Uk Unit II Cse Split Up

8/13/2019 Uk Unit II Cse Split Up

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SRI MANAKULA VINAYAGAR ENGINEERING COLLEGE DEPARTMENT OF CSE

UNIT II

IntroductionElementary Economic AnalysisInterest Formulas and their Applications

- ComparisonsPresent Worth MethodFuture Worth MethodAnnual Equivalent MethodRate of Return

Method

UNITII

2 MARKS

1. WHAT IS ECONOMIC ANALYSIS? (Dec2012) (Apr 2012)

Meaning: Asystematic approach to determining theoptimum use of scarceresources,involving comparison of

two or more alternatives in achieving a specificobjective under the givenassumptions andconstraints.

Economic analysis takes intoaccount theopportunity costs of resourcesemployed andattempts tomeasure in

monetaryterms the private andsocial costs andbenefits of aproject to thecommunity oreconomy.

Economic Analysis: Business Cycles, Monetary & Fiscal Policy, Economic Indicators, World Events& Foreign Trade, Inflation, Public Sentiment, GDP Growth, Unemployment, Productivity, Capacity

Utilization, etc.

Industry Analysis: Industry Structure, Competition, Supply-Demand Relationships, Product QualityCost Elements, Government Regulation, Business Cycle Exposure, etc.

Analysis of the Individual Firm: Forecasts of Earnings, Dividends and discount rates, BalanceSheet/Income Statement Analysis, Management, Research, Return, Risk, etc

2. WRITE SHORT NOTES ON THE TYPES OF INTEREST RATE? (Apr2012)

1. Simple interest rate

2. Compound interest rate.

1. Simple interest rate: In simple interest, the interest is calculated, based on the initial deposit for every

interest period.

2. Compound interest rate. In Compound interest, the interest for the current period is computed based on the

amount at the beginning of the current period.The notations which are used in various interest formulae are as follows:

P = principal amount n = No of interest periods I = interest rate (It may be compounded monthly, quarterly, semiannually or annually) F = future amount at the end of year n A = equal amount deposited at the end of every interest period G = uniform amount which will be added/subtracted period after period to/from the amount of deposi

A1 at the end of period 1

3. WHAT IS SIMPLE INTEREST?

Simple interest is calculated on the original principalonly. Accumulated interest from prior periods is no

used in calculations for the following periods. Simple interest is normally used for a single period of less than a

year, such as 30 or 60 days.

Simple Interest = p * i * n

where:

p = principal (original amount borrowed or loaned)
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i = interest rate for one period n = number of periods

Example 1: You borrow $10,000 for 3 years at 5% simple annual interest.

interest = p * i * n = 10,000 * .05 * 3 = 1,500

Example 2: You borrow $10,000 for 60 days at 5% simple interest per year (assume a 365 day year).

interest = p * i * n = 10,000 * .05 * (60/365) = 82.1917

4. WHAT IS COMPOUND INTEREST?

Compound interest is calculated each period on the original principal and all interestaccumulated during

past periods. Although the interest may be stated as a yearly rate, the compounding periods can be yearly

semiannually, quarterly, or even continuously. You can think of compound interest as a series of back-to-back

simple interest contracts. The interest earned in each period is added to the principal of the previous period to

become the principal for the next period.

Example 1: You borrow $10,000 for three years at 5% annual interest compounded annually:

Interest year 1= p * i * n = 10,000 * .05 * 1 = 500 Interest year 2 = (p2= p1+ i1) * i * n = (10,000 + 500) * .05 * 1 = 525 Interest year 3 =(p3= p2+ i2) * i * n = (10,500 + 525) *.05 * 1 = 551.25

Total interest earned over the three years = 500 + 525 + 551.25 = 1,576.25.

Compare this to 1,500 earned over the same number of years using simple interest.

The power of compounding can have an astonishing effect on the accumulation of wealth. This table shows the

results of making a one-time investment of $10,000 for 30 years using 12% simple interest, and 12% interest

compounded yearly and quarterly.

Type of Interest Principal Plus Interest Earned

Simple 46,000.00

Compounded Yearly 299,599.22

Compounded Quarterly 347,109.87

You can solve a variety of compounding problems including leases, loans, mortgages, and annuities by using

thepresent value,future value,present value of an annuity,andfuture value of an annuityformulas.

5. STATE THE EIGHT TYPES OF INTEREST FORMULAS.

1. Single-Payment Compound Amount

2. Single-Payment Present Worth Amount

3. Equal-Payment Series Compound Amount

4. Equal-Payment Series Sinking Fund

5. Equal-Payment Series Present Worth Amount

6. Equal-Payment Series Capital Recovery Amount

7. Uniform Gradient Series Annual Equivalent Amount

8. Effective Interest Rate

6. WRITE SHORT NOTES ON SINGLE-PAYMENT COMPOUND AMOUNT?
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The objective is to find the single future sum (F) of the initial payment (P) made at time 0 after n periods at an

interest rate I compounded every period.

Formula:

F = P(1+i)^n = P(F/P,i,n)

Where,

(F/P,i,n) is called single-payment compound amount factor.

Example:

A person deposits a sum of Rs.20,000 at the interest rate of 18% compounded annually for 10

years. Find the maturity value after 10 years.

Solution:

P = Rs.20,000

i = 18% compounded annually

n = 10 years

F = P(1+i)^n = P(F/P,i,n)

= 20,000 (1+0.18)^10

= 20,000*5.234 = Rs.1,04,680

7. WRITE SHORT NOTES ON SINGLE-PAYMENT PRESENT WORTH AMOUNT?

The objective is to find the present worth amount (P) of a single future sum (F) which will be received

after n periods at an interest rate of i compounded at the end of every interest period.

Formula:

P = F/((1+i)^n) = F(P/F,i,n)

where,

(P/F,i,n) is termed as single-payment present worth factor.

Example:

A person wishes to have a future sum of Rs.1,00,000 for his sons education after 10 years from

now. What is the single-payment that he should deposit now so that he gets the desired amount after 10 years?The bank gives 15% interest rate compounded annually.

Solution:

F = Rs.1,00,000

i = 15%, compounded annually

n= 10 years

P = F/((1+i)^n) = F(P/F,i,n)

= 1,00,000((1+0.15)^10)

= 1,00,000 * 0.2472

= Rs.24,720

8. WRITE SHORT NOTES ON EQUAL-PAYMENT SERIES COMPOUND AMOUNT?

The objective is to find the future worth of n equal payments which are made at the end of every interest

period till the end of the nth interest period at an interest rate of i compounded at the end of each interest period.

Formula:

F = A(((1+i)^n)-1)/i = A(F/A,i,n)

Where,

(F/A,i,n) is termed as equal-payment series compound factor.


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Example:

A person who is now 35 years old is planning for his retired life. He plans to invest an equal sum

of Rs.10,000 at the end of every year for the next 25 years starting from the end of the next year. The bank gives

20% interest rate, compounded annually. Find the maturity value of his account when he is 60 years old.

Solution:

A = Rs.10,000

n = 25 years

i = 20%

F = A(((1+i)^n)-1)/i

= A(F/A,i,n)

= 10,000(F/A,20%,25)

= 10,000*471.981

= Rs.47,19,810

9. WRITE SHORT NOTES ON EQUAL-PAYMENT SERIES SINKING FUND?The objective is to find the equivalent amount (A) that should be deposited at the end of every interest

period for n interest periods to realize a future sum (F) at the end of the nth interest period at an interest rate of i

Formula:

A = F(i/((1+i)^n)-1) = F(A/F,i,n)

Where,

(A/F,i,n) is called as equal-payment series sinking fund factor.

Example:

A company has to replace a present facility after 15 years at an outlay of Rs.5,00,000. It plans to

deposit an equal amount at the end of every year for the next 15 years at an interest rate of 18% compoundedannually. Find the equivalent amount that must be deposited at the end of every year for the next 15 years.

