MER 160 - Design of Thermal Fluid Systems

INTRODUCTION TO ENGINEERING ECONOMICS

Professor BrunoWinter Term 2005

Economic Value

• Need to determine the “value” of an engineering project.– “Should We Do It?”

• Guiding criterion – most often economic value.

• A project can be an “engineering success” but still be a failure.

Cost Benefit Analysis

• Typically we will decide to invest in an engineering project if its benefits outweigh its costs.

• For simple economic analyses we are only concerned with monetary costs and benefits.

Engineering Costs

• Various Costs associated with a project:– Capital Expenditures - 1 time cost at start of

project– Operation and Maintenance (O&M) - periodic

investment that includes labor, expendable supplies, energy, etc.

– Replacement Costs - costs of major equipment that must be replaced as parts wear out.

– Salvage Costs - money you receive when you sell the used equipment:

Cash Flow Diagrams: An Important Tool

Income

time

Initial Capital Cost

ReplacementCosts

Operating &Maintenance

Costs

Salvage“Costs”

- Arrows up represent “income” or “profits” or “payoffs”

- Arrows down represent “costs” or “investments” or “loans”

- The “x axis” represents time, most typically in years

Time Value of Money…Or “I’ll gladly pay you Tuesday for a hamburger today.”

Simple Example: If I offered to give you $10,000 today or $10,000 ten years from now, which would you choose?

Slightly Tougher Example: If I offered to give you $10,000 today or $35,000 ten years from now, which would you chose?

A still tougher example:You are an engineer faced with the

responsibility of buying new production equipment…Which alternative do you pick?

Cost Type Alternative A Alternative B Alternative CCapital $1,200,000 $2,200,000 $1,900,000O&M $430,000 $250,000 $370,000Replacement $26,000 $11,000 $12,000Salvage $9,000 $12,000 $11,000

In order to get a rational answer we need to account for the time value of $$

Engineering Economics

• Earning Power of Money - A dollar in hand today is worth more than a dollar received 1 year from now.

• We need methods for evaluating projects that account for the time value of money.

Interest

Interest is the money paid for the use of borrowed money or the return obtainable by productive investment.

Interest Rate = (Interest accrued per unit Time) / (Original Amount)

Interest Rate• Time Value of Money is based on the idea

that borrowed money should be returned with an extra amount called interest

• The magnitude of the US IR varies but is generally 2-3% > inflation rate

InterestSimple Interest: Interest for an interest period is

calculated using only the original principle

Compound Interest: The interest for an interest period is calculated on the principle plus the total amount of interest accumulated in previous periods.

“interest on top of interest”

Compound interest is the general practice of the business world.

Compounding FrequencyTypically interest is expressed based on

compounding which occurs once per year.

If compounding occurs m times per year, then the effective annual interest rate ieff is related to the nominal annual interest rate i:

ieff = (1+i/m)m - 1

ExampleThe nominal interest rate is 8% per year, and the compounding period is 6-months. What is the effective annual rate?

Equivalence

Different sums of money at different times can be equal in economic value.

i.e. $100 today with i = 6% is equivalent to $106 in one year.

Equivalence depends on the interest rate!

Time Value of MoneyIf P dollars are invested in account that makes

i percent interest per time period and the interest is compounded at the end of each of n periods then:

F = P(1+i)n

P =Present Value (in dollars)

F = Future Value (in dollars)

P

Ft=0

t=n

Factors

Single Payment Compound Amount Factor (future worth)

(F/P, i%, n) :

Single Payment Present Worth Factor (P/F, i%, n):

neffi

PF

)1(

neffiF

P

)1(

1

n is in years if the ieff is used.

Example - Factors

How much inheritance to be received 20 years from now is equivalent to receiving $10,000 now? The interest rate is 8% per year compounded each 6-months.

AnnuitiesAn Annuity is a series of equal amount money

transactions occurring at equal time periodsOrdinary Annuity - one that occurs at the end

of each time period

neffeff

neff

ii

i

AP

)1(

1)1(

1)1(

)1(

neff

neffeff

i

ii

PA

Uniform Series Present Worth

FactorCapital

Recovery Factor

Annuities

Can Relate an Annuity to a future value:

eff

neff

i

i

AF 1)1(

1)1(

n

eff

eff

i

i

FA

Uniform Series Compound

Amount Factor

Uniform Series Sinking Fund Factor

Annuity Example

EXAMPLE:

How much money can you borrow now if you agree to repay the loan in 10 end of year payments of $3000, starting one year from now at an interest rate of 18% per year?

Factors

Fortunately these factors are tabulated…

And Excel has nice built in functions to calculate them too