
Ans.
r = .327, Beta = .856, Expected Return = 12% , Required Return = 11.99
PORTFOLIO SCANNER QUESTION
Que. 1
(a) Security-A offers an expected rate of return of 14% with a standard deviation of 8%.
Security-B offers an expected rate of return of 1l% with a standard deviation of 6%. If
an investor wishes to construct a portfolio with a 12.8% expected return, what
percentage of the portfolio will consist of Security-A? (Dec, 10) (4 Marks)
Answer
(a) Security A offers an expected rate of return of 14% with a standard deviation
Solution
Security A
Security B
Return
14%
11%
Risk
8%
6%
We know,
Rp = R a × W a + R b × W b
Where;
Rp = Return of portfolio
Page | 444
Ra = Return on Security A
Wa= Weight of security A (y)
Rb= Return on security B
Wb = Weight of security B (1-y)
12.8=14y x +11× (1-y)
14y+11-11y = 12.8
3y = 1.8
Y = .6
So, Wa = .6, Wb = .4
Thus, the percentage of security A in the portfolio will be 60%
Que 2
A Portfolio Manager has three stocks in his portfolio. Following information is available in
respect of his portfolio:
Company
Investment (Rs)
β
X Ltd,
6,00,000
1.3
Y Ltd.
3,00,000
1.4
Z Ltd.
1,00,000
0.9
Expected return on the market portfolio is 15% and the risk free rate of interest is 60%
On the basis of Capital Asset Pricing Model (CAPM) compute the following:
(i)
(ii)
Expected return of the portfolio; and
Expected β of the portfolio
(Dec, 11) (8 Marks)
Answer
Expected rate of Individual Securities
ra = rf + βa (rm - rf)
Page | 445
Where,
Rf = Risk free rate = 6%
βa = Beta of the security
Rm = Expected market return = 15%
ra of X Ltd. = .06+ 1.3(.15 -.03) =.06 + .117 =.177
ra of Y Ltd. = .06 +1.4(.15 - .06) = .06 + .126 = .186
ra of Z Ltd. = .06 + 0.9(.15 - .06) = .06 + .081 = .141
Expected rate of Portfolio
ra
W × ra
0.6
βa
1.3
0.117
0.1 002
3,00,000
0.3
1.4
0.1 88
0.0558
1,00,000
0.1
0.9
0.141
0.0141
Company
Amount (Rs.)
Weight (w)
X Ltd
6,00,000
Y Ltd.
Z Ltd.
10,00,000
0.17 61
So the expected return of the portfolio is 0.1761 or 17.61%
Expected β of the portfolio
βp = β1W1 + β2W2 + βaWa
= 1.3 × 0.6 + 1.4 × 0.3 + 0.9 × 0.1
= .78 + .48 + .09
βp = 1.29
Question 3
A Ltd., and B Ltd., has the following risk and return estimates
RA
RB
σA
σB
(Correlation coefficient) = rAB
20%
22%
18%
15%
-.50
Calculate the proportion of investment in A Ltd., and B Ltd., to minimize the risk of Portfolio.
Page | 446
Answer
1. Basic Values of Factors for Determination of Portfolio Risk
Standard Deviation of Security A
σA
18%
15%
Correlation co-efficient of Securities A and B
σB
Weight of Security A
WA
X
Weight of Security B
WB
1-x
Standard Deviation of Security B
-.50
2. Computation of Investment in Security A (WA)
𝜎𝐵 2 − 𝐶𝑂𝑉
𝐴𝐵
Proportion or Investment in A Ltd., = 𝜎𝐴2 +𝜎𝐵 2 + 2𝐶𝑂𝑉
𝐴𝐵
Proportion of Investment in B Ltd., WB= 1 - WA
(a)
Computation of Covariance
covAB= rAB x σA σB
= -.50 x 18 x 15 = - 135
(b)
Proportion of investment in A Ltd.
(𝜎𝐵)2 − 𝐶𝑜𝑉𝐴𝐵
𝑊𝐴 =
(𝜎𝐴)2 + (𝜎𝐵)2 − 2 𝐶𝑜𝑉𝐴𝐵
(15)2 − (−135)
=
(15)2 + (18)2 − 2 (−135)
(c)
= .44
Proportion of investment in B Ltd.
→ WB = 1 - 0.44 = 0.56
MULTIPLE CHOICE QUESTIONS
Page | 447
1.
Security Analysis is a process of estimating................. for individual securities.
a) Return and risk
b) Risk and correlation
c) Correlation and co-efficient
d) Return and co-efficient
2.
Which of the following is correct formula to calculate returns of listed security?
a) [(P, - P0) + D] ÷ [P0 x 100]
b) [(P,' P0) + D] ÷ [P, x 100]
c) [(P,-P0)-D] ÷ [P0x100]
d) [(P, - P0) + D (1 -1)] ÷ [P0 x 100]
3.
A risk associated with project and way considered by well diversified stockholder
is classified as a) Expected risk
b) Beta risk
c) Industry risk
d) Returning risk
4.
Standard deviation determine a) Systematic risk of a security
b) Unsystematic risk of security
c) Total risk of security
d) Premium of security
5.
Standard deviation is a deviation from a) Arithmetic mean
b) Harmonic mean
c) Median mean
d) Mode mean
6.
