Engineering Economy is the discipline concerned with the ...
Engineering Economy
I. Introduction
Engineering Economy is the discipline concerned with the economic aspects of engineering; it involves the systematic evaluation of the costs and benefits of proposed technical projects. The principles and methodology of engineering economy are an integral part of the daily management and operation of private-sector companies and corporations, regulated public utilities, government units or agencies, and nonprofit organizations. These principles are utilized to analyze alternative uses of financial resource, particularly in relation to the physical assets and the operation of an organization. Last, but certainly not least, engineering economy will prove to be invaluable to you in assessing the economic merits of alternative uses of your personal funds.
A. Principles of Engineering Economy
PRINCIPLE 1 -- DEVELOP THE ALTERNATIVES: The Choice (decision) is among alternatives. The alternatives need to be identified and then defined for subsequent analysis.
PRINCIPLE 2 -- FOCUS ON THE DIFFERENCES: Only the differences in expected future outcomes among the alternatives are relevant to their comparison and should be considered in the decision.
PRINCIPLE 3 -- USE A CONSISTENT VIEWPOINT: The prospective outcomes of the alternatives, economic and other, should be consistently developed from a defined viewpoint.
PRINCIPLE 4 -- USE A COMMON UNIT OF MEASURE: Using a common unit of measurement to enumerate as many of the prospective outcomes as possible will make easier the analysis and comparison of the alternatives.
PRINCIPLE 5 -- CONSIDER ALL RELEVANT CRITERIA: Selection of a preferred alternative (decision making) requires the use of a criterion (or several criteria). The decision process should consider both the outcomes enumerated in the monetary unit and those expressed in some other unit of measurement or made explicit in a descriptive manner.
|Category |Economic criterion |
|Fixed input |Maximize the benefits or other outputs. |
|Fixed output |Minimize the costs or other inputs. |
|Neither input nor output fixed |Maximize the profits (benefits or other outputs minus costs or other inputs). |
PRINCIPLE 6 -- MAKE UNCERTAINTY EXPLICIT: Uncertainty is inherent in projecting the future outcomes of the alternatives and should be recognized in their analysis and comparison.
PRINCIPLE 7 -- REVISIT YOUR DECISIONS: Improved decision-making results from an adaptive process; to the extent practicable, the initial projected outcomes of the selected alternative should be subsequently compared with actual results achieved.
B. Engineering Economic Analysis Procedure
1. Problem recognition, formulation, and evaluation.
2. Development of the feasible alternatives.
3. Development of the cash flows for each alternative.
4. Selection of a criterion (or criteria).
5. Analysis and comparison of the alternatives.
6. Selection of the preferred alternative.
7. Performance monitoring and post-evaluation of results.
II. Cost Concepts
Fixed costs are those unaffected by changes in activity level over a feasible range of operations for the capacity available.
Variable costs are those associated with an operation that vary in total with the quantity of output or other measures of activity level.
An incremental cost is the additional cost that results from increasing the output of a system by one unit.
Recurring costs are those that are repetitive and occur when an organization produces similar goods or services on a continuing basis.
Nonrecurring costs are those that are not repetitive, even though the total expenditure may be cumulative over a relatively short period of time.
Direct costs are those that can be reasonably measured and allocated to a specific output or work activity.
Indirect costs are those that are difficult to attribute or allocate to a specific output or work activity.
Standard costs are representative costs per unit of output that are established in advance of actual production or service delivery.
Cash cost (involving real expenditure) versus book cost.
A 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.
An opportunity cost is incurred because of the use of limited resources, such that the opportunity to use those resources to monetary gain in an alternative use is foregone.
Life-cycle cost refers to a summation of all the costs, recurring and nonrecurring, related to a product, structure, system, or service during its life span.
III. Money-Time Relationships
A. Time Value of Money
• Purchasing power of money
• Earning power of money
B. Simple Interest
I = (P)(N)(i)
where: P = principal amount lent or borrowed
N = number of interest periods (e.g., years)
i = interest rate per interest period.
C. Compound Interest
Whenever the interest charge for any interest period is based on the remaining principal amount plus any accumulated interest charges up to the beginning of that period, the interest is said to be compound.