Solution:

F = Rs.5,00,000

n= 15 years

i = 18%

A = F(i/((1+i)^n)-1) = F(A/F,i,n)

= 5,00,000(A/F,18%,15)

= 5,00,000 * 0.0164

= Rs.8,200

10. WRITE SHORT NOTES ON EQUAL-PAYMENT SERIES PRESENT WORTH AMOUNT?

The objective of this mode of investment is to find the present worth of an equal

Payment made at the end of every interest period for n interest periods at an interest rate of i compounded at the

end of every interest period.

Formula:

P=A((1+i)^n)-1/i(1+i)^n = A(P/A,i,n)

Where,

(P/A,i,n) is called equal-payment series present worth factor.


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Example:

A company wants to set up a reserve which will help the company to have an annual equivalent

amount of Rs.10,00,000 for the next 20 years towards its employees welfare measures. The reserve is assumed

to grow at the rate of 15% annually. Find the single-payment that must be made now as the reserve amount.

Solution:

A = Rs.10,00,000

i = 15%

n = 20 years

P = A((1+i)^n)-1/i(1+i)^n = A(P/A,i,n)

= 10,00,000 * (P/A,15%,20)

= 10,00,000 * 6.2593

= Rs.62,59,300

11. WRITE SHORT NOTES ON EQUAL-PAYMENT SERIES CAPITAL RECOVERY AMOUNT?

The Objective is to find the annual equivalent amount (A) which is to be recovered at the end of everyinterest period for n interest periods for a loan (P) which is sanctioned now at an interest rate of i compounded

at the end of every interest period.

Formula:

A = P(i(1+i)^n)/((1+i)^n)-1 = P(A/P,i,n)

Where,

(A/P,i,n) is called equal-payment series capital recovery factor.

Example:

A bank gives a loan to a company to purchase an equipment worth Rs.10,00,000 at an interest

rate of 18% compounded annually. This amount should be repaid in 15 yearly equal installments. Find theinstallment amount that the company has to pay to the bank.

Solution:

P = Rs.10,00,000

I = 18%

N = 15 years

A = P(i(1+i)^n)/((1+i)^n)-1 = P(A/P,i,n)

= 10,00,000*(A/P,18%,15)

= 10,00,000 * 0.1964

= Rs.1,96,400

12. WRITE SHORT NOTES ON UNIFORM GRADIENT SERIES ANNUAL EQUIVALENT

AMOUNT?

The objective of this type is to find the annual equivalent amount of a series with an amount A1 at the

end of the first year and with an equal increment (G) at the end of each of the following n-1 years with an

interest rate i compounded annually.

Formula:

A = A1 + G(((1+i)^n)-in-1)/(i(1+i)^n)-i

= A1 + G(A/G,i,n)


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Where,

(A/G,i,n) is called uniform gradient series factor.

Example:

A person is planning for his retired life. He has 10 more years of service. He would like to

deposit 20% of his salary, which is Rs.4,000, at the end of the first year, and thereafter he wishes to deposit the

amount with an annual increase of Rs.500 for the next 9 years with an interest rate of 15%. Find the total

amount at the end of the 10thyear of the above series.

Solution:

A1 = Rs.4,000

G = Rs.500

i = 15%

n = 10 years

A = A1 + G(((1+i)^n)-in-1)/(i(1+i)^n)-i

= A1 + G(A/G,i,n)

= 4,000+500(A/G,15%,10)

= 4,000+500*3.3832

= Rs.5,691.60This is equivalent to paying an equivalent amount of Rs.5,691.60 at the end of every year for the next 10 years.

The future worth sum of this revised at the end of the 10thyear is obtained follows

F = A(F/A,i,n)

= A(F/A,15%,10)

= 5,691.60(20.304)

= Rs.1,15,562.25

13. WRITE SHORT NOTES ON EFFECTIVE INTEREST RATE?

Let i be the nominal interest rate compounded annually. But, in practice, the compounding may occur

less than a year. For example, compounding may be monthly, quarterly, or semi-annually. Compoundingmonthly means that the interest is computed at the end of every month. There are 12 interest periods in a year if

the interest is compounded monthly. Under such situations, the formula to compute the effective interest rate,

which is compounded annually, is

Formula:

R = ((1+i/C)^c)-1

Where,

i = the nominal interest rate C = the number of interest periods in a year

Example:

A person invests a sum of Rs.5,000 in a bank at a nominal interest rate of 12% for 10 years. The

compounding is quarterly. Find the maturity amount of the deposit after 10 years.

Solution:

P = Rs.5,000

n = 10 years

i = 12% (Nominal interest rate)

Method 1:

No. of interest periods per year = 4

No. of interest periods in 10 years = 10*4 = 40

Revised No. of periods (No. of quarters), N = 40


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Interest rate per quarter, r = 12%/4

= 3%, compounded quarterly.

F = P(1+r)^N = 5,000(1+0.03)^40

= Rs.16,310.19

Method 2:

No. of interest periods per year, C = 4

Effective interest rate, R = (1+i/C)^C1

= (1+12%/4)^41

= 12.55%, compounded annually.

F = P(1+R)^n = 5,000(1+0.1255)^10

= Rs.16,308.91

14. WRITE SHORT NOTES ON ANNUAL EQUIVALENT METHOD?

In the annual equivalent method of comparison, first the annual equivalent cost or the revenue of eachalternative will be computed. Then the alternative with the maximum annual equivalent revenue in the case ofrevenue-based comparison or with the minimum annual equivalent cost in the case of cost-based comparisonswill be selected as the best alternative.

15. WRITE SHORT NOTES ON REVENUE.DOMINATED CASH FLOW DIAGRAM?

A generalized revenue-dominated cash flow diagram to demonstrate the annual equivalent method ofcomparison is presented in fig.1. S

R0 R1 R2 R3 .Rj Rn

0 1 2 3 .j n

P Fig.1.1. Revenue-dominated cash flow diagram.In the above cash flow diagram,

o Pis an initial investmento Rjis the net revenue at the end of the jth yearo Sis the salvage value at the end of the nth year.

The first step is to find the net present worth of the cash flow diagram using the following expression at a giveninterest rate, i.

PW(i) = - P + R1 / (1+i)1

+R2 / (1+i)2+Rj / (1+i)

j++Rn/(1+i)

n+ S/(1+i)

n

In the above formula, the expenditure is assigned with a negative sign and the revenues are assigned with a

positive sign.In the second step, the annual equivalent revenue is computed using the following formula:

i(1+i)n

A = PW(i) = PW(i) (A/P, i, n)

(1+i)n-1

Where (A/P, i, n) is called equal payment series capital recovery factor.


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If we have some more alternatives which are to be compared with this alternative, then the corresponding

annual equivalent revenues are to be computed and compared. Finally, the alternative with the maximum annual

equivalent revenue should be selected as the best alternative.

16. WRITE SHORT NOTES ON COST-DOMINATED CASH FLOW DIAGRAM?

A generalized cost-dominated cash flow diagram to demonstrate the annual equivalent method of comparison is

illustrated in fig.1.2.

S

0 1 2 .j . .

. . n

C0 C1 C2 .Cj Cn

P

Fig.1.2. Cost-dominated cash flow diagram.

In fig 1.2, P represents an initial investment, Cj the net cost of operation and maintenance at the end of the jth

year, and S the salvage value at the end of the nth year.

The first step is to find the net present worth of the cash flow diagram using the following relation for a

given interest rate, i.

PW(i) = P + C1 / (1+i)1

+C2 / (1+i)2+Cj / (1+i)

j++Cn/(1+i)

n- S/(1+i)

n

In the above formula, each expenditure is assigned with positive sign and the salvage value with negative

sign. Then, in the second step, the annual equivalent cost is computed using the following equations:

i(1+i)n

A = PW(i) = PW(i) (A/P, i, n)

(1+i) n-1

Where (A/P, i, n) is called as equal-payment series capital recovery factor.

