Engineering Economy with Sample Problems PDF

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ENGINEERING ECONOMICS Basic Economic Environment and Concept Economics is the study or science of the production, distribution and consumption of goods and services. Economy the cost or profit situation regarding a practical enterprise or project, as in economy studies, engineering economy, project ...

Description

ENGINEERING ECONOMICS Basic Economic Environment and Concept Economics - is the study or science of the production, distribution and consumption of goods and services.

Economy - the cost or profit situation regarding a practical enterprise or project, as in economy studies, engineering economy, project economy.

Engineering economy: a. The discipline concerned with economic aspects of engineering; it involves the systematic evaluation of the costs and benefits of proposed technical projects; b. The application of engineering or mathematical analysis and synthesis to economic decisions; c. A body of knowledge and concerned with the evaluation of the worth of commodities and services; d. The economic analysis of engineering alternatives.

Cost Terminology Fixed costs - are those unaffected by changes in activity level over a feasible range of operations for the capacity or capability available. Typical fixed costs include insurance and taxes on facilities, general management and administrative salaries, license fees, and interest costs on borrowed capital. Variable costs - are those associated with an operation that varies in total with the quantity of output or other measures of activity level. For example, the costs of material and labor used in a product or service are variable costs – because they vary in total with the number of output units – even though the costs per unit stay the same. Incremental cost, or incremental revenue - is the additional cost, or revenue, that results from increasing the output of a system by one (or more) units. Incremental cost is often associated with “go/no go” decisions that involve a limited change in output or activity level. Recurring costs - are those that are repetitive and occur when an organization produces similar goods or services on a continuing basis. Variable costs are also recurring costs, because they repeat with each unit of output. However, recurring costs are not limited to variable costs. A fixed cost that is paid on a repeatable basis is a recurring cost. For example, in an organization providing architectural and engineering services, office space for rental – which is a fixed cost – is also a recurring cost. Nonrecurring costs – are those that are not repetitive, even though the total expenditure may be cumulative over a relatively short period of time. Typically, nonrecurring costs involve developing or establishing a capability or capacity to operate. For example, the purchase cost for real estate upon which a plant will be built is a nonrecurring cost, as is the cost of constructing the plant itself. Direct Costs – are those that can be reasonably measured and allocated to a specific output or work activity. The labor and material costs directly associated with a product, service, or

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construction activity are direct costs. For example, the materials needed to make a pair of scissors would be a direct cost. Indirect costs – are those that are difficult to attribute or allocate to a specific output or work activity. The term normally refers to type of costs that would involve too much effort to allocate directly to a specific output. In this usage, they are costs allocated through a selected formula (such as, proportional to direct labor hours, direct labor dollars, or direct material dollars to the outputs or work activities. For example, the costs of common tools, general supplies, and equipment maintenance in a plant are treated as indirect costs. Overhead consists of plant operating costs that are not direct labor or direct material costs. Examples of overhead include electricity, general repairs, property taxes, and supervision. Standard costs – are representative costs per unit of unit of output that are established in advance of actual production or service delivery. They are developed from the direct labor hours, materials, and support functions (with their established costs per unit) planned for the production or delivery process. Cash cost – a cost that involves payment of cash (and results in a cash flow) to distinguish it from one that does not involve a cash transaction and is reflected in the accounting system as a noncash cost. This noncash cost is often referred to as a book cost. Sunk cost – is one that has occurred in the past and has no relevance to estimates of future costs and revenues related to an alternative course of action. Opportunity cost – is the cost of the best rejected (i.e., foregone) opportunity and is often hidden or implied. It is incurred because of the use of limited resources, such that the opportunity to use those resources to monetary advantage in an alternative use is foregone. For example, suppose that a project involves the use of vacant warehouse space presently owned by a company. The cost for that space to the project should be the income or savings that possible alternative uses of the space may bring to the firm. In other words, the opportunity cost for the warehouse space should be the income derived from the best alternative use of the space. Life-Cycle cost –this term refers to a summation of all costs, recurring and nonrecurring, related to a product, structure, system, or service during its life span.