D. Equivalence
Economic equivalence is established when there is no difference between a future payment, or a series of future payments, and a present sum of money.
E. Notation and Cash Flow Diagram
In compound interest calculations, the following notation is used:
P = Present sum of money;
F = Future sum of money
A = End-of-period cash flows
i = effective interest per interest period
n = Number of compounding periods
F. Basic Interest Formulas (Discrete Compounding / Discrete Cash Flows)
|Known |To find |Formula |Examples |
|P |F | |A person borrows $10,000 for five years at 12% interest|
| | |or (F/P, i, n) |rate. How much he/she must repay at the end of the |
| | | |fifth year? |
|F |P |or (P/F, i, n) |A person wishes to have $5,000 ten years from now. |
| | | |What amount should be deposited now in an account that |
| | | |pays 8% interest? |
|P |A |or (A/P, i, n) |What is the monthly payment to repay a mortgage of |
| | | |$70,000 at 0.75% interest rate per month for 15 years? |
|A |P |or (P/A, i, n) |How much should be deposited in a fund (with 8% |
| | | |interest) now to provide for 10 end-of-year withdraws |
| | | |of $10,000? |
|F |A |or (A/F, i, n) |How much money should be deposited each year (with 8% |
| | | |interest) in order to have $1,000,000 at time of |
| | | |retirement 25 years from now. |
|A |F |or (F/A, i, n) |If $2,000 is deposited in an IRA account that earns 10%|
| | | |interest, how much money will be accumulated in 20 |
| | | |years? |
Problem 3-15, 3-18, 3-27, 3-30, 3-36
G. Interest Formulas Relating a Uniform Gradient of Cash Flows
|Known |To find |Formula |Examples |
|G |F | |A person decided to invest $0 this year, $1000 |
| | |or (F/G, i, n) |next year, $2000 the following year, and |
| | | |increase by $1000 a year thereafter earning 10%|
| | | |interest rate. How much will he/she accumulate|
| | | |after 20 years? |
|G |P | |What amount should be deposited now in an |
| | |or (P/G, i, n) |account that pays 8% interest to pay $200 two |
| | | |years from now, $400 three years from now, and |
| | | |increase $200 a year thereafter? |
|G |A | |A person decided to invest $0 this year, $1000 |
| | |or (A/G, i, n) |next year, $2000 the following year, and |
| | | |increase by $1000 a year thereafter earning 10%|
| | | |interest rate for 20 years. What is the |
| | | |equivalent amount if the money was deposited |
| | | |equally? |
Problem 3-50
H. Interest Formulas when n=( or i=0
|Interest Formula |n=( |i=0 |
|(F/P, i, n) |( |1 |
|(P/F, i, n) |0 |1 |
|(A/P, i, n) |i |1/n |
|(P/A, i, n) |1/i |n |
|(A/F, i, n) |0 |1/n |
|(F/A, i, n) |( |n |
|(A/G, i, n) |1/i |(n-1)/2 |
|(P/G, i, n) |1/i2 |n (n-1)/2 |
I. Interest Formulas Relating a Geometric Gradient of Cash Flows
|Known |To find |Formula |Examples |
|A1, g |P | |You would like to set up a scholarship to award $2000 this|
| | | |year, $2200 next year, and increase by 10% a year |
| | | |thereafter earning 8% interest rate. How much should be |
| | | |deposited now? |
|A1, g |F | |A person decided to invest $1000 this year, $1050 next |
| | | |year, and increase by 5% a year thereafter earning 10% |
| | | |interest rate. How much will he/she accumulate after 20 |
| | | |years? |
|A1, g |A | |A 5-year contract calls for $100,000 the first year and |
| | | |then increases 10% per year. What is the equivalent |
| | | |annual salary with interest rate of 8%? |
Problem 3-15, 3-66, 3-69
J. Nominal and Effective Interest Rate
Unless otherwise noted, the interest rate is usually expressed in terms of annual rate. If the interests are compounded more than once a year, the actual interest accumulated in a year is higher than the quoted (nominal) rate. The actual rate of interest earned on the principal during one year is known as the effective rate. The relationship between effective interest rate, i, and nominal interest rate, r, is
[pic]
where: m = number of compounding periods per year
(m=2 for semi-annually compounding, 4 for quarterly, 12 for monthly, 52 for weekly, 365 for daily)
Problem 3-39, 3-87
K. Interest Formulas for Continuous Compounding and Discrete Cash Flows
If the interests are compounded continuously, the relationship between effective interest rate, i, and nominal interest rate, r, is
[pic]
IV. Evaluation of Single Alternative
A. Determining the Minimum Attractive Rate of Return (MARR)
Deciding factors:
• Supply of capital (amount, sources, costs of funds, etc.)
