Investment Decisions
Study Note - 6
INVESTMENT DECISIONS
6.1 Cost Benefits Risk Analysis For Projects
This Section includes :
Techniques of Risk Analysis
Convention Techniques
Statistical Techniques
INTRODUCTION :
In the capital budgeting decisions, if there is an element of risk involved, it must be considered
while evaluating investment proposals. There are several techniques available to analyse the
risk perception of capital budgeting proposals. These techniques differ in their approach and
methodology to analyse risk in the evaluation process.
TECHNIQUES OF RISK ANALYSIS :
Conventional Techniques
1. Risk Adjusted Discount Rate
2. Certainty Equivalents Approach
3. Sensitivity Analysis
Statistical Techniques
1. Probability Distribution Approach
2. Simulation Analysis
3. Decision Tree Approach
CONVENTIONAL TECHNIQUES :
There are several conventional techniques which attempt to incorporate the risk or capital
budgeting proposals. Some of these techniques have been discussed hereunder.
1. Risk Adjusted Discount Rate (RADR)
Every firm is basically risk averse and tries to avoid risk. However, it may be ready to take risk
provided it is rewarded for undertaking risk by higher returns. So, more risky the investment
is, the greater would be the expected return. The expected return is expressed in terms of
discount rate which is also termed as the minimum required rate of return generated by a
proposal if it is to be accepted. Therefore, there is a positive correlation between risk of a
proposal and the discount rate.
A firm at any point of time has a risk level emanating from the existing investment. The firm
also has a discount rate to reflect that level of risk. In case, there is no risk of the existing
investment, then the discount rate may be known as the risk free discount rate. If the risk level
of the new proposal is higher than the risk level of the existing investment, then the discount
rate to be applied to find out the present values of the cash flows of the proposals having
varying degree of risk should be evaluate at different discount rates. The difference between
the discount rate applied to a riskless proposal and to a risky proposal is known as risk premium.
RADR attempts to incorporate risk by modifying the discount rate. A risk premium is added
to the riskless discount rate, to reflect the risk inherent in the project. The reasoning behind
adding the risk premium is quire simple. i.e., the greater the risk, the higher should be the
desired return from a proposal. The RADR approach to handle risk in a capital budgeting
decision process is a more direct method. The RADR is based on the premise that riskiness of
a proposal may be taken care of, by adjusting the discount rate. The cash flows from a more
risky proposal should be discounted at a relatively higher discount rate as compared to other
proposals whose cash flows are less risky. The RADR may be expressed in terms of Equation
RADR = Risk Free Return + Premium for facing the Risk
The risk free discount rate is described as the rate of return on the government securities. Since
all the business proposals have higher degree of risk as computed to zero degree of risk of
government securities, the RADR is always greater than the risk free rate. Moreover, as the
risk of a proposal increases, the risk adjustment premium also increases. The relationship
between the risk free rate, the risk premium, the RADR and the risk return line has been explained
in the figure below :
Risk-free rate, Risk Premium and Risk-return relationship.
Return
Risk Adjustment
Premium
Risk-free
Rate
C
B
A
O X1 X2
Risk-Return Line
Risk
The figures reflects that if the risk of proposal is zero, then the minimum required rate of
return, i.e., the discount rate will be just equal to the risk free rate, i.e., OA. However, as the
risk increases, say, up to X1, then the required rate of return also increases from OA to OB. The
component AB is known as the risk adjustment premium. Similarly, if the level of risk of a
proposal is X2, then the risk premium may be AC and the discount rate for such proposal will
Investment Decisions
be equal to OC. The risk premium being added to the risk free rate reflects the greater risk
attached to a proposal. As the risk increases, the risk premium also increases and the RADR
also increases. The RADR is used to find out the risk adjusted NPV of the proposal as per
Equation
RANPV = 0
1 [1 ]
C
Ra
n CFi
i
−
+ Σ=
RANPV = Risk adjusted NPV
CF1 = Cash inflows occurring at different points of time
C0 = Initial cash outflow
Ra = Risk adjusted discount rate.
Difference between the NPV method, discussed in the previous chapter, and the RADR is that
the rate of discount used in RADR, i.e., Ra is higher than the original discount rate, i.e., R. The
RADR reflects the return that must be earned by a proposal to compensate the firm for undertaking
the risk. The higher the risk of a proposal, the higher the RADR would be and therefore
the lower the NPV of a given set of cash flows. The decision rule of RADR is that a firm should
select the proposal if the RANPV is positive or even zero and reject the proposal if it is negative.
In case of mutually exclusive proposals, the rule may be : select the alternative which has
the highest positive RANPV. In case, the firm is applying the IRR technique for evaluation of
capital budgeting proposals, then IRR of the project can be compared with the RADR, i.e., the
minimum required rate of return to accept or reject the proposal.
Evaluation of RADR Approach— The RADR approach considers the time value of money
and explicitly incorporates the risk involved in the project by making the discount rate as a
function of the proposal’s risk. The RADR helps finding out the expected future wealth generated
by a risk project over and above the RADR, However, the RADR suffers from the basic
shortcoming relating to the determination of the risk adjustment premium or the RADR itself.
Moreover, the RADR does not adjust the future cash flows which are risky and uncertain.
2. Certainty Equivalents (CE)
The CE approach to incorporate the risk is to adjust the cash flows of a proposal to reflect the
riskiness. The CE approach attempts at adjusting the future cash flows instead of adjusting the
discount rates. The expected future cash flows which are taken as risky and uncertain are
converted into certainty cash flows. Initiatively, more risky cash flows will be adjusted down
lower than the less risky cash flows. The extent of adjustment will vary and it can be either
subjective or based on a risk return model. These adjusted cash flows are then discounted at
risk free discount rate to find out the NPV of the proposal. The procedure for the CE approach
can be explained as follows:
1. Estimate the future cash flows from the proposal. These cash flows do have some degree
of risk involved.
2. Calculate the CE factors for different years. These CE factors reflect the proportion of the
future cash flow a finance manager would be ready to accept now in exchange for the
future cash flow. For example, cash inflow of Rs. 10,000 is receivable after 2 years. However,
if the inflow is available right now, the firm may be ready to accept even 70% of Rs.
10,000, i.e., Rs.7,000 only. This 70% or 0.7 is the CE factor. The CE factor will be different
from year to year. The higher the riskiness of cash flow, the lower would be the CE
factor.
3. The expected cash flows for different years as calculated in step 1 above are multiplied
by the respective CE factors and the resultant figures are described as certainty equivalent
cash flows.
4. Once all the cash flows are reduced to CE cash flows, then these CE cash flows are discounted
at risk free rate to find out the NPV of the proposal.
The CE approach may be described in terms of Equation
RANPV = 0
[1 ] 1
C
kf
ai CFi n
i
−
+ Σ=
Where RANPV = Risk adjusted NPV of the proposal
ai = CE factors for different years
CFi = Expected cash flows for different years
Kf = Risk free discount rate
Co = Initial Cash Outflow
In the above equation, the value of a1 i.e., the CE factors will vary between 0 and 1, and will
vary inversely to risk. The greater the risk involve (may be due to time factor or otherwise), the
lower will be the value of a.
The decision rule associated with the CE approach is that accept a proposal with positive CE
NPV. In case of mutually exclusive proposals, the rule is that the proposal having the highest
positive CE NPV is accepted. If a firm is using IRR technique to evaluate the capital budgeting
proposals, then the IRR of the CE cash flows can be calculated and computed with the minimum
required rate of return to make an appropriate decision.
Evaluation of CE Approach— The CE approach explicitly recognises the risk and incorporates
it by deflating the cash flows to CE cash flows. This approach seems to be conceptually superior
to the RADR and does not assume that risk increases over time at a constant rate. But the
CE approach involves the determination of CE factors which is a tedious job.
Comparison of RADR and CE Approach—Both the RADR and the CE approach attempt to
incorporate the project risk, of course, in a different way. The RADR incorporates the risk by
increasing the discount rate, i.e., deals with the denominator of the NPV formula. The CE
approach incorporates the risk by deflating the expected cash flows to CE cash flows and it
deals with the numerator of the NPV formula. In case of RADR, there is an implied assumphttp://
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tion that the risk of the proposal increases at a constant rate over the life of the project. On the
other hand, the CE approach incorporates the different degrees of risk involved for different
years.
The RADR tends to club together the risk free rate, the risk involved and the risk premium,
while the CE approach maintains a distinction between the risk free rate and the risk. The
discount rate in CE approach is taken as the risk free discount rate and is constant while the
risk is incorporated by adjusting the cash flows.
Both the RADR and the CE approach attempt to incorporate the risk, yet they differ in their
approach. The relative position of these two techniques have been presented in the following
figure which shows that RADR converts the risky cash flows into present values in one stroke,
while the CE approach makes separate adjustments for time and the risk.
Future Cash Flows [Risky]
Certainty Equivalent
[Adjustment for Risk]
Time value of Money
[Adjustment for Time]
Risk-Adjusted Discount Rate
[Adjustment for Risk and Time]
Present Value
3. Sensititivity Analysis (SA)
The NPV of a project is based upon the series of cash flows and the discount factor. Both these
determinants depend upon so many variables such as sales revenue, input cost, competition,
etc. Given the level of all these variables, there will be a series of cash flows and there will be
NPV of the proposal. If any of these variables changes, the value of the NPV will also change.
It means that the value of NPV is sensitive to all these variables. However, the value of NPV
will not change in the same proportion for a given change in any one of these variables. For
some variables, the NPV may be less sensitive while for others, the NPV may be more sensitive.
The Sensitivity Analysis (SA) deals with the consideration of sensitivity of the NPV in
relation to different variables contributing to the NPV. The following steps are required to
find out the sensitivity of NPV to different variables:
(a) Based on the expectations about the future, the cash flows are estimated in respect of the
proposal. NPV of the proposal is calculated on the basis of these cash flows.