Investment with lower standard deviation carries
a) High risk
b) Less risk
c) Infinite risk
d) Avoidable risk
7.
The beta of the market is:
a) -1.0
b) 0
Page | 448
c) 1.0
d) 0.5
8.
Non-systematic risk is furthermore identified as a) No diversifiable risk
b) Market risk
c) Random risk
d) Company specific risk
9.
Beta is measure of a) Non-diversifiable risk
b) Diversifiable risk
c) Toted risk
d) Covariance
10.
Beta, β, of risk-free investment is
a) Zero
b) 1
c) -1
d) None of these.
11.
Which of the following is diversifiable risk?
a) Inflation Risk
b) Interest Rate Risk
c) Risk due to restructuring of company
d) All of the above.
12.
Which of the following is not a non-diversification
a) Industrial recession
b) Lock-out in a company
c) Political Instability
d) Both (a) and (c).
13.
Which of the following is true?
a) Risk can never be reduced to zero in real life
b) Diversification always reduces risk to zero
c) Diversification does not affect risk
d) None of the above.
14.
Standard deviation can be used to measure
Page | 449
a) Risk of an investment
b) Return of an investment
c) Both(a)&(b)
d) None of (a) and (b).
15.
Which of the following is true?
a) Higher the Beta, lower the risk
b) Higher the Beta, higher the risk
c) Risk is constant
d) Beta is constant.
16.
Amount of risk-reduction in a portfolio depends upon
a) Market movement
b) Degree of correlation
c) No. of shares
d) Both (b) and (c).
17.
Portfolio risk will be when two components of a portfolio stand perfectly
positively correlated and will be when the same are perfectly negatively
correlated.
a) Minimum; Maximum
b) Maximum; Minimum
c) Minimum; Less
d) Maximum; More
18.
Risk-Return trade off implies
a) Minimization of Risk
b) Maximization of Risk
c) Ignorance of Risk
d) Optimization of Risk
19.
Risk of a portfolio depends on
a) Risk of elements
b) Correlation of return
c) Proportion of elements
d) All of the above.
20.
Systematic risk of a security can be measured by
a) Coefficient of variation
b) Standard Deviation
Page | 450
c) Beta
d) Range.
21.
Which of the following is unsystematic risk to a firm?
a) Inflation
b) Surcharge of Income-tax
c) Interest Rate
d) Scarcity of Raw Material.
22.
Which of the following is diversifiable through diversification?
a) Systematic
b) Unsystematic
c) Both of the above
d) None of the above
23.
A beta of 1.15 for a security would indicate that a) Security is trading 15% higher than market index
b) Security is 15% riskier than index/market.
c) Security is 15% less risky than index/market.
d) Security and market has covariance of 0.15.
24.
Choice of correlation coefficient is between a) 0 to 1
b) 0 to 2
c) Minus 1 to +1
d) Minus 1 to 3
25.
A beta of 0.8 for a security would indicate that a) Security is 20% riskier than index/market.
b) Security is 80% less risky than index/market.
c) Security is 20% less risky than index/market.
d) Security is 80% riskier than index/market
26.
Which is the beta for a treasury stock?
a) Zero
b) One
c) Greater than one
d) Less than one
27.
An aggressive share would have a beta
Page | 451
a) Equal to Zero
b) Greater than one
c) Less than Zero
d) Equal to one
28.
An amount invested is Rs 1500 and an amount received is Rs 2000 then return
would be
a) Rs 500.00
b) -Rs 500.00
c) Rs 3,500.00
d) -Rs 3,500.00
29.
Risk on a stock portfolio which cannot be eliminated or reduced by placing it in
diversified portfolio is classified as
a) diversifiable risk
b) market risk
c) stock risk
d) portfolio risk
30.
An opposite of perfect positive correlation + 1.0 is called
a) negative correlation
b) multiple correlation
c) divisor correlation
d) none of above
31.
Standard deviation is divided by expected rate of return is used to calculate
a) coefficient of variation
b) coefficient of deviation
c) coefficient of standard
d) coefficient of return
32.
Standard deviation is 18% and expected return is 15.5% then coefficient of
variation would be
a) 0.86%
b) 1.16%
c) 2.50%
d) -2.50%
33.
An expected final stock price is Rs 70 and an expected capital gain is Rs 25 then
an original investment would be
Page | 452
a) Rs 45.00
b) -Rs 45.00
c) Rs 95.00
d) -Rs 95.00
34.
Paid dividend is Rs 20 and dividend yield is 40% then current price would be
a) 60.00%
b) Rs 60.00
c) Rs 50.00
d) 2.00%
35.
An original investment is Rs 30 and an expected capital gain is Rs 10 then an
expected final stock price will be
a) Rs 20.00
b) Rs 40.00
c) -Rs 40.00
d) -Rs 20.00
36.
An expected final stock price is Rs 45 and an original investment is Rs 25 then an
expected capital gain will be
a) Rs 75.00
b) -Rs 75.00
c) -Rs 20.00
d) Rs 20.00
37.
An expected dividend yield is added into expected growth rate to calculate
a) dividend return
b) expected rate of return
c) expected capital
d) invested capital
38.
Dividend yield is 25% and current price is Rs 40 then dividend will be
a) Rs 50.00
b) Rs 10.00
c) Rs 65.00
d) Rs 15.00
39.
