DECISION Assignment

8/8/2019 DECISION Assignment

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DECISION ANALYSIS

INTRODUCTION:

A decision is defined as the selection by the decision-maker of an act, considered to

be best according to some pre-designated standard, from among the several

available options.

Decision-making problem:

There are certain essential elements which are common to all such problems. These

are:

Course of action: A decision is made from a set of defined alternative

courses of action. These are also called actions, acts or strategies.

State-of-nature: These are the consequences of any courses of

action are dependent upon certain factors beyond the control of thedecision-maker.

Uncertainty: This is indicated in terms of probabilities assigned to the

occurrence of events.

Payoff: It measures the net benefit to the decision- maker that

accrues from a given combination of decision alternatives and events.

Payoff table: Suppose the problem under consideration has n

possible events (state of nature) denoted by E1, E2 En and m alternativesacts (strategies) denoted by A1, A2, ..Am. Then the payoff corresponding

to strategy Aj of the decision-maker under the event (state-of-nature) Ei will

be denoted by aij (i=1,2..,n;j=1,2,.,m).

DECISION-MAKING PROCESS:

Step 1: Determine the various alternative courses of action from which the final

decision is to be made.

Step 2: Identify the possible outcomes called the state-of-nature for the decision

problems. The events are beyond the control of the decision-maker.

Step 3: Determine the payoff function which describes the consequences resulting

from the different combinations of the act and events.

Step 4: Construct the regret opportunity loss table. An opportunity loss occurs due

to failure of not adopting best available course of action.The opportunity loss values

are calculated separately ofr each outcomes (state-of nature) by first locating the

most favorable course of action for that outcomes and then determining the


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departure of the payoff value for that course of action and payoff value for the best

possible course of action that could have been selected.

Consider a fixed state-of nature Ei (i=1, 2 ,3..n) for which the payoff

corresponding to the n courses of action are given by Pi1, Pi2,.Pm. Let M1 be

the payoff for the least possible occur of action. The opportunity loss table will beshown as follows:

State-of-nature

Events

Conditional opportunity loss (decision alternatives)

A1 A2 A3 .. Am

E1 M1 p11 M1 p12 M1 p13 ..

M1 p1m

E2 M2 p21 M2 p22 M2 p23 .. M2 p2m

E3 M3 P31 M3 p32 M3 p33 .. M3

p3m

. . . .

. . . .

En Mn pn1 Mn pn2 Mn pn3 .. Mn

pnm

DECISION-MAKING ENVIRONMENT:

Decision-making is used to determine optimum strategies where a decision-maker

is faced with several decision alternatives. We may come across several decision-

making situations:

Decision under certainty: Whenever there exists only one outcome

for a decision, we are dealing with the category. Examples-linear

programming, transportation etc.

Decision under conflict: In many cases neither state-of nature arecompletely known nor are they completely uncertain. Partial

knowledge is available and therefore it may be termed as decision-

making under `partial uncertainty`. An example of this is the situation

of conflict involving two or more competitors marketing the same

product.


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Decision under uncertainty: These refer to situations where more

than one outcome can result from any single decision.

Decision under risk:This refers todecision situations wherein

decision-maker chooses from among several possible outcomes where

probabilities of occurrence can be stated objectively from the pastdata.

DECISIONS UNDER UNCERTAINTY:

Under uncertainty, only payoffs are known and nothing is known about the

likelihood of each state of nature.

1. THE LAPLACE PRINCIPLE

The Laplace uses all the information by assessing value equal probabilities to thepossible payoffs for each action and then selecting that alternatives which

corresponds to the maximum expected payoff.

The basic steps of this are :

Step 1: Assign equal probabilities (1/n) to each payoff of a strategy( having n

possible payoffs)

Step 2: Determine the expected payoff value for each alternatives.

Step 3: Select that alternatives which corresponds to the maximum of the above

expected payoffs.