(b) Variables which have a bearing on the cash flows of a proposal are identified. For example,
some of these variables may be selling price, cost of inputs, market share, market
growth rate, etc.,
(c) To find out the effect of change in any of these variables on the value of NPV. This
exercise should be performed for all the factors individually. For example, in case of a
project involving the product sale, the effect of change in different variables such as
number of units sold, selling price, discount rate, etc., can be taken up on the NPV or IRR
of the Project. This information can be used in conjunction with the basic capital budgeting
analysis to decide whether or not to take up the project.
The sensitivity of a capital budgeting proposal, in general, may be analysed with reference to
a. level of revenues,
b. the expected growth rate in revenues,
c. the operating margin, and
d. the working capital requirements as a percentage of revenue, etc., With each such variable,
the NPV and IRR of a proposal may be ascertained by keeping the other variables
unchanged.
Evaluation of Sensitivity Analysis—SA helps in identifying the different variables having
effect on the NPV of a proposal. It helps in establishing the sensitivity or vulnerability of the
proposal to a given variable and showing areas where additional analysis may be undertaken
before a proposal is finally selected. The final decision on whether or not to take up the proposal
will be based on the regular capital budgeting analysis and the information generated by
the sensitivity analysis. It is entirely possible that a decision maker, when faced with the
results from the SA. might decide to override a proposal originally approved by capital budgeting
analysis. He may point out that a small change in any one variable makes the proposal
unacceptable. However, SA has some limitations as follows.
1. It may be observed that the SA is neither a risk measuring nor a risk-reducing technique.
It does not provide any clear cut decision rule.
2. Moreover, the study of effect of variations in one variable by keeping other variables
constant may not be very effective as the variable may be interdependent. The variables
are often related and move together, e.g., the selling price and the expected sales volume
are interrelated.
3. The analysis presents the results for range of values, without providing any sense of the
likelihood of these values occurring.
STATISTICAL TEHNIQUES :
The different techniques discussed above fail to measure and quantify the risk in precise terms.
There are certain statistical techniques available to measure and incorporate risk in a capital
budgeting decision process. These techniques can be used to evaluate the risk-return charachttp://
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teristics of a capital budgeting proposal. The most important concept used in these statistical
techniques is that of probability. Therefore, before analysing the statistical techniques of incorporating
risk, the concept of probability must also be understood.
The Concept of Probability—The probability may be defined as the likelihood of happening
or non-happening of an event. It may be described as measure of chance of happening or nonhappening
of an event.
1. Probability Distribution
The probability distribution may be defined as a set of possible cash flows that may occur at a
point of time and their probabilities of occurrence. In probability distribution, given above for
year 1, there are 4 possible cash inflows. The probabilities given for these cash inflows can be
interpreted as follows :
There is a 20% chance that the cash inflows will be Rs1,00,000; there is 40% chance that the
cash inflows will be Rs1,50,000 and so on. The probabilities can be assigned on the basis of
past experience or historical data. If the decision maker foresees a risk in the proposal then he
has to prepare a separate probability distribution to summarize the possible cash flow for each
year through the economic life of the proposal. The next step is to find out the expected value
of probability distribution for each year.
Expected Value of a Probability Distribution
The initial step required in evaluating a risky proposal is to find out the expected value of
probability distribution for each year. For this, each cash flow of the probability distribution is
multiplied by the respective probability of the cash flow and then adding the resulting products.
This final figure is then considered as the expected value of the cash flow for that year for
which the probability distribution has been considered. This procedure is to be adopted for
the probability distributions for all the years and then the expected value of cash inflows are
discounted at an appropriate discount rate to find out the NPV of the proposal. This has been
presented in following equation.
RANPV = 0
[1 ]
1
1
C
k
EVCF n
i
−
+ Σ=
Where NPV = Net present value of the proposal,
EVCFi = Expected value of cash inflows for different years, and
k = Discount Rate.
Co = Intital Cash Outflow
2. Simulation
The dictionary meaning (WEBSTER) of SIMULATION is “to assume the mere appearance of without
the reality”. Thus the appearance is true but not real, which implies that simulation is imitation
of reality. Simulation is the representation of a system by a model which will react to change in
a similar way to that which is being simulated. This evolves a decision maker to predict the
outcome of particular decision through testing it via the model. Normally simulation techniques
are used to solve problems involving uncertainty. There are several techniques of simulation
that are in use. However, ‘Monte-carlo’method is very popular as it is very simple and easy to
use. The technique uses random numbers and is used to solve problems which involves
conditions of uncertainty.
In simulation, a computer would normally be lised to build and run the model. This prticularly
important in this area, since meaningful information can be extracted from the simulation only
after a number of runs with different random numbers. If we are interested in the steady state
of die moodel, the simulation must be allowed to proceed for a long period of simulated time
so that average volumes of the relevant statistics may be calculated. If the period is too short,
the initial start up fluctuations can affect the mean values.
3. Decision Tree Approach
The evaluation of a project frequently requires a sequential decision-making process where
the accept-reject decision is make in several stages. Instead of taking a decision once for all, it
is broken up into several parts and stages. At each stage there may be more than one option
available and the firm may have to decide every time that which option is to be taken for. This
can be explained with the help of simple situation.
A firm is considering to launch a new product and to install a plant with capacity of 10,000
units a month. It is hopeful of selling the entire production. However, if due to one or the
other factor, the demand is not generated to lift even the break-even level of production, then
the firm will face a heavy loss. In this case, it will be better for the firm to first install a pilot
project and go for test marketing. If the product is accepted by the market, full-fledged plant
may be installed in the next stage. This is a two-stage decision. The first occurs before the test
market. At that point, cash flows related to both the test and to the production must be considered.
After the test, another decision must be made. At this point, the cash flows related to the
market test are sunk costs and are irrelevant to the decision to be made. At this second point,
the decision to be made cannot affect the cash flows already make in connection with the
market test.
An analytical technique used in sequential decisions is decision tree. The decision tree approach
gets its name because of the resemblance with a tree having number of branches. A
decision tree is a branching diagram representing a decision problem as a series of decisions to
be taken under conditions of uncertainty. A decision presently being considered depends
upon the past decision and their outcomes. The decision trees are the diagrams that permit the
various decisions alternatives, their outcomes and probabilities of their occurrences to be
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mapped in a clear fashion. In a typical decision tree, the project is broken down into clearly
defined stages and the possible outcomes at each stage are listed along with the probabilities
and cash flows effect of each outcome.
Steps in Decision Tree Approach
While constructing a decision tree for a given problem, the following steps may be required:
1. Break the Project into clearly defined stages. For example, a computer software company
may take up the project of new package in different stages, i.e., research and development,
market testing, limited production and then full production.
2. List all the possible outcomes at each stage. Specify the probability of each outcome at
each stage base on information available. This task will become progressively more difficult
as more and more stages are introduced.
3. Specify the effect of each outcome on the expected cash flows form the project.
4. Evaluate the optimal action to be taken at each stage in the decision tree, based on the
outcome at the previous stage and its effect on cash flow.
6.2 Designing Capital Structure
This Section includes :
Capital structure and financial structure
Features of An Appropriate Capital Structure
Determinants of capital structure
INTRODUCTION :
A firm needs funds for long term requirements and working capital. These funds are raised
through different sources both short term and long term. The long term funds required by a
firm are mobilized through owners funds (equity share, preference shares and retained
earnings) and long term debt(debentures and bonds). A mix of various long term sources of
funds employed by a firm is called capital structure.
According to Gerestenberg, “Capital structure of a company refers to the composition or makeup
of its capitalization and it includes all long term capital resources, viz, loans, bonds, shares
and reserves”. Thus capital structure is made up of debt and equity securities and refers to
permanent financing of a firm.
Financial manager has to plan the appropriate mix of different securities in total capitalization
in such a way as to minimize the cost of capital and maximize the earnings per share to the
equity shareholders. There may be four fundamental patterns of capital structure as follows:
i. Equity capital only(including Reserves and Surplus)
ii. Equity and preference capital
iii. Equity, preference and long term debt i.e. debentures, bonds and loans from
financial institutions etc.
iv. Equity and long term debt.
CAPITAL STRUCTURE AND FINANCIAL STRUCTURE :
Some authors use capital structure and financial structure interchangeably. But, both are
different concepts. Financial structure refers to the way in which the total assets of a firm are
financed. In other words, financial structure refers to the entire liabilities side of the balance
sheet. But, capital structure represents only long term sources of funds and excludes all short
term debt and current liabilities. Thus, financial structure is a broader one and capital structure
is only part of it.
FEATURES OF AN APPROPRIATE CAPITAL STRUCTURE :
A capital structure will be considered to be appropriate if it possesses following features:
1. Profitability— The capital structure of the company should be most profitable. The most
profitable capital structure is one that tends to minimize cost of financing and maximize
earnings per equity share.
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2. Solvency— The pattern of capital structure should be so devised as to ensure that the firm
does not run the risk of becoming insolvent. Excess use of debt threatens the solvency of
the company. The debt content should not, therefore, be such that it increases risk beyond
manageable limits.
3. Flexibility— The capital structure should be such that it can be easily maneuvered to meet
the requirements of changing conditions. Moreover, it should also be possible for the
company to provide funds whenever needed to finance its profitable activities.
4. Conservatism— The capital structure should be conservative in the sense that the debt
content in the total capital structure does not exceed the limit which the company can bear.
In other words, it should be such as is commensurate with the company’s ability to generate
future cash flows.
5. Control— The capital structure should be so devised that it involves minimum risk of loss
control of the company.
The above principles regarding an appropriate capital structure or as a matter of fact militant
to each other. For example, raising of funds through debt is cheaper and, is therefore, in
accordance with principle of profitability, but it is risky and, therefore, goes against the
principle of solvency and conservatism. The prudent financial manager should try to have
the best out of the circumstances within which the company is operating. The relative
importance of each of the above feature will also vary from company to company. For
example, one company may give more importance to flexibility as compared to conservatism
while the other may consider solvency to be more important than profitability. However,
the fact remains that each finance manager has to make a satisfactory compromise between
the management’s desire for funds and the trend in the supply of funds.