An expected dividend yield is 5.5% and expected rate of return is 11.5% then
constant growth rate would be
a) 2.09%
Page | 453
b) -6.00%
c) 17.50%
d) 6.00%
40.
This type of risk is avoidable through proper diversification.
a) portfolio risk
b) systematic risk
c) unsystematic risk
d) total risk
41.
Beta is the slope of”
a) The security market line.
b) The capital market line.
c) A characteristic line.
d) The CAPM.
42.
Capital Asset Pricing Model (CAPM) provides the link between a) Return and total risk
b) Risk and covariance
c) Return and non-diversifiable risk
d) Return and diversifiable risk
43.
Which of the following investment advice will you provide to your client investor
if CAPM Return < Expected return?
a) Sell
b) Hold
c) Buy
d) Short
44.
Which of the following investment advice will you provide to your client investor
if CAPM Return > Expected return?
a) Sell
b) Buy
c) Hold
d) None of the above
45.
If expected return is more than required return as per CAPM, then a) Security is overvalued and hence can be bought
b) Security is correctly priced and hence should be hold
c) Security is undervalued and hence can be sold
Page | 454
d) Security is undervalued and hence can be bought
46.
Which of the following investment advice will you provide to your client investor
if CAPM Return = Expected return?
a) Sell
b) Buy
c) Hold
d) Put
47.
Capital asset pricing theory asserts that portfolio returns are best explained by:
a) Economic factors
b) Systematic risk
c) Specific risk
d) Diversification
48.
................................is also called specific risk.
a) Systematic risk
b) Unsystematic risk
c) Covariance
d) Coefficient
49.
Systematic Risk is a) Uncontrollable
b) Controllable
c) Avoidable
d) Voidable
50.
Covariance between Security X and Security Y is zero. This indicate that a) There is strong relationship between the movements in returns of two securities.
b) There is positive relationship between the movements in returns of two
securities.
c) There is no distinct relationship between the movements in returns of two
securities.
d) There is negative relationship between the movements in returns of two
securities.
51.
According to the CAPM, overpriced securities have:
a) Negative alphas
b) Positive alphas
Page | 455
c) Zero betas
d) Zero alphas
52.
Negative covariance indicates that a) Returns on two assets bear a tendency to off-set each other, i.e. if return on A is
above par, return on B is likely to be below par. If return on A is below par, return
on B is likely to be above par.
b) Returns on two assets tend to go together, ie. if return on A is above par, return
on B is also likely to be above par.
c) There is no distinct relationship between the movements in returns of two
securities.
d) There is unnecessary relationship between the movements in returns of two
securities.
53.
Positive Covariance indicates that a) Returns on two assets bear a tendency to off-set each other ie. if return on A is
above par, return on B is likely to be below par. If return on A is below par, return
on B is likely to be above par.
b) There is no distinct relationship between the movements in returns of two
securities.
c) Returns on two assets tend to go together, le. if return on A is above par, return
on B is also likely to be above par.
d) Higher discount rate should be used in capital budgeting to discount the cash
flow.
54.
Alpha is an indicator of the extent to which the a) Actual return of a security deviates from those predicated by market experts.
b) Actual return of a security deviates from those predicated by derivative market
c) Actual return of a security deviates from those predicated by its beta value.
d) Actual return of a security deviates from those predicated by its probable
distribution value.
55.
Negative alpha value indicates that a) Expected return is less than required return as per CAPM and hence security is
overvalued. Such security should be sold.
b) Expected return is less than required return as per CAPM and hence security is
undervalued. Such security should be bought.
c) Expected return is more than required return as per CAPM and hence security is
undervalued. Such security should be bought.
Page | 456
d) Expected return is equal to required return as per CAPM and hence security is
correctly valued. Such security should be hold.
56.
Which of the following describe the relationship between expected rate of return
and the beta?
a) Security Market Line
b) characteristic Line
c) Capital Market Line
d) None of the above
57.
Which of the following describes the relationship between systematic risk and
return?
a) Arbitrage Pricing Theory
b) Capital Assets Pricing Model
c) Harry Marketing Model
d) Capital Market Line
58.
Which of the following describes the relationship between expected rate of return
and the standard deviation?
a) Characteristic Line
b) Capital Market Line
c) Security Market Line
d) None of the above
59.
Consider following two statements:
P. Beta coefficient is the measure of risk in CML.
Q. Standard deviation determines the risk factors of the SML.
Select correct answer from the options given below.
a) Statement P is true and Statement Q is false.
b) Statement Q is true and Statement P is false.
c) Both Statement P and Statement Q are true.
d) Both Statement P and Statement Q are false.
60.
Security Market Line graphs defines a) Efficient portfolios
b) Non-efficient portfolios
c) Disposable portfolios
d) Both efficient and non-efficient portfolios.
Page | 457
61.
According to the capital market line, the expected return of any efficient portfolio
is a function of:
a) Unsystematic risk
b) Systematic risk
c) Unique risk
d) Total risk
62.
The X-axis of the Security Market Line (SML) chart represents a) Expected return
b) Risk in terms of beta
c) Standard deviation
d) Co-efficient
63.
If an asset’s expected return plots above the security market line, the asset is:
a) Overpriced
b) Under priced
c) Fairly priced (if it has an unusually large amount of unique risk)
d) Both the first and third answers.
64.
