11

What is Engineering Economics?What is Engineering Economics?

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What is Engineering Economics?What is Engineering Economics?

Subset of General EconomicsSubset of General Economics Different from general economics situations Different from general economics situations

- - project drivenproject driven Analysis performed by technical Analysis performed by technical

professionals (not economists)professionals (not economists) Requires advanced technical knowledge in Requires advanced technical knowledge in

some casessome cases

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Lots of Questions: Project/$ drivenLots of Questions: Project/$ driven Why do this Why do this at allat all? ?

Is there a need for the project?Is there a need for the project? Why do it Why do it nownow??

Can it be delayed? Can we afford it now?Can it be delayed? Can we afford it now? Why do it Why do it this waythis way??

Is this the best alternative? Is this the optimal Is this the best alternative? Is this the optimal solution?solution?

Will the Will the project payproject pay?? Will we run a loss or make a profit?Will we run a loss or make a profit?

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Sample Engineering ProjectSample Engineering Project

Hydro:Hydro: expensive initiallyexpensive initially far away from load far away from load

centres (high centres (high transmission cost)transmission cost)

no fuel requiredno fuel required longer lifelonger life no pollutionno pollution

ThermalThermal less expensive initiallyless expensive initially can be near load centrescan be near load centres

require fuelrequire fuel shorter lifeshorter life can cause pollutioncan cause pollution

Hydro vs. Thermal power

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Other examplesOther examples

BuyBuy vs. vs. rentrent (car, house, equipment) (car, house, equipment)

Good quality (Good quality (expensiveexpensive) but longer life vs. ) but longer life vs. poor quality (poor quality (cheapcheap) but shorter life) but shorter life car, shoes, computerscar, shoes, computers

InvestmentsInvestments decisions - GIC, RRSP, Bonds, decisions - GIC, RRSP, Bonds, Stocks and SharesStocks and Shares

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Steps in Engineering Economics StudySteps in Engineering Economics Study

Define alternatives in physical termsDefine alternatives in physical terms Cost and revenue estimatesCost and revenue estimates All money estimates placed on a comparable basisAll money estimates placed on a comparable basis

appropriate interest rate usedappropriate interest rate used time horizon (economic life)time horizon (economic life)

Recommend choice among alternativesRecommend choice among alternatives

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Engineering Economics on the WebEngineering Economics on the Web The discipline that translates engineering The discipline that translates engineering

technology into a form that permits evaluation by technology into a form that permits evaluation by businesses or investors.businesses or investors.

The application of economic principles to The application of economic principles to engineering problems, for example in comparing engineering problems, for example in comparing the comparative costs of two alternative capital the comparative costs of two alternative capital projects or in determining the optimum projects or in determining the optimum engineering course from the cost aspect.engineering course from the cost aspect.

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The Time Value of MoneyThe Time Value of Money

Would you prefer to Would you prefer to

have have $1 million$1 million nownow or or

$1 million$1 million 100 years100 years

from now?from now?

Of course, we would Of course, we would all prefer the money all prefer the money nownow!!

This illustrates that This illustrates that there is an inherent there is an inherent monetary value monetary value attached to time.attached to time.

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What is Time Value?What is Time Value? We say that money has a time We say that money has a time

value because that money can be value because that money can be invested with the expectation of invested with the expectation of earning a positive rate of returnearning a positive rate of return

In other words, “In other words, “a dollar received a dollar received today is worth more than a dollar today is worth more than a dollar to be received tomorrowto be received tomorrow””

That is because today’s dollar That is because today’s dollar can be invested so that we have can be invested so that we have more than one dollar tomorrowmore than one dollar tomorrow

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What is The Time Value of Money?What is The Time Value of Money?

A dollar received today is worth more than a A dollar received today is worth more than a dollar received tomorrowdollar received tomorrow This is because a dollar received today can This is because a dollar received today can

be invested to earn interestbe invested to earn interest The amount of interest earned depends on The amount of interest earned depends on

the rate of return that can be earned on the the rate of return that can be earned on the investmentinvestment

Time value of money quantifies the value of a Time value of money quantifies the value of a dollar through timedollar through time

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Uses of Time Value of MoneyUses of Time Value of Money

Time Value of Money, is a concept Time Value of Money, is a concept that is used in all aspects of finance that is used in all aspects of finance including:including:

Stock valuationStock valuation Financial analysis of firmsFinancial analysis of firms Accept/reject decisions for project Accept/reject decisions for project

managementmanagement And many others!And many others!

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The Terminology of Time ValueThe Terminology of Time Value Present Value Present Value - An amount of money today, - An amount of money today,

or the current value of a future cash flowor the current value of a future cash flow Future Value Future Value - An amount of money at some - An amount of money at some

future time periodfuture time period PeriodPeriod - A length of time (often a year, but - A length of time (often a year, but

can be a month, week, day, hour, etc.)can be a month, week, day, hour, etc.) Interest Rate Interest Rate - The compensation paid to a - The compensation paid to a

lender (or saver) for the use of funds expressed lender (or saver) for the use of funds expressed as a percentage for a period (normally as a percentage for a period (normally expressed as an annual rate)expressed as an annual rate)

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AbbreviationsAbbreviations

PV - Present valuePV - Present value FV - Future valueFV - Future value Pmt - Per period payment amountPmt - Per period payment amount i - The interest rate per periodi - The interest rate per period

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$$

Purchasing Power and ValuePurchasing Power and Value

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N = 0 $100

N = 1 $104(inflation rate = 4%)

N = 0 $100

N = 1 $106(earning rate =6%)

Case 2: Earning power exceeds inflation

N = 0 $100

N = 1 $108(inflation rate = 8%)