As in the previous case, if we have some more alternatives which are to be compared with this alternative,

then the corresponding annual equivalent costs are to be computed and compared. Finally, the alternative with

the minimum annual equivalent cost should be selected as best alternative.

If we have some non-standard cash flow diagram, then we have to follow the general procedure for

converting each and every transaction to time zero and then convert the net present worth into annual equivalentcost/revenue depending on the type of the cash flow diagram. Such procedure is to be applied to all the

alternatives and finally, the best alternative is to be selected.

17. WRITE SHORT NOTES ON RATE OF RETURN METHOD?

The rate of return of a cash flow pattern is the interest rate at which the present worth of that cash flow pattern

reduces to zero. In this method of comparison, the rate of return for each alternative is computed. Then the

alternative which has the highest rate of return is selected as the best alternative.


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In this type of analysis, the expenditures are always assigned with a negative sign and the

revenues/inflows are assigned with a positive sign.

A generalized cash flow diagram to demonstrate the rate of return method of comparison is presented in

fig2.1. S

R0 R1 R2 R3 Rj Rn

0 1 2 3 .j n

P Fig.1.1. generalized cash flow diagram.In the above cash flow diagram, P - represents an initial investment, Rj - the net revenue at the end of the jth year S - the salvage value at the end of the nth year.

The first step is to find the net present worth of the cash flow diagram using the following expression at agiveintrest rate, i.

PW(i) = - P + R1 / (1+i)1

+R2 / (1+i)2+Rj / (1+i)

j++Rn/(1+i)

n+ S/(1+i)

n

18. WRITE SHORT NOTES ON PRESENT WORTH METHOD? (Dec2012)

In this method of comparison, the cash flows of each flow will be reduced to time zero by assuming an

interest rate i. Then depending on the type of decision, the best alternative will be selected by comparing the

present worth amounts of the alternatives. The sign of various amounts at different points in time in a cash flow

diagram is to be decided based on the type of the decision problem.

In a cost dominated cash flow diagram, the cost will be assigned with positive sign and the profits

revenue, salvage value (all inflows), etc will be assigned with negative sign. In a revenue/profit dominated cashflow diagram, the cost will be assigned with negative sign and the profits, revenue, salvage value (all inflows),

etc will be assigned with positive sign. In case the decision is to select the alternative with the minimum cost,

then the alternative with the least present worth amount will be selected. On the other hand if the decision is to

select the alternative with the maximum cost, then the alternative with the maximum present worth amount will

be selected.

19. WRITE SHORT NOTES ON FUTURE WORTH METHOD?

In the future worth method of comparison of alternatives, the future worth of various alternatives will be

computed. Then, the alternative with the maximum future worth of net revenue or with the minimum future

worth of net cost will be selected as the best alternative for implementation

20. DIFFERENCE BETWEEN SIMPLE AND COMPOUND INTEREST?

Simple Interest is calculated from the principal only (the amount that you deposited)Compound Interest is calculated from the remaining balance (this includes the principal plus any interest

that you earned that still remains in the account).

A very simple example shows the dif ference:

Assume you put $5,000 in the bank. Assume the interest rate is 3.75% per year. Assume you withdraw the money at the end of 3 years.


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With simple interest, the interest each year is calculated from the principal you put in the bank which is$5,000. The interest that you already earned is not used in the calculation.

With compound interest, the interest each year is calculated from the remaining balance. This includesyour principal plus any interest that you previously earned that still remains in the account.

21. WHAT ARE THE OBJECTIVES OF ECONOMIC ANALYSIS?

The economic analysis of a project helps select and design projects that contribute to the welfare of acountry. Various tools of economic analysis help determine the economic and fiscal impact of the project

including the impact on society and the major stakeholders involved, as well as the projects risks andsustainability. A good economic analysis answers the following questions:

What is the objective of the project? This helps identify tools for the analysis. A clearly defined objective also helps in identifying the

possible alternatives to the project. What will be the impact of the project? This question concerns a counterfactual as the difference between the situation with or without the

project is crucial for assessing the incremental costs and benefits of the project. Are there any alternatives to the project? If so how would costs and benefits of the alternatives to

achieve the same goal compare to the project in question? Is there economic justification of each separable component of the project? Who gains and who loses if the project is implemented? The analysis has to make sure that the most benefit accrues to the poor. What is the fiscal impact of the project? Is the project financially sustainable and what are the risks involved? Are there any other externalities? What is the environmental impact of the project?

22. WHAT IS INTEREST? (April2012)

Interest is the price paid for using someone elses money. It is thus the fee for the privilege of borrowing

money. The fee represents the price a person pays for the ability to spend / consume in the present instead of

having to wait for the future to do so. You pay for the opportunity to use money today that would otherwise take

time to accumulate.

A simple example to use is that when a person puts money in the bank and leaves it there, the bank pays theperson interest for allowing the bank to use it. If the person borrows money from the bank, the bank will charge

the person interest for using his or her money.

The Oxford dictionary defines interest as: The charge made for borrowing a sum of money. The interest rate is

the charge made, expressed as a percentage of the total sum loaned, for a stated period of time.

11 MARKS

1. EXPLAIN ECONOMIC ANALYSIS INDICATORS.

Business Cycle of Economic Activity: The business cycle is usually a graph of economic activity. The graph

shown below would have all of the characteristics of a typical business cycle: Peaks, troughs, periods of

expansion, periods of reduced economic activity. This interest rate graph of 6-month T-Bill rates is a good

example of how the economy's activity is tracked.

GOVERNMENT POLICY: Monetary & Fiscal.

Monetary Policy - The Federal Reserve's primary policy variables. Money Supply and InteresRates. See my notes on the Fed to get a more complete definition.

Fiscal Policy - Congress primary policy variables. Taxing and Spending. The US government iknown for its deficits (spending more than income), many believe that this is sound economic

policy. Great political debates have arisen out of deficit spending conversations. For the first time in

over 30 years, the federal government ran a surplus (income exceeded spending) in year 2000.

Coincident Indicators -Economic indicators that change direction at roughly the same time as the general


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economy.

Employees on Non-Agricultural Payrolls Personal Income Less Transfer Payments Industrial Production Manufacturing and Trade Sales

Lagging Indicators - Economic indicators that usually change direction after business conditions have

changed.

Average duration of unemployment, in weeks Ratio, manufacturing and trade inventories to sales Change in labor cost per unit of output in manufacturing Average Prime Rate charged by Banks Commercial and Industrial Loans Outstanding Ratio, consumer installment credit outstanding to personal income Changes in Consumer Price Index for services

OTHER ECONOMIC INDICATORS

Public Attitudes - Consumer confidence. Domestic Legislation - Laws and regulations. Inflation - A general increase in the price of goods and services. Gross Domestic Product (GDP) Growth - GDP is the measure of output from US factories and

related consumption in the US. It does not include products made by US companies in foreign

markets.

Unemployment - The percent of the population that wants to work and are currently not working. Productivity - Output per worker. Capacity Utilization - Output by the firm.

2. EXPLAIN THE METHODS OR TECHNIQUES AVAILABLE FOR ECONOMIC ANALYSIS.An economic theory derives laws or generalizations through two methods (1) Deductive Method and (2)

Inductive Method. These two ways of deriving economic generalizations are now explained in brief.

1. Deductive Method.

The deductive method is also named as analytical, abstract or prior method. The deductive method consists in

deriving conclusions from general truths. It takes a few general principles and applies them to draw conclusions

For instance, if we accept the general proposition that man is entirely motivated by self-interest. Rashid is a

man. therefore, the inference will be drawn that Rashid is motivated by self-interest. In applying the deductive

method of economic analysis, we proceed from general to particular.

