Advanced Engineering Economy & Costing.pptx

7/27/2019 Advanced Engineering Economy & Costing.pptx

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Advanced Engineering Economy &

Costing

D.Prakash

Adminstrative block; Room no: [email protected]

0932120816
mailto:[email protected]:[email protected]


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Aim

To develop economic and cost analysis models for decisions

making.

Course Description

Formulation of economic problems models. Analysis of

capital Investments, Decision analysis methods: decision tree

analysis, multi-attribute decisions, probabilistic analysis andsensitivity/risk analysis.

Stochastic techniques and risk to evaluate design

alternatives, Capital budgeting models: multi-criteria optimization,

certainty equivalence. Replacement analysis.

Costing techniques applicable in manufacturing: activitybased costing, life cycle costing, theory of constraints, cost of

quality.


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3

ENGINEERING ECONOMICS INVOLVES:FORMULATING, ESTIMATING, AND

EVALUATING ECONOMIC OUTCOMES

WHEN CHOICES ORALTERNATIVES AREAVAILABLE

What Kinds of Questions Can

Engineering Economics Answer?


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4

How Does It Do This?

BY USING SPECIFIC

MATHEMATICAL RELATIONSHIPSTO COMPARE THE CASH FLOWS OF THE

DIFFERENT ALTERNATIVES

(typically using spreadsheets)


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5

Where Does Engineering

Economics Fit?Here is an approach to problem-solving:

Understand the problem

Collect all relevant data/information

Define the feasible alternatives

Evaluate each alternative

Select the best alternative

Implement and monitor the decision


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6

Where Does Engineering

Economics Fit?1. Understand the Problem

2. Collect all relevant data/information (difficult!)

3. Define the feasible alternatives

4. Evaluate each alternative

5. Select the best alternative

6. Implement and monitorThis is the major role of

engineering economics


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Contemporary Engineering Economics, 4thedition, 2007

7

What Makes the Engineering Economic

Decision Difficult? - Predicting the Future

Estimating a Required

investment

Forecasting a product

demand Estimating a selling price

Estimating a

manufacturing cost

Estimating a product life


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8

Create & Design

Engineering Projects

Evaluate

Expected

Profitability

Timing of

Cash Flows Degree of

Financial Risk

Analyze

Production Methods

Engineering Safety

Environmental Impacts

Market Assessment

Evaluate

Impact on

Financial Statements

Firms Market Value

Stock Price

Role of Engineers in Business


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The five main types of engineering economic decisions are

(1) service improvement,

(2) equipment and process selection,(3) equipment replacement,

(4) new product and product expansion, and

(5) cost reduction.


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10

Present

FuturePast

Engineering EconomyAccounting

Evaluating past performance Evaluating and predicting future events

Accounting Vs. Engineering Economics


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11

Fundamental Principles of Engineering

Economics

Principle 1: A nearby dollar is worth more

than a distant dollar

Principle 2: All it counts is the differences

among alternatives

Principle 3: Marginal revenue must exceed

marginal cost

Principle 4: Additional risk is not taken

without the expected additional return


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12

Principle 1: A nearby dollar is worth more

than a distant dollar

Today 6-month later


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Contemporary Engineering Economics, 4thedition, 2007 13

Principle 2: All it counts is the differences

among alternatives

Option MonthlyFuelCost

MonthlyMaintenance

Cashoutlay atsigning

Monthlypayment

SalvageValue atend ofyear 3

Buy $960 $550 $6,500 $350 $9,000

Lease $960 $550 $2,400 $550 0

Irrelevant items in decision making


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14

Principle 3: Marginal revenue must exceed

marginal cost

Manufacturing cost

Sales revenueMarginal

revenue

Marginal

cost

1 unit

1 unit


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Contemporary Engineering Economics, 4thedition, 2007 15

Principle 4: Additional risk is not taken

without the expected additional return

Investment Class Potential

Risk

Expected

Return

Savings account(cash)

Low/None 1.5%

Bond (debt) Moderate 4.8%

Stock (equity) High 11.5%


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Simple Methods

Simple Payback Period (SPP)- The timerequired for savings to offset first costs.