The Security Market Line (SML) is a line drawn on a chart that serves as a
graphical representation of the Capital Asset Pricing Model, which shows
different levels of ............ of various marketable securities plotted against the
expected return.
a) Systematic risk
b) Unsystematic risk
c) Total risk
d) Free risk
65.
If a market is inefficient, as new information is received about a
security____________.
a) nothing will happen
b) the stock price will fall at first and then later rise
c) there will be a lag in the adjustment of the stock price
d) there will be negative demand for the stock
66.
The highest level of market efficiency is_____________.
a) weak form efficiency
b) semi-strong form efficiency
c) random walk efficiency
Page | 458
d) strong form efficiency
67.
The weak form of the EMH is supported if successive price changes over time
are________.
a) independent of each other
b) negative
c) positive
d) lagged
68.
If an investor searches for patterns in security returns by examining various
techniques applied to a set of data, this is known as__________.
a) fundamental analysis
b) technical analysis
c) data mining
d) random-walk theory
69.
The Markowitz model identifies the efficient set of portfolios, which offers the
____________.
a) highest return for any given level of risk or the lowest risk for any given level
of return
b) least-risk portfolio for a conservative, middle-aged investor
c) long-run approach to wealth accumulation for a young investor
d) risk-free alternative for risk-averse investors
70.
The Markowitz model identifies the efficient set of portfolios, which offers the
____________
a) highest return for any given level of risk or the lowest risk for any given level
of return
b) least-risk portfolio for a conservative, middle-aged investor
c) long-run approach to wealth accumulation for a young investor
d) risk-free alternative for risk-averse investors
71.
................................suggests that stock price changes are uncertain and are
independent of each other, so the past movement or trend of a stock price or
market cannot be used to predict its future movement.
a) Technical analysis theory
b) Random walk theory
c) Efficient market theory
d) Fundamental Market theory
Page | 459
72.
Dow Jones theory was formulated by a) John P. Dow
b) Charles H. Dow
c) James T. Dow
d) Michel R. Dow
73.
According to Dow Jones theory, share prices demonstrate a pattern over 4 to 5
years. These patterns can be divided into three distinct cyclical trends a) Preliminary, primary and secondary trends
b) Preliminary, bullish and bearish trends
c) Primary, secondary and minor trends
d) Primary, secondary and major trends.
74.
Efficient-market hypothesis (EMH) was developed bya) Professor Eugene Fama
b) Professor Miller
c) Professor Mark Linter
d) Professor Marshall
75.
A portfolio which lies below the efficient frontier is described as________________.
a) optimal
b) unattainable
c) dominant
d) sub-optimal
76.
Portfolios lying on the upper right portion of the efficient frontier are likely to be
chosen by_______________.
a) aggressive investors
b) conservative investors
c) risk-averse investors
d) defensive investors
77.
According to Markowitz, an efficient portfolio is one that has the_________________.
a) largest expected return for the smallest level of risk
b) largest expected return and zero risk
c) largest expected return for a given level of risk
d) smallest level of risk
78.
The relevant risk for a well-diversified portfolio is____________.
a) interest rate risk
Page | 460
b) inflation risk
c) business risk
d) market risk
79.
Beta is the slope of”
a) The security market line.
b) The capital market line.
c) A characteristic line.
d) The CAPM.
80.
The risk-free security has a beta equal to, while the market portfolio's beta is
equal to.
a) Zero; one.
b) Less than zero; more than zero.
c) One; less than one.
d) One; more than one.
81.
Beta measures the ___________.
a) Investment risk rate
b) Financial risk
c) Market risk
d) Market and finance risk
82.
If an investor states that Intel is overvalued at 65 times, he is referring
to___________.
a) earnings per share
b) dividend yield
c) book value
d) P/E ratio
83.
Markets which deals with high liquid and short term debt securities are classified
as
a) capital markets
b) money markets
c) liquid markets
d) short-term markets
84.
Type of financial securities that matures in less than a year are classified as
a) money market securities
b) capital market securities
Page | 461
c) saving intermediaries
d) discounted intermediaries
85.
Market risk premium is 8% and risk free return is 7% then market required
return would be
a) 15.00%
b) 1.00%
c) 5.60%
d) 1.14%
86.
Treasury yielded by bond is 7% and market required return is 13% then market
risk premium will be
a) 2.16%
b) 20.00%
c) 6.00%
d) 0.53%
87.
In capital asset pricing model, stock with high standard deviation tend to have
a) low variation
b) low beta
c) high beta
d) high variation
88.
In capital asset pricing model, covariance between stock and market is divided by
variance of market returns is used to calculate
a) sales turnover of company
b) risk rate of company
c) beta coefficient of company
d) weighted mean of company
89.
An average return of portfolio divided by its standard deviation is classified as
a) Jensen's alpha
b) Treynor's variance to volatility ratio
c) Sharpe's reward to variability ratio
d) Treynor's reward to volatility ratio
90.
An efficient set of portfolios represented through graph is classified as an
a) attained frontier
b) efficient frontier
c) inefficient frontier
Page | 462
d) unattained frontier
91.
92.
Expected Return on the market in 16% and Risk free rate is 6%, which of the
following projects be accepted.
a) A:β = 0.50, Return = 11.5%
b) B: β = 1.25, Return = 18.0%
c) C: β = 1, Return = 15.5%
d) D: β = 2, return = 25.0%
Risk avoidable through proper diversification is known as
a) Portfolio Risk
b) Unsystematic Risk
c) Systematic Risk
d) Total Risk
93.