• Demand of capital (number of projects, investment amount, risk, etc.)
• Cost of administration
• Type of organization
B. Net Present Worth (NPW) Method
NPW = PW(cash inflows) ( PW(cash outflows)
Project is acceptable if NPW ( 0
1) Special Application: Bond Value
VN = C(P/F, i, N) + rZ (P/A, i, N)
where: VN = Present value of the bond
C = Redemption or disposal price (usually equal to Z)
Z = Face (or par) value
r = bond rate per interest period
N = Number of periods before redemption.
i = bond yield rate per period
2) Capitalized Worth (when n = ()
[pic]
Problem 4-6, 4-12
C. Net Future Worth (NFW) Method
NFW = FW(cash inflows) ( FW(cash outflows)
Project is acceptable if NFW ( 0
D. Annual Equivalent Worth (AEW) Method
AEW = AE(cash inflows) ( AE(cash outflows)
Project is acceptable if AEW ( 0
1) Capital Recovery (CR) Amount (Loss in value + Interest on capital)
CR = I (A/P, i, N) ( S (A/F, i, N)
= (I ( S)(A/P, i, N) + S ( i)
= (I ( S)(A/F, i, N) + I ( i)
where I = Initial investment
S = Salvage value at the end of the recovery period
N = Recovery period
Problem 4-20
E. Internal Rate of Return (IRR) Method
• Both cash inflows and outflows must be present;
• ((cash inflows) ( ((cash outflows) for investment cases
Searching for the IRR:
Goal: To find an interest rate, so that
NPW = 0;
NFW = 0; or
EAW = 0.
Trial-and-error routine
Interpolation
Project is acceptable if IRR ( MARR.
Problem 4-24, 4-44
F. Payback Period Method
• Simple payback period
• Discounted payback period
Problem 4-48
G. Spreadsheet Applications
Irregular Cash Flows
|Net Present Value |=NPV(Rate, Values) |
|Internal Rate of Return |=IRR(Values, Guess) |
Single Payment Compounding
|Future Value |(F/P, i, n) |=FV(rate, nper, pmt, PV, type) |
|Present Value |(P/F, i, n) |=PV(rate, nper, pmt, FV, type) |
|Effective Interest Rate | |=RATE(nper, pmt, PV, FV, type, guess) |
|Periods to reach FV | |=NPER(Rate, pmt, PV, FV, type) |
Uniform Series Annuities
|Annuity Payment |(A/P, i, n) |=PMT(rate, nper, PV, FV, type) |
| |(A/F, i, n) |=PMT(rate, nper, PV, FV, type) |
|Present Value |(P/A, i, n) |=PV(rate, nper, pmt, FV, type) |
|Future Value |(F/A, i, n) |=FV(Rate, nper, pmt, PV, type) |
|Annuity Rate | |=RATE(nper, pmt, PV, FV, type, guess) |
|Yield (Bond) | |=YIELD(See Excel Help screen) |
|Annuity Term | |=NPER(Rate,pmt,PV,FV,type) |
|Periods to reach FV | |=NPER(Rate, pmt, PV, FV, type) |
Uniform Loan Payments
|Uniform Loan Pmt |=PMT(rate, nper, PV, FV, type) |
|Remaining Balance |=PV(Rate, Remaining periods, pmt, FV, type) |
|Interest in Period |=IPMT(Rate, per, nper, PV, FV, type) |
|Principal in Period |=PPMT(Rate, per, nper, PV, FV, type) |
V. Comparing Multiple Alternatives
A. Types of Alternatives
• Mutually Exclusive: Selecting one alternative precludes selecting any other alternative.