Simple Return on Investment (ROI)- The

simple percent return the project pays over itslife.

These methods are simple because they do

not consider the time value of money. Simple methods are OK for investments that

are very good and pay off over short timeperiods.


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17

Time Value of Money

Money has value Money can be leased or rented

Thepayment is called interest

If you put $100 in a bank at 9% interest for one time periodyou will receive back your original $100 plus $9

Original amount to be returned = $100

Interest to be returned = $100 x .09 = $9


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18

Compound Interest

Interest that is computed on the original

unpaid debt and the unpaid interest Compound interest is most commonly used

in practice

Total interest earned = In = P (1+i)n - P Where,

P present sum of money

i interest rate

n number of periods (years)

I2 = $100 x (1+.09)2 - $100 = $18.81


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Present and Future Value

Present Value is the value now of an amount

of money Freceived n years in the future.

Future Value is value n years in the future of

an amount of money Preceived now.

If we can earn interest rate i on investments,

the relationship between P and F is:

F = P(1 + i)n or P = F/(1 + i)n


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ECONOMIC MODELS

Economic modeling is at the heart of economic theory.

Modeling provides a logical,abstract template to helporganize the analyst's thoughts.

The model helps the economist logically isolate and

sort out complicated chains of cause and effect andinfluence between the numerous interacting elementsin an economy.

Through the use of a model, the economist canexperiment, at least logically, producing differentscenarios, attempting to evaluate the effect ofalternative policy options, or weighing the logicalintegrity of arguments presented in prose.


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Types of Models

visual models,

Mathematical models,

Empirical models,

Simulation models.


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1. Visual Models - Visual models are simply pictures of anabstract economy; graphs with lines and curves that tell an economic story


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2. Mathematical Models

The most formal and abstract of the economic models are the purely

mathematical models. These are systems of simultaneous equations with anequal or greater number of economic variables.


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3.Empirical Models

Empirical models are mathematical modelsdesigned to be used with data. Thefundamental

model is mathematical, exactly as describedabove. With an empirical model, however,

data is gathered for the variables, and using

accepted statistical techniques, the data areused to

provide estimates of the model's values.


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"What will happen to investment if income

rises one percent?" The purely mathematicalmodel might only allow the analyst to say,"Logically, it should rise.

The user of the empirical model, on the otherhand, using actual historical data forinvestment, income, and the other variables inthe model, might be able to say,

"By my best estimate, investment should rise byabout two percent."


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4.Simulation Models

Simulation models, which must be used with computers,

embody the very best features of mathematical models

without requiring that the user be proficient in mathematics.

The models are fundamentally mathematical (the equations

of the model are programmed in a programming language like

Pascal or C++) but the mathematical complexity is transparentto the user.

The simulation model usually starts with initial or "default"

values assigned by the program or the user, then certain

variables are changed or initialized, then a computersimulation is done.

The simulation, of course, is a solution of the model's

equations. The user can usually alter a whole range of

variables at will.


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The computerized simulation model can show

the interaction of numerous variables all at

once, including hidden feedback and

secondary effects that are not so apparent inpurely mathematical or visual models.

Macroeconomic simulation model calledHMCMacroSim


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Static and Dynamic Models

Most of the models used in economics are

comparative statics models. Some of the more

sophisticated models in macroeconomics and

business cycle analysis are dynamic models.


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The initial equilibrium (point 'a') identifiesthe price and

level of output that would obtain, given assumptions aboutsupply and demand and the level of inflationaryexpectations.

Then the model is shocked by introducing a higher level ofexpectations, demonstrating a new equilibrium at point 'b'.