2. THE MAXIMIN OR MININMAX PRINCIPLE

The maximin is based upon the conservative approach to assume that the worst

possible is going to happen. The decision maker consider each strategy and locates

the minimum payoff for each; and then select that alternatives which maximizes the

minimum payoff.

This consist of two steps:

Step 1: Determine the minimum assured payoff for each alternative.

Step 2: Choose that alternative which corresponds to the maximum of above

minimum payoffs.

When dealing with the costs , the maximum cost associated with each alternative

criterion used is the Minimax and carried out in two steps:

Step 1: Determine the maximum possible cost for each alternative.


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Step 2: Choose the alternative which corresponds to the minimum of the above

costs.

3. THE MAXIMAX OR MINIMIN PRINCIPLE

The maximax is based upon extreme optimism .The decision maker selects that

particular strategy which corresponds to the maximum of the maximum payoffs for

each strategy.

The maximax consist of the following steps:

Step1: Determine the maximum possible payoff for each alternative.

Step 2: Select that alternative which corresponds to the maximum of the above

maximum payoffs.

4.THE HURWIEZ CRITERION

:Hurwiez Criterion stipulates that a decision maker`s view may fall somewhere

between the extreme pessimism o maximum criterion and the extreme optimism of

the maximum criterion. The criterion provides a mechanism by which a balance

between extreme pessimism and extreme optimism is made b y weighing them

with certain degrees of optimism and pessimism.

The basic steps for this criterion is summarized as

Step1: Choose an appropriate degree of optimism (or pessimism) of the decision-

maker.

Step2 : Determine the maximum as well as minimum payoff for each alternative

and obtain the quantities.

DECISION UNDER RISK:

When a decision maker chooses from among several options whose probabilities of

occurrence can stated, he is said to take decision under risk. The probability of

various outcomes may be determined objectively from past data. However, past

records may not be available to arrive at the objective probabilities. In many cases

the decision-maker may, on the basis of his experience and judgment, be able toassign subjective probabilities to the various outcomes. The problem can then be

solved as decision problem under risk.

Under condition o risk, the most popular decision criterion for evaluating the

alternatives is the expected monetary value or expected opportunity loss of the

expected payoff.


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INVESTMENT ANALYSIS

INTRODUCTION

Every individual or firm wishes to know how 'best' to invest money to attain the

maximum gain. To achieve this objective, a proper investment analysis is to be

made. It

involves the consideration of investment proposals, estimation of their cash flows,

evaluation of cash flows, selection of the proposals based on some criterion and

finally the continuous revaluation of these proposals (projects).

This chapter is focused on financial decision-making problems arising out of an

investment decision, and provides detailed steps necessary for the analysis of such

problems. The chapter begins with a consideration of the time value of money,

followed

by the investment analysis, i.e., the question of making capital budgeting decisions.

Thereafter, interrelations between cost, revenue, volume, and the profit planning

(i.e., break-even analysis)have been discussed.

TIME VALUE OF MONEY

One of the basic concepts of finance is the notion that money has time value.This is

because money today is more valuable than the same amount at 'some future date.We can

always put available funds to some use and" make them grow into higher sums, so

that a

larger sum would be available later on. A rational decision-maker would not value

the


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opportunity to receive some amount of money now, equally, with the opportunity to

have

the same amount of money at some future date. This phenomenon is known as the

decision

maker's 'time preference of money'.

The time preference for money is generally expressed by means of an interest rate.

For

exam pie, if the time preference rate of an individual is 10%, he may forego the

opportunity

of receiving Rs. 100 now if he' is offered Rs. 110 after one year. There, amounts to

pay him

the current principal (Rs. 100) plus the interest that would accrue on it after oneyear

@ 10% p.a. Like individuals, firms also have time preference (or discount rate).

They use

this rate in evaluating the alternative decisions.

Compound Value

Consider the situation, when the investments involve more than one year.