An interest yield = 7.9% and capital gains yield = 2.5% then total rate of return is
a) 10.00%
b) 3.16%
c) 0.31%
d) 5.40%
94.
The expected return on an investment in stock is___________.
a) the expected dividend payments
b) the anticipated capital gains
c) the sum of expected dividends and capital gains
d) less than the realized return
95.
The expected return on an investment in stock is___________.
a) the expected dividend payments
b) the anticipated capital gains
c) the sum of expected dividends and capital gains
d) less than the realized return
96.
A company is considering two securities X and Y.
Security X
Return
Probability
(%)
30
0.1
Security Y
Return
Probability
(%)
30
0.2
Page | 463
60
120
150
0.4
0.4
0.1
60
120
150
0.3
0.3
0.2
Compute expected return of Security X & Security Y
a)
b)
c)
d)
97.
Security X
90%
80%
90%
80%
Security Y
80%
90%
90%
80%
A company is considering two securities X and Y.
Security X
Return
Probability
(%)
30
0.1
60
0.4
120
0.4
150
0.1
Security Y
Return
Probability
(%)
30
0.2
60
0.3
120
0.3
150
0.2
Compute expected risk of Security X & Security Y
a)
b)
c)
d)
98.
Risk (X)
37.94
36.04%
39.74%
36%
Risk (Y)
44.49%
44%
49.44%
35%
You have estimated the probability distribution of expected future return for
Stocks.
Stock X
Probability Return
0.1
-10%
0.2
10
0.4
15
Stock Y
Probability Return
0.2
2%
0.2
7
0.3
12
Page | 464
0.2
0.1
20
40
0.2
0.1
15
16
Compute expected return of X and Y
a)
b)
c)
d)
99.
15%
10%
12%
14%
11.61%
15%
13.26%
15%
You have estimated the probability distribution of expected future return for
Stocks.
Stock X
Probability Return
0.1
-10%
0.2
10
0.4
15
0.2
20
0.1
40
Stock Y
Probability Return
0.2
2%
0.2
7
0.3
12
0.2
15
0.1
16
Compute expected return of X and Y
a)
b)
c)
d)
10%
9%
10%
8%
6%
8%
4.93%
6%
100. Suppose risk free rate is 4% and k is 2.5%. If an investor takes 13% risk, he can
expect a return of a) 32.5%
b) 52%
c) 10%
d) 36.5%
101. Yogesh invest Rs.1,25,000 in shares of BABA Ltd., a listed company. At the end of
period investment value is Rs.1,32,000. He gets dividend of Rs.8,000. Return from
investment is Page | 465
a) 11%
b) 12%
c) 13%
d) 14%
102. X and Y are two securities in portfolio for which following information is
available.
Security X
Security Y
Return
12%
1896
SD
10%
1596
Correlation coefficient is + 0.5. Calculate the risk of portfolio using 20:80 weights.
a) 12.13%
b) 13.21%
c) 13.12%
d) 12.31%
103. K and H are two securities in portfolio for which following information is
available.
Security K
Security H
Variance
100
225
SD
10%
15%
Correlation coefficient is + 0.5. At what weight portfolio risk will be lowest.
a) 87.51 : 12.49
b) 58.71:41.29
c) 84.17:15.83
d) 14.29:85.71
104. Standard deviation of Security X and Market are 12% & 16% respectively.
Covariance of Security X with Market is +96. What is market sensitivity index of
Security X?
a) 0.407
b) 0.873
c) 0.375
Page | 466
d) 0.573
105. Return on XM Ltd. shares has a standard deviation of 23%, as against the
standard deviation of the market at 19%. Correlation co-efficient between market
and stock of XM Ltd. is 0.8. Compute the systematic risk of XM Ltd.’s shares.
a) 96.84%
b) 18.4%
c) 25.78%
d) 64.85%
106. Pavan has invested in four securities. Amount invested and beta of each security
is as follows:
Security
A
B
C
D
Rs.
25,000
50,000
40,000
35,000
Beta
0.80
1.20
1.40
1.75
Compute portfolio beta.
a) 1.524
b) 1.874
c) 0.789
d) 1.315
107. Expected return of Security A is 22% while that of Security B is 24%. Beta of
Security A is 0.86 while that of Security B is 1.24. What is risk free rate, so that
both securities are correctly priced?
a) 14.74%
b) 17.47%
c) 14.71%
d) 14.00%
108. Expected return of Security A is 20% while that of Security B is 25%. Beta of
Security A is 0.85 while that of Security B is 1.25.
What is market rate of return?
a) 21.875%
b) 22.385%
Page | 467
c) 18.655%
d) 20.555%
109. Calculate the required return on the security from the following information:
Standard deviation
2.5%
Market standard deviation
2.0%
Risk free rate of return
13%
Expected rate of return on
15%
market portfolio
Correlation coefficient of
0.8
portfolio with the market
a) 16%
b) 15%
c) 14%
d) 12%
110. A financial consultant has gathered following facts for H Ltd.
Systematic risk of the firm is 1.4.