Obviously this movement in equilibria and the shift in themodel's solution happened over time, but neither thevisual model nor its mathematical counterpart candemonstrate what happened in the interim. The modelshows only the starting point and the ending point.

The comparative statics approach is roughly analogous tousing snapshots from a camera to record developmentsduring a dynamic event. With each snapshot a static butinformative picture is presented.

i d l


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Dynamic Model


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Why Comparative Statics Models are

Usually Used?

The answer is simple - comparative statics modelsare much easier to solve.

Any student of calculus knows the difficulty of

solving systems of difference or (especially)differential equations.

The latter, as soon as they achieve any complexity,are sometimes impossible to solve.

Therefore dynamic models must be kept extremelysimple and are therefore so elementary that moreis lost than gained.


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Simple dynamic models, nonetheless, often providevaluable insights into the complex interactions betweenvariables over time.

They can capture remarkably subtle feedback effects thatare easily missed by static models.

It should be noted that dynamic models are much easier tosimulate on computers than they are to solve outright.

The user can experiment with an endless variety of valuesand assumptions to see whether results obtained are

realistic or insightful. Since computers are now powerfuland cheaper, the importance of dynamic simulation modelsshould gradually grow in importance.


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Expectations-Enhanced Models

Economic models often incorporate economicexpectations, such as inflationary expectations. Suchmodels are called expectations-enhanced models.

Generally, expectations-enhanced models include oneor more variables based upon economic expectationsabout future values.

For example, if consumers, for whatever reason,

expect the inflation rate to be much higher next yearthan this year, they are said to have formedinflationary expectations.


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There are many types of expectations found in

economics.

In addition to inflationary expectations,

economists might consider interest rate

expectations, income expectations, and

wealth expectations. This list is hardly

exhaustive.


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Adaptive Expectations

The theory of adaptive expectations presumes thatexpectations are primarily learned from experience.

For example, the theory of adaptive expectationswould say that if consumers begin to actually see

prices rising, say from three percent to five percent toseven percent, over a period of, say, two years, theywill begin to form robust expectations of inflationaryexpectations perhaps even expectations of double-digit inflation.

The same theory might claim that consumers willexpect an economic recovery to begin only after ampleevidence that the turning point has been passed.


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Rational Expectations

The theory of rational expectations presumes thatexpectations are formed when economic agents see newdevelopments in the economy and they logically deduceexpectations based upon the information they have.

For example, if the Federal Reserve System were tosuddenly increase the money supply, according to thetheory of rational expectations, consumers wouldimmediately form inflationary expectations, not becauseprices are actually rising, but because they deduce thatexcessive money supply growth is likely to cause inflation.

The theory of rational expectations emphasizes the effectsof changes in economic policy upon expectations, althoughthe theory is not restricted to policy decisions alone.


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The Limitations of Models

Improper Assumptions

Oversimplification

Mathematical Intractability


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The Model as an "Image" of Economic Activity

Two important points are being made here:

1. This model, like most in economies, is not an applied model, where anyone actually uses it to

determine appropriate prices and levels of production. (To be more specific, it is not an

applied management model; corporations don't use these models to make pricing decisions).

Instead, the model represents a type of consistent behavior that economists see in the market

place, and it presents an image of that behavior. It allows an economist to both ask and answer

the question, "What would we expect to happen in a market where prices are too high or too

low? What kind of adjustment would take place, and why?

2. The market reactions of the economic decision-makers are not undertaken by virtue of their

use of this model or any other, but is instead motivated by their necessary response tomarket signals that tell them that they must alter their decisions.

The model, therefore, simply captures their responses to a series of market signals.


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Analysis of capital investment

Present value method

Future value technique

Annual equivalent cost method

Rate of return method


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Present value method

Using the compound interest formulas bring allbenefits and costs to present worth

Select the alternative if its net present worth 0

Net present worth =Present worth of benefits Present worth of costs

Present Worth Analysis


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A construction enterprise is investigating the

purchase of a new dump truck. Interest rate is 9%.The cash flow for the dump truck are as follows:

First cost = $50,000, annual operating cost = $2000,

annual income = $9,000, salvage value is $10,000, life

= 10 years. Is this investment worth undertaking? P = $50,000, A = annual net income = $9,000 - $2,000

= $7,000, S = 10,000, n = 10.

