# ENGINEERING ECONOMICS AND MANAGEMENT BOOK PDF

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Course G ENGINEERING ECONOMIC AND MANAGEMENT To include in his analytical framework economic concepts as inflation, TEXTBOOK. Financial Management. Time period: assets, liability, and the double entry book keeping. The project is within the topic Engineering Economics and. Engineering Economics and Management is the textbook which covers complete syllabus of the subject for the Gujarat Technological University (GTU) students.

Skip to main content. Log In Sign Up. Engineering Economics by Panneer Selvam. Wajeeh Rehman. Engineering Economics R. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher.

If there is an advancement in technology used in the manufacture of the product in the long run, there will be a reduction in the production cost per unit. This will enable the manufacturer to have a greater profit margin per unit at the prevailing price of the product. Hence, the producer will be tempted to supply more quantity to the market.

Weather also has a direct bearing on the supply of products. For example, demand for woollen products will increase during winter. This means the prices of woollen goods will be incresed in winter. So, naturally, manufacturers will supply more volume of woollen goods during winter.

If the price of TV sets is lowered significantly, then its demand would naturally go up. As a result, the demand for associated products like VCDs would also go up. Engineering is the application of science.

It establishes varied application systems based on different scientific principles. From the discussions in the previous section, it is clear that price has a major role in deciding the demand and supply of a product.

The following section discusses the different types of efficiency and their impact on the operation of businesses and the definition and scope of engineering economics. The efficiency can be classified into technical efficiency and economic efficiency. Technical efficiency It is the ratio of the output to input of a physical system. The physical system may be a diesel engine, a machine working in a shop floor, a furnace, etc.

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This is mainly due to frictional loss and incomplete combustion of fuel, which are considered to be unavoidable phenomena in the working of a diesel engine. Economic efficiency Economic efficiency is the ratio of output to input of a business system. There are several ways of improving productivity. Increased output for the same input. In this strategy, the output is increased while keeping the input constant. Let us assume that in a steel plant, the layout of the existing facilities is not proper.

By slightly altering the location of the billet-making section, and bringing it closer to the furnace which produces hot metal, the scale formation at the top of ladles will be considerably reduced. The molten metal is usually carried in ladles to the billet-making section. In the long run, this would give more yield in terms of tonnes of billet produced. In this exercise, there is no extra cost involved. The only task is the relocation of the billet-making facility which involves an insignificant cost.

Decreased input for the same output. In this strategy, the input is decreased to produce the same output. Let us assume that there exists a substitute raw material to manufacture a product and it is available at a lower price. If we can identify such a material and use it for manufacturing the product, then certainly it will reduce the input. In this exercise, the job of the purchase department is to identify an alternate substitute material. The process of identification does not involve any extra cost.

So, the productivity ratio will increase because of the decreased input by way of using cheaper raw materials to produce the same output. Less proportionate increase in output is more than that of the input. Consider the example of introducing a new product into the existing product mix of an organization.

If we examine these two increases closely, the proportionate increase in the revenue will be more than the proportionate increase in the input cost. Hence, there will be a net increase in the productivity ratio. When proportionate decrease in input is more than that of the output. Let us consider the converse of the previous example, i. This will result in the following: Simultaneous increase in output and decrease in input. Let us assume that there are advanced automated technologies like robots and automated guided vehicle system AGVS , available in the market which can be employed in the organization we are interested in.

If we employ these modern tools, then: Initially, the cost on equipment would be very high. But, in the long run, the reduction in the operation cost would break-even the high initial investment and offer more savings on the input. The increased production will yield more revenue. In this example, in the long run, there is an increase in the revenue and a decrease in the input.

Hence, the productivity ratio will increase at a faster rate. In the process of managing organizations, the managers at different levels should take appropriate economic decisions which will help in minimizing investment, operating and maintenance expenditures besides increasing the revenue, savings and other related gains of the organization. Introduction 7 Scope The issues that are covered in this book are elementary economic analysis, interest formulae, bases for comparing alternatives, present worth method, future worth method, annual equivalent method, rate of return method, replacement analysis, depreciation, evaluation of public alternatives, inflation adjusted investment decisions, make or buy decisions, inventory control, project management, value engineering, and linear programming.