DETERMINANTS OF CAPITAL STRUCTURE :
The following are the factors influencing the capital structure
The capital structure of a firm depends on a number of factors and these factors are of different
importance. Moreover, the influence of individual factors of a firm changes over a period of
time. Generally, the following factors should be considered while determining the capital
structure of a company.
i. Trading on equity and EBIT-EPS analysis
The use of long term debt and preference share capital, which are fixed income bearing securities,
along with equity share capital is called financial leverage or trading on equity. The use of long
term debt capital increases the earnings per share as long as the return on investment is greater
than the cost of debt. Preference share capital will also result in increasing EPS. But the leverage
effect is more pronounced in case of debt because of two reasons:
a. Cost of debt is usually lower than the cost of preference share capital,
b. The interest paid on debt is tax deductible.
Because of its effects on the earnings per share, financial leverage is one of the important
considerations in planning the capital structure of a company, the companies with high level
of Earnings Before Interest and Taxes (EBIT) can make profitable use of the high degree of
leverage to increase the return on the shareholders equity. The EBIT-EPS analysis is one
important tool in the hands of the financial manager to get an insight into the firms capital
structure planning. He can analyse the possible fluctuations in EBIT and their impact on EPS
under different financing plans.
Under favorable conditions, financial leverage increases EPS, however it can also increase
financial risk to shareholders. Therefore, the firm should employ debt to such an extent that
financial risk does not spoil the leverage effect.
ii. Growth and stability of sales
This is another important factor which influences the capital structure of a firm. Stability of
sales ensures stable earnings, so that the firm will not face any difficulty in meeting its fixed
commitments of interest payment and repayment of debt. So the firm can raise a higher level
of debt. In the same way, the rate of growth in sales also affects the capital structure decision.
Usually, greater the rate of growth of sales, greater can be the use of the debt in the financing of
a firm. On the other hand, the firm should be very careful in employing debt capital if its sales
are highly fluctuating and declining.
iii. Cost of Capital
Cost of capital is another important factor that should be kept in mind while designing the
capital structure of a firm. The capital structure should be designed in such a way that the
firm’s overall cost of capital is the minimum. Cost of capital is the minimum return expected
by its suppliers. Of all the sources of capital, equity capital is the costliest as the equity
shareholders bear the highest risk. On the other hand, debt capital is the cheapest source because
the interest is paid on it by the firm whether it makes profits or not. Moreover, interest on debt
capital is tax deductible which makes it further cheaper. Preference share capital is also cheaper
than equity capital as the dividends are paid at a fixed rate on preference shares. So, the overall
cost of capital depends on the proportion in which the capital is mobilized from different
sources of finance. Hence, capital structure should be designed carefully so that over all cost of
capital is minimized.
iv. Cash flow ability
A firm which has the ability of generating larger and stable cash inflows will be able to employ
more debt capital. The firm has to meet fixed charges in the form of interest on debt capital,
fixed preference dividend and the principal amount, when it becomes due. The firm can meet
these fixed obligations only when it has adequate cash inflows. Whenever a firm wants to raise
additional funds, it should estimate the future cash inflows to ensure the coverage of fixed
charges. Fixed charges coverage ratio and interest coverage ratio are relevant for this purpose.
Here, one important point to be considered is that it is the cash flow ability of the firm and not
the earning capacity alone (as indicated by EBIT) that should be taken into view while designing
the capital structure. A firm may have adequate profits (EBIT) but it may not have adequate
cash inflows to meet its fixed charges obligation. Some times, inadequacy of cash inflows may
lead the firm to the point of insolvency, when it fails to meet its payment obligations in time.
Therefore debt capacity of the firm is determined by its cash flow ability.
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v. Control
Some times, the designing of capital structure of a firm is influenced by the desire of the existing
management to retain the control over the firm. Whenever additional funds are required, the
management of the firm wants to raise the funds without any loss of control over the firm. If
equity shares are issued for raising funds, the control of the existing shareholders is diluted.
Because of this, they may raise the funds by issuing fixed charge bearing debt and preference
share capital, as preference shareholders and debt holders do not have any voting right. The
Debt financing is advisable from the point of view of control. But overdependence on debt
capital may result in heavy burden of interest and fixed charges and may lead to liquidation of
the company.
vi. Flexibility
Flexibility means the firm’s ability to adapt its capital structure to the needs of the changing
conditions. Capital structure should flexible enough to raise additional funds whenever
required, without much delay and cost. The capital structure of the firm must be designed in
such a way that it is possible to substitute one form of financing for another to economise the
use of funds. Preference shares and debentures offer the highest flexibility in the capital
structure, as they can be redeemed at the discretion of the firm.
vii. Size of the firm
The size of the firm influences the capital structure design of a firm. Small companies find it
very difficult to mobilise long-term debt, as they have to face higher rate of interest and
inconvenient terms. Hence, small firms make their capital structure very inflexible and depend
on share capital and retained earnings for their long-term funds. Since their capital structure is
small, small firms cannot go to the capital market frequently for the issue of equity shares, as it
carries a greater danger of loss of control over the firm to others. Hence, the small firms
sometimes limit the growth of their business and any additional fund requirements met through
retained earnings only. However, a large firm has relative flexibility in capital structure
designing. It has the facility of obtaining long-term debt at relatively lower rate of interest and
convenient terms. More, the large firms have relatively an easy access to the capital market.
viii. Marketability and timing
Capital market conditions may change from time to time. Sometimes there maybe depression
and at over times there may be boom condition in the market. The firm should decide whether
to go for equity issue or debt capital by taking market sentiments into consideration. In the
case of depressed conditions in the share market, the firm should not issue equity shares but
go for debt capital. On the other hand, under boom conditions, it becomes easy for the firm to
mobilise funds by issuing equity shares.
The internal conditions of a firm may also determine the marketability of securities. For example,
a highly levered firm may find it difficult to raise additional debt. In the same way, a firm may
find it very difficult to mobilise funds by issuing any kind of security in the market merely
because of its small size.
ix. Floatation costs
Floatation costs are not a very significant factor in the determination of capital structure. These
costs are incurred when the funds are raised externally. They include cost of the issue of
prospectus, brokerage, commissions, etc. Generally, the cost of floatation for debt is less than
for equity. So, there may be a temptation for debt capital. There will be no floatation cost for
retained earnings. As is said earlier, floatation costs are not a significant factor except for small
companies.
Floatation costs can be an important consideration in deciding the size of the issue of securities,
because these costs as a percentage of funds raised will decline with the size of the issue.
Hence, greater the size of the issue, more will be the savings in terms of floatation costs.
However, a large issue affects the firm’s financial flexibility.
x. Purpose of financing
The purpose for which funds are raised should also be considered while determining the sources
of capital structure. If funds are raised for productive purpose, debt capital is appropriate as
the interest can be paid out of profits generated from the investment. But, if it is for unproductive
purpose, equity should be preferred.
xi. Legal requirements
The various guidelines issued by the Government from time to time regarding the issue of
shares and debentures should be kept in mind while determining the capital structure of a
firm. These legal restrictions are very significant as they give a framework within which capital
structure decisions should be made.
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6.3 Capital Investment Real Options
This Section includes :
Real Option-Key Concept
Terms and Definitions
Factors Affecting Value of an Option
Real Options in Capital Investment Decisious
Comparison of Options Pricing Models
INTRODUCTION :
A real option is the right, but not the obligation, to undertake some business decision, typically
the option to make a capital investment. For example, the opportunity to invest in the expansion
of a firm’s factory is a real option. In contrast to financial options, a real option is not often
tradable - e.g. the factory owner cannot sell the right to extend his factory to another party,
only he can make this decision. However, some real options can be sold, e.g., ownership of a
vacant plot of land is a real option to develop that land in the future. Some real options are
proprietary (owned or exercisable by a single individual or a company); others are shared (can
be exercised by many parties). Therefore, a project may have a portfolio of embedded real
options; some of them can be mutually exclusive.
REAL OPTION-KEY CONCEPT :
The terminology “real option” is relatively new, whereas business operators have been making
capital investment decisions for centuries. However, the description of such opportunities
as real options has occurred at the same time as thinking about such decisions in new, more
analytically-based, ways. As such, the terminology “real option” is closely tied to these new
methods. The term “real option” was coined by Professor Stewart Myers at the MIT Sloan
School of Management.
The concept of real options was popularized by Michael J. Mauboussin, the chief U.S. investment
strategist for Credit Suisse First Boston and an adjunct professor of Finance at the Columbia
School of Business. Mauboussin uses real options to explain the gap between the stock
market prices and the “intrinsic value” for those businesses as calculated by traditional financial
analysis.
Additionally, with real option analysis, uncertainty inherent in investment projects is usually
accounted for by risk-adjusting probabilities (a technique known as the Equivalent Martingale
approach). Cash flows can then be discounted at the risk-free rate. With regular DCF analysis,
on the other hand, this uncertainty is accounted for by adjusting the discount rate, using e.g.
the cost of capital or the cash flows (using certainty equivalents). These methods normally do
not properly account for changes in risk over a project’s lifecycle and fail to appropriately
adapt the risk adjustment. More importantly, the real options approach forces decision makers
to be more explicit about the assumptions underlying their projections.
In business strategy, real options have been advanced by the construction of option space,
where volatility is compared with value-to-cost. Latest advances in real option valuation are
FACTORS WHICH AFFECT THE VALUE OF AN OPTION :
The factors which affect the value of an option are given below
Symbol
Factor as it relates to stock
option value Factor as it relates to capital budgeting
PO
Price of the underlying asset
(i.e., stock price)
PV of expected operation CFs discounted at
the project's cost of capital
X Exercise price
For call options-the initial investment.