Evaluate net present worth = present worth ofbenefits present worth of costs



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Present worth of benefits = $9,000(PA,9%,10) =

$9,000(6.418) = $57,762

Present worth of costs = $50,000 +

$2,000(PA,9%,10) - $10,000(PF,9%,10)= $50,000 +

$2,000(6..418) - $10,000(.4224) = $58,612

Net present worth = $57,762 - $58,612 < 0 do not

invest


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Future value technique

The future value technique of evaluating

alternatives is almost identical to the present

value method except that all costs andrevenues are stated in terms of future value.


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Annual equivalent cost method

The annual equivalent cost method of evaluating alternativeprojects states all costs and revenues over the useful life ofthe project in terms of an equal annual payment series

1. It requires less effort and fewer calculations.

2. It eliminates the problem of alternatives with incompatibleuseful lives.

3. It allows for much more sophistication when consideringinflation, increasing equipment cost, equipment depreciationschedules, etc.


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Rate of Return (ROR)

The rate of return (ROR) method of comparing

alternatives calculates the interest rate for each

alternative and selects the highest ROR.

ROR evaluates INVESTED capital and the costs of

operation and maintenance as opposed to revenues

or benefits received from the project.


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Cost-Benefit Analysis

Project is considered acceptable ifB C 0 or B/C 1. Example (FEIM):

The initial cost of a proposed project is $40M, thecapitalized perpetual annual cost is $12M, the

capitalized benefit is $49M, and the residual value is$0. Should the project be undertaken?

B = $49M, C = $40M + $12M + $0 B C = $49M $52M = $3M < 0

The project should not be undertaken.


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Rational Decision-Making Process

1. Recognize a decision problem

2. Define the goals or objectives

3. Collect all the relevant

information

4. Identify a set of feasibledecision alternatives

5. Select the decision criterion to

use



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Which Car to Lease?

Saturn vs. Honda

1. Recognize a decision problem

2. Define the goals or objectives

3. Collect all the relevant

information

4. Identify a set of feasibledecision alternatives

5. Select the decision criterion

to use


Need a car

Want mechanical security

Gather technical as well

as financial data

Choose between Saturn

and Honda

Want minimum total cash

outlay Select Honda


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Financial Data Required to Make an Economic

Decision


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Predicting the Future

Estimating a Required

investment

Forecasting a product

demand

Estimating a selling price

Estimating a

manufacturing cost

Estimating a product life

Types of Strategic Engineering


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Contemporary Engineering Economics, 4th

edition, 2007 55

Types of Strategic EngineeringEconomic Decisions in Manufacturing

SectorService Improvement

Equipment and Process Selection

Equipment Replacement

New Product and Product Expansion

Cost Reduction

S i I t H lth


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edition, 2007 56

Service Improvement - Healthcare

Delivery

Which plan is moreeconomically viable?

Traditional Plan: Patients

visit each service provider.

New Plan: Each service

provider visits patients

: patient

: service provider


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edition, 2007 57

Equipment & Process Selection

How do you choose between the Plastic SMC

and the Steel sheet stock for an auto body

panel?

The choice of material will dictate themanufacturing process for an automotive

body panel as well as manufacturing costs.


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edition, 2007 58

Equipment Replacement Problem

Now is the time to

replace the old machine?

If not, when is the right

time to replace the old

equipment?


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edition, 2007 59

New Product and Product Expansion

Shall we build or acquire

a new facility to meet the

increased demand?

Is it worth spending

money to market a new

product?