Variable cost varies with the volume of production while overhead cost is fixed, irrespective of the production volume. Variable cost can be further classified into direct material cost, direct labour cost, and direct expenses. The overhead cost can be classified into factory overhead, administration overhead, selling overhead, and distribution overhead.

Direct material costs are those costs of materials that are used to produce the product. Direct labour cost is the amount of wages paid to the direct labour involved in the production activities. Direct expenses are those expenses that vary in relation to the production volume, other than the direct material costs and direct labour costs.

Overhead cost is the aggregate of indirect material costs, indirect labour costs and indirect expenses. Administration overhead includes all the costs that are incurred in administering the business. Selling overhead is the total expense that is incurred in the promotional activities and the expenses relating to sales force. Distribution overhead is the total cost of shipping the items from the factory site to the customer sites. The selling price of a product is derived as shown below: Let the cost of producing 20 units of a product be Rs.

Then the marginal cost of producing the 21st unit is Rs. Let, the revenue of selling 20 units of a product be Rs. Then, the marginal revenue of selling the 21st unit is Rs.

Let us assume that an equipment has been purchased for Rs. If it is considered for replacement, then its present value is not Rs. Instead, its present market value should be taken as the present value of the equipment for further analysis. So, the purchase value of the equipment in the past is known as its sunk cost. The sunk cost should not be considered for any analysis done from nowonwards. If the same money is invested in some other alternative Y , it may fetch some return.

Since the money is invested in the selected alternative X , one has to forego the return from the other alternative Y. The amount that is foregone by not investing in the other alternative Y is known as the opportunity cost of the selected alternative X.

So the opportunity cost of an alternative is the return that will be foregone by not investing the same money in another alternative. Consider that a person has invested a sum of Rs. Let the expected annual return by this alternative be Rs. Then, the corresponding total return per year for the investment in the bank is Rs. This return is greater than the return from shares. The foregone excess return of Rs. The corresponding volume of production on the X-axis is known as the break-even sales quantity.

At the intersection point, the total cost is equal to the total revenue. This point is also called the no-loss or no-gain situation. For any production quantity which is less than the break-even quantity, the total cost is more than the total revenue.

Hence, the firm will be making loss. Hence, the firm will be making profit. The margin of safety M. Profit M. Define economics. Also discuss the flow of goods, services, resources and money payments in a simple economy with the help of a suitable diagram. Illustrate the effect of price on demand and supply; illustrate with the help of a diagram. Discuss the factors which influence demand and supply. Distinguish between technical efficiency and economic efficiency by giving examples.

What are the ways by which the economic efficiency can be improved? Give the definition and scope of engineering economics. Clearly explain the method of deriving the selling price of a product. Define the following costs with examples: Define break-even point. Draw a break-even chart and explain its components. Krishna Company Ltd. Consider the following data of a company for the year One can manage many of these decision problems by using simple economic analysis.

For example, an industry can source its raw materials from a nearby place or from a far-off place. In this problem, the following factors will affect the decision: This would certainly add cost to the product. On the other hand, consider another alternative of sourcing the raw materials from a far-off place with the following characteristics: Under such a situation, the procurement of the raw material should be decided in such a way that the overall cost is minimized.

Among various elements of cost, raw material cost is most significant and it forms a major portion of the total cost of any product. So, any attempt to find a suitable raw material will bring a reduction in the total cost in any one or combinations of the following ways: In this process, if the new raw material provides any additional benefit, then it should be treated as its welcoming feature.

This concept is demonstrated with two numerical problems. Either material will provide equal service, but the aluminium casting will weigh 1. The aluminium can be cast for Rs. The cost of machining per unit is Rs. Every kilogram of excess weight is associated with a penalty of Rs. Which material should be specified and what is the economic advantage of the selection per unit?

