Ch 10-1© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Cost Analysis and Estimatingfor Engineering and Management

Chapter 10

Engineering Economy

Ch 10-2© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Overview

Methods to Determine Project Returns Impact of Time Value of Money (Interest)

Simple and Compound Interest CalculationsMethods to Evaluate Projects

Various Rates of Return Evaluation of Replacement Alternatives Tax Effects on Decisions

Ch 10-3© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Money

All Projects Require Money All Should Return Money (Payback) When Large Sums of Money or

Longer Times Are Involved –

Interest Becomes Important Decisions Are Based on Money

Ch 10-4© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Capital

Monetary Assets Should Be Employed to Earn a Return Invested

In Ordinary Financial TransactionsIn Some Endeavor (Production/Service)

Need to Evaluate Investments

Ch 10-5© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Monitoring Return Ways to Express Return

Total DollarsRatio with SalesReturn on Investment

Calculation of ReturnAverage Annual Rate of ReturnPayback PeriodEngineering-Economy Rate of Return

Ch 10-6© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Average Annual Rate of Return

Yearly After Tax Profit from Activity Total Investment in the Activity

Alternately

Eq 10.1

Eq 10.2

% ,100 valueinvestment

yearper earnings=return

% ,100

investment average

life economicinvestment total- earnings average=return

Ch 10-7© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Payback Period

How Many Years to Earn Back the Investment

Capital Liquidity Importance

Eq 10.3 years ,earningsafter tax annual

investmentnet =payback

Ch 10-8© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Payback Caveats

Assumes Equal Annual Earnings Does Not Account for

InterestDepreciation / Obsolescence Earnings After Payback

Ch 10-9© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Interest

Choice of InvestmentsTraditional (Bank, Stock Market, etc.)Capital into Endeavor (Equipment, etc.)

Time Value of Money Interest Calculations

SimpleCompound

Ch 10-10© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Simple Interest

Interest

I = Pni Total Including Principal

F = P + I = P(1+ni) Payments Are at the End of the Periods

Ch 10-11© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Compound Interest Interest Adds to Principal

Interest Earns Interest In Subsequent Periods

Single Payment Compound Amount Factor

(1+i)n

Used In All Variations

Ch 10-12© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Various Interest Calculations

Net Present Worth Net Future Worth Net Equivalent Annual Worth Rate of Return All Generally Yield Consistent

Recommendations

Ch 10-13© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Set Up for Discussions Example Situation

Investment $1025, for 3 Years

Factors Can Be Calculated or Found In Tables (10% and 20% in Appendices)

Year Cost Revenue

0 $1025 $0

1 0 450

2 0 425

3 0 400

Ch 10-14© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Net Present Worth Convert All Amounts to Present Value

 Period

 n

PW Factor at 10%

 

Cash Flow

 Amount

Year 1 to zero 1 0.9091 $450 $409

Year 2 to zero 2 0.8264 425 351

Year 3 to zero 3 0.7513 400 301

Total       $1061

Less proposed investment

0 1.0000 1025 1025

Net present worth

      $36

Ch 10-15© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Net Future Worth Convert All Amounts to Future Value

  

Period

  n

Compound Amount

Factor 10% 

 Cash Flow

  

AmountYear 1 to 3 2 1.2100 $450 $545

Year 2 to 3 1 1.1000 425 468

Year 3 0 1.0000 400 400        $1413

Compounded to terminal year at 10%

       

3 1.3310 1025 1364

Net future worth       $ 49

Ch 10-16© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Net Equivalent Annual Worth

Find Present Value of Receipts Calculate Annual Equivalent

Calculate Net Annual Equivalent Worth

427$4868.2

1061

0.7513+0.8264+0.9091

1061 =

14$4868.2

1025427=

Ch 10-17© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Net Equivalent Annual Worth Example

  AmountAnticipated annual receipts $427Less equal annual equivalent worth 14Equal annual receipts $413

1025 1.10 = $1128Less payment 413  715

715 1.10 = $787Less payment 413  374

374 1.10 = $413Less payment 413  0

Ch 10-18© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Rate of Return

Other Methods Assume an Interest Rate Find the Interest Rate to Yield Same

Return as Investment Found By Trial-and-Error or Interpolation

Ch 10-19© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Example at 5%

Ch 10-20© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Example at 15%

Ch 10-21© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Interpolate

Ch 10-22© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Compare the Methods

Compare Present and Future Worths Rate of Return Finds Actual Interest

Other Methods Assume an Interest

Method Amount

Net present worth at 10% $36

Net future worth at 10% $49

Net annual equivalent worth at 10% $14

Rate of return 12.3%

Ch 10-23© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Engineering Economy

P, F, A, i, and n Functional Notation

F=P(P/F, i%, n)P/F means, Find P Given F

6 Methods (Equations)2 Single Payment4 Uniform Payment Series

Ch 10-24© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Single Payment Methods

F P i n ( )1

P F i n ( )1

Factor Name Functional Notation

Equation Equation Number

Compound-amount factor

(F/P, i%, n) (10.7)

Present-worth factor

(P/F, i%, n) (10.8)

Ch 10-25© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Single Payment Diagrams

Ch 10-26© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Uniform Payment Series

A Fi

i n

( )1 1

A Pi i

i

n

n

( )

( )

1

1 1

F Ai

i

n

( )1 1

P Ai

i i

n

n

( )

( )

1 1

1

Factor Name Functional Notation

Equation Equation Number

Sinking-fund factor 

(A/F, i%, n) (10.9)

Capital-recovery factor 

(A/P, i%, n) (10.10)

Compound-amount factor 

(F/A, i%, n) (10.11)

Present-worth factor 

(P/A, i%, n) (10.12)

Ch 10-27© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Uniform Series Diagrams