For put options-the value of the project's assets
if sold or shifted to a more valuable use
T Time until the option expires
Time until the option expires or is no longer
Available
K rf Risk-free rate of interest
Risk-free rate of interest (use the yield on U.S.
T-bills
E
Standard deviation of the
underlying asset (volatility of stock
price)
Project risk - standard deviation of the
operating cash flow as a percent of total
investment
models that incorporate fuzzy logic and option valuation in fuzzy real option valuation models.
TERMS AND DEFINITIONS
Strategic NPV = Passive NPV + Present value of options arising from the active management
of the firm’s investment opportunities
The terms used in the study of real options are given below
An option is a right to buy or sell a particular good for a limited time at a specified price (the
exercise price). A call option is the right to buy. A put option is the right to sell.
The expiration date is the date when the option matures. An American option is exercisable
anytime until the end of the expiration date while a European option is exercised only at the
expiration date.
The writer of an option contract sells the call or put option while the buyer purchases the
option contract from the seller. For real options, the firm is the implied buyer and the market
is the implied seller. No actual contract is traded.
A call option is out-of-the-money when the price of the underlying assets is below the exercise
price of the call and in-the-money when the price of the underlying assets is above the
striking price of the call. The opposite is true for a put option, which is outof-the-money
when the price of the underlying assets is above the striking price of the call and in-themoney
when the price of the underlying assets is below the striking price of the call.
Buyers may hold a long (buy) or short (write) position in the option.
Investment Decisions
REAL OPTIONS IN CAPITAL INVESTMENT DECISIONS :
Option: Valued as a
wait & learn more before investing call
default during construction (staged investment) a series of put options
alter operating scale (expand, restart) call
alter operating scale (contract, shut down) put
Abandon put
switch inputs or outputs call + put
grow and build-on previous investments call
A COMPARISON OF OPTIONS PRICING MODELS :
Binominal Model Black-Scholes Model
description
*assumes that the time to an option's
maturity can be divided into a number of
subintervals, in each of which, there are only
two possible price changes
the binomial model
estimated over an
finite number of sub-intervals
Advantages
*easier for executives to understand *bigger
range of applications (B-S model cannot be
used in all cases)
*similar in structure to a decision tree but a
much more concise representation of
complex relationships
easy to calculate with tables
disadvantages
*more than one or two sub-intervals
requires computer simulation
*not easy to explain to executives
not easy to explain to executives
6.4 Venture Capital
This Section includes :
Features of Venture Capital
Modes of Finance by Venture Capitalists
INTRODUCTION :
Venture capital is a form of equity financing especially designed for funding high risk and
high reward projects.
There is a common perception that venture capital is a means of financing high technology
projects. However, venture capital is investment of long term finance made in :
1. Ventures promoted by technically or professionally qualified but unproven entrepreneurs,
or
2. Venture seeking to harness commercially unproven technology. Or
3. High risk ventures.
The term ‘venture capital’ represents financial investment in a highly risky project with the
objective of earning a high rate of return.
FEATURES OF VENTURE CAPITAL :
The main features of venture can be summarised as follows:
1. High Degree of risk
Venture capital financing is, invariably, an investment in a highly risky project with the
objective of earning a high rate of return.
2. Equity Participation
Venture capital financing is, invariably, an actual or potential equity participation wherein
the object of venture capital is to make capital gain by selling the share once the form become
profitable.
3. Long term Investment
Venture capital financing is a long term investment. It generally taken a long period to
encash the investment in securities made by the venture capitalists.
4. Participation in Management
In addition to provide capital, venture capital funds take an active interest in the
management of the form that of a traditional lender or banker. It is also different from that
of accompany stock market investor who merely trades in the shares of a company without
participating in their management. It has been rightly said, “Venture capital combines the
qualities of banker, stock market investor and entrepreneur in one”.
Investment Decisions
5. Achieve Social Objectives
It is different from the development capital provided by several central and state level government
bodies in that the profit objective is the motive behind the financing. But venture
capital profits generate employment, and balanced regional growth indirectly due to setting
up successful new business.
6. Investment is Illiquid
A venture capital is not subject to repayment on demand as with an overdraft or following
a loan repayment schedule. The investment is realized only when the company is sold or
achieves a stock market listing. It is lost when the company goes into liquidation.
MODES OF FINANCE BY VENTURE CAPITALISTS :
1. Equity
Most of the venture capital funds provide financial support to entrepreneurs in the form of
equity by financial 49% of the total equity. This is to ensure that the ownership and overall
control remains with the entrepreneur. Since there is a great uncertainty about the generation
of cash inflows in the initial years, equity financing is the safest mode of financing. A
debt instrument on the other hand requires periodical servicing of dept.
2 Conditional Loan
From a venture capitalist point of view, equity is an unsecured instrument hence a less
preferable option than a secured debt instrument. A conditional loan usually involves either
no interest at all or a coupon payment at nominal rate. In addition, a royalty at agreed
rates payable to the lender on the sales turnover. As the units picks up in sales levels, the
interest rate are increased and royalty amounts are decreased.
3 Convertible Loans
The convertible loan is subordinate to all other loans which may increased to be converted
into equity if interest payments are not made within agreed time limit.
Stages of Investment/Financing
A) Early Stage Financing
This stages including the following :
1. Seed Capital and R & D Projects
Venture capitalists are more often interested in providing seed finance i.e making provision
of very small amounts for finance needed to turn into a business.
Research and development activities are required to be undertaken before a product is to be
launched. External finance is often required by the entrepreneur during the development of
the product. The financial risk increase progressively as the research phase moves into the
development phase, where a sample of the product is tested before it is finally commercialized.
Venture capitalists / firms / funds are always ready to undertake risks and make
investment in such R & D projects promising higher returns in future.
2. Start Ups
The most risky aspect of venture capital is the launch of a new business after the Research
and Development activities are over. At this stage, the entrepreneur and his product or
services are as yet untried. The finance required usually falls short of his own resources.
Start ups may include mew industries / businesses set up by the experienced persons in
the area in which they have knowledge. Others may result from the research bodies or large
corporations, where a venture capitalist joins with an industrially experienced or corporate
partner. Still other start ups occur when a new company with inadequate financial resources
to commercialise new technology is promoted by an existing company.
3. Second Round Financing
It refers to the stage when product has already been launched in the market but has not
earned enough profit to attract new investors. Additional funds are needed at this stage to
meet the growing needs of business. Venture Capital Institutions (VCIs) provide large funds
at this stage than at other early stage financing in the form of debt. The time scale of investment
is usually three to seven years.
B) Later stage Financing
Those established business which require additional support but cannot raise capital through
public issue approach venture capital funds for financing expansion, buyouts and turnarounds
or for development capital.
1. Development Capital
It refers to the financing of an enterprise which has overcome the highly risky stage and
have recorded profits but cannot go public, thus needs financial support. Funds are needed
for the purchases of new equipment / plant, expansion of marketing and distributing facilities,
launching one to three into new regions and so on. The time scale of investment is
usually one to three years and falls in medium risk category.
2. Expansion Financial
Venture capitalists perceive low risk in ventures requiring finance for expansion purpose
either by growth implying bigger factory, large warehouse, new factories, new products or
mew markets or through purchases of exiting business. The time frame of investment is
usually from one to three years. It represents the last round of financing before a planned
exit.
3. Buyouts
It refers to the transfer of management control by creating a separate business by separating
it from their existing owners. It may be of two types.
(i) Management Buyouts (MBOs)
(ii) Management Buyins(MBIs)
Investment Decisions
(i) In Management Buyouts (MBOs) - Venture capital institutions provide funds to unable
the current operating management / investors to acquire an existing product line
/ business. They represent an important part of the activity of VCIs.
(ii) Management Buyins - are funds provide to enable an outside group of manager (s) to
buy an existing company. It involves parties: a management team, a target company
and an investor (i.e Venture capital institution). MBIs are more risky than MBOs and
hence are less popular because it is difficult for new management to assess the actual
potential of target company. Usually, MBIs are able to target the weaker or
underperforming companies.
4. Replacement capital
VCIs another aspect of financing is to provide funds for the purchases of existing share of
owners. This may be due to a verity of reasons including personal need of finance, conflict
in the family, or need for association of a well known name. The time scale of investment is
one to three years and involve low risk.
5. Turnarounds
Such form of venture capital financing involves medium to high risk and a time scale of
three to five years. It involves buying the control of a sick company which required very
specialized skills. It may require rescheduling of all the company’s borrowings, change in
management or even a change in ownership. A very active “hands on” approach is required
in the initial crisis period where the venture capitalists may appoint its own chairman
or nominate its directors on the board.
In a nutshell, venture capital firms finance both early and stage investment to maintain a
balance between risk and profitability. Venture capitalists evaluate technology and study
potential markets besides considering the capability of the promoter to implement the project
while undertaking early stage investment. In later stage investment in new markets and
track record of the business / entrepreneur is closely examined.
6.5 Hybrid Finance
This Section includes :
Preferred Stock
Trust Preferred Securities
Convertible Debentures
Warrants
Innovative Hybrid
INTRODUCTION :
Equity and debt lie at the two ends of the spectrum of financing. In between lie hybrid sources
of financing which partake some characteristics of equity and some characteristics of debt. The
important forms of hybrid financing are preference capital, warrants, convertible debentures,
and innovative hybrids.
Preference capital ordinarily carries a fixed rate of dividend which is payable at the discretion
of directors when the company has distributable surplus.
A warranty gives its holder the right to subscribe to the equity share of a company during a
certain period at a specified price.
A convertible debenture is a debenture that is convertible, partially or fully, into equity shares.
The conversion may be compulsory or optional.
An innovative hybrid is a hybrid security whose payoff is linked to some general economic
variable like the interest rate, exchange rate, or commodity index.