• Independent: The choice of an alternative is independent of the choice of any other alternatives.
• Contingent: The acceptance of an alternative is conditional on the selection of one or more other alternatives.
B. Study (Analysis) Period
• Service period required
• Useful life of the shorter (or longer)-lived alternative
• Company policy
❑ Case 1: Useful lives are the same for all alternatives and equal to study period
❑ Case 2: Useful lives are different among the alternatives and at least one does not equal to study period
o Repeatability assumption
o Co-terminated assumption
C. Useful Lives Equal to Study Period
❑ Net Present Worth (NPW) Method
Maximize NPW ( 0
❑ Net Future Worth (NFW) Method
Maximize NFW ( 0
❑ Annual Equivalent Worth (AEW) Method
Maximize EAW ( 0
❑ Internal Rate of Return (IRR) Method
Incremental Analysis
Problem 5-10, 5-14, 5-16
D. Useful Lives Are Different Among Alternatives
o Repeatability assumption
o Co-terminated assumption
Problem 5-16, 5-22, 5-24, 5-26, 5-28
E. Combinations of Projects to Form Mutually Exclusive Alternatives
Problem 5-32, 5-34
VI. Evaluating Projects with the Benefit/Cost (B/C) Ratio Method
B/C Ratio = [pic]
Criteria: B/C Ratio ( 1 (Single Alternative)
Incremental Analysis for Multiple Alternatives
❑ Conventional B/C Ratio:
o Benefit = Benefits – Disbenefits
o Cost = Capital Recovery Amount + Operating & Maintenance
❑ Modified B/C Ratio
o Benefit = Benefits – Disbenefits – Operating & Maintenance
o Cost = Capital Recovery Amount
Problem 6-8, 6-14, 6-16, 6-18
VII. Depreciation and Income Taxes
A. Depreciation
Depreciation is the decrease in value of physical properties with the passage of time and use. More specifically, depreciation is an accounting concept that establishes an annual deduction against before-tax income such that the effect of time and use on an asset's value can be reflected in a firm's financial statements.
Requirements for depreciable property:
▪ It must be used in business or held to produce income.
▪ It must have a determinable useful life, and the life must be longer than one year.
▪ It must be something that wears out, decays, gets used up, becomes obsolete, or loses value from natural causes.
▪ It is not inventory, stock in trade, or investment property.
Cost Basis (B): The initial cost of acquiring an asset (purchase price plus sales taxes), including transportation, installation and any other normal costs of making the asset serviceable for its intended use. (Also known as unadjusted cost basis)
Adjusted Cost Basis: The original basis of asset, adjusted by allowable increases or decreases, is used to compute depreciation and depletion deductions.
Book Value (BV): The worth of a depreciable property as shown on the accounting records of a company. It is the original cost basis of the property, including any adjustment, less all allowable depreciation or depletion deductions.
Market Value (MV): The amount that will be paid by a willing buyer to a willing seller for a property in an open market.
Recovery period: The number of years over which the cost basis of a property is recovered through the accounting process.
Salvage Value (SV): The estimated value of property at the end of its useful life. Under MACRS, the SV of a depreciable property is defined to be zero.
B. Classical Depreciation Methods
❑ Straight-Line (SL) Depreciation
[pic]
❑ Sum-Of-Years'-Digits (SOYD) Depreciation
[pic]
[pic]
❑ Declining Balance (DB) Depreciation
[pic]
❑ Declining Balance with Switchover to Straight-Line (DB ( SL) Depreciation
C. Modified Accelerated Cost Recovery System (MACRS)
❑ General Depreciation System (GDS): Main system
❑ Alternative Depreciation System (ADS):
o Longer recovery period
o Uses only SL method of depreciation
o For property placed in any tax-exempt use and property used predominantly outside U.S.