The classical and neo-classical school-. of economists notably, Ricardo. Senior, Cairnes, J.S. Mill, Malthus

Marshall, Pigou, applied the deductive method in their economic investigations.

The main steps involved in deductive logic are as under_

(1) Perception of the problem to be inquired into. In the process of deriving economic

generalizations, the analyst must have a clear and precise idea of the problem to be inquired into.

(2) Defining of terms. The next step in this direction is to define clearly the technical

terms to be used in economic analysis. Further, the assumptions made for a theory should also be precise.

(3) Deducing hypothesis from the assumptions. The third step in deriving generalizations is deducing

hypothesis from the assumptions taken.


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(4) Testing of hypothesis. Before establishing laws or generalizations, the hypothesis should be verified

through direct observations of events in the real world and through statistical methods. (Their is an inverse

relationship between price and .quantity demanded of a good is a well established generalization).

Merits of Deductive Method.

The main merits of deductive method are as under:

(1) This method is near to reality. It is less time consuming and less expensive.

(2) The use of mathematical techniques in deducing theories of economics brings exactness and clarity in

economic analysis.

(3) There being limited scope of experimentation in economics, the method helps in deriving economic

theories.

(4) The method is simple because it is analytical.

Demerits of deductive method.

(1) The deductive method is simple and precise only if the underlying assumptions are valid. More often the

assumptions turn out to be based on half truths or have no relation to reality. The conclusions drawn from such

assumptions will, therefore, be misleading.

(2) Professor Learner describes the deductive method as armchair analysis. According to him, the premises

from which inferences are drawn may not hold good at all times, and places. As such deductive reasonings arenot applicable universally.

(3) The deductive method is highly abstract. It require a great deal of care to avoid bad, logic or faulty

economic reasoning. As the deductive method employed by the classical and neo-classical economists led to

many facile conclusions due to reliance on imperfect and incorrect assumptions, therefore, under the German

Historical School of economists, a sharp reaction began against this method. They advocated a more realistic

method for economic analysis known as inductive method.

2. Inductive Method.Inductive method which is also called empirical method was adopted by the istorical

School of economists. It involves-the process of reasoning from articular facts to general principle. This

method derives economic generalizations n the basis of (1) Experimentations (2) Observations and (3)

Statistical methods.Systematically arranged and the general conclusions are drawn from them. For example, we observe 200

persons in the market. We find that nearly 195 persons buy from the cheapest shops, Out of the 5 which

remains, 4 persons buy local products even at higher rate just to patronise their own products, while the fifth is a

fool. From this observation, we can easily draw conclusions that people like to buy from a cheaper shop unless

they are guided by patriotism or they are devoid of commonsense.

T.he main steps involved in the application of inductive method are: (i) observation (ii) formation of hypothesis

(iii) generalization and (iv) verification. Merits of inductivemethod.

(1) It is based on facts as such the method is realistic.

(2) In order to test the economic principles, the method makes use of statistical techniques. The inductive

method is, therefore, more-reliable.

(3) Inductive method is dynamic. The changing economic phenomenon are analysed and on the basis of

collected data, conclusions and solutions are drawn from them.

(4) Induction method also helps in future investigations. Demerits of inductive method.

The main weaknesses of this method are as under.-

(1) If conclusions are drawn from insufficient data, the generalizations obtained may befaulty.

(2) The collection of data itself is not an easy task. The sources and methods employed

in the collection of data differ from investigator to investigator. The results, therefore,may differ even with the

same problem.


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(3) The inductive method is time-consuming and expensive.

3. EXPLAIN THE TYPES OF ECONOMIC ANALYSIS.

Policymakers have a variety of economic analyses at their disposal to help them assess policies and programs

Cost analysis,fiscal impact analysis,cost-effectiveness analysis,andcost-benefit analysisare among the most

commonly used tools. This document describes these four types of economic analysis, compares and contrasts

them, and explains which circumstances warrant their use.

Cost analysis

Cost analysis provides a complete accounting of the expenses related to a given policy or program decision. It

supplies the most basic cost information that both decision makers and practitioners require and forms the

foundation of all other economic analyses.

A cost analysis sounds simple, but it requires effort to perform a cost analysis thoroughly. Analysts frequently

identify only the most obvious costs, such as staff salaries, and fail to account for many others. A complete cost

analysis needs to consider:

Direct costs,like equipment and fringe benefits, in addition to staff salaries; Indirect costsoroverhead,such as central support services;

For new programs or policies, start-up expenditures and one-time costs, including hiring and training; Future costs, including wage increases, contributions for increasing pension and insurance expenses

and other escalating costs; and

Capital costs,including debt service.For more details, see the sectionKnow your costs.

Fiscal impact analysis

A fiscal impact analysis is a comprehensive study of all governmental revenues, expenditures, and savings that

will result from the proposed policy or program. State and local fiscal offices routinely produce fiscal impact

analyses, which are also called fiscal notes when they are prepared for draft legislation. This type of analysis

helps policymakers determine whether a proposed initiative is affordable from a budgetary standpoint.

Cost-effectiveness analysisA fiscal impact analysis can help you assess how a program or policy will affect your budget but it wont tell

you whether the program or policy is an efficient use of resources. There may be less expensive options that

produce equivalent results. To evaluate which program or policy creates the result you want at the lowest cost

use cost-effectiveness analysis (CEA).

Suppose that youre comparing two job-training programs, both of which serve 1,000 ex-offenders per year

After doing a comprehensive cost analysis, you find that Program A costs $10 million and Program B $7.5

million annually (see Figure 1). Program A, which costs $10,000 per client, is more expensive than Program B

which costs $7,500 per client. Program A, however, places more of its clients in permanent employment than

Program B. The appropriate measure of the programs cost-effectiveness is the total program cost divided by

the desired outcome, in this case, the total number of job placements. The results show that Program A is more

cost-effective, i.e., a better use of resources, because its cost per placement ($13,333) is lower than Program Bs

($15,000).

Figure 1

Indicator Total Cost ClientsCost per

Client

Placement

RatePlacements

Cost per

Placement

Program

A $ 10,000,000 1,000 $ 10,000 75% 750 $ 13,333
http://cbkb.org/basics/glossary/#cost%20analysishttp://cbkb.org/basics/glossary/#cost%20analysishttp://cbkb.org/basics/glossary/#fiahttp://cbkb.org/basics/glossary/#fiahttp://cbkb.org/basics/glossary/#fiahttp://cbkb.org/basics/glossary/#ceahttp://cbkb.org/basics/glossary/#ceahttp://cbkb.org/basics/glossary/#ceahttp://cbkb.org/basics/glossary/#cbahttp://cbkb.org/basics/glossary/#cbahttp://cbkb.org/basics/glossary/#cbahttp://cbkb.org/basics/glossary/#directhttp://cbkb.org/basics/glossary/#indirecthttp://cbkb.org/basics/glossary/#indirecthttp://cbkb.org/basics/glossary/#overheadhttp://cbkb.org/basics/glossary/#overheadhttp://cbkb.org/basics/glossary/#overheadhttp://cbkb.org/basics/glossary/#capitalhttp://cbkb.org/basics/glossary/#capitalhttp://cbkb.org/toolkit/types-of-economic-analysis/#knowhttp://cbkb.org/toolkit/types-of-economic-analysis/#knowhttp://cbkb.org/toolkit/types-of-economic-analysis/#knowhttp://cbkb.org/toolkit/types-of-economic-analysis/#knowhttp://cbkb.org/basics/glossary/#capitalhttp://cbkb.org/basics/glossary/#overheadhttp://cbkb.org/basics/glossary/#indirecthttp://cbkb.org/basics/glossary/#directhttp://cbkb.org/basics/glossary/#cbahttp://cbkb.org/basics/glossary/#ceahttp://cbkb.org/basics/glossary/#fiahttp://cbkb.org/basics/glossary/#cost%20analysis


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Program

B $ 7,500,000 1,000 $ 7,500 50% 500 $ 15,000

Note that CEA is a valuable tool for weighing programs or policies with similar outcomes, but it should not be

used to compare programs that have different outcomes.