Let the

interest, as it becomes due, is added to the principal, and the amount, thus,

obtained forms

the principal for the next time period. Then, the mode of interest

computation is called

Compound Interest. The time period after which the interest is added each

time to the

principal to form the new principal is called Conversion Periodand amount

received after

the last conversion period is called the Compound Value. The difference of

the compound


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value and the original sum borrowed is the amount ofCompound Interestfor

given

can version periods.

Let P be the principal. r the rate of interest in percentage per conversionperiod, and

J7 is the number of conversion periods. Then the amount after Ist conversion

period will

be P + P x r, i.e., P (I + r). Similarly, compound amount after 2nd conversion

period will be P (I + r) + P (I + r) x r, i.e., P (I + r)2. In general, compound

amount after nth

conversion period= P

(I + r) n.

The factor (I + r)n is also sometimes called the accumulation factor.

Present Value

The present value (PV) is the amount of money that represents the sum of

principal

and interest ifP (i.e., principal) is required to be invested now at a certain

ratecompounded over a number of time periods at a specific rate for each time

period.

The present value of the amount A (n) due at the end ofn interest periods at

the rate

ofr(in percentage per conversion period) may be obtained by solving for P,

the following

A (n) = P (1 + r)^n or P = A (n) x, (I + r)^-n


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Continuous Compounding

In most of the investments; the interest is payable quarterly, half-yearly or at

the end

of some other fraction of the year. Let the annual year be composed of f

such periods.

Then, an n-year period shall be equivalent c o n x fperiods. If an amount P is

invested at

the interest rate r% per I I fyear, the compound value at the end of 11 years

shall be

A (n) = P ( 1 + r / f )^ n f

By continuous compounding we mean compounding over an infinitely large

number of

periods (i.e., f infinity ). An example of it could be the rate of return that

a firm earns on its

initial investments, since it enables it to receivecontinuous inflow of earnings

throughoutthe year or over a specified time horizon.

ANNUITIES AND SINKING FUND

Instead of investing a lump sum amount initially, once may invest a constant

amount

annually (or monthly) or at equal intervals for a designated period of time.

The investment

is generally assumed to be made at the end of each period. The constant

periodic sums are

called annuities. A recurring deposit amount in Post Office/Bank, payment of

insurance

premium, etc., are the examples of annuity. It may be noted that-


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(a)The size of each payment of an annuity is called theperiodic payment.

(b)An annuity which is payable forever, i.e., which never terminates is called

perpetuity.

(c)The total time from the beginning of the first payment period to the end of

last

payment period is known as the term of annuity.

(d)The algebraic sum of payments and the accumulated interest is known as

the amount of annuity.

(e) The present value of an annuity is the sum of the present values of its

installments.

Amount ofan Annuity

The amount of annuity refers to the terminal value of the sequence of

payments,

including principal and compound interest, at the end of the term of annuity.

To obtain

the amount of annuity, letP =

the periodic payment. r=

the rate of interest,and

n = the interval, or the term of annuity, or the number of payments.

The first payment, being made at the end of the first time period, shall carry

accumulated interest for (n - I) time periods, the second one would similarly

carry

interest for (n - 2) time periods, and so on. The last payment would not carry

any interest,

because it is made at the end of the term. Thus, the amount of an ordinary

annuity of Rs. p

per period for n periods at the rate ofrper period is given by


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A(n, 1') = p(1 + r)^n-I-+ p(1 + r)^n-2 + ... + p(l + 1') + P

Multiplying this equation on both sides by (I + r), we get

(I + r)A(n. 1') = p(1 + r)n + p(l + r)n-I + ... + pel + 1')2 + p(1 + 1')

On subtraction, these equations yields

[(1+r)-1]A (n,r)=p(1+r)^n-p

A (n, r) = p[(1+r)^n-1] / r

Types of Annuities

In general, there are two types of annuities, namely annuity certain and

annuity

contingent.

1. Annuity Certain. When payments are to be made unconditionally for a

certain

fixed period of time. The annuity is known as annuity certain. This type of

annuity can. be

further sub-divided into following three categories:

(a) Annuity Immediate. If the payments fall due at the end of each period,

the

annuityis called an immediate or ordinary annuity.