|Asset Class |Description of Assets |Class Life |Recovery Period |
| | | |GDS |ADS |
|00.11 |Office furniture and equipment |10 |7 |10 |
|00.12 |Information systems, including computers |6 |5 |5 |
|00.22 |Automobiles, taxis |3 |5 |5 |
|00.23 |Buses |9 |5 |9 |
|00.241 |Light general purpose trucks |4 |5 |5 |
|00.242 |Heavy general purpose trucks |6 |5 |6 |
|00.26 |Tractor units for use over the road |4 |3 |4 |
|10.0 |Mining |10 |7 |10 |
|13.2 |Production of petroleum and natural gas |14 |7 |14 |
|13.3 |Petroleum refining |16 |10 |16 |
|15.0 |Construction |6 |5 |6 |
|22.3 |Manufacture of carpets |9 |5 |9 |
|24.4 |Manufacture of wood products |10 |7 |10 |
|28.0 |Manufacture of chemicals and allied products |9.5 |5 |9.5 |
|30.1 |Manufacture of rubber products |14 |7 |14 |
|32.2 |Manufacture of cement |20 |15 |20 |
|34.0 |Manufacture of fabricated metal products |12 |7 |12 |
|36.0 |Manufacture of electronic components, products, & systems |6 |5 |6 |
|37.11 |Manufacture of motor vehicles |12 |7 |12 |
|37.2 |Manufacture of aerospace products |10 |7 |10 |
|48.12 |Telephone central office equipment |18 |10 |18 |
|49.13 |Electric utility steam production plant |28 |20 |28 |
|49.21 |Gas utility distribution facilities |35 |20 |35 |
GDS Recovery rate for Personal Property
|If the recovery year |3-year |5-year |7-year |10-year class |15-year class |20-year class |
|is: |class |class |class | | | |
| 1 |33.33 |20.00 |14.29 |10.00 |5.00 |3.750 |
| 2 |44.45 |32.00 |24.49 |18.00 |9.50 |7.219 |
| 3 |*14.81 |19.20 |17.49 |14.40 |8.55 |6.677 |
| 4 | 7.41 |*11.52 |12.49 |11.52 |7.70 |6.177 |
| 5 | |11.52 |*8.93 | 9.22 |6.93 |5.713 |
| 6 | |5.76 |8.92 | 7.37 |6.23 |5.285 |
| 7 | | |8.93 |*6.55 |*5.90 |4.888 |
| 8 | | | 4.46 |6.55 |5.90 |4.522 |
| 9 | | | |6.56 |5.91 |*4.462 |
| 10 | | | |6.55 |5.90 |4.461 |
| 11 | | | |3.28 |5.91 |4.462 |
| 12 | | | | |5.90 |4.461 |
| 13 | | | | |5.91 |4.462 |
| 14 | | | | |5.90 |4.461 |
| 15 | | | | |5.91 |4.462 |
| 16 | | | | |2.95 |4.461 |
| 17 | | | | | |4.462 |
| 18 | | | | | |4.461 |
| 19 | | | | | |4.462 |
| 20 | | | | | |4.461 |
| 21 | | | | | |2.231 |
Computation Method:
The 3-, 5-, 7-, and 10-year classes are based on double declining balance (DDB) depreciation with conversion to straight-line depreciation in the year with the asterisk (*) to maximize the deduction. The 15- and 20-year classes are based on 150% declining balance depreciation with conversion to straight-line depreciation in the year with the asterisk (*) to maximize the deduction. The half-year convention applies, with all property treated as placed in service in the middle of the year. Thus a half-year of depreciation is allowed in the first recovery year and a half-year of depreciation when the property is disposed of or retired from service, or in the last recovery year.