Cost-benefit analysis

Cost-benefit analysis (CBA) is a method for comparing the economic pros and cons of policies and programs to

help policymakers identify the best or most valuable options to pursue. A characteristic feature of CBA is that it

monetizes,or puts into dollar terms, all the benefits and all the costs associated with an initiative so that they can

be directly compared. Policies and programs whose benefits outweigh their costs generatenet benefits.

In contrast to CEA, CBA allows you to compare initiatives that have different purposessuch as a reduction in

victimization or an improvement in program participants reading scoresbecause the outcomes have been

monetized. In contrast to fiscal impact analysis, CBA evaluates the costs and benefits of programs and policies

from multiple perspectives, not just that of government agencies. For example, when evaluating a crimina

justice program using CBA, the costs and benefits to victims, offenders, program participants, family members

and communities need to be factored in.

Costs and benefits are measured over a long-term horizon, and future dollars are discounted to reflect thetime

value of money, that is, the concept that money is worth more to us in the present than at some point in thefuture. The result of a cost-benefit analysis is typically presented as a benefit-cost ratio that indicates the benefit

received for every dollar invested, providing a bottom-line summary of the net benefit to society.

See Figure 2 for a simple comparison of the kind of information each type of economic analysis can provide.

Figure 2

Type of economic

analysis

Information provided

Cost analysis How much something costs

Fiscal-impact analysis How your budget will be affected

Cost-effectiveness analysis How many outputs you get for yourdollar

Cost-benefit analysis How much benefits outweigh costs

Know your costs

Direct costso Staff salary plus fringe benefits (e.g., health insurance, employers share of social security

workers compensation, unemployment insurance, pension contribution, vacation wages)

o Equipment, such as computers and office supplieso Rent, occupancy, office maintenance, and other space-related costso Training

Indirect costso Executive staffo Central support (e.g., human resources, fiscal, information technology)

Start-up and one-time costs (e.g., furniture, equipment, consultants) Future costs

o Wage increases, including anticipated collective-bargaining settlementso Additional pension contributionso Anticipated health-insurance escalation

Capital expenses
http://cbkb.org/basics/glossary/#monetizehttp://cbkb.org/basics/glossary/#monetizehttp://cbkb.org/basics/glossary/#netbenhttp://cbkb.org/basics/glossary/#netbenhttp://cbkb.org/basics/glossary/#netbenhttp://cbkb.org/toolkit/perspectives/http://cbkb.org/toolkit/perspectives/http://cbkb.org/basics/glossary/#timevaluehttp://cbkb.org/basics/glossary/#timevaluehttp://cbkb.org/basics/glossary/#timevaluehttp://cbkb.org/basics/glossary/#timevaluehttp://cbkb.org/basics/glossary/#timevaluehttp://cbkb.org/basics/glossary/#timevaluehttp://cbkb.org/toolkit/perspectives/http://cbkb.org/basics/glossary/#netbenhttp://cbkb.org/basics/glossary/#monetize


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o Project planning, design, development, and professional serviceso Real estate, materials, and constructiono Contingencyo Debt service

4. EXPLAIN THE TOOLS OF ECONOMIC ANALYSIS.

Opportunity Cost:opportunity cost = the value of the best alternative that is forgone when an item or activity is

chosen

opportunity cost is subjective calculation requires time and information sunk costs need to be considered

Comparative Advantage: absolute advantage versus comparative advantage

results in specialization creates a division of labor leads to exchange (barter)

Production Possibilities: The Production Possibilities Curve the alternative combinations of final goods and services that could be produced in a given time period

with all available resources and technology.

each point on the production possibilities curve depicts an alternative mix of output.the production possibilities curve illustrates two essential principles:

Scarce resourcesthere is a limit to the amount we can produce in a given time period with available

resources and technology.

Opportunity costs We can obtain additional quantities of any desired good only by reducing the

potential production of another good.

Increasing Opportunity Costs

the shape of the production possibilities curve reflects another limitation on our choices. why do opportunity costs increase? because it is difficult to move resources from one industry to

another.

the law of increasing opportunity cost says that we must give up ever-increasing quantities of othergoods and services in order to get more of a particular good.

Efficiency

increasing opportunity costs arent a sign of inefficiency. efficiency means getting the most from what youve got that is, using factors of production in the

most productive way.

maximum output of a good from the resources used in production. theresno guarantee, of course, that well always use resources efficiently. a production possibilities curve shows potential output, not necessarily actual output. if we are inefficient, actual output will be less than the potential output

Economic Growth

an increase in output (real GDP); an expansion of production possibilities. all output combinations that lie outside the production possibilities curve are unattainable with available

resources and technology.


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over time, population increases and we get more labor. Also, if we continue building factories andmachinery, the stock of available capital will also increase.

the quality of labor and capital can also increase if we train workers and pursue new technologies.5. EXPLAIN ANNUAL EQUIVALENT METHOD.

In the annual equivalent method of comparison, first the annual equivalent cost or the revenue of eachalternative will be computed. Then the alternative with the maximum annual equivalent revenue in the case of

revenue-based comparison or with the minimum annual equivalent cost in the case of cost-based comparisonswill be selected as the best alternative.

Revenue.dominated cash f low diagram?

A generalized revenue-dominated cash flow diagram to demonstrate the annual equivalent method ofcomparison is presented in fig.1.

S

R0 R1 R2 R3 .Rj Rn

0 1 2 3 .j n

P

Fig.1.1. Revenue-dominated cash flow diagram.

In the above cash flow diagram,o Pis an initial investmento Rjis the net revenue at the end of the jth yearo Sis the salvage value at the end of the nth year.

The first step is to find the net present worth of the cash flow diagram using the following expression at a giveninterest rate, i.

PW(i) = - P + R1 / (1+i)1

+R2 / (1+i)2+Rj / (1+i)

j++Rn/(1+i)

n+ S/(1+i)

n

In the above formula, the expenditure is assigned with a negative sign and the revenues are assigned with a

positive sign.

In the second step, the annual equivalent revenue is computed using the following formula:

i(1+i)n

A = PW(i) = PW(i) (A/P, i, n)

(1+i) n-1

Where (A/P, i, n) is called equal payment series capital recovery factor.

If we have some more alternatives which are to be compared with this alternative, then the corresponding

annual equivalent revenues are to be computed and compared. Finally, the alternative with the maximum annual

equivalent revenue should be selected as the best alternative.

Cost-dominated cash flow diagram

A generalized cost-dominated cash flow diagram to demonstrate the annual equivalent method of comparison is

illustrated in fig.1.2.


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S

0 1 2 .j . .

. . n

C0 C1 C2 .Cj Cn

P

Fig.1.2. Cost-dominated cash flow diagram.

In fig 1.2, P represents an initial investment, Cj the net cost of operation and maintenance at the end of the jth

year, and S the salvage value at the end of the nth year.

The first step is to find the net present worth of the cash flow diagram using the following relation for a

given interest rate, i.

PW(i) = P + C1 / (1+i)1

+C2 / (1+i)2+Cj / (1+i)

j++Cn/(1+i)

n- S/(1+i)

n

In the above formula, each expenditure is assigned with positive sign and the salvage value with negative

sign. Then, in the second step, the annual equivalent cost is computed using the following equations:

i(1+i)n

A = PW(i) = PW(i) (A/P, i, n)

(1+i) n-1

Where (A/P, i, n) is called as equal-payment series capital recovery factor.

As in the previous case, if we have some more alternatives which are to be compared with this alternative,

then the corresponding annual equivalent costs are to be computed and compared. Finally, the alternative withthe minimum annual equivalent cost should be selected as best alternative.