T p f Str t i E i ri E i


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edition, 2007 60

Types of Strategic Engineering Economic

Decisions in Service Sector

Commercial Transportation

Logistics and Distribution

Healthcare Industry

Electronic Markets and Auctions

Financial Engineering

Retails

Hospitality and Entertainment Customer Service and Maintenance


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Which Material to Choose?

New plant design Upgrade old plant

A i


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Alternative 1

Description

Cash flows oversome time period

Analysis using an

engineeringeconomy model

Evaluatedalternative 1

Noneconomic issues-environmental considerations

Alternative2

Description

Cash flows oversome time period

Analysis using anengineering

economy model

Evaluatedalternative2

Income, cost estimationsFinancing strategiesTax laws

Planning horizonInterest

Measure of worth

Calculated value ofmeasure of worth

I select alternative 2

Rate of return (Alt 2)>Rate of return (Alt 1)

Alternatives

Methods of Economic Selection

Example 7 2


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Compare the following machines on the basis of their equivalent

uniform annual cost. Use an interest rate of 18% per year.

Comparison point New Machine Used Machine

Capital cost 44000 m.u. 23000 m.u.

Annual operating

cost7000 m.u. 9000 m.u.

Annual repair cost210 m.u. 350 m.u.

Overhauling 2500 m.u. every 5 years 1900 m.u. every 2 years

Salvage value 4000 m.u. after 15 years 3000 m.u. after 8 years

Example 7.2

Cash flows of the two machines.


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0 1 2 3 4 5 6 7 8 9 10 11 12 1513 14

i = 18%

m.u.2500 m.u.2500m.u.7210/year

m.u.44000-2500

New machine

m.u.4000

m.u.2500

EUACnew = 7,210 + (440002500) (A/P, 18%, 15) + 2500 (A/P, 18%, 5) 4000 (A/F, 18%, 15)

= 7210 + 41500 (0.18 (1.1815) / (1.18151)) + 2500 (0.18 (1.185) / (1.1851))

4000 (0.18/ (1.1815-1))

EUACnew = 16094.55 m.u. per year.


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EUACused = 9350 + (230001900) (A/P, 18%, 8) + 1900 (A/P, 18%, 2) 3000 (A/F, 18%, 8)

= 21100 (0.18 (1.18)8 / (1.1881)) + 9350 + 1900 (0.18 (1.18)2 / (1.1821))

3000 (0.18 / (1.1881))

= 15542.4 m.u. per year.

1 2 3 4

0

5

i= 18 %

6 7 8

m.u.23000

m.u.9350/year

m.u.1900 m.u.1900 m.u.1900

se mac ne

m.u.3000


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Since we have found that: EUACused


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Spreadsheet Solution for example 7.2


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Analysis

The acceptance or rejection of a project based on the IRR criterion

is made by comparing the calculated rate with the required rate of return,or cutoff rate established by the firm. If the IRR exceeds the required ratethe project should be accepted; if not, it should be rejected.

If the required rate of return is the return investors expect the

organization to earn on new projects, then accepting a project with an IRRgreater than the required rate should result in an increase of the firmsvalue.


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Analysis

There are several reasons for the widespread popularity of the IRR as an

evaluation criterion:

Perhaps the primary advantage offered by the technique is that

it provides a single figure which can be used as a measure of

project value.

Furthermore, IRR is expressed as a percentage value. Most

managers and engineers prefer to think of economic decisions

in terms of percentages as compared with absolute values

provided by present, future, and annual value calculations.


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Analysis

Another advantage offered by the IRR method is related to the

calculation procedure itself:

As its name suggests, the IRR is determined internally for

each project and is a function of the magnitude and timing of the

cash flows.

Some evaluators find this superior to selecting a rateprior to calculation of the criterion, such as in the profitability index

and the present, future, and annual value determinations. In other

words, the IRR eliminates the need to have an external interest

rate supplied for calculation purposes.