N = 0 $100

N = 1 $106(earning rate =6%)

Case 1: Inflation exceeds earning power

Cost of RefrigeratorAccount Value

N = 0 $100

N = 1 $104(inflation rate = 4%)

N = 0 $100

N = 1 $106(earning rate =6%)

Case 2: Earning power exceeds inflation

N = 0 $100

N = 1 $108(inflation rate = 8%)

N = 0 $100

N = 1 $106(earning rate =6%)

Case 1: Inflation exceeds earning power

Cost of RefrigeratorAccount Value

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TimelinesTimelines

0 1 2 3 4 5

PV FV

Today

A timeline is a graphical device used to clarify the A timeline is a graphical device used to clarify the timing of the cash flows for an investmenttiming of the cash flows for an investment

Each tick represents one time periodEach tick represents one time period

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Calculating the Future ValueCalculating the Future Value Suppose that you have an extra $100 today that you Suppose that you have an extra $100 today that you

wish to invest for one year. If you can earn 10% per wish to invest for one year. If you can earn 10% per year on your investment, how much will you have in year on your investment, how much will you have in one year?one year?

0 1 2 3 4 5

-100 ?

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Calculating the Future ValueCalculating the Future Value

Suppose that at the end of year 1 you decide to extend Suppose that at the end of year 1 you decide to extend the investment for a second year. How much will the investment for a second year. How much will you have accumulated at the end of year 2?you have accumulated at the end of year 2?

0 1 2 3 4 5

-110 ?

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Generalizing the Future ValueGeneralizing the Future Value

Recognizing the pattern that is developing, we Recognizing the pattern that is developing, we can generalize the future value calculationscan generalize the future value calculations

If you extended the investment for a third year, you would have:

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Compound InterestCompound Interest Note from the example that the future value is Note from the example that the future value is

increasing at an increasing rateincreasing at an increasing rate In other words, In other words, the amount of the amount of interestinterest earned each earned each

year is increasingyear is increasing Year 1: $10Year 1: $10 Year 2: $11Year 2: $11 Year 3: $12.10Year 3: $12.10

The reason for the increase is that each year you are The reason for the increase is that each year you are earning interest on the interest that was earned in earning interest on the interest that was earned in previous years in addition to the interest on the previous years in addition to the interest on the original original principle amountprinciple amount

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Compound Interest GraphicallyCompound Interest Graphically

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Years

Fut

ure

Val

ue

5%

10%

15%

20%

3833.76

1636.65

672.75

265.33

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The Magic of CompoundingThe Magic of Compounding

On Nov. 25, 1626 Peter Minuit, purchased Manhattan from the On Nov. 25, 1626 Peter Minuit, purchased Manhattan from the Indians for $24 worth of beads and other trinkets. Was this a Indians for $24 worth of beads and other trinkets. Was this a good deal for the Indians?good deal for the Indians?

This happened about 378 years ago, so if they could earn 5% per This happened about 378 years ago, so if they could earn 5% per year they would in 2005 haveyear they would in 2005 have

If they could have earned 10% per year, they would now have:

378$106,000,000,000,000,000 24(1.10)

$ 3782,400,000,000 24(1.05)

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Calculating the Present ValueCalculating the Present Value

So far, we have seen how to calculate the So far, we have seen how to calculate the future value of an investmentfuture value of an investment

But we can turn this around to find the amount But we can turn this around to find the amount that needs to be invested to achieve some that needs to be invested to achieve some desired future value: desired future value:

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Present Value: An ExamplePresent Value: An Example Your Your fivefive-year old daughter -year old daughter

has just announced her desire has just announced her desire to attend college. After some to attend college. After some research, you determine that research, you determine that you will need about you will need about $100,000$100,000 on her on her 1818th birthday to pay th birthday to pay for four years of college. If for four years of college. If you can earn you can earn 8%8% per year on per year on your investments, how much your investments, how much do you need to invest today do you need to invest today to achieve your goal?to achieve your goal?

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Continuous CompoundingContinuous Compounding

There is no reason why we need to stop increasing the There is no reason why we need to stop increasing the compounding frequency at dailycompounding frequency at daily

We could compound every hour, minute, or second We could compound every hour, minute, or second We can also compound every instant (i.e., We can also compound every instant (i.e.,

continuously):continuously):

Here, F is the future value, P is the present value, r is the annual rate of interest, t is the total number of years, and e is a constant equal to about 2.718

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Continuous CompoundingContinuous Compounding

Suppose that the Fourth National Bank is offering to Suppose that the Fourth National Bank is offering to pay 10% per year compounded continuously. What pay 10% per year compounded continuously. What is the future value of your $1,000 investment?is the future value of your $1,000 investment?

This is even better than daily compounding The basic rule of compounding is: The more

frequently interest is compounded, the higher the future value

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Continuous CompoundingContinuous Compounding

Suppose that the Fourth National Bank is offering to Suppose that the Fourth National Bank is offering to pay 10% per year compounded continuously. If you pay 10% per year compounded continuously. If you plan to leave the money in the account for 5 years, plan to leave the money in the account for 5 years, what is the future value of your $1,000 investment?what is the future value of your $1,000 investment?

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SummarySummary Engineering EconomicsEngineering Economics The Time Value of MoneyThe Time Value of Money Calculating the Future/Present ValueCalculating the Future/Present Value Simple/Compound InterestSimple/Compound Interest

Self-Study: Simple Interest P+P*N*5% Self-Study: Simple Interest P+P*N*5% 1+1=21+1=2 Required: Slides/Book Chapter 2.1 2.2 2.3 2.5Required: Slides/Book Chapter 2.1 2.2 2.3 2.5

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