If we have some non-standard cash flow diagram, then we have to follow the general procedure for

converting each and every transaction to time zero and then convert the net present worth into annual equivalent

cost/revenue depending on the type of the cash flow diagram. Such procedure is to be applied to all the

alternatives and finally, the best alternative is to be selected.

Al ternative Approach

Instead of first finding the present worth and then figuring out the annual equivalent cost/revenue, an alternative

method which is as explained below can be used. In each of the cases present in sections 1.2 and 1.3, in the first

step, one can find the future worth of the cash flow diagram of each of the alternatives. Then, in the second stepthe annual equivalent cost/revenue can be obtained using the equation:

i

A = F = A(A/F, i, n)

(1+i) n-1

Where (A/F, i, n) is called equal-payment series sinking fund factor.


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Example For Annual Equivalent Method

In this section, the application of the annual equivalent method is demonstrated with several numerical

examples.

Eg:1.

A company provides a car to its chief executive. The owner of the company is concerned about the increasing

cost of petrol. The cost per liter of petrol for the first year of operation is Rs.21. He feels that the cost of petrol

is increasing by re.1 every year. His experience with his company car indicates that it averages 9km per liter of

petrol. The executives expects to drive an averages of 20,000km each year for next four years. What is the

annual equivalent cost of fuel for this period of time?. If he is offered similar service with same quality on rental

basis at Rs.60,000 per year, should the owner continue to provide company car for his executive or alternatively

provide a rental car to his executive? Assume i=18%. If the rental car is preferred, then the company car wil

find some other use within the company.

Solution

Average number of km run/year = 20,000km

Number of km/liter of petrol = 9km

Therefore,

Petrol consumption/year = 20,000/9= 2222.2litre

Cost/litre of petrol for the 1styear = Rs 21

Cost/litre of petrol for the 2ndyear = Rs 21.00 + Re1.00

= Rs 22.00

Cost/litre of petrol for the 3rd year = Rs 22.00 + Re1.00

= Rs 23.00

Cost/litre of petrol for the 4thyear = Rs 23+ Re 1.00

= Rs 24.00

Fuel expenditure for 1styear = 2222.2 X 21 = Rs. 46,666.20

Fuel expenditure for 2nd year = 2222.2 X 22 = Rs. 48,888.40Fuel expenditure for 3rd year = 2222.2 X 23 = Rs. 51,110.60

Fuel expenditure for 4th year = 2222.2 X 24 = Rs. 53,332.80

The annual equal increment of the above expenditures in Rs.2,222.20

0 1 2 3 4

A1

A1+G

A1+2G

A1+3G

Fig 1.3.uniform gradient series cash flow diagram

In fig 1.3, A1 = Rs. 46,666.20 and G = Rs.2222.20

A = AI+G(A/G, 18%, 4)

= 46,666,20 + 2222.2(1.2947)

= Rs.49,543.28


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The proposal of using the company car by spending for petrol by the company will cost an annual equivalent

amont of Rs 49,543.28 for four years. This amount is less than the annual rental value of Rs.60,000. Therefore

the company should continue to provide its own car to its executive.

6. EXPLAIN RATE OF RETURN METHOD.

The rate of return of a cash flow pattern is the interest rate at which the present worth of that cash flow pattern

reduces to zero. In this method of comparison, the rate of return for each alternative is computed. Then the

alternative which has the highest rate of return is selected as the best alternative.

In this type of analysis, the expenditures are always assigned with a negative sign and the

revenues/inflows are assigned with a positive sign.

A generalized cash flow diagram to demonstrate the rate of return method of comparison is presented in

fig2.1.

S

R0 R1 R2 R3 Rj Rn

0 1 2 3 .j n

P

Fig.1.1. generalized cash flow diagram.

In the above cash flow diagram, P - represents an initial investment, Rj - the net revenue at the end of the jth year S - the salvage value at the end of the nth year.

The first step is to find the net present worth of the cash flow diagram using the following expression at agiveintrest rate, i.

PW(i) = - P + R1 / (1+i)1

+R2 / (1+i)2+Rj / (1+i)

j++Rn/(1+i)

n+ S/(1+i)

n

Now, the above function is to be evaluated for different values of I until the present worth function reducesto zero, as shown in fig.1.2.

In the figure, the present worth goes on decreasing when the interest rate is increased. The value of I atwhich the present worth curve cuts the X-axis is the rate of return of the given proposal/project. It will be very

difficult to find the exact value of i at which the present worth function reduces to zero.

PositiveRate of Return

Present worthPW(i)


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0 2 4 6 8 10 12 14 16 18 . .

Negative interest rate(i%)

Fig.2.2present worth function graph

So, one has to start with an intuitive value of I and check whether the present worth function is positive.

If so, increase the value of I until PW(i) becomes negative. Then, the rate of return is determined byinterpolation method in the range of values of I for which the sign of the present worth function changes from

positive to negative.

ADVANTAGES AND DI SADVANTAGES OF RATE OF RETURN METHOD:

Advantages:

1. Accounting rate of return is simple and straightforward to compute.2. Likepayback period,this method of investment appraisal is easy to calculate.3. It recognizes the profitability factor of investment.4. It focuses on accounting net operating income. Creditors and investors use accounting net operating

income to evaluate the performance of management.

Disadvantages:

1. Accounting rate of return method does not take into account the time value of money. Under this methoda dollar in hand and a dollar to be received in future are considered of equal value.

2. Cash is very important for every business. If an investment quickly generates cash inflow, the companycan invest in other profitable projects. But accounting rate of return method focus on accounting net

operating income rather than cash flow.

3. The accounting rate of return does not remain constant over useful life for many pro4. It ignorestime value of money.Suppose, if we use ARR to compare two projects having equal initia

investments. The project which has higher annual income in the latter years of its useful life may rankhigher than the one having higher annual income in the beginning years, even if the present value of the

income generated by the latter project is higher.

5. It can be calculated in different ways. Thus there is problem of consistency.6. It uses accounting income rather than cash flow information. Thus it is not suitable for projects which

having high maintenance costs because their viability also depends upon timely cash inflows.

TYPES OF RATE OF RETURN METHOD

PAYBACK PERIOD METHOD

Payback period is the time in which the initial cash outflow of an investment is expected to be recovered from

the cash inflows generated by the investment. It is one of the simplest investment appraisal techniques.

Formula

The formula to calculate payback period of a project depends on whether the cash flow per period from the

project is even or uneven. In case they are even, the formula to calculate payback period is:

Payback Period =Initial Investment

Cash Inflow per Period

When cash inflows are uneven, we need to calculate the cumulative net cash flow for each period and then use

the following formula for payback period:
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Payback Period = A +B

C

In the above formula,

Ais the last period with a negative cumulative cash flow;

Bis the absolute value of cumulative cash flow at the end of the period A;

Cis the total cash flow during the period after A

Both of the above situations are applied in the following examples.

Decision Rule

Accept the project only if its payback period is LESS than the target payback period.

Examples

Example 1: Even Cash Flows

Company C is planning to undertake a project requiring initial investment of $105 million. The project is

expected to generate $25 million per year for 7 years. Calculate the payback period of the project.

Solution

Payback Period = Initial Investment Annual Cash Flow = $105M $25M = 4.2 years

Example 2: Uneven Cash Flows

Company C is planning to undertake another project requiring initial investment of $50 million and is expected

to generate $10 million in Year 1, $13 million in Year 2, $16 million in year 3, $19 million in Year 4 and $22

million in Year 5. Calculate the payback value of the project.