PREFERRED STOCK :
Preferred stock is a hybrid corporate security. It represents an equity interest in the issuing
company. Unlike common stock, which pays a variable dividend depending on the corporation’s
earnings, preferred stock pays a fixed quarterly dividend based on a stated par value.
For example, an XYZ corporation might issue preferred stock with a par value of Rs 50.00
and paying a quarterly 2% dividend. This would translate into a Rs 1.00 dividend paid each
quarter.
Most corporations do not issue preferred shares. Those that do, often issue multiple classes of
preferred shares over time. There are three naming conventions used for distinguishing between
the different preferred issues of a corporation.
1) Annualized dividend: the shares in our example would be called XYZ Rs 4.00 preferred.
2) Annualized dividend yield: the shares in our example would be called XYZ 8% preferred.
3) A letter indicating the order of issuance: If the shares in our example were the
corporation’s third preferred issuance, they would be called XYZ preferred C.
Investment Decisions
With fixed dividends, preferred shares resemble fixed income instruments. As they don’t mature,
they most resemble a perpetuity. Preferred shareholders generally don’t have voting rights.
Also, the board of directors have less of a fiduciary obligation to preferred shareholders than
to common shareholders. Some Delaware court decisions have treated the board’s obligation
to preferred shareholders as purely contractual.
Preferred stock differs from fixed income instruments in their tax treatment. Interest payments
are an expense, so they are tax deductible for the corporation. Dividends are distributions of
earnings, so they are not tax deductible. Also, depending on the investor’s tax jurisdiction,
dividends may be taxed differently from interest income.
When it is first issued, preferred stock is priced by the market based on prevailing interest
rates. Generally, the issuer will set the preferred’s dividend yield so it issues at a price close to
par. After issuance, the preferred shares trade in the stock market just like common stock.
Credit rating agencies rate preferred stocks based on the issuing corporation’s ability to pay
dividends. Market prices of highly rated issues tend to fluctuate with interest rates. Prices of
lower rated issues - just like prices of lower rated bonds - tend to fluctuate with the issuing
corporation’s fortunes.
Preferred stock is subordinate to all the issuing corporation’s fixed income obligations. If the
issuer is not current on the fixed income obligations, it can pay no preferred dividends. If the
issuer is liquidated, creditors must be paid in full before preferred stockholders can receive
anything. However, preferred shares are superior to common shares. No dividends may be
paid to holders of common stock unless dividends to preferred shareholders are also paid in
full. In liquidation, preferred shareholders are entitled to at least their par value before common
shareholders can receive anything.
Unlike fixed income instruments, failure of a corporation to make preferred dividend payments
cannot force the firm into bankruptcy. However, while dividends are not being paid,
mandatory restrictions may be placed on management and preferred shareholders may be
granted the right to vote for a number of board members. Because it is dependent on dividends
not being paid, this is called contingent voting.
Most preferred stock is cumulative. This means that, if a dividend is ever missed, it must eventually
be made up to investors. No dividends can be paid to common stockholders until all
missed dividends have been paid to preferred stockholders. If preferred shares are issued with
no obligation to make up missed dividends, the shares are called non-cumulative.
Callable preferred stock has an embedded option allowing the issuer to call shares, either at
par or at a slight premium above par. In a typical arrangement, shares are not callable for the
first few years following issuance but can be called, perhaps with a month’s notice, any time
thereafter. As with callable bonds, the price behavior of callable preferreds depends on whether
the call option is in-the-money or out-of-the-money as well as the financial strength of the
issuer.
Most preferred stock is issued with a sinking fund provision that requires that the issuer set
aside funds to gradually retire the issue over time.
There are a number of other variations on preferred stock:
a. Adjustable-rate preferred stock (ARPS) has a dividend yield that, instead of being fixed,
floats with specified interest rates according to some formula.
b. Convertible preferred stock has an embedded option that allows the holder to exchange
each preferred share for a specified number of common shares. Convertible preferred
is usually callable. This allows the issuers to call the stock and force preferred shareholders
to choose between accepting either par value or common shares. This is called
a forced conversion.
c. Participating preferred stock pays a regular fixed dividend plus an additional dividend
if the common stock dividend exceeds some specified value. Today, this feature
is rare.
TRUST PREFERRED SECURITIES :
1. Trust preferred securities (TruPS) are cumulative preferred stock issued by bank holding
companies through a special purpose vehicle. The special purpose vehicle is wholly owned
by the bank holding company and is usually a trust. It sells the TruPS to investors and uses
the proceeds to purchase a subordinated note from the bank holding company. This becomes
its sole asset and cash flows from the note largely mirror the dividends payable on
the TruPS. The note has an initial maturity of at least 30 years. Dividends are paid quarterly
or semi-annually. Dividends may be deferred for at least five years without creating an
event of default or acceleration.
2. From a tax standpoint, TruPS have a significant advantage over the direct issuance of preferred
shares. This is because dividends on preferred shares are not deductible as a business
expense, but interest on a subordinated note is. In this regard, the TruPS behaves like debt.
In another regard, it behaves like equity.
3. Initially, TruPS were only issued by larger bank holding companies. This changed in 2000,
when several institutions issued TruPS, which were pooled in a CDO. Since then, the TruPS
CDO market has grown dramatically and has become a significant source of capital for
small and medium sized bank holding companies.
4. TruPS are also issued by insurance holding companies and REITS. Those securities have
also been packaged in CDOs.
CONVERTIBLE DEBENTURES :
A convertible debenture is a debenture that can be changed into a specified number of ordinary
shares at the option of the owner. A company is, in fact, issuing equity shares in future
whenever it offers convertible debentures. The most notable feature of this debenture is that it
promises a fixed income associated with debenture as well as chance of capital gains associated
with equity share after the owner has exercised his conversion option. Because of this
combination of fixed income and capital gains in the convertible debenture, it has been called
hybrid security.
Investment Decisions
Characteristics of Convertible Debentures
When a company issues a convertible debenture, it clearly specifies conversion terms which
indicate the number of equity shares in exchange for the convertible debenture, the price at
which conversion will take place and the time when the conversion option can be exercised.
Conversion ratio and conversion price The conversion ratio is the number of ordinary shares
that an investor can receive when he exchange his convertible debenture. In other words, the
number of ordinary shares per one convertible security is called the conversion ratio. The conversion
price is the price paid for the ordinary share at the time of conversion. If you know the
par value of the convertible security and its conversion price, you can easily find out the conversion
ratio:
Conversion ratio = Par value of convertible debenture / Conversion price
Valuation of Convertible Debentures
The valuation of convertible debentures is more complex than the valuation of non-convertible
securities since they combine features of both ordinary shares and fixed-income securities.
The market value of a convertible debenture will thus depend on: market price of ordinary
share, conversion value, and the value of the non-convertible or straight debentures, called
investment value.
Conversion value The conversion value of a convertible debenture is equal to the conversion
ration multiplied by the ordinary share’s market price. Thus:
Conversion value = Conversion Ratio share price.
Market Value of convertible debenture The convertible securities are traded (bought and
sold) in the stock market until they are converted into equity shares. The price at which the
convertible security sells is called its market value. In India, the secondary market for debentures
–including both convertible and non-convertible — is still in a developing stage.
What is the relationship between a convertible debenture’s market value, its investment value
and its conversion value? A convertible debenture’s market value depends on both investment
and conversion value. More importantly, its market value cannot be less than its investment
value or its conversion value. The difference between the convertible debenture’s market
value and the higher of the conversion or the NCD value (investment value) is called the conversion
premium. Thus:
Conversion Premium =
[Market value −Conversionor Investment value]
Conversion or investment value
Value of a convertible debenture
Why issue convertible debentures?
At least four reasons can be cited for issuing the convertible debentures. They are:
Sweetening fixed-income securities
Deferred equity financing
Avoiding earnings dilution
Raising low cost capital
WARRANTS :
A warrant entitles the purchaser to buy a fixed number of ordinary shares at a particular price
during a specified time period. Warrants are generally issued along with debentures issue as
‘sweetners.’ In USA, warrants have been in the past mainly by financially weaker firms to
attract investors. Now, of course, warrants are used by large, profitable companies as a part of
a major financing package. Warrants may also be used in conjunction with ordinary or
preference shares. The purpose is the same, that is, to improve the marketability of the issue.
Detachability
A warrant can be either detachable or non-detachable. If a warrant can be sold separately from
the debenture (or preference share) to which it was originally attached, it is called a detachable
warrant. A debenture holder may sell his warrant when its price increases but continue holding
the debenture. The DFPC warrant is a detachable warrant. The company will list it separately,
and it will be traded on the stock exchanges. A non-detachable warrant cannot be sold separately
from the debenture to which it was originally attached.
500
600
1000 1500 2000
Market value of
convertible debenture
Market Price of Share
Investment Decisions
Right Warrants entitle to purchase ordinary shares. Therefore, the holders of warrants are not
the shareholders of the company until they exercise their options. Therefore, they do not have
rights of ordinary shareholders, such as the right to vote or receive dividends. Once they exercise
their warrants and buy ordinary shares, they became the company’s ordinary shareholders.
Valuation of Warrants
A warrant is an option to buy a stated number of a company’s ordinary shares at a given
exercise price on or before a specified maturity date. Thus, it is similar to an American call
option. As a call option, its market value will be dependent on the market price of the ordinary
share and the exercise price. The market price of a company’s ordinary share is a function of its
expected performance and that of the economy as a whole. Thus, a warrant’s market price will
in general depend on the issuing company’s performance and the general economic conditions.
Theoretical Value
The theoretical value of a warrant can be found out if we know the ordinary share’s market
price and warrant’s exercise price and exercise ratio. There exist two possibilities with regard
to the ordinary share’s price and the exercise price. Either the ordinary share’s price is greater
or lesser than the exercise price. If the share price is equal to or greater than the exercise price,
then a warrant’s theoretical value is given as follows:
Warrant’s Theoretical value = (Share price – Exercise price)* Exercise ratio.