Elementary Economic Analysis 17 Solution a Cost of using aluminium metal for the jet engine part: Hence, aluminium is suggested for making the jet engine part. The different materials used to manufacture the tables and their costs are given in Table 2. Table 2. The wooden top therefore could be replaced with a granite top. This would require additional wood for the frame and legs to take the extra weight of the granite top.

The materials and labour requirements along with cost details to manufacture a table with granite top are given in Table 2.

Compute the cost of manufacture of the table under each of the alternatives described above and suggest the best alternative. Also, find the economic advantage of the best alternative. Hence, the table with granite top should be selected by the manufacturer. Design is an important factor which decides the cost of the product for a specified level of performance of that product.

The elementary economic analysis applied to the selection of design for a product is illustrated with two example problems. Either design will serve the purpose and will involve the same material and manufacturing cost except for the lathe and grinder operations. Design A will require 16 hours of lathe time and 4.

Design B will require 7 hours of lathe time and 12 hours of grinder time per 1, units. The operating cost of the lathe including labour is Rs. The operating cost of the grinder including labour is Rs.

Which design should be adopted if 1,00, units are required per year and what is the economic advantage of the best alternative? Hence, design B is recommended for making the tapered fastening pin.

The chief engineer of refinery operations is not satisfied with the preliminary design for storage tanks to be used as part of a plant expansion programme. From a graph of the article, the engineer found that the present ratio of height to diameter of 1. The cost for the tank design as originally submitted was estimated to be Rs. What are the optimum tank dimensions if the volume remains the same as for the original design? What total savings may be expected through the redesign?

Hence, it is assumed that the price of raw material is location dependent. While sourcing a raw material, the cost of transportation is to be considered in conjunction with the price of the raw material. This concept is demonstrated with a numerical example. Either steel or aluminium window frames will satisfy the design criteria. Because of the remote location of the building site and lack of building materials in Alpha State, the window frames will be purchased in Beta State and transported for a distance of 2, km to the site.

The price of window frames of the type required is Rs. The weight of steel window frames is 75 kg each and that of aluminium window frame is 28 kg each. The shipping rate is Re 1 per kg per km. Which design should be specified and what is the economic advantage of the selection?

Hence, aluminium window frame is recommended. The process sequence of a component which has been planned in the past is not static.

It is always subject to modification with a view to minimize the cost of manufacturing the component. The steps in process planning are as follows: Analyze the part drawing to get an overall picture of what is required. Make recommendations to or consult with product engineers on product design changes. List the basic operations required to produce the part to the drawing or specifications.

Determine the most practical and economical manufacturing method and the form or tooling required for each operation. Devise the best way to combine the operations and put them in sequence. Specify the gauging required for the process.

Steps 3—5 aim to determine the most practical and economical sequence of operations to produce a component. This concept is demonstrated with a numerical problem. Solution a Cost of component using process sequence 1. The process sequence 1 of the component is as follows: Turning — Milling — Shaping — Drilling The calculations for the cost of the above process sequence are summarized in Table 2.

The process sequence 2 of the component is as follows: Turning — Milling — Drilling The calculations for the cost of the above process sequence are given in Table 2. The process sequence 3 of the component is as follows: Only CNC operations The calculations for the cost of the above process sequence are summarized in Table 2.

Therefore, it should be selected for manufacturing the component. List and explain the different situations deserving elementary economic analysis. Explain the steps in the process planning. In the design of an aircraft jet engine part, the designer has a choice of specifying either an aluminium alloy casting or a steel casting. Either material will provide equal service, but the aluminium casting will weigh 5 kg as compared with 7 kg for the steel casting. The aluminium part can be cast for Rs.

Two alternatives are under consideration for a hexagonal bolt fastening pin. Either design will serve equally well and will involve the same material and manufacturing cost except for the lathe and grinder operations. Elementary Economic Analysis 25 Design A will require 20 hours of lathe time and 8 hours of grinder time per 10, units.