Solution (cash flows in millions) Cumulative

Cash FlowYear Cash Flow

0 (50) (50)

1 10 (40)

2 13 (27)

3 16 (11)

4 19 8

5 22 30

Payback Period

= 3 + (|-$11M| $19M)

= 3 + ($11M $19M)

3 + 0.58

3.58 years

Advantages of payback period are:

1. Payback period is very simple to calculate.


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2. It can be a measure of risk inherent in a project. Since cash flows that occur later in a project's life areconsidered more uncertain, payback period provides an indication of how certain the project cash

inflows are.

3. For companies facing liquidity problems, it provides a good ranking of projects that would return moneyearly.

Disadvantages of payback period are:

1. Payback period does not take into account thetime value of money which is a serious drawback since itcan lead to wrong decisions. A variation of payback method that attempts to remove this drawback is

calleddiscounted payback period method.

2. It does not take into account, the cash flows that occur after the payback period.ACCOUNTING RATE OF RETURN

The accounting rate of return has two different formulas that can be used to derive the return of the project. The

first formula is the following:

expressed as a percentage and where:

Average Annual Profit is the annual cash inflow that the project will generate after deductingdepreciation.

Initial Investment is the capital expenditure that is required to undertake the project.For the second formula, the initial investment will need to be replaced by the average investment. Therefore, the

accounting rate of return becomes:

expressed as a percentage and where:

Average Investment is the capital expenditure that is required to undertake the project plus the finalscrap value of the machinery divided by two.

Accounting Rate of Return example

Example: A company is trying to decide whether is should accept a project with the following details: The initial capital expenditure requirements are $100,000 for a machine that will have a five years useful

life.

Depreciation is calculated on a straight line basis. The scrap value of the machine is $10,000 The project is expected to have $30,000 profit

Using the first way to calculate the accounting rate of return, depreciation can be calculated as:

or ($100,000-$10,000)/5=$18,000. Therefore, the annual profit is $30,000-$18,000=$12,000. The accounting

rate of return can be therefore calculated as (12,000/100,000)%=12%

Using the second formula (the average investment method), the annual profit will be the same but the

denominator will be:

or: (100,000 + 10,000)/2=55,000. Therefore, the accounting rate of return will be:

12,000/55,000=21.8%.

Advantages of accounting rate of return

The advantages of the accounting rate of return as follows:

ARR offers a straightforward way to calculate the required return of the project. It offers a certain degree of comparability between projects.
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Disadvantages of accounting rate of return

The disadvantages of the accounting rate of return are as follows:

It does not take into account the time value of money or in other words it does not recognize that $1 nowwill not have the same buying power tomorrow

It can not (or should not) be used as the only way to appraise a project. The net present value should bealso calculated as calculating only the return of a project can give a distorted image when projects that

have significantly different capital expenditure are compared.

It uses accounting figures which can be affected by judgment, accounting policies and non cash items(depreciation).

There are two ways to calculate the accounting rate of return which causes a problem of comparability.INTERNAL RATE OF RETURN METHOD

Internal rate of returnis that method of capital budgeting in which we can calculate IRR and compare it with

cut off rate for selecting any project. It has following advantages and disadvantages. First we will discuss the

advantages of Internal rate of return (IRR)

Advantages of Internal Rate of Return1. Perfect Use of Time Value of Money Theory: Time value of money means interest and it should high

because we are sacrifice of money for specific time. IRR is nothing but shows high interest rate which we

expect from our investment. So, we can say, IRR is the perfect use of time value of money theory

2. All Cash Flows are Equally Important : It is good method of capital budgeting in which we give equal

importance to all the cash flows not earlier or later. We just create its relation with different rate and want to

know where is present value of cash inflow is equal to present value of cash outflow

3. Uniform Ranking: There is no base for selecting any particular rate in internal rate of return.

4. Maximum profitability of Shareholder: If there is only project which we have to select, if we check its IRR

and it is higher than its cut off rate, then it will give maximum profitability to shareholder

5. Not Need to Calculate Cost of Capital: In this method, we need not to calculate cost of capital because

without calculating cost of capital, we can check the profitability capability of any project.

Disadvantages of I nternal Rate of Retur n:

1. To understand IRR is difficult: It is difficult to understand it because many student can not understand why

are calculating different rate in it and it becomes more difficult when real value of IRR will be two experimental

rate because of not equalize present value of cash inflow with present value of cash outflow

2. Unrealistic Assumption: For calculating IRR we create one assumption. We think that if we invest out

money on this IRR, after receiving profit, we can easily reinvest our investments profit on same IRR. We seem

to be unrealistic assumption.

3. Not Helpful for comparing two mutually exclusive investment: IRR is not good for comparing two projec
http://www.svtuition.org/2010/03/internal-rate-of-return.htmlhttp://www.svtuition.org/2010/03/internal-rate-of-return.htmlhttp://www.svtuition.org/2010/03/internal-rate-of-return.htmlhttp://www.svtuition.org/2010/03/internal-rate-of-return.htmlhttp://www.svtuition.org/2010/03/internal-rate-of-return.htmlhttp://www.svtuition.org/2010/05/time-value-of-money.htmlhttp://www.svtuition.org/2010/05/time-value-of-money.htmlhttp://www.svtuition.org/2009/06/capital-budgeting-and-its-importance.htmlhttp://www.svtuition.org/2009/06/capital-budgeting-and-its-importance.htmlhttp://www.svtuition.org/2010/03/present-value.htmlhttp://www.svtuition.org/2010/03/cut-off-rate.htmlhttp://www.svtuition.org/2010/03/cut-off-rate.htmlhttp://www.svtuition.org/2009/06/cost-of-capital-and-methods-of.htmlhttp://www.svtuition.org/2009/06/cost-of-capital-and-methods-of.htmlhttp://www.svtuition.org/2009/06/cost-of-capital-and-methods-of.htmlhttp://www.svtuition.org/2010/03/cut-off-rate.htmlhttp://www.svtuition.org/2010/03/present-value.htmlhttp://www.svtuition.org/2009/06/capital-budgeting-and-its-importance.htmlhttp://www.svtuition.org/2010/05/time-value-of-money.htmlhttp://www.svtuition.org/2010/03/internal-rate-of-return.htmlhttp://www.svtuition.org/2010/03/internal-rate-of-return.html


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Example

EXAMPLES

In this section the concept of rate of return calculation is demonstrated with suitable examples.

Eg:1

A person is planning a new business. The initial outlay and cash flow pattern for the new business are listed

below. The expected life of the business is five years. Find the rate of return for the new business.

Period 0 1 2 3 4 5Cash flow(Rs) 1,00,000 30,000 30,000 30,000 30,000 30,000

Solution:

Initial investment = Rs 1,00,000 Annual equal revenue = Rs 30,000 Life = 5 years

The cash flow diagram for this situation is illustrated in fig 2.3

30,000 30,000 30,000 30,000 30,000

0 1 2 3 4 5

1,00,000

Fig.2.3. cash flow diagram

The present worth function for the business is

PW(i) = -1,00,000+30,000(P/A, i ,5)

When i=10%,
http://3.bp.blogspot.com/_DJEIRrK4tl4/S-FaCtT1rRI/AAAAAAAAFK0/aLEwjgfsbqQ/s1600/IRR+is+bad.PNG


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PW(10%) = -1,00,000+30,000(P/A, 10, 5)

= -1,00,000+30,000(3.7908)

= Rs 13,724.

When i=15%,

PW(10%) = -1,00,000+30,000(P/A, 15, 5)

= -1,00,000+30,000(3.3522)

= Rs 566.

When i=18%,

PW(18%) = -1,00,000+30,000(P/A, 18, 5)

= -1,00,000+30,000(3.1272)

= Rs -6,184.

i = 15% + 566-0 x (3%)

566-(-6184)

= 15%+0.252%

= 15.252%

Therefore, the rate of return for the new business is 15.252%.

7. EXPLAIN PRESENT WORTH METHOD.

In this method of comparison, the cash flows of each flow will be reduced to time zero by assuming an

interest rate i. Then depending on the type of decision, the best alternative will be selected by comparing the

present worth amounts of the alternatives. The sign of various amounts at different points in time in a cash flow

diagram is to be decided based on the type of the decision problem.