The General Economic Environment There are numerous general economic concepts that must be taken into account in engineering studies. In broad terms, economics deals with the interactions between people and wealth, and engineering is concerned with the cost-effective use of scientific knowledge to benefit mankind.

Consumer and Producer Goods and Services Consumer goods and services are those products or services that are directly used by people to satisfy their wants. Food, clothing, homes, cars, television sets, haircuts, and medial services are examples. Producer goods and services are used to produce consumer goods and services or other producer goods. Machine tools, factory building, buses, and farm machinery are example.

Measure of Economic Worth Goods and services are produced and desired because directly or indirectly they have utility – the power to satisfy human wants and needs. Thus, they may be used or consumed directly, or they may be used to produce other goods or services that may, in turn, be use directly. Utility is

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most commonly measured in terms of value, expressed in some medium of exchange as the price that must be paid to obtain the particular item.

Necessities, Luxuries, and Price Demand Goods and services may be divided into two types – necessities and luxuries. Necessities are those products or services that are required to support human life and activities that will be purchased in somewhat the same quantity even though the price varies considerably. Luxuries are those products or services that are desired by humans and will be purchase if money is available after the required necessities have been obtained. Obviously, these terms are relative, because, for most goods and services, what one person considers a necessity may be considered a luxury by another. For example, a person living in one community may find that an automobile is a necessity to get to and from work. If the same person lived and worked in a different city, adequate public transportation might be available, and an automobile would be a luxury. For all goods and services, there is a relationship between the price that must be paid and the quantity that will be demanded or purchased. As the selling price per unit ( p) is increased, there will be less demand ( D) for the product, and as the selling price is decreased, the demand will increase. The relationship between price and demand can be expressed as linear function: p = a – bD

for 0 ≤ D ≤ a/b, a > 0, b > 0

Eqn. 1

where a is the intercept on the price axis and – b is the slope. Thus, b is the amount by which demand increases for each unit decrease in p. Both a and b are constants. It follows that, a - p D=

(b ≠ 0)

Eqn. 2

b Demand is the need, want or desire for a product backed by the money to purchase it. In economic analysis, demand is always based on “willingness and ability to pay” for a product, not merely want or need for the product. The demand for a product is inversely proportional to its selling price, i.e., as the selling price is increased, there will be less demand for the product; and as the selling price is decreased, the demand will increase. Supply is the amount of a product made available for sale. If the selling price for a product is high, more producers will be willing to work harder and risk more capital in order to reap more profit. However, if the selling price for a product declines, capitalists will not produce as much because of the smaller profit they can obtain for their labor and risk. Therefore, the relationship between price and supply is that they are directly proportional, i.e., the bigger the selling price, the more supply; and the smaller the selling price, the less is the supply. THE LAW OF SUPPLY AND DEMAND The law of supply and demand may be stated as follows: “Under conditions of perfect competition, the price at which any given product will be supplied and purchased is the price that will result in the supply and the demand being equal.”

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Competition Perfect competition occurs in a situation in which any given product supplied by a large number of vendors and there is no restriction on additional vendors entering the market. Under such conditions, there is assurance of complete freedom on the part of both buyer and seller. Perfect competition may never occur in actual practice, because of a multitude of factors that impose some degree of limitation upon the actions of buyers or sellers, or both. Monopoly is at the opposite pole of perfect competition. A perfect monopoly exists when a unique product or service is only available from a single vendor and that vendor can prevent the entry of all others into the market. Under such conditions, the buyer is at the complete mercy of the vendor in terms of the availability and price of the product. Perfect monopolies rarely occur in practice, because (1) few products are so unique that substitutes cannot be used satisfactorily, and (2) governmental regulations prohibit monopolies if they are unduly restrictive.