182 days Treasury bill yield is 8%
Expected yield on market portfolio is 13%. Calculate expected return based on
capital asset pricing model (CAPM).
a) 18%
b) 17%
c) 16%
d) 15%
111. As an Investment Manager you are given the following information:
Particulars
p
Cement Ltd. 0.8
Steel Ltd.
0.7
Liquor Ltd.
0.5
GOI bonds
0.99
Risk free return may be taken at 14%.
Expected rate of return on market portfolio is 26.33%. Average return on portfolio =
Rs.
a) 23.86%
b) 22.63%
c) 26.21%
d) 23.22%
Page | 468
112. Following details are gathered by the investor:
Standard deviation
2.80%
Market standard deviation
2.30%
Risk free rate of return
8%
Expected rate of return on market portfolio
18%
Correlation coefficient of portfolio with the market
0.8
Required return on security is a) 14.77%
b) 17.74%
c) 15.84%
d) 20.65%
113. The following data relate to two securities, A and B:
A
B
Expected return
22%
17%
Beta factor (P)
1.5
0.7
Assume RF = 10% and RM = 18%.
Find out whether the securities, A and B are correctly priced?
Security A
Security B
Undervalued
Overvalued
b) Overvalued
Undervalued
c)
Undervalued
a)
Correctly valued
d) Overvalued
Correctly valued
114. Security-A offers an expected rate of return of 14% with a standard deviation of
8%. Security-B offers an expected rate of return of 11 % with a standard
deviation of 6%. If an investor wishes to construct a portfolio with a 12.8%
expected return, what percentage of the portfolio will consist of Security-A &
Security-B?
a) 40:60
Page | 469
b) 60:40
c) 70:30
d) 30:70
115. Mohan has a portfolio of 6 securities, each with a market value of Rs. 10,000. The
current beta (β) of the portfolio is 1.30 and (β) of the riskiest security is 1.80,
Mohan wishes to reduce his portfolio (β) to 1.15 by selling the riskiest security
and replacing it with another security with a lower (β). What must be the (β) of
the replacement security?
a) 0.8
b) 0.7
c) 0.9
d) 1.1
116. You are analyzing the beta for ABC Ltd. and have divided the Company into four
broad business groups, with market values and betas for each group.
Business Group
Market value of Equity (Rs.)
Beta
Main Frames
100 billion
1.10
Laptop
100 billion
1.50
Software
50 billion
2.00
Printers
150 billion
1.00
Estimate the beta for ABC Ltd. as a company.
a) 1.275
b) 1.825
c) 1.645
d) 0.895
117. Following details are available for EX Ltd. & FX Ltd. securities.
Probability
Return in %
Security EX
Security FX
0.5
20%
16%
0.3
30%
40%
0.2
40%
30%
Page | 470
Covariance between Security EX and Security FX is a) 85
b) 58
c) -58
d) -54
118. You have been given following data for Security X:
Probability
0.05
0.20
0.50
0.20
0.05
Return
7%
10%
13.5%
17%
20%
Calculate standard deviation of security.
a) 3.02%
b) 3.36%
c) 4.57%
d) 4.12%
119. Following data is available for the Security P & Q.
Probability
Return in %
Security P
Security Q
0.15
15%
5%
0.70
10%
10%
0.15
5%
15%
Correlation Coefficient for the above two securities is a) -0.9899
b) -0.9989
c) +0.8999
d) +0.9989
120. X and Y are two securities in portfolio for which following information is
available.
Page | 471
Security X
Security Y
Return
15%
22.5%
SD (a)
8%
10%
Correlation coefficient is + 0.7.
What weight you will assign to the Security Y so that portfolio risk is lowest?
a) 15.3896
b) 84.6296
c) 82.4696
d) 20.1896
Page | 472
Answers 1
A
21
D
41
C
61
D
81
C
101
B
2
3
4
5
A
B
C
A
22
23
24
25
B
B
C
C
42
43
44
45
C
C
A
D
62
63
64
65
B
B
A
C
82
83
84
85
D
B
A
A
102
103
104
105
C
D
C
B
6
7
8
9
B
C
D
A
26
27
28
29
A
B
A
B
46
47
48
49
C
B
B
A
66
67
68
69
D
D
B
A
86
87
88
89
C
C
C
C
106
107
108
109
D
B
A
B
10
11
12
A
C
B
30
31
32
A
A
B
50
51
52
C
A
A
70
71
72
A
B
B
90
91
92
B
A
B
110
111
112
D
D
B
13
14
15
16
A
A
B
B
33
34
35
36
A
C
B
D
53
54
55
56
C
C
A
A
73
74
75
76
C
A
D
A
93
94
95
96
B
C
C
C
113
114
115
116
C
B
C
D
17
18
19
20
B
D
D
C
37
38
39
40
B
B
D
C
57
58
59
60
B
B
D
D
77
78
79
80
C
D
C
A
97
98
99
100
A
A
C
D
117
118
119
120
B
A
C
B
State whether each of the following statements is True (T) or False (F).
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
Principal objective of making investment is return, hence, risk can be ignored by an
investor.
Return includes only the interest or dividend received from an investment.
Holding period return includes the capital gain as well as revenue return.
If more than one value of return is expected, then expected return can be
ascertained with the help of probabilities.
Risk refers to possibility of loss from an investment.
Business risk arises because of competition in the market.
Financial risk of a firm depends upon composition of capital structure.
Systematic risk is diversifiable.