In a cost dominated cash flow diagram, the cost will be assigned with positive sign and the profits

revenue, salvage value (all inflows), etc will be assigned with negative sign. In a revenue/profit dominated cash

flow diagram, the cost will be assigned with negative sign and the profits, revenue, salvage value (all inflows),

etc will be assigned with positive sign.

In case the decision is to select the alternative with the minimum cost, then the alternative with the least

present worth amount will be selected. On the other hand if the decision is to select the alternative with the

maximum cost, then the alternative with the maximum present worth amount will be selected.

Revenue- dominated cash f low diagram

A generalized revenue-dominated cash flow diagram to demonstrate the present worth method of

comparison is presented in figure1.

S

R1 R2 R3 .Rj Rn

0 1 2 3 .j n

P

Fig: 1 Revenue-dominated cash flow diagram

In the above figure, P represents an initial investment and Rj the net revenue at the end of the j thyear

The interest rate is i, compounded annually. S is the salvage value at the end of the n thyear. To find the present

worth of the above cash flow diagram for a given interest rate, the formula is


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PW(i) = -P+R1[1/(1+i)1]+ R2[1/(1+i)

2]+.+R

j[1/(1+i)

j]+Rn[1/(1+i)

n]+S[1+(1+i)

n]

In this formula, expenditure is assigned a negative sign and revenues are assigned a positive sign. If we

have some more alternatives which are to be compared with this alternative, then the corresponding present

worth amounts are to be computed and compared. Finally, the alternative with the maximum present worth

amount should be selected as the best alternative.

Cost- Dominated Cash F low Diagram

A generalized cost-dominated cash flow diagram to demonstrate the present worth method of

comparison is presented in figure1. n

0 1 2 .j . .

P

C1 C2 .Cj

Cn

Fig: 1 Cost-dominated cash flow diagram

In the above figure, P represents an initial investment and Cj the net cost of operation and maintenance at the

end of the jthyear. S is the salvage value at the end of the nthyear. To find the present worth amount of the

above cash flow diagram for a given interest rate i, the formula is

PW(i) = P+C1[1/(1+i)1]+ C2[1/(1+i)

2]+.+Cj[1/(1+i)

j]+Cn[1/(1+i)

n]-S[1+(1+i)

n]

In this formula, expenditure is assigned a positive sign and revenues are assigned a negative sign. If wehave some more alternatives which are to be compared with this alternative, then the corresponding present

worth amounts are to be computed and compared. Finally, the alternative with the minimum present worth


8. EXPLAIN FUTURE WORTH METHOD.

In the future worth method of comparison of alternatives, the future worth of various alternatives will be

computed. Then, the alternative with the maximum future worth of net revenue or with the minimum future

worth of net cost will be selected as the best alternative for implementation.

Revenue- dominated cash f low diagram.

A generalized revenue-dominated cash flow diagram to demonstrate the future worth method of


S

R1 R2 R3 .Rj Rn

0 1 2 3 .j n


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P

Fig: 1 Revenue-dominated cash flow diagram

In the above figure, P represents an initial investment and Rj the net revenue at the end of the j thyear. S

is the salvage value at the end of the nthyear. To find the future worth of the above cash flow diagram for a

given interest rate i, the formula is

FW(i) = -P(1+i)n]+ R1[1/(1+i)

n-1]+R2[1/(1+i)

n]+.+Rj[1/(1+i)

n-j]++Rn+S

In this formula, expenditure is assigned a negative sign and revenues are assigned a positive sign. If we

have some more alternatives which are to be compared with this alternative, then the corresponding future

worth amounts are to be computed and compared. Finally, the alternative with the maximum future worth


Cost- dominated cash fl ow diagram:

A generalized cost-dominated cash flow diagram to demonstrate the present worth method of


S

0 1 2 .j . . n

P C1 C2 .Cj Cn

Fig: 1 Cost-dominated cash flow diagram

In the above figure, P represents an initial investment and Cj the net cost of operation and maintenance

at the end of the jthyear. S is the salvage value at the end of the n thyear. To find the future worth amount of the

above cash flow diagram for a given interest rate i, the formula isFW(i) = P(1+i)

n+C1(1+i)

n-1]+ C2(1+i)

n-2+.+Cj(1+i)

n-j]++Cn-S

In this formula, expenditure is assigned a positive sign and revenues are assigned a negative sign. If we

have some more alternatives which are to be compared with this alternative, then the corresponding future

worth amounts are to be computed and compared. Finally, the alternative with the minimum future worth


9. EXPLAIN INTEREST FORMULAS AND THEIR APPLICATIONS

In most cases, when you borrow money the lender charges you some form of interest. There are four different

types of interest:

flat charge simple interest complex interest compound interest

Below we explain the way each of the interests work including compound interest formula, as well as the

formulas for calculating other interest types.


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Flat charge

The lender simply charges you a set fee to borrow money. This form of interest is almost never used today

although it is not uncommon for financial institutions to charge an administration or set-up fee when you

borrow money.

Simple interest

E.g. Simple interest is calculated by multiplying the amount of your debt by the interest rate. This form of

interest is often charged by family or friends and not by financial institutions. It isnt effected by the repayment

period. Its a fairly straight forward calculation.

E.g. If you borrow $5,000 at 10 % simple interest then you would repay $5,500 ($5,000 plus $500 (10 % of

$5,000).

Complex interest

Complex interest is calculated by multiplying the amount of debt outstanding by the interest rate. The difference

here is that the interest rate is applied to the debt at a specific point in time and the amount you pay will depend

on the amount of your original loan that remains outstanding. Commercial lenders (banks, finance companies

credit cards, etc) charge this type of interest.

If you borrow $5,000 at 10% per annum for 36 months your monthly payment would be $161.34. At the end of

the first month you would owe $41.67 interest ($5,000 x 10% /12 months). At the end of the second month yourloan balance would be $4,880.33 ($5,000 + $41.67 $161.34). Your interest charge for the second month

would be $40.67 ($4,880.33 x 10% / 12 months). By the end of the loan the total interest you would pay is equal

to $808.09.

Compound interest

Compound interest is the interest charged on any unpaid interest. This is the most expensive type of interest of

all. Commercial lenders (banks, finance companies, credit cards, etc) charge this type of interest. The following

example explains how to use compound interest formula to calculate the total cost of borrowing if interest is

calculated as compound interest.

E.g. Use the same example as above, except you dont make any payments for 6 months. At the end of the first

month you would owe $5,041.67 ($5,000 plus unpaid interest of $41.67). At the end of the second month youwould owe $5,083.68 ($5,000 plus $41.67 plus $42.01 interest). In the second month you paid $0.34 interest on

the unpaid interest from the first month. At the end of 6 months you will owe $5,255.26 ($5,000 you borrowed

plus unpaid interest of $255.26). The total cost of borrowing with compound interest, if you then made

payments for 36 months, would be $849.35.

There could be a significant difference in your total cost of borrowing depending on whether compound interes

formulaor some other type of interest calculation is used. Make certain that you know what rate and what type

of interest you are being charged on your debtstake interest in the interest you pay!

(UNIT I I COMPLETED)

11 MARKS UNIVERSITY QUESTIONS

1. Explain the usesfulness of economic analysis. (Dec 2012) (Refer P.No. )2. Explain the basic economic analysis method. (Dec 2012) / (April 2012)(Refer P.No. 11)3. Explain interest formula and their applications. (April 2012)(Refer P.No. 11)4. Explain the objectives of economic analysis and the types of rate of return method.

(April 2010)(Refer P.No. 10 & 19)

5. Explain the advantages of rate of return method and compare present and future method.


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(April 2010) (Refer P.No. 20, 21, 22)

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