Design B will require 10 hours of lathe time and 22 hours of grinder time per 10, units. Which design should be adopted if 10,00, units are required per year and what is the economic advantage of the best alternative? A building contractor can source door frames from either a nearby shop or a far-off forest area. The cost details are as summarized in the following table. The total requirement of wood for the construction work is 75 tons.

Also find the economic advantage of the best decision. Consider Example 2. Rework this example if the ratio of the height to diameter corresponding to the minimum cost is 6: The process planning engineer of a firm listed down the sequences of operations, as shown in the following table to produce a component: Sequence Process sequence 1 Turning — Milling — Shaping — Drilling 2 Turning — Milling — Drilling 3 All operations are performed with CNC machine The details of process time for the components for various operations and their machine hour rates are tabulated now.

Operation Machine hour Process sequence rate Rs. It represents the growth of capital per unit period. The period may be a month, a quarter, semiannual or a year. So, the total amount at the end of the first year will be Rs. Hence the total amount at the end of the second year will be Rs. The process will continue thus till the specified number of years.

Table 3. The maturity value at the end of the fifth year is Rs. This means that the amount Rs. This is diagrammatically shown in Fig. This explanation assumes that the inflation is at zero percentage. Alternatively, the above concept may be discussed as follows: If we want Rs.

A detailed working is shown in Table 3. Similarly, if we want Rs. Also, this concept can be stated as follows: A person has received a prize from a finance company during the recent festival contest.

But the prize will be given in either of the following two modes: Spot payment of Rs. If this option is followed, the equivalent amount for Rs. This example clearly demonstrates the time value of money. To simplify all these computations, it is extremely important to know how to use interest formulas more effectively.

Before discussing the effective application of the interest formulas for investment-decision making, the various interest formulas are presented first. Interest rate can be classified into simple interest rate and compound interest rate. In simple interest, the interest is calculated, based on the initial deposit for every interest period.

In this case, calculation of interest on interest is not applicable. In compound interest, the interest for the current period is computed based on the amount principal plus interest up to the end of the previous period at the beginning of the current period.

The notations which are used in various interest formulae are as follows: The cash flow diagram of this situation is shown in Fig. Interest Formulas and Their Applications 29 F. Find the maturity value after 10 years.

The corresponding cash flow diagram is shown in Fig. What is the single-payment that he should deposit now so that he gets the desired amount after 10 years?

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In Fig. He plans to invest an equal sum of Rs. Find the maturity value of his account when he is 60 years old. Find the equivalent amount that must be deposited at the end of every year for the next 15 years.

Find the single-payment that must be made now as the reserve amount. The corresponding cash flow diagram is illustrated in Fig. This amount should be repaid in 15 yearly equal installments. Find the installment amount that the company has to pay to the bank. Find the total amount at the end of the 10th year of the above series.

The cash flow diagram is shown in Fig. The future worth sum of this revised series at the end of the 10th year is obtained as follows: He has 10 more years of service. He would like to deposit Rs. But, in practice, the compounding may occur less than a year.

For example, compounding may be monthly, quarterly, or semi-annually. Compounding monthly means that the interest is computed at the end of every month.

The compounding is quarterly. Find the maturity amount of the deposit after 10 years. Let us assume that an organization has a huge sum of money for potential investment and there are three different projects whose initial outlay and annual revenues during their lives are known. The executive has to select the best alternative among these three competing projects.

Interest Formulas and Their Applications 39 There are several bases for comparing the worthiness of the projects. These bases are: Present worth method 2. Future worth method 3. Annual equivalent method 4. Rate of return method These methods are discussed in detail in Chapters 4—7. Explain the time value of money. Give practical applications of various interest formulas.

A person deposits a sum of Rs. Find the future amount of the deposited money at the time of admitting his son in the professional course. A person needs a sum of Rs.

A person who is just 30 years old is planning for his retired life. A company is planning to expand its business after 5 years from now. The expected money required for the expansion programme is Rs. The company can invest Rs. If not, find the difference in amounts for which the company should make some other arrangement after 5 years.