Systematic risk remains fixed irrespective of number of securities in portfolio.
Degree of risk and risk premium are positively related.
Page | 473
(xi)
(xii)
(xiii)
(xiv)
(xv)
(xvi)
(xvii)
(xviii)
(xix)
(xx)
(xxi)
No investor is ready to take risk in whatsoever situation.
Standard deviation is better than coefficient of variation as measure of risk.
Higher risk may be assumed by an investor if the.
Variation in expected return from an investment is known as risk.
Capital Market Line show the MP of shares at the exchanges.
CAPM establishes that the return of a security –is related to risk of that security.
β and σ cannot be used interchangeably.
β is a measure of expected return of a security.
Security Market Line is the graphical presentation of security prices.
CML and SML have same shape and conveys same ideas.
CAPM can be used for risk-return relationship of any type of asset.
Answers (i) F, (ii) F, (iii) T, (iv) T, (v) F, (vi) T, (vii) T, (viii) F, (ix) T, (x) T, (xi) F, (xii) F,
(xiii) F, (xiv) T, (xv) F, (xvi) T, (xvii) T, (xviii) F, (xix) F, (xx) F ,(xxi)T
Page | 474
TABLE 1 : pRESENTVALUE OF RUPEE ONE { r vf)
YEAR
YEAR
YEAR
YEAR
YEAR
YEAR
YEAR
YEAR
YEAR
YEAR
1
2
3
4
5
6
7
I
9
10
0.9524
0.9070
0.8638
0,7B3s
o.7462
o-710'7
0.6768
o.6446
0-6 r 39
0.9534
0.8900
0.8396
0.7921
o.7 473
0 7050
0.665 t
0.627 4
o 5919
0-9346
0.8734
0_81 63
0.7629
0.7130
0.6663
0.6227
0.5820
Bo/"
0.9259
0.8573
0.7938
0.7350
0.6806
0.6302
0.5835
9%
0.9 174
0.841 7
o.7722
0.7084
0.6499
0.5963
10'/"
0.9091
0.8264
0.7513
0.6830
0.6209
11.h
0.9009
0.81 16
0.7312
0.6587
12.h
0.8929
o.7972
o.7118-
13%
0.8850
0.7831
14%
o-8172
15./.
RATE
YEAR
YEAR
YEAR
YEAR
YEAR
12
13
14
15
0_5847
o.5568
0.5303
0.5051
0.481 0
0.5584
0,5268
0.4970
0.4688
0.4423
0_41 73
o.sa cg
0_5083
o.47 51
0.4440
0.41 50
0.3878
0-3624
0.5403
0.5002
0-4632
0.4289
0.3971
0.3677
0.3405
o.3152
0.5470
0,5019
o..1604
o.4224
0,3875
0.3555
0.3262
o.2992
o.2745
0.564 5
0.51 32
0.4665
a.4241
. 0-385s
0.3505
0.31 86
0.2897
0,2633
0.2394
0.5935
o.5346
0.4817
.0_4339
0.3009
o.3522
0.3173
0.2858
o.2575
o.izzo
0.2090
0.6355
0.5674
0.5066
0.4523
0.4039
0.3606
0.3220
0.2875
0-2567
o ?292
0.2046
0.1827
0_693't
0,6133
0.5425
0.4803
o.4251
o.3762
0.3329
0.2946
0.2607
0 2307
o 2042
0_ 1 807
0.1 599
0.7695
0.6750
0.592 r
0.5194
0.4556
b.ssgo
0.3506
0.3075
0 2697
0.2365
0,2076
0.1 82 1
0.1 597
0.1401
0-86S6
0.7561
0.6575
0,571 B
o.49t2
0 4323
0 3759
0_3269
o 2843
o.2472
0.2 r49
0_ 1 869
0_ 1 625
0.r413
o.1229
160
o.8621
0.7432
o.6407
0.5523
0.4761
0.4104
0-3538
o.3050
o 2630
0.2261
0.1 954
0.1 685
0.'1452
o.1252
0.1 079
6%
11',',"
0 8547
0,7305
o.6244
0-5337
0.4561
0.3898
0_3332
o,2844
o.24'34
0 2080
0.11't 8
0.1 520
0.1 2S9
0.1110
0_0949
lBo/o
0_8475
0.718 2
0.6086
0_5158
0.4371
0.3704
0.3139
0.2660
o ??55
0.1911
0 1619
0 1312
0.1 1 63
o 0985
0.0835
19r"
0 8403
0 7062
0.5934
o..1987
0.,1190
0.3521
0 2959
o.248 7
0.20e0
0 1756
().1476
0.1240
01042
0 0876
0.0736
20%
0.8333
0.6944
4.5187
0_4823
0.4019
0 3349
o 2i.)1
0 2:r2 6
0 1938
0. 101 5
01340
0 112?