Premium
The difference between the warrant’s market value and its theoretical value is called the
premium. It can be found as follows:
Premium =
Warrant's market value − warrant's theoretical value
Warrant's theoretical value
Market Value of a Warrant
100
80
60
40
20
0
10 50 100
Warrant’s market Price
Warrant’s
Theoretical Price
Exercise price
Premium
INNOVATIVE HYBRIDS :
A hybrid debt security is a debt security combined with a derivative such as forward, swap, or
option. Historically, the most common form of hybrid security has been the convertible bond.
From the beginning of the eighties, however, a new breed of hybrid securities has become very
popular, particularly in the US. The distinctive feature of these securities is that the payoffs
instead of being related to the stock price of the issuing company (as is the case with a convertible
bond), are linked to some general economic variable like the interest rate, exchange rate,
commodity price, stock market index, and so on.
Hybrids are essentially devices for managing risk. Examples of different types of hybrids are
given below:
Hybrids to manage commodity risk— This hybrids includes a zero coupon bond and a call
option. This type of hybrid issued in 1986.
Hybrids to manage foreign exchange risk— This is the dual currency bond which includes
principle amount in one currency and interest in other country currency.
Hybrids to manage interest rate risk— This hybrid is divides into two parts. They are:
1. A Floating rate bullet repayment note and
2. A plain interest swap for double the principle.
Illustration 1 :
A company is considering taking up of one of the two projects A and B. both projects have the
same life, require equal investment of Rs.80 crores each and both are estimated to have almost
the same yield. As the company is new to this type of business, the cash flows arising from the
projects cannot be estimated with certainty. An attempt was, therefore, made to use probability
to analyse the pattern of cash flow from either project during the first year of operation. This
pattern is likely to continue during the life of these projects. The results of the analysis are as
follows :
Project A Probability Project B probability
Cash flows (Rs.crores) Cash flows (Rs.crores)
12 0.1 8 0.1
14 0.2 12 0.25
16 0.4 16 0.30
18 0.2 20 0.25
20 0.1 24 0.10
Which project should the company take up? Show workings to justify your answer.
COST-VOLUME-PROFIT
ANALYSIS
Investment Decisions
Calculation of Standard Deviation
Project A
Cash Probability(P) EV= X × P (x − x) P(x − x)2
flow(X)
12 0.1 1.2 -4 16 1.6
14 0.2 2.8 -2 4 0.8
16 0.4 6.4 0 0 0
18 0.2 3.6 2 4 0.8
20 0.1 2.0 4 16 1.6
80 EV=16.00 Variance = 20.8
x = 80/5 =16
Standard deviation of Project A = 4.8 = Rs. 2.19 crores
Project B
Cash Probability(P) EV= X × P (x − x) P(x − x)2
flow(X)
8 0.10 0.8 -8 64 6.4
12 0.25 3.0 -4 16 4.0
16 0.30 4.8 0 0 0
20 0.25 5.0 4 16 4.0
24 0.10 2.4 8 64 6.4
80 EV=16.0 Variance=20.8
x = 80/5 =16
Standard deviation of Project A = 20.8 = Rs. 4.56 crores
= ×100
Expected Value of Profit
Standard deviation
Coefficient of variation
. %
16
2.19 100
Project a =13 69 = ×
. %
.
Pr oject B 28 5
16
4 56 100 = × =
Analysis : Project B is more risky than project A and the risk involved in it is more than double.
Hence Project A is advisable.
Illustration 2 – The management of Power Tech. Ltd. must choose whether to go ahead with
either of two mutually exclusive projects A and B. The expected profits are as follows :
Particulars Profit if there is Profit/(loss) if here
strrong demand is weak demand
Option A (Rs.) 4,000 (1.000)
Option B (Rs.) 1,500 500
Probability of demand 0.3 0.7
a. What would be the decision. based on expected values. if no information about demand
were available?
b. What is the value of perfect information about demand?
a. If there were no information to help with the decision. the project with the higher EV of
profit would be selected.
(Rs.)
Project A Project B
Probability Profit EV Profit EV
0.3 4,000 1,200 1,500 450
0.7 (1.000) (700) 500 350
1.0 500 800
Analysis : Project B would be selected. This is clearly the better option if demand turns out to
be weak. However, if demand wrere to turn out o be strong, Project A would be more profitable.
There is a 30% chance that this could happen.
b. Perrect information will indicate for certain whether demand will be weak or strong. If
demand is forecast ‘weak’ Project B would be selected. If demand is forecast as ‘strong’,
Project A would be selected, and perfect information would improve the profit from
Rs. 1.500, which would have been earned by selecting B. 10 Rs. 4,000.
Forecast Project
demand Probability chosen Profit EV of profit
Weak 0.7 B 500 350
Strong 0.3 A 4.000 1.200
EV of profit with perfect information 1.550
The Value of Perfect Information derives from the 0.3 probability that if demand is going to be
strong, the information would reveal this fact, and the decision is changed from ‘choose B’to
‘choose A’ thereby earning Rs. 2.500 more profit. The EV of the Value of Perfect Information is
therefore 0.3×Rs. 2,500 = Rs. 750. Another way of making this same calculation is as follows :
COST-VOLUME-PROFIT
ANALYSIS
Investment Decisions
(Rs.)
EV of profit without Perfect Information (i.e., choose B all the time) 800
EV of profit with Perfect Information 1,550
Value of Perfect Information 750
Analysis : Provide that the information does not cost more than Rs. 750 to collect, it would be
worth having.
Illustration 3 – A manager is trying to decide which of three mutually exclusive projects to
undertake. Each of the projects could lead to varying net profits which are classified as outcomes
I, II and III. The manager has constructed the following pay-off table or matrix (a conditional
profit table).
Net profit if outcome turns out to be :
Project I II III
A 50,000 65.000 80.000
B 70.000 60 ,000 75,000
C 90,000 80,000 55,000
Probability 0.2 0.6 0.2
Which project should be undertaken?
If the project with the highest EV of profit were chosen, this would be project C. (Rs.)
Outcome Probability Project A Projecr B Projecr C
EV EV EV
I 0.2 10.000 14,000 18,000
II 0.6 39,000 36.000 48,000
III 0.2 16.000 15,000 11,000
1.0 65,000 65,000 77.000
However, if the maximum criterion were applied, the assessment would be as follows :
Project Selected The worst outcome Profit (Rs.)
that could happen
A I 50,000
B II 60,000
C III 55,000
Analysis : By choosing B, wer are ‘guaranteed’ a profit of at least Rs. 60,000, which is more than
we would get from project A or C if the worst outcome were to occur for them. The decision
would therefore be to choose project B.
IlIustralion 4 – XYZ Ltd. is considering a project with the following expected cash flows. Initial
investment Rs. 1,00,000 Expected cash inflows 1st year Rs. 70,000; 2nd year Rs. 60.000; 3rd year
Rs. 45,000. The cost of capital is 10%. Due to uncertainly of future cashflows, the management
decides to reduce the cash inflows to certainty equivalent by taking only 80%, 70% and 60%
respectively. Is it worth while to take up the project?
Caiculalion of Certainty Equivalents of Cash Inflow :
Ist year 70,000 × 80/100 = Rs. 56.000
2nd year 60,000 × 70/100 = Rs, 42,000
3rd year 45.000 × 60/100 = Rs. 27,000
Caicuialion of Risk Adjusted NPV of the Project :
Year Cash flow (Rs.) P.Y. factor (10%) P.V. (Rs.)
0 (1,00,000) 1.000 (1,00,000)
1 56.000 0.909 50,904
2 42,000 0.826 34,692
3 27,000 0.751 20,277
NPV = 5,873
Decision : The NPV of the project is positive and. therefore, the project can be selected.
Illustration 5 – A Production Manager is planning to produce a new product and he wishes to
estimate the raw material requirement for that new product. On the basis of usage for a similar
product introduced previously, he has developed a frequency distribution of demand in tonnes
per day for a two month period. Used this data to simulate the raw material usage requirements
for 7 days. Compute also expected value and comment on the result.
Demand Frequency
Tonnes/day No. of days
10 6
11 18
12 15
13 12
14 6
15 3
COST-VOLUME-PROFIT
ANALYSIS
Investment Decisions
Demand Frequency Probability Cumulative Random
Tonnes/day No. of days Probability Numbers
10 6 0.10 0.10 00.09
11 18 0.30 0.40 10.39
12 15 0.25 0.45 40.64
13 12 0.20 0.85 65.84
14 6 0.10 0.95 85.94
15 3 0.05 1.00 95.99
60 1.00
The first seven random numbers (two digits only) are simulated :
Random No. Corresponding demand
Tonnes/day
27 11
13 11
80 13
10 11
54 12
60 12
49 12
82
Mean requirement per = 82 / 7 = 11.7 Tonnes
The expected value (EV) = (10×0.1)+(11×0.3)+(12×0.25)+(13×0.2)+(14×0.1)+(15×0.05)
= 12.05 Tonnes
The difference = 12.05 - 11.7 = 0.35
This indicate that the small sample size of only 7 hadys had resulted in some error. A much
larger sample should be taken and several samplex should be simulated before the simulation
results are used for decision making.
Illustration 6 – The Financial Controller of Super Stocks Ltd. has drawn the following projections
with probability distributions :
Wages & salaries Probability Raw material Probability Sales revenue Probability
(Rs. ’000)
10 - 12 0.3 6 - 8 0.2 30 - 34 0.1
10 - 12 0.5 8 - 10 0.3 34 - 38 0.3
10 - 12 0.2 10 - 12 0.3 38 - 42 0.4
12 - 14 0.2 42 - 46 0.6
Your are required to simulate the cash flow projecton from the following random numbers :
Wages and salaries 2 7 9 2 9 2
Raw materials 4 4 1 0 3 4
Sales Revenue 0 6 6 8 0 2
Simulation of Cash flow projection
Random number allocation
Wages and Salaries Raw Materials Values Revenue
Midpoint Cum. Random Midpoint Cum. Random Midpoint Cum. Random
(Rs. ’000) Prob. Nos. (Rs. ’000) Prob. Nos. (Rs. ’000) Prob. Nos.