The Total Revenue Function The total revenue, TR that will result from a business venture during a given period is the product of the selling price per unit, p, and the number of units sold, D. Thus TR = price X demand = p (D)

Eqn. 3

If the relationship between price and demand as given in Eqn. 1 is used, TR = (a - bD)D = aD - bD

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for ≤ D ≤ a/b, a > 0, b > 0

Eqn. 4

From calculus the demand, Ď that will produce maximum total revenue can be obtained by solving dTR = a - 2bD = 0

Eqn. 5

dD Thus a Ď=

Eqn. 6 2b

To guarantee that Ď maximizes the total revenue, check the second derivative to be sure it is negative. 2

d TR = - 2b dD

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Cost, Volume, and Breakeven Point Relationships Fixed costs remain constant over a wide range of activities as long as the business does not permanently discontinue operations, but variable costs vary in total with the volume of output. Thus, at any demand D, total cost is CT = CF + CV Where:

Eqn. 7

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CF = fixed costs CV = variable costs For the linear relationship assumed here, CV = (Cν) (D) Where: Cν = variable cost per unit

Eqn. 8

We consider two scenarios for finding breakeven points. In the first scenario, demand is a function of price. The second scenario assumes that price and demand are independent of each other. Scenario 1. When total revenue and total cost, as given in Eqns. 7 and 8 are combined, the typical results as a function of demand are depicted. At breakeven point D’1, total revenue is equal to total cost, and an increase in demand will result in a profit for the operation. Then at optimal demand, D*, profit is maximized (Eqn. 10). At breakeven point D’2, total revenue and total cost are again equal, but additional volume will result in an operating loss instead of a profit. Obviously, the conditions for which breakeven and maximum profit occurs are our primary interest. First, at any volume (demand), D, Profit (loss) = total revenue - total costs = (aD - bD2) - (CF + CνD) = - CF + (a - Cν) D - bD

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for 0 ≤ D ≤ a/b

Eqn. 9

In order for a profit to occur, and to achieve the typical results, two conditions must be met: 1. (a – Cν) > 0; that is, the price per unit that will result in no demand has to be greater than the variable cost per unit (this avoids negative demand). 2. Total revenue (TR) must exceed total cost (CT) for the period involved. If these conditions are met, we can find the optimal de4mand at which maximum profit will 2

occur by taking the first derivative of profit = - CF + (a – Cν) D – bD with respect to D and it equal to zero: d (profit) =0 dD a - Cν D* =

Eqn. 10 2b

Where: D* = optimal value of D that maximizes profit

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To ensure that we have maximized profit (rather than minimized it); the sign of the second derivative must be negative. Checking this, we find that 2

d (profit) = - 2b dD

2

which will be negative for b > 0 (as earlier specified). (Also, recall that in cost minimization problems a positive signed second derivative is necessary to guarantee a minimum – valued optimal cost solution). An economic breakeven point for an operation occurs when total revenue equals total cost. Then for total revenue and total cost, as used in the development of Eqns. 9 and 10 and at any demand D,

Total revenue = total cost

(breakeven point)

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aD – bD = CF + CνD 2

-bD + (a – Cν) D – CF = 0

Eqn. 11

Because Eqn. 11 is a quadratic equation with one unknown ( D), we can solve for the breakeven points D’1 and D’2 (the roots of the equation). ½

- (a – Cν) ± [(a – Cν)2 – 4(-b) (-CF)] D’ =

Eqn. 12 2(-b)

With the conditions for the profit satisfied (Eqn. 9), the quantity in the brackets of the numerator (the discriminant) in Eqn. 12 will be greater than zero. This will ensure that D’1 and D’2 have real positive and unequal values. - (a – Cν) + [(a – Cν)2 – 4(-b) (-CF)]

½

D’1 = 2(-b) and - (a – Cν) - [(a – Cν)2 – 4(-b) (-CF)]

½

D’2 = 2(-b) Scenario 2. When the price per unit (p) for a product or service can be represented more simply as being independent of demand (versus being a linear function of demand, as assumed in Eqn. 1) and is greater than the variable cost per unit ( Cν), a single breakeven points results. Then under the assumption that demand is immediately met, total revenue TR = p (D).