A financial institution introduces a plan to pay a sum of Rs. Find the annual equivalent amount that a person should invest at the end of every year for the next 10 years to receive Rs.

The money required for the expansion programme is Rs. A company wants to set-up a reserve which will help it to have an annual equivalent amount of Rs. Find the single-payment that must be made as the reserve amount now. An automobile company recently advertised its car for a down payment of Rs. Alternatively, the car can be taken home by customers without making any payment, but they have to pay an equal yearly amount of Rs. Suggest the best alternative to the customers.

A company takes a loan of Rs.

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Find the equal installment amount that should be paid for the next 20 years. A bank gives loan to a company to purchase an equipment which is worth of Rs. This amount should be repaid in 25 yearly equal installments. A working woman is planning for her retired life. She has 20 more years of service. Find the total amount at the end of the 15th year of the above series.

Consider the following cash flow diagram. A person is planning for his retired life. Interest Formulas and Their Applications 41 A person invests a sum of Rs. The compounding is monthly.

Find the maturity amount of the deposit after 15 years. 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 costs outflows will be assigned with positive sign and the profit, revenue, salvage value all inflows , etc.

The costs outflows will be assigned with negative 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 profit, then the alternative with the maximum present worth will be selected. S R1 R2 R3.

The interest rate is i, compounded annually. S is the salvage value at the end of the nth year. 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. Finally, the alternative with the minimum present worth amount should be selected as the best alternative.

It has identified three different technologies for meeting the goal. The initial outlay and annual revenues with respect to each of the technologies are summarized in Table 4.

Table 4. Therefore, technology 2 is suggested for implementation to expand the production. The details of the bids for the elevators are as follows: Alpha Elevator Inc. Solution Bid 1: The cash flow diagram of bid 1 is shown in Fig. The present worth of the above cash flow diagram is computed as follows: Beta Elevator Inc.

Hence, bid 1 is to be selected for implementation. That is, the elevator from Alpha Elevator Inc. Proposal End of years 0 1 2 3 4 A Rs. Which proposal should be selected? The cash flow diagram of proposal A is shown in Fig.

The cash flow diagram of the proposal B is shown in Fig. Therefore, select proposal B. If it is purchased under down payment, the cost of the machine is Rs. Solution There are two alternatives available for the company: Down payment of Rs. The cash flow diagram of the second alternative is shown in Fig. Hence, the company should select the second alternative to buy the fully automated granite cutting machine. In plan 1, the company pays Rs. In plan 2, for every Rs.

Solution Plan 1. The cash flow diagram for plan 1 is illustrated in Fig. The cash flow diagram for plan 2 is shown in Fig. Innovative Investment Ltd. Which is the best investment alternative? At the end of the life of the business, the salvage value is zero.

A project involves an initial outlay of Rs. The salvage value at the end of the life of the project after five years is Rs. End Maintenance and Revenue of year operating expense Rs. Find the present worth of the following cash flow series. Consider the following cash flow series over a year period. End of year Cash flow Rs. The cost of erecting an oil well is Rs. The annual equivalent yield from the oil well is Rs. The salvage value after its useful life of 10 years is Rs. The details of the feasibility report of a project are as shown below.

You are asked to advise the best alternative for the customers based on the present worth method of comparison.

The cash flows of two project proposals are as given below. Each of the project has an expected life of 10 years. Initial Annual Salvage outlay equivalent value after revenue 10 years Rs. Project 1 —7,50, 2,00, 50, Project 2 —9,50, 2,25, 1,00, 9. A company has two alternatives for satisfying its daily travel requirements of its employees for the next five years: Renting a vehicle at a cost of Rs.

Alternative 2: Buying a vehicle for Rs. The salvage value of the vehicle after five years is Rs. She would like to have an annual equivalent amount of Rs. Find the single amount that should be deposited now so that she receives the above mentioned annual equivalent amount at the end of every year for 20 years after her retirement.

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. Finally, the alternative with the maximum future worth amount should be selected as the best alternative.