Ch 10-28© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Uniform Series Diagrams

Ch 10-29© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Assumptions

Cash Flow at Year End (Lump Sum) Ignore Inflation Special Handling of Taxes Constant Interest Rate Predetermined MARR Save Non-Quantifiable Effects for End

Ch 10-30© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Interest

Cost of Using Capital Internal Rate of Return (IRR) Minimum Acceptable Rate of Return

(MARR) External Rate of Return (ERR) Percentage Showing Yield on Different

Uses of Capital

Ch 10-31© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

IRR

Based Solely on Project’s Cash FlowBefore Taxes

Find IRR for Present Worth of $0 Required IRR < the Projected IRR

Approve Project Compare Alternatives

Ch 10-32© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

MARR

Rate Set By Management Sets Lower Limit on Acceptable Return Rations Capital to Avoid Unproductive

Investments

Ch 10-33© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Comparison of Alternatives Feasible Alternatives Mutually Exclusive “Do Nothing” Is an Alternative May Omit Costs/Revenues If the Same Find Alternative with Highest Return or

Lowest Cost Equal/Unequal Lives Handled Differently

Ch 10-34© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Equal Life Example (i=10%)  Automatic Semiautomatic

Investment cost $1,250,000 $800,000

Annual Utilities 570,000 480,000

Labor, annual 50,000 700,000

Floor space 80,000 50,000

Maintenance 140,000 90,000

Equipment life 5 years 5 years

Ch 10-35© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Cash Flows

Ch 10-36© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Comparison for Example  Automatic Semiautomatic

Annual capital recovery cost, P(A/P, 10%,5)

$329,750 $211,040

Annual cost 1,002,500 1,478,000

Comparative annual cost $1,332,250 $1,689,040

Ch 10-37© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Unequal Life

Comparison Must Be for Equal OutputExtra Cost Involved with Extra Output

Different Useful Lives for AlternativesAnalysis Period Common Multiple of Useful Lives

Example I1 – 3 Years, I2 – 4 YearsCommon Multiple = 12 Years

Ch 10-38© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Unequal Life ExampleInvestments I1 I2

Initial cost $230,000 $320,000

Annual operating cost 25,000 0

Salvage value 0 40,000

Economic life, year 3 4

Multiple of lives 12 12

Repeated investments 3 2

MARR before taxes 10% 10%

Ch 10-39© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

12 Year Cash Flow

Ch 10-40© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Comparison

Present Worth for 12 Years

PW (I1) = – $800,520

PW (I2) = – $629,116 Select Investment 2, Lower Cost

Assuming Revenues Are Equal Study Period May Be Excessive Situation May Vary from Assumptions

Ch 10-41© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Restricted Life Project Limited to 2 Years Assume Salvage Value = $0

PW(I1) = – $273,388

PW(I2) = – $320,000 Compare to Include Salvage Value

(320,000-273,338)/(P/F,10%,2)=$56,400 Decision Depends on Salvage Cost of I2

Ch 10-42© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Replacement

Existing Alternative In Operation Economic Facts Are Different for

Challenger Equipment Life – Period of Lower Cost Need Value for Existing Equipment

Don’t Use Book or Trade In ValueNeed the Market Value

Ch 10-43© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Equivalent Annual Cost for Replacement

Includes Resale Value (Fs)

Or

Eq 10.13 + )%, ,/)(( iFniPAFPEAC ss

) %, /()%,,/( niFAFniPAPEAC ss

Ch 10-44© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Example i = 20%, Life = 4 Years

  

Year

Defender (D) Challenger (C)

Operating cost

 

Salvage value

Operating cost

Salvage value

0   $120,000   $350,000

1 $34,000 70,000 $3000 310,000

2 39,000 40,000 10,000 270,000

3 46,000 25,000 12,000 240,000

4 56,000 10,000 15,000 210,000

5     20,000 170,000

6     31,000 120,000

Ch 10-45© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Results

Existing (Defender)

EAC(D) = – $86,618 Challenger

EAC(C) = – $105,208 Challenger Has Higher Cost

Don’t Replace

Ch 10-46© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Effects of Taxes

Taxable IncomeBefore Tax Cash Flow Less Depreciation and Other Charges

Rate of ReturnAfter Tax MARR (Before Tax MARR)(1-t)

Before Tax MARR = 20%, t = 38%

After Tax MARR = About 12.4% Timing of Cash Flow Has Impacts

Ch 10-47© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Considerations for After Tax Analysis

Costs, Savings, Revenues Depreciation Taxable Income Cash Flow Effects Engineering Economy Analysis Decision Process

Consider Non-Economic Factors

Ch 10-48© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

After Tax ExampleYr

End  

Before Tax

 

 Dep.

 

Deductible Charges

 

35% Tax Savings

 

After Tax Cash Flow

            

0 -$3       -$3

1 -25 $3.3 -$28.3 -$9.9 -15.1

2 -14 3.3 -17.3 -6.1 -7.9

3 -14 3.4 -17.4 -6.1 -7.9

3 2       2           

0 -$28       -$28

1 -7 9.2 -$16.2 -$5.7 -1.3

2 -7 12.6 -19.6 -6.9 -0.1

3 -7 6.2 -13.2 -4.6 -2.4

Defender

Challenger

Ch 10-49© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Outcome

EAC(D) = – $11.1 MillionEAC(C) = – $12.5 Million

Different Depreciation Methods UsedFavor Challenger

Costs Represent DisbursementsThus Positive Costs

Select Challenger

Ch 10-50© 2004 Pearson Education, Inc.Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management

Summary

Methods of Project Alternative Evaluation

How to Use and Apply Interest Calculations

How to Evaluate Replacements What Is the Impact of Taxes for

Economic Decisions