(b) Annuity Due. If the payments fall due at the beginning of each period, the

annuity is called annuity due. In this annuity, the first payment falls due at

the

beginning of first interval, the second payment falls due at the beginning of

the

second interval, and so on. Premium on life insurance policies illustrate the

point.


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(c) Deferred or Reversionary Annuity. If the money is allowed to accumulate

for a

certain period and the payments begin after the lapse of that period, the

annuity is

called deferred or reversionary annuity. For example, when the house

building

loan is granted to a person, the repayment of loan begins after the expiry of,

may

be, a year or two from the date of grant of loan.

2. Annuity Contingent. Annuities, in which the payments are to be made

till thehappening of an event such as construction of house building. marriage of a

girl, are the

examples ofannuity contingency.

Present Value of an Annuity. The present value or capital value of an annuity

'A' is

the sum of the present values of all payments. It represents the amount that

must beinvested now to purchase, the payments due in future.

It may he noted that the interest is compounded at the end of each payment

period.

Let us, now, consider an annuity of11 payments ofy(rupees) each, where

the interest

rate per period is rand the first payment is due one period from now. Then,

the present

value of the annuity is given by

Pv= x(1+r)^-1 + x(1+r)^-2 + + x(1+r)^-n


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Multiplying this equation on both sides by (I + rt' and thensubtracting it from

the

above equation. we get

PV- PV(I+ r)^-1=x(1+ r) -I - x(1 + r)^-n+1

Hence, pv=x*

Present Value of a Perpetual Annuity For a perpetuity, there is no end to

the

periodic payments, Under the conditions, therefore.. /1 -7 00, This

implies that

(I + r)^ -n-7 0, So, the present value of a perpetuity of Rs, xper year @ r%

per annum

is given by

PVP= (A / r)

Where PVP = present value of perpetuity.

A = constant annual cash flow.

r = rate of interest.

Present Value for a Deferred Annuity For an annuity in respect of which

the first

payment is scheduled to begin after the lapse ofa certain time period, the

present value

can be obtained in a similar way as for the ordinary annuity. To -illustrate, let

the annuity

begins in 'I' years from now (so that the first paymentwould, as usual, be

made at the end

of the first year at that, time), the 'present value of the successive payments

would be

x(I +r)^-(1+I), x(I + r)^-(l+2), and so on.

Thus,


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PV=x(I + r) -i+1 +x(l + r) -1+2 + ... +x(I + r) -i+n

To obtain the value ofPVwe first multiply this equation by (I + r) and then

subtract

the above equation from it. -Thus, we get

PV=x/r(1+r)^-1 [1-(1+r)^-n]

Sinking Fund

A sinking fund is a fund that is created for a sequence of periodic payments

over a

time period at a specified interest rate, The amount in such a fund is usually

used for

repair of buildings, replacement of an equipment, expansion of an

enterprise, and so on,

IfA is the amount to be saved, and P, the periodic payment: then size of the

sinking

fund is computed by using the following formula

A = R [(1+i)n-1]/i R = Ai/(1+i)n -1

R = Ai/(1+i)n -1

R : periodic payment.

A : periodic payment R is required to accumulate a sum of A dollars.

n: number of periods.

i: interest rate.

METHODS OF INVESTMENT ANALYSIS

An efficient allocation of capital is one of the most important functions of a

financial


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management. This function involves the firm's desire to commit its funds in

long tern

assets and other profitable activities. Such investment decisions are of

considerably important, because they influence the wealth of the firm,

determine the size, set up the pace and direction of its growth and affects

business risk.

Investment decisions of a firm influence its wealth-it will increase if the'

investment

proposals are profitable, otherwise it would decrease. Now, to evaluate an

investment

proposal the study of the following components is necessary:

a)The initial cash outflow.

b ) The returns (or net cash-inflows calculated on yearly basis) over the

economic life

of the asset.