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Problems: 1. Find the demand, Ď that maximizes total revenue if the equation for price is given by 50,000- 200D? Ans. Ď = 125 units 2. A company produces an electronic time switch that is used in consumer and commercial products made by several other manufacturing firms. The fixed cost ( CF) is $73,000 per month, and the variable cost ( Cν) is $83 per unit. The selling price per unit is p = $180 – 0.02D, based on Eqn 1. For this situation (a) determine the optimal volume for this product and confirm that a profit occurs (instead of loss) at this demand; and (b) find the volumes at which breakeven occurs; that is what is the range of profitable range? Ans. (a) D* = 2,425 units per month (b) D’1 = 932 units per month, D’2 = 3,918 units per month. 3. Suppose we know that p = 1,000 – D/5, where p = price in dollars and D = annual 2

demand. The total cost per year can be approximated by $1,000 + 2D (a) Determine the value of D that maximizes profit (b) Show in part (a) that profit has been maximized rather than minimized. Ans. (a) D* = 227 units per year 2

d (profit) (b)

= - 4.4 2

dD 4. A company produces circuit boards used to update outdated computer equipment. The fixed cost is $42,000 per month and the variable cost is $53 per circuit board. The selling price per unit is p = $150 – 0.02 D. Maximum output of the plant is 4,000 units per month. (a) Determine optimum demand for this product (b) What is the maximum profit per month? (c) What is the company’s range of profitable demand? Ans. (a) D* = 2425 circuit boards per month (b) Max profit = $75,612.5 per month (c) 480 to 4,369 circuit boards per month 5. A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately D = 780 – 10 p units (D is the demand or quantity sold per month, and p is the price in dollars). The fixed cost is $800 per month, and the variable cost is $300 per unit produced. What number of units, D*, should be produced per month and sold to maximize net profit? What is the maximum profit per month related to the product? Ans. D* = 240 units per month Maximum profit = $4,960 per month 6. A company estimates that as it increases its sales volume by decreasing the selling price 2

of its product, revenue = aD – bD (where D represents the units of demand per month, with 0 ≤ D ≤ a/b). The fixed cost is $1,000 per month, and the variable cost is $4 per unit.

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If a = $6 and b = $0.001, determine the sales volume for maximum profit, and the maximum profit per month. Ans. D* = 1,000 units per month Maximum profit = $0 per month

Principles of Money – Time Relationship Capital – refers to wealth in the form of money or property that can be used to produce more wealth. Two basic categories of capital: 1. Equity capital – is that owned by individuals who have invested their money or property in a business project or venture in the hope of receiving a profit. 2. Debt capital – often called borrowed capital, is obtained from lenders e.g., through the sale of bonds) for investment. SIMPLE INTEREST Suppose a debtor loans money from a creditor. The debtor must pay the creditor the original amount loaned plus an additional sum called interest. For the debtor, interest is the payment for the use of the borrowed capital while for the creditor; it is the income from the invested capital. Simple Interest (denoted as I) is defined as the interest on a loan or principal that is based only on the original amount of the loan or principal. This means that the interest charges grow in linear function over a period of time. This is usually used for short-term loans where the period of the loan is measured in days rather than years. It can be calculated using the following formula: I = Pin

Eqn. 13

where: P = principal/loan I = interest i = interest rate n = period The future amount of the principal may be calculated by adding the interest (I) to the principal (P). F=P+I or: F = P + Pin Thus, F = P(1+in)

Eqn. 14

There are two types of simple interest namely, ordinary interest and exact simple interest. Ordinary simple interest is based on one banker’s year. A banker year is composed of 12 months of 30 days each which is equivalent to a total of 360 days in a year. The value of n that is used in the preceding formulas may be calculated as

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d n=

Eqn. 15 360

where: d = number of days the principal was invested Exact simple interest is based on the exact number of days in a given year. A normal year has 365 days while a leap year (which occurs once every 4 years) has 366 days. Unlike the ordinary simple interest, the number of days in a month is based on the actual number of days each month contains in our Gregorian calendar. To determine the year whether leap year or not, one has to divide the year by 4. If it is exactly divisible by 4, the year to be leap year otherwise it will be considered just a normal year with 365 days. However,...