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 amount should be selected as the best alternative. End of year Alternative 0 1 2 3 4 A Rs. Thus, alternative A should be selected. He must decide which of the several alternatives to select in trying to obtain a desirable return on his investment. After much study and calculation, he decides that the two best alternatives are as given in the following table: Build Build soft gas station ice-cream stand First cost Rs.

Thus, building the gas station is the best alternative. Therefore, alternative 2 must be selected. Thus, none of the two alternatives should be selected. It has received tenders from three different original manufacturers of annealing furnace. The details are as follows. Manufacturer 1 2 3 Initial cost Rs. Krishna castings should buy the annealing furnace from manufacturer 2. Use future worth method of comparison. The cash flow diagram of machine A is given in Fig. The future worth function of Fig.

The cash flow diagram of the machine B is illustrated in Fig. The future worth function of Fig 5. Therefore, machine A should be selected. A suburban taxi company is considering buying taxis with diesel engines instead of petrol engines. The cars average 50, km a year, with a useful life of three years for the taxi with the petrol engine and four years for the diesel taxi.

Other comparative information are as follows: Diesel Petrol Vehicle cost Rs. A motorcycle is sold for Rs. The motorcycle dealer is willing to sell it on the following terms: Consider the following two mutually exclusive alternatives. A B Cost Rs. A company must decide whether to buy machine A or machine B: Use the future worth method of comparison.

Due to increasing awareness of customers, two different television manufacturing companies started a marketing war. The details of advertisements of the companies are as follows: Alpha Finance Company is coming with an option of accepting Rs.

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Beta Finance Company is coming with a similar option of accepting Rs. An insurance company gives an endowment policy for a person aged 30 years. The yearly premium for an insured sum of Rs. The policy will mature after 25 years. Also, the person is entitled for a bonus of Rs. If a person survives till the end of the 25th year: 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 comparison will be selected as the best alternative.

The first step is to find the net present worth of the cash flow diagram using the following expression for a given interest rate, i: 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. 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. Then, in the second step, the annual equivalent cost is computed using the following equation: Finally, the alternative with the minimum annual equivalent cost should be selected as the best alternative.

Such procedure is to be applied to all the alternatives and finally, the best alternative is to be selected. In each of the cases presented in Sections 6. The owner of the company is concerned about the increasing cost of petrol. The cost per litre of petrol for the first year of operation is Rs. He feels that the cost of petrol will be increasing by Re. His experience with his company car indicates that it averages 9 km per litre of petrol. The executive expects to drive an average of 20, km each year for the next four years.

What is the annual equivalent cost of fuel over this period of time?. If he is offered similar service with the same quality on rental basis at Rs. If the rental car is preferred, then the company car will find some other use within the company.

The cash flow diagram for this situation is depicted in Fig. This amount is less than the annual rental value of Rs. Therefore, the company should continue to provide its own car to its executive. Three original manufacturers have responded to its tender whose particulars are tabulated as follows: Manufacturer Down payment Yearly equal No.

The annual equivalent cost of manufacturer 3 is less than that of manufacturer 1 and manufacturer 2. Therefore, the company should buy the advanced machine centre from manufacturer 3. The life of both alternatives is estimated to be 5 years with the following investments, annual returns and salvage values.

Alternative A B Investment Rs. The annual equivalent revenue expression of the above cash flow diagram is as follows: Thus, the company should select alternative B. The following data are to be used in the analysis: Base your answer on annual equivalent cost. The cash flow diagram of machine X is illustrated in Fig.

The cash flow diagram of machine Y is depicted in Fig. So, machine X is the more cost effective machine.

Data on the routes are as follows: Around the lake Under the lake Length 15 km 5 km First cost Rs. Therefore, select the route around the lake for laying the power line.

The cars average 60, km a year with a useful life of three years for the petrol taxi and four years for the diesel taxi. Other comparative details are as follows: Therefore, the taxi company should buy cars with diesel engine. Comparison is done on common multiple lives of 12 years. The company will reimburse their salesman each month the fuel cost and maintenance cost. Ramu has decided to drive a low-priced automobile. He finds, however, that there are two different ways of obtaining the automobile.