(c) The economic life of the asset. Economic life is usually shorter than

durable lifedue to technological advancements.

(d) Minimum return desired on such investment, called "cut-off point".

The most widely used methods of evaluating an investment proposal can be

grouped

into the following two major categories:

I. Traditional Methods these include (a) Payback Period method, and (b)

Average

Rate of Return method.

2. Discounted Cash Flow (DCF) Methods These include (e) Net Present

Value


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(NPV) method, (d) Internal Rate of Return (IRR) method, and (e) Discounted

Payback Period method.

(a) Payback Period Method Payback period is the number of years

required torecover the cash invested in a project. If the annual cash inflows are same,

.the payback

period can be computed dividing the cash invested by the annual cash

inflow; if unequal,

it can be calculated by adding up the cash inflows until the total is equal to

the initial cost

invested.

Illustration, A project requires a cash outlay of Rs. 60.000 and yields an

annual cash inflow of

R s .12.000 For 7 years. What is its payback period?

(p) =Cash outlay (P)/ average met cash inflow per year(R)

60,000/12000 = 5 years

It may be noted that the proposal will be accepted, only if payback period is

5 years or less.

(b) Average Rate of Return Method The average rate of return is an

accounting

method. It is calculated as the ratio of the average annual profits, after

taxes, to the average investment in the project. For instance, if the average

annual book profits (after

taxes and depreciation) are estimated at Rs. 20;000 and net investment for a

new equipment is Rs. 1,00.000; then the average rate of return would be

Rs. 20,000/Rs. 1,00,000', i.e., 0.20 or 2Q%.


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where CF represents that Cash Flow generated in particular time

period

N represents the last time period.

R represents IRR value.

T h e computed IRR is compared with the required rate of return, If the

calculated rate

exceeds the required rate, the proposal is accepted; otherwise it is rejected.

Note: The value of r in the above equation is determined by trial and error.

We select any rate of interest to compute PI' or cash inflows. If the calculated

PVof cash inflows is lower than the PVof cash outflows a lower rateinterest

is to be tried. On the other hand. a higher rate should be tried. if the PI' of

cash inflows is higher than, the PI' or cash outflows, The process is to be

repeated till the NI'V becomes zero.

RemarkI: may be observed that the IRR formula is same as used for the NPV

method with the difference

that in the NPVmethod, the required rate of return 'is assumed to be known

and then the NPV is calculated whereas in the IRR method the value ofr

has to be determined such that the NPVis zero.

(c) Discounted Payback Period Method The payback period is defined as

the

number of years required to recover the original investment. In the case of

discounted payback period we consider the discounted present values of

future cash inflows and find

out the number of years required to recover the initial investment. If

discounted payback


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Chance node 1 Low demand (8

lakh*0.4 = 3.2lakh)

Medium demand(18 lakhs*0.3=5.4lakh)

Large demand

(22lakhs*0.3=6.6lakhs)

Decision node 1 Low demand

(meet demand) no expansion required (4*0.4=1.6lakh)

Chance node 2 further

expansion for medium demand (0.5*16=8lakhs)

Decision

node2

Large demand

(0.5*19=9.5lakhs)

Build large plant

10 lakhs

Build small

plant 4lakhs


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lumColumn2 Column3 Column4 Column5

no. Decision Returns Earned Total Returns Decisionreturn earned -investment

for small demand (8*0.4=3.2lakhs)

Build Largeplant

for medium demand(18*0.3=5.4lakhs)

15.2lakhs - 10lakhs =5.2 lakhs SELECT

for large demand(22*0.3=6.6lakhs)

if small demand meet demand(4*0.4=1.6lakhs)

for further medium and large

demandBuild smallplant

19.1lakhs - (4+4+8)=3.1lakhs REJECT

expansion for medium demand(16*0.5=8lakhs)

expansion for large demand(19*0.5=9.5lakhs)

From both th options we can observe that the action 1 is more profitable. Sothe company should go ahead with building large plant as it involves lesscost and more profit.


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DECISION Assignment