11 0.3 0-2 7 0.2 0-1 32 0.1 0
13 0.8 3-7 9 0.5 2-4 36 0.4 1-3
15 1.0 8-9 11 0.8 5-7 40 0.8 4-7
13 1.0 8-9 44 1.0 8-9
Simulation of cash flow (Rs. ’000)
Month Wages & Raw Sales Fixed Net Cash Cash balance
salaries materials revenues costs flow (O B Rs.50)
1 11 9 32 14 –2 48
2 13 9 40 14 +4 52
3 15 7 40 14 +4 56
4 11 7 44 14 +12 68
5 15 9 32 14 –6 62
6 15 9 36 14 –2 60
From the above simulation it will be observed that there are 3 months which have net cash
outflows, the probability of net cash outflows can therefore be estimated as 3/6=0.5. From the
above table, the estimated cash balance at the end of sixth month is Rs. 60,000.
(b) Expected Value Method of Cash Flows Projection
EV of salaries and wages = (11×0.3)+(13×0.5)+(15×0.2) = 12,800
EV of Raw materials = (7×0.2)+(9×0.3)+(11×0.3)+(13×0.2) = 10,000
EV of sales revenue = (32×0.1)+(36×0.3)+(40×0.3)+(44×0.2) = 34,800
Expected net cash inflow per month = 34,800–12,800–10,000–14,000 = Rs. 2,000
Expected net cash inflow per month = 50,000 + (2,000×6) = Rs. 62,000
The difference between Rs. 60,000 and rs. 62,000 is due to smaple errors. If a number of simulation
iterations were carried out then the mean of the balances predicted should approach the expected
value more and closely as the number was increased.
COST-VOLUME-PROFIT
ANALYSIS
Investment Decisions
Illustration 7 – Infoway Ltd. is considering the purchase of an automatic pack machine to replace
the 2 machines which are curently used to pack Product X. The new machine would result in
reduced labour costs because of the more automated natrue of the process and in addition,
would permit production levels to be increased by creating greater capacity at the packing
stage with an anticipated rise in the demand for Product X, it has been estimated that the new
machine will lead to increased profits in each of the next 3 years. Due to uncertainty in demand
however, the annual cash flows (including savings) resulting from purchase of the new machine
cannot be fixed with certainty and have therefore, been estimated probabilically as follows :
Annual cost flows :
Year 1 Probability Year 2 Probability Year 3 Probability
10 0.3 10 0.1 10 0.3
15 0.4 20 0.2 20 0.5
20 0.3 30 0.4 30 0.2
40 0.3
Because of the overall uncertainty in the sales of Product X, it has been decided that only 3
years fash flows will be considered in deciding whether to purchase the new machine. After
allowing for the scrap valu fo the existing machines, the net cost of the new machine will be
42,000. The effects of taxation should be ignored.
Required :
a. Ignoring the time value of money, identify which combionations of annual cash flows will
lead to an overall negative net cash flow, and determine the total probalility of this occurring.
b. One the basis of the average cost flow for each year, calculate the net present value of the
new machine gives that the company’s cost of capital is 15%. Relevant discount factors are
as follows :
Year Discount factor
1 0.8696
2 0.7561
3. 0.6575
c. Analyse the risk inherent in this situation by simulating the net present value calculation.
You should use the random number given at the end of the illustration in 5 sets of cash
flows. On he basis of your simulation results what is the expected net prestn value and
what is the probability of the new machine yielding a negative net present value ?
Set 1 Set 2 Set 3 Set 4 Set 5
Year 1 4 7 6 5 0
Year 2 2 4 8 0 1
Year 3 7 9 4 0 3
a. If the total cash flow in years 1, 2 and 3 is less than Rs. 42,000, the net cash flow will be
negative. The combinations of cash flow which total less than Rs. 42,000 are given in table
below :
Cash flow (Rs. ’000)
Year 1 Year 1 Year 1 Total Probility
10 10 10 30 0.3×0.1×0.3 = 0.009
10 10 20 40 0.3×0.1×0.5 = 0.015
10 20 10 40 0.3×0.2×0.3 = 0.018
15 10 10 35 0.4×0.1×0.3 = 0.012
20 10 10 40 0.3×0.1×0.3 = 0.009
Total = 0.063
The probability of a negative cash flow is 0.063
b. Expected cash flow = S [Cash flow×Probality]
(Rs. ’000)
Year 1 EV = (10×0.3) + (15×0.4) + (20×0.3) 15
Year 2 EV = (10×0.1) + (20×0.2) + (30×0.4) + (40×0.3) 29
Year 3 EV = (10×0.3) + (20×0.5) + (30×0.2) 19
P.V. of the cash = (15×0.8696) + (29×0.7561) + (19×0.6575) = 47.4634
The net present value of the new machine = 47,463 – 42,000 = Rs. 5,463
c. Allocate random number ranges to the cash flows for each year.
Cashflow (R. ’000) Probability Random number
Year 1 10 0.3 0.2
15 0.4 3.6
20 0.3 7.9
Year 2 10 0.1 0
20 0.2 1-2
30 0.4 3-6
40 0.3 7-9
Year 3 10 0.3 0.2
20 0.5 3-7
30 0.2 8-9
COST-VOLUME-PROFIT
ANALYSIS
Investment Decisions
We can now carryou the simulation. (Rs. 000)
Year 1 Year 2 Year 3
Number Random Cash DCF Random Cash DCF Random Cash DCF Net PV
1 4 15 13.044 2 20 15.122 7 20 13.150 -6.684
2 7 20 17.392 4 30 22.683 9 30 19.725 17.800
3 6 15 13.044 8 40 30.244 4 20 13.150 14.438
4 5 15 13.044 0 10 7.561 0 10 6.575 -14.820
5 0 10 8.696 1 20 15.122 3 20 13.150 -5.032
Total 11.702
The average net present value of the cash flow = 11,702/5 = Rs. 2,340.40
Thre out of the five simulations produced negative NPV, therefore, we estimate the probability
of a negative NPV as 3/5=0.6. Since the simulation is small, the estimates are unlikely to be
reliable.
Illustration 8 – A Research project of Continental Fibers Ltd. is in progress with a view to
deloping a new product for commercial launch. There are several aspects to this issue.
1. The project may be aborted or it may be allowed to continue.
2. If it is continued it may or may not resutlt in a potentially marketable new product.
3. If it does result in a marketable product the organisation may choose to launch it
immediately or to postpone the launch.
4. Competition may or might be able to match the organisation’s endeavours.
The Manager represent points at which decisions need to be made, while the circles represent
subsequent events. It can be seen that each decision, combined with the states of nature that are
assumed to prevail, produces distinct outcomes.
The next step is to introduce quantitative data, so let us assume the following :
a. It will cost an estimated Rs. 50,000 to continue the project which is itself probabilistic.
b. If the Company decides to postpone the launch of the product (assuming the project is
successful) and competitors enter the market there will be a loss of current business
amounting to Rs. 1,25,000.
c. If the project is successful and an immediate launch is undertaken, the company will generte
incremental cash flows of Rs. 4,50,000 if competitiors stayout of the market, but only Rs.
2,50,000 if competitors enter the market.
Taking the branch dealing with the immediate launch of a successful project as an example, the
xpected value is derived as follows : (Rs.)
2,50,000×0.7 1,75,000
4,50,000×0.3 1,35,000
Expected value 3,10,000
The expected value for continuing the project of Rs. 1,56,000 calculated as follows : (Rs.)
3,10,000×0.6 1,86,000
(–) 75,000×0.4 (30,000)
Expected value 1,56,000
FIGURE 1 : BASIC DECISION TREE
Competiors enter
Competiors stayout
Immediately
launch
Postpone
launch
Decision 2
Failure
Abort project
Success
Continue
project
Decision 1
Competiors enter
Competiors stayout
Competiors enter
Competiors stayout
Competiors stayout
Competiors stayout
COST-VOLUME-PROFIT
ANALYSIS
Investment Decisions
FIGURE 2 : DECISION TREE WITH QUANTIFIED OUTCOMES
Competiors enter
Competiors stayout
Immediately
launch
Postpone
launch
Decision 2
Failure
Abort project
Success
Continue
project
Decision 1
Competiors enter
Competiors stayout
Competiors enter
Competiors stayout
Competiors stayout
Competiors stayout
A comparison of this pay-ff with the expected value of aborting the project [(–) Rs. 62,500]
shows the desirability of continuing with the project.
The decision branches will be drawn as broken lines emerging from square nodes and the
outcomes of a trail as solid lines emerging from round nodes. The square nodes, from which
the decision brances are drawn, represent the points at which decision maker selects his decision.
The round nodes represents the points at which the outcome of the decision arises. The decision
maker has no control over the outcome and can only estimate the probability of the various
outcomes actually occurring. When all of the decisions and outcomes have been represented
on the tree, each of the possible routes through tree is considered and the monetary payoff is
shown at the end of each route. Any costs incurred by the decisions are indicated along the
appropriate branches.
Where,
RRRp = Required rate of return on the project
R = Risk free rate of return
R = Market return
= Project beta
Illustration 9 – A project had an equity beta of 1.2 and was going to be financed by a combination
of 3 debt and 70% equity (assume debt beta = 0). Calculate the Project Beta. Assume Rt = 10%
and Rα = 18%.
β2 D = ⎟⎠
⎞
⎜⎝
⎛
+
× + ⎟⎠
⎞
⎜⎝
⎛
+
×
D E
D
debt
D E
E
β Equity β
= (1.2×0.70)+(0×0.30) = 0.84
RRR2 = Rt p (Rm Rt ) +β −
= 10% + 0.84 (18%–10%) = 10% + 6.72% = 16.72%
So, the riskness of this investment suggests that the project should earn a required rate of
return of about 16.7% (greater than the market rate of return).