In either case, the fuel cost and maintenance cost are borne by the company. The monthly charge is Rs. At the end of the three-year period, the car is returned to the leasing company.

If the car could be sold for Rs. The monthly equivalent cost of alternative 1 is less than that of alternative 2. Hence, the salesman should purchase the car for cash.

She estimates that it will have a five year useful life and no salvage value at the end of equipment life. The dealer, who is a friend has offered Jothi Lakshimi two alternative ways to pay for the equipment.

Hence, Jothi Lakshimi should select alternative 2 for purchasing the home equipment. Brand Tyre warranty Price per tyre months Rs. This is months. The annual equivalent cost of brand C is less than that of other brands.

Hence, it should be used in the vehicles of the trucking company. It should be replaced four times during the month period. A company has three proposals for expanding its business operations. The details are as follows: Alternative Initial cost Annual revenue Life Rs. An automobile dealer has recently advertised for its new car.

There are three alternatives of purchasing the car which are explained below. Alternative 1 The customer can take delivery of a car after making a down payment of Rs. The remaining money should be paid in 36 equal monthly installments of Rs. Alternative 3 The customer can take delivery of the car by making full payment of Rs. Use the annual equivalent method. A small-scale industry is in the process of buying a milling machine. The purchase value of the milling machine is Rs. It has identified two banks for loan to purchase the milling machine.

In Urban Bank, the loan is to be repaid in 60 equal monthly installments of Rs. In State Bank, the loan is to be repaid in 40 equal monthly installments of Rs. Suggest the most economical loan scheme for the company, based on the annual equivalent method of comparison. There are two alternatives of replacing a machine. The details of the alternatives are as follows: Alternative 1 Purchase value of the new machine: A company receives two options for purchasing a copier machine for its office.

Option 1 Make a down payment of Rs. The remaining money is to be paid in 24 equal monthly installments of Rs. Find the best alternative using the annual equivalent method of comparison. 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. A generalized cash flow diagram to demonstrate the rate of return method of comparison is presented in Fig. Rj Rn 0. In the above cash flow diagram, P represents an initial investment, Rj the net revenue 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 expression at a given interest rate, i.

In the figure, the present worth goes on decreasing when the interest rate is increased.

It will be very difficult to find the exact value of i at which the present worth function reduces to zero. 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 by interpolation method in the range of values of i for which the sign of the present worth function changes from positive to negative. The initial outlay and cash flow pattern for the new business are as 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 5 Cash flow —1,00, 30, 30, 30, 30, 30, Rs. The life of the project is 10 years with no salvage value at the end of its life.

The initial outlay of the project is Rs. The annual net profit is Rs. The life of all the three alternatives is estimated to be five years with negligible salvage value. Alternative A1 A2 A3 Rate of return So, it should not be considered for comparison.

The remaining two alternatives are qualified for consideration. Among the alternatives A1 and A2, the rate of return of alternative A1 is greater than that of alternative A2. Hence, alternative A1 should be selected. The amounts are in rupees. It has two alternatives for the expansion programme and the corresponding cash flows are tabulated below.

Each alternative has a life of five years and a negligible salvage value. Suggest the best alternative to the company. Initial investment Yearly revenue Rs. The formula for the net present worth of alternative 2 is: Consider the following cash flow of a project: Year 0 1 2 3 4 5 Cash flow —10, 4, 4, 5, 5, 6, Find the rate of return of the project. At the end of the 10th year, the salvage value of the business is Rs.

Find the rate of return of the business. A company is in the process of selecting the best alternative among the following three mutually exclusive alternatives: Alternative Initial Annual revenue Life investment Rs. A shipping firm is considering the purchase of a materials handling system for unloading ships at a dock. The firm has reduced their choice to three different systems, all of which are expected to provide the same unloading speed. The initial costs and the operating costs estimated for each system are now tabulated.

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