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Multiple Roots Case

One of the disconcerting aspects associated with the internal rate of return is that

more than one interest rate may satisfy the calculation. The solution procedure for IRR

is essentially the solution for an nth degree polynomial of the form:

NPV = 0 = A0 + A1X + A2X2 + A3X

3 + .... + AnXn

whereX= 1/(1 + r)

For a polynomial of this type there may be n different real roots, or values ofr,

which satisfy the equation. Multiple positive rates of return may occur when the

annual cash flows have more than one change in sign.


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Multiple Roots Case

The following example illustrates the possibility of multiple rates which satisfy the definition of IRR:

Suppose a mining operation has a remaining life of eight years, but an investment is considered to increase the production rate. This will result indepleting the deposit in six years. Assuming the following cash flows, is the investment justified?

Because there are two sign reversals in the cash flows, Descartes Rule of Signs indicates there area maximum of two real roots to the IRR polynomial.

Solving for these roots by trial and error yields the following:

Year 0 1 2 3 4 5 6 7 8

Existing 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0

Proposed (15.0) 16.0 16.0 16.0 16.0 15.0 15.0 - -

Difference (15.0) 6.0 6.0 6.0 6.0 5.0 5.0 (10.0) (10.0)


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Multiple Roots CaseGraphically this appears as shown in the following figure:

The rates at which NPV = 0 are, by definition, the internal rates of return. By interpolation, the two solving rates of return for this example are approximately 4.5 and 12.3%

Rate 0% 4% 5% 10% 12% 15%

NPV (1.00) (0.07) 0.06 0.05 0.03 (0.25)


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Multiple Roots Case

Should the firm invest in the project or not?

If both rates were above the firm's required rate of return there would be no

problem and the firm would accept the project.

However, what if the required rate of return is 10%? Which of the calculated

IRR values is correct? The answers to these questions are that they are both

mathematically correct, but they are meaningless from an economic standpoint.

Neither of these rates can be considered an adequate measure of the project's

rate of return because a project can not earn more than one rate of return over

its life. Therefore, the calculation of an IRR value(s) does not always enable the

decision-maker to make accept/reject decisions on investment proposals.

M lti l R t C


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Multiple Roots Case

How often this problem of multiple rates actually occurs?

The possibility of multiple-rate occurrences is perhaps more prevalent in thecase of new mining ventures than in most other industries. The negative cash flows

are typically the result of anticipated periods of reduced market prices, major

capital expenditures for equipment replacement, expansion programs, and/or

major environmental expenditures, particularly at the end of project life.

Because of the possibility of multiple rates and the reinvestment assumptionwhen using-the IRR to rank projects, the evaluator must carefully consider the

exclusive use of this technique for decision-making.


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Sensitivity and Breakeven Analysis:

These techniques are used to see howsensitive a decision is to estimates for thevarious parameters.

BREAKEVEN ANALYSIS is done to locateconditions under which various alternativesare equally desirable. Examples include singlevs. multi-stage construction ,hours of

equipment utilization, production volumerequired, and equipment replacement analysis


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Break-Even Analysis

Excel using a Goal Seek function

Analytical Approach


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Excel Using a Goal Seek Function

Goal Seek

Set cell:

To value:

By changing cell:

Ok Cancel

? X

$F$5

0

$B$6

NPW

Breakeven Value

Demand

1

2

A B C D E F G

Example 10.3 Break-Even Analysis


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2345678

910111213141516171819

2021222324

2627

293031

32333435363738

4041

Input Data (Base): Output Analysis:

Unit Price ($) 50$ Output (NPW) $0Demand 1429.39Var. cost ($/unit) 15$Fixed cost ($) 10,000$

Salvage ($) 40,000$Tax rate (%) 40%MARR (%) 15%

0 1 2 3 4 5Income StatementRevenues:

Unit Price 50$ 50$ 50$ 50$ 50$Demand (units) 1429.39 1429.39 1429.39 1429.39 1429.39Sales Revenue 71,470$ 71,470$ 71,470$ 71,470$ 71,470$