Many companies introduce the concept of discounting risky cashflows at different rates when
they introduce variable risk premiums for different types of investments. They set different
required rates of return, or hurdle rates, for their investment projects depending on the nature
of the investment. This is usually in the form of a premium on what is considered the basic
company cost of capital. In some cases they take the four broad categories of investment projects
and they assess the degree of risk generally associated with each type of investment. Thus a
company may set up a decision rule which gives the following risk premiums :
1. Safety and maintenance investments (financing decision) - no
risk as it is simply a financing decision to choose the investment
with the lowest cost = Zero risk premium
2. Cost-savmg inveslments - low risk = 3% risk premium
3. Expansion investments - moderate risk as taking existing products
into new markets or new products into existing markets = 6% riks premium
4. Diversilicauon investments - high risk as expanding with new
products into new markets = 9% risk premium
Sometimes the decision rule will not be on the basis of what type of investment it is, but rather
on a subjective measure of how risky the investment is. For example. all new investments in a
company could be divided into high risk investments with a risk premium of 9 per cent ;
moderate risk investments, with a risk premium of 6 per cent ; low risk with a risk premium of
3 per cent ; and finally those investments with zero risk which are discounted at the company
cost of borrowing.
The CAPM approach provides a theoretically correct, comprehensive approach to risk-adjusted
RRR determination. However, the model's assumptions have been criticised as unrealistic and
it is complex to use and relies on th availability and accuracy of much information which is
external to the organisation.
COST-VOLUME-PROFIT
ANALYSIS
Investment Decisions
Illustration 10 – A publishing house has brought out a new monthly magazine which sells at
Rs.25 per copy. The cost of production it is Rs.20 per copy. A news stand estimates the sales
pattern
of the magazine as under:
Demand copies Probability
0 <>
200 <>
400 <>
600 <>
800 <>
1000 <>
The news stand has contracted for 500 copies of the magazine per month from the publisher.
The unsold copies are returnable to the publisher who will take them back at cost less Rs. 2 per
copy for handling charges.
The news stand manager wants to simulate the pattern of demand and profitability. The
following random number may be used for simulation:
27 15 56 17 98 71
51 32 62 83 96 69
You are required to:
(i) Allocate random numbers to the demand pattern forecast by the news stand.
(ii) Simulate twelve months sales and calculate the monthly and annual profit / loss.
(iii) Calculate the loss on loss on sales.
(a) Profit per copy of the magazines = 25 - 20 = Rs. 5. If unsold copy is returned, loss per copy
= Rs. 2.
(i) Allocation of Random Numbers
Demand Probability Cumulative Random Nos.
probability allocated
0 <>
200 <>
400 <>
600 <>
800 <>
1000 <>
(ii) Simulation of monthly pattern of demand and profitability
Month Random Demand Sales Returned Profit on Net Lost Loss
Numbers copies copies sales return profit/ sale
loss copies
Rs. Rs. Rs.
1 27 300 300 200 1,500 400 1,000 -
2 15 100 100 400 500 800 (300) -
3 56 500 500 - 2,500 - 2,500 -
4 17 100 100 400 500 800 (300) -
5 98 1100 500 - 2,500 - 2,500 600
6 71 500 500 - 2,500 - 2,500 -
7 51 500 500 - 2,500 - 2,500 -
8 32 300 300 200 1,500 400 1,500 -
9 62 500 500 - 2,500 - 2,500 -
10 83 700 500 - 2,500 - 2,500 200
11 96 1100 500 - 2,500 - 2,500 600
12 69 500 500 - 2,500 - 2,500 -
24,000 2,400 21,600 1,400
(ii) Loss due to lost sales= 1400 copes x Rs. 5= Rs.7,000
Illustration 11 – A company manufacture 30 items per day. The sale of these items depends
upon demand which has the following distribution:
Sales ( Units) 27 28 29 30 31 32
Probability 0.10 0.15 0.20 0.35 0.15 0.05
The production cost and sale price of each unit are Rs. 40 and Rs. 50 respectively. Any unsold
product is to be disposed off at a loss of Rs. 15 per unit. These is penalty of Rs. 5 per unit if the
demand
is the demand is not met.
Using the following random numbers estimate total / loss for the company for next 10 days:
10, 99, 65, 99, 95, 01, 79, 11, 16, 20
If the company decides to produce 29 items per day, what is the advantage to the company?
Alignment of Random Numbers
Sales (Units) Probability Cumulative Random numbers
probability assigned
27 0.10 0.10 00 - 09
28 0.15 0.25 10 - 24
29 0.20 0.45 25 - 44
30 0.35 0.80 45 - 79
31 0.15 0.95 80 - 94
32 0.05 1.00 95 - 99
COST-VOLUME-PROFIT
ANALYSIS
Investment Decisions
Let us now simulate the demand for next 10 days using the given number in order to estimate
the total profit /loss for the company. Since the production cost each item is Rs. 40 and sale
price is Rs. 50,
therefore the profit per unit of the sold item will be Rs. 10. Therefore is a loss of Rs. 15 per unit
associated with each unsold unit and penalty of Rs. 5 per unit if the demand is nit met.
Accordingly, the
profit/loss for next ten days are calculated in column (iv) of the table below if the company
manufacture 30items per days.
Day Random EstimatedProfit/Loss per day when Profit/Loss per day when
number saleproduction = 30 items per day production = 29 items per day
1 10 28 (28 X 10) -(2 X 15) = 250 (28 X 10) -(1X 15) = 265
2 99 32 (30 X 10) -(2 X 5) = 290 (29 X 10) -(3 X 5) = 275
3 65 30 (30 X 10) = 300 (29 X 10) -(1 X 5) = 285
4 99 32 (30 X 10) -(2 X 5) = 290 (29 X 10) -(3 X 5) = 275
5 95 32 (30 X 10) -(2 X 5) = 290 (29 X 10) -(3 X 5) = 275
6 01 27 (27 X 10) -(3 X 15) = 225 (27 X 10) -(2 X 15) = 240
7 79 30 (30 X 10) = 300 (29 X 10) -(1 X 5) = 285
8 11 28 (28 X 10) -(2 X 15) = 250 (28 X 10) -(1X 15) = 265
9 16 28 (28 X 10) -(2 X 15) = 250 (28 X 10) -(1X 15) = 265
10 20 28 (28 X 10) -(2 X 15) = 250 (28 X 10) -(1X 15) = 265
Total Profit Rs. 2695 Rs. 2695
The total profit for next 10 days will be Rs. 2695 if the company manufacture 30 items per day.
In case, the company decides to produce 29 items per day, then the profit of the company for
next 10 days
is calculated in column (v) of the above table. It is evident from this table that there is no
additional profit or loss if the production is reduced to 29 items per day since the total profit
remains unchangedi.e Rs. 2695.
Illustration 12 – A company uses a high grade raw material. The consumption pattern is
probabilities as given below and it takes two months to replenish stocks:
Consumption per month (tons) 1 2 3 4
Probability 0.15 0.30 0.45 0.10
The cost of placing an order is Rs.1,000 and the cost of carrying stocks is Rs. 50 per month per
ton. The average carrying costs are calculated on the stocks held at the end of each month.
The company has two options for the purchase of raw materials as under :
Option I. Order for 5 tons when the closing inventory of the month plus outstanding order is
less than 8 tons.
Option II. Order for 8 tons when the closing inventory of the month plus outstanding order is
less than 8 tons.
Currently in 1st April 2002, the company has a stock of 8 tons of raw materials plus 6 tons
ordered two months ago. The order quantity is expected to be received next month.
Using the random numbers given below, simulate 12 months consumption till 31-3-2003 and
advise the company as to which purchase option should be accepted such that the inventory
costs are minimum.
Random numbers are : 88, 41, 67, 63, 48, 74, 27, 16, 11, 64, 49, 21
Demand (Tons) Probability Cumulative Random Nos.
Probability allocated
1 0.15 0.15 00 - 14
2 0.30 0.45 15 - 44
3 0.45 0.90 45 - 89
4 0.10 1.00 90 - 99
Option - I
RN Demand Opening Receipts Closing Op. Stock Order Cl. Stock
Stock Stock on Order on Order
88 3 8 - 5 - - 6
41 2 5 6 9 - - -
67 3 9 - 6 - 5 5
63 3 6 - 3 5 - 5
48 3 3 - 0 5 5 10
74 3 0 5 2 5 5 10
27 2 2 - 0 10 - 10
16 2 0 5 3 5 - 5
11 1 3 5 7 - 5 5
64 3 7 - 4 5 - 5
49 3 4 - 1 5 5 10
21 2 1 5 4 5 - 5
44
(Rs.)
No. of order placed 5 Ordering cost (5 × 1000) 5,000
Closing stock 44 Carrying cost (44 × 50)2,200
Total Cost 7,200
COST-VOLUME-PROFIT
ANALYSIS
Investment Decisions
Option - II
RN Demand Opening Receipts Closing Op. Stock Order Cl. Stock
Stock Stock on Order on Order
88 2 8 - 5 - - 6
41 2 5 6 9 - - -
67 3 9 - 6 - 8 8
63 3 6 - 3 8 - 8
48 3 3 - 0 8 - 8
74 3 0 8 5 - 8 8
27 2 3 - 3 8 - 8
16 2 3 - 1 8 - 8
11 1 1 8 8 - - -
64 3 8 - 5 - 8 8
49 3 5 - 2 8 - 8
21 2 2 - 0 8 - 8
47
(Rs.)
No. of order 3 Ordering cost (3 × 1000) 3,000
Closing stock 47 Carrying cost (47 X 50) 2,350
Total 5,350
Analysis: Since the cost of inventory is less in Option II, it is suggested to implement.
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