0.0935
tj 0779
0.0649
21%
o.8264
0.6830
0.564 5
0 4665
0.3855
0.3186
0 26:13
O 21 r-6
o.1 739
[j. ] 480
0.1 228
01015
0.08 39
0 u693
o.0573
22%
0,8 197
0.6719
0.5507
0.451.1
0.370n
0 3033
0.24ti6
0.203I
01b70
0 1309
o 1127
0.0920
0.075.1
00618
0.0507
0.8130
0.6610
o.537 4
0 4369
0-3552
0.2888
o.234 B
0. r 909
Q 1552
o.1262
0 1026
0.083.1
0 0678
0 0551
o.o44B
0,8065
0_6504
0_524 5
0.4230
0.3.1 1 1
0.2751
o.2218
0.1 789
o 14.13
Ll 116,1
0.0938
0.ot57
0.001 0
o r)492
o.0397
0.8000
0.6400
0.5120
0.4096
o.3277
0 .2671
0.2097
0. 1 678
o.1 342
0.'r 074
0 0859
0.068 7
0.0550
0 0440
0.0352
.
TABLE 2 : pRESENTVALUE OF ANANNUTTY oF RUPEE oNE
YEAR
YEAR
.YEAR
YEAR
1
2
3
4
o.9524
1.8594
2.7232
3.5460
o.9434
r.8334
2.6730
0.9346
1.8080
8./"
o.slss
90/o
t f u fi €)
I
YEAR
YEAR
YEAR
YEAR
YEAR
YEAR
YEAR
YEAR
YEAR
6
7
I
I
10
11
12
13
14
15
4.3?95
5.0757
5.7864
6.4632
7. l 078
7.1217
E.3064
8.8633
9.3936
9.8986
1
3.4651
4.21?4
4.9173
5.5A24
6.2098
6.8017
7.360I
7 -8869
8.3838
8.A527
9.2950
9.7 122
2.6243
3.3872
4.100?
4-7665
5.3893
5.971 3
6.51 52
7.0236
7.4987
7.9427
8.3577
8.7455
9.1 079
I.za:a
l-ct t t
3.3121
3-9927
4.6229
5.2064
5.7466
6.2469
6.7101
7.1 390
7.5361
7.9038
8.2442
8.5595
o-9174
1 .759 r
2.5313
3.2357
3.8897
4.4859
5.0330
5.5348
5.9952
6.4177
6.8052
7.'t607
7-4869
7.7862
8.0607
10y.
0_9091
1.7355
2,4869
3.1 6S9
3.7908
r1.3553
4,8684
5.3349
5.75S0
6,1 446
6-4951
6.813 7
7.'to34
1.3667
7.6061
1ft"
0.9009
1-7125
2_4437
3.1024
3.6950
4.2305
4.7122
-5.146
1
5.5370
5.8892
6,2065
6.4924
6.749S
6.981
I
7.1 909
12Yo
o 8929
1 .6901
2.'4018
3.0373
3,6048
4 _1114
4_5638
4.9676
5.3282
5.6502
5.5377
6. t 944
6.4235
6.6282
6.8 109'
l3Vo
o,8850
1 -668
I
2-3612
2.9-745
3_517?
3,9975
4.4226
4.7988
5,1317
5-4262
5.6869
5-91 76
6.1218
6_3025
6.4624
1 40/o
o_8772
1.6467
2;3216
2.9137
3.4331
3.8887
4,2883
4.6389
4.9464
5.2161
5.4527
5.6m3
5-8424
6.O021
6.142?
150/o
0_8696
1.6257
2.2832
2,8550
3.3522
3.7845
4. 1 604
4.4A73
4 _7716
5-0188
5_2337
5.4206
5.5831
5.7245
5.8474
r6%
0.8621
1.6052
2.2459
2.7982
3.684 7
4.0386
4.3436
4,6065
4-8332
5.0286
5.1 97 1
5.3423
5.4675
5-5755
0.8547
1.5852
2.2096
2.7 432
3.5892
3.9224
4.2072
4.4506
4.6586
4.8364
4.9884
5.1 1 83
5.2293
B9;
0.8475
1.5656
2.11 43
2 6901
3.4976
3.81r5
4.0776
4.3030
4.494 1
4.6560
4.7932
4_9095
5,O08 1
5,0916
19%
0.8403
1 5465
2 1399
2.6346
3.0576
3.4098
3.7 051
3,9544
4_r 633
4-3389
4,4865
4.6105
4.7 141
4,8023
4.8759
20"h
0_8333
1 5278
2. 1 065
2.5887
2.9906
3.3255
3.e'046
3.8372
4.0310
4.1925
4 _327 1
4.43!2
q J.)t
I
4,6106
4 D / 3)
o.8264
1
-5095
2.0139
2.5404
2.9200
3.2446
3 5079
3.7256
3.9054
4.054 1
4_1 769
4.2184
4.3624
4.4317
4,4 890
o.6'197
1 4915
?.0422
2.4936
2.8636
3.1 669
3.4155
3.6193
3.7863
3.9237
4 _0354
4.127 4
4.2028
4.2G46
4.31 52
o.B 1 30
1.4740
2.0114
2.4483
2.8035
3.0923
3.3270
3.5179
3_6731
3.7993
3.90 r I
3.9852
4_0530
4. 1 082
4.1530
24"A
0.8065
1-4568
1.S8'13
2_4043
2.7 454
3.0205
3.2423
3.4212
3.5655
3_681 9
J.t tJl
3.851 4
3.9124
3.9616
4.0013
lzsv,
0.8000
1 4400
1,S520
2,36 r 6
2.68 9 3
2.951 4
3. 1611
3.3289
3.4 031
3.5705
3.6564
3 -7 251
3-7801
3.8241
3.8S3
RATE
E"h
1
YEAR
3. l 993
YEAR
0-3797