Expenses:Unit Variable Cost 15$ 15$ 15$ 15$ 15$Variable Cost 21,441 21,441 21,441 21,441 21,441Fixed Cost 10,000 10,000 10,000 10,000 10,000Depreciation 17,863 30,613 21,863 15,613 5,581

Taxable Income 22,166$ 9,416$ 18,166$ 24,416$ 34,448$Income Taxes (40%) 8,866 3,766 7,266 9,766 13,779

Net Income 13,299$ 5,649$ 10,899$ 14,649$ 20,669$

Cash Flow Statement

Operating Activities:Net Income 13,299 5,649 10,899 14,649 20,669Depreciation 17,863 30,613 21,863 15,613 5,581

Investment Activities:Investment (125,000)Salvage 40,000Gains Tax (2,613)

Net Cash Flow (125,000)$ 31,162$ 36,262$ 32,762$ 30,262$ 63,636$

Goal Seek

FunctionParameters

Analytical Approach


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Analytical ApproachUnknown Sales Units (X)

0 1 2 3 4 5

Cash Inflows:

Net salvage 37,389

X(1-0.4)($50) 30X 30X 30X 30X 30X

0.4 (dep) 7,145 12,245 8,745 6,245 2,230Cash outflows:

Investment -125,000

-X(1-0.4)($15) -9X -9X -9X -9X -9X

-(0.6)($10,000) -6,000 -6,000 -6,000 -6,000 -6,000

Net Cash Flow -125,000 21X+

1,145

21X+6,245

21X+

2,745

21X+

245

21X+

33,617


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PW of cash inflows

PW(15%)Inflow= (PW of after-tax net revenue)

+ (PW of net salvage value)+ (PW of tax savings from depreciation

= 30X(P/A, 15%, 5) + $37,389(P/F, 15%, 5)

+ $7,145(P/F, 15%,1) + $12,245(P/F, 15%, 2)

+ $8,745(P/F, 15%, 3) + $6,245(P/F, 15%, 4)

+ $2,230(P/F, 15%,5)

= 30X(P/A, 15%, 5) + $44,490

= 100.5650X+ $44,490

PW of cash outflows:


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PW of cash outflows:

PW(15%)Outflow = (PW of capital expenditure_

+ (PW) of after-tax expenses

= $125,000 + (9X+$6,000)(P/A, 15%, 5)= 30.1694X+ $145,113

The NPW:

PW (15%) = 100.5650X+ $44,490

- (30.1694X+ $145,113)

=70.3956X- $100,623.

Breakeven volume:

PW (15%) = 70.3956X- $100,623 = 0

Xb =1,430 units.


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Demand

PW of

inflow

PW of

Outflow NPW

X

100.5650X

- $44,49030.1694

X

+ $145,11370.3956

X

-$100,623

0 $44,490 $145,113 100,623

500 94,773 160,198 65,425

1000 145,055 175,282 30,2271429 188,197 188,225 28

1430 188,298 188,255 43

1500 195,338 190,367 4,970

2000 245,620 205,452 40,168

2500 295,903 220,537 75,366


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Outflow

Break-Even Analysis Chart

0 300 600 900 1200 1500 1800 2100 2400

$350,000

300,000

250,000

200,000

150,000

100,000

50,000

0

-50,000

-100,000

Profit

Loss

Break-even Volume

Xb=1430

Annual Sales Units (X)

PW

(15%

)

Scenario Analysis


85/85

Scenario Analysis

Variable

Considered

Worst-

Case

Scenario

Most-Likely-

Case

Scenario

Best-Case

Scenario

Unit demand 1,600 2,000 2,400

Unit price ($) 48 50 53Variable cost ($) 17 15 12

Fixed Cost ($) 11,000 10,000 8,000

Salvage value ($) 30,000 40,000 50,000

PW (15%) -$5,856 $40,169 $104,295

Advanced Engineering Economy & Costing.pptx

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