MACRS Classes of Depreciable Real Property
❑ GDS
o 27.5-Years Residential rental property (does not include hotels and motels)
o 39.0-Years Nonresidential real property
❑ ADS
o 40.0-Years Nonresidential real property
GDS Recovery rate for Personal Property
Recovery Percentage for Residential Rental Property
|Recovery |Month placed in service |
|Year |1 |
|Year |1 |
|Over |Not over |This |plus |over |
|0 |25,750 | |15% |0 |
|25,750 |62,450 |3,862.50 |28% |25,750 |
|62,450 |130,250 |14,138.50 |31% |62,450 |
|130,250 |283,150 |35,156.50 |36% |130,250 |
|Over 283,150 |90,200.50 |39.6% |283,150 |
If your filling status is Married file jointly or Qualifying widow(er)
|Taxable Income |Your tax is |
|Over |Not over |This |plus |over |
|0 |43,050 | |15% |0 |
|43,050 |104,050 |6,457.50 |28% |43,050 |
|104,050 |158,550 |23,537.50 |31% |104,050 |
|158,550 |283,150 |40,432.50 |36% |158,550 |
|Over 283,150 |85,288.50 |39.6% |283,150 |
If your filling status is Married file separately
|Taxable Income |Your tax is |
|Over |Not over |This |plus |over |
|0 |21,525 | |15% |0 |
|21,525 |52,025 |3,228.75 |28% |21,525 |
|52,025 |79,275 |11,768.75 |31% |52,025 |
|79,275 |141,575 |20,216.25 |36% |79,275 |
|Over 141,575 |42,644.25 |39.6% |141,575 |
If your filling status is Head of household
|Taxable Income |Your tax is |
|Over |Not over |This |plus |over |
|0 |34,550 | |15% |0 |
|34,550 |89,150 |5,182.50 |28% |34,550 |
|89,150 |144,400 |20,470.50 |31% |89,150 |
|144,400 |283,150 |37,598.00 |36% |144,400 |
|Over 283,150 |87,548.00 |39.6% |283,150 |
Corporate Tax Rates (1999)
|Taxable Income |Rate |Income Tax |
|Not over 50,000 |15% |15% over 0 |
|50,000-75,000 |25% |7,500 + 25% over 50,000 |
|75,000-100,000 |34% |13,750 + 34% over 75,000 |
|100,000-335,000 |39% |22,250 + 39% over 100,000 |
|335,000-10 million |34% |113,900 + 34% over 335,000 |
|10 million-15 million |35% |3,400,000 + 35% over 10 mil. |
|15 mil. - 18,333,333 |38% |5,150,000 + 38% over 15 mil. |
|over 18,333,333 |35% |35% over 0 |
E. Gain (Loss) on the Disposal of an Asset
F. After-Tax Cash Flow Analysis
G. Spreadsheet Applications
|Depreciation | |
|Double Declining Bal. |=DDB(Cost, Salvage, Life, Period, factor) |
|Straight Line |=SLN(Cost, Salvage, Life) |
|Sum-of-Years Digits |=SYD(Cost, Salvage, Life, Period) |
Problem 7-24, 7-32, 7-38, 7-40
VIII. Estimating Cash Flows
Problem 8-16
IX. Inflation and Price Changes
A. Consumer Price Index (CPI)
General price inflation, which is defined here as an increase in the prices paid for goods and services bringing about a reduction in the purchasing power of the monetary unit, is a business reality that can affect the economic comparison of alternatives.
[pic]
B. Basic Concepts
Actual Dollars (A$): The dollar amount associated with a cash flow as of the time it occurs.
Real Dollars (R$): The dollar amount expressed in term of the same purchasing power relative to a particular time with a cash flow as of the time it occurs. (or Constant Dollars)
General Price Inflation Rate (f): A measure of the change in the purchasing power of a dollar during a specific period of time.
Combined (Nominal) Interest Rate (ic): The money paid for the use of capital, normally expressed as a nominal rate that includes a market adjustment for the anticipated general price inflation rate in the economy.
Real Interest Rate (ir): The money paid for the use of capital, normally expressed as a nominal rate that does not include a market adjustment for the anticipated general price inflation rate in the economy.
Base Time Period (b): The base time period used to define the purchasing power of real (constant) dollar.
[pic]
[pic]
Problem 9-24, 9-30
X. Dealing with Uncertainty
o Breakeven Analysis
o Sensitivity analysis
o Optimistic-pessimistic estimation
o Risk-adjusted MARR
o Reduction of useful life
XI. Replacement Analysis
Replacement analysis
o Defender
o Challenger
Determination of Economic Life
Problem 11-8, 11-14
Incremental Analysis
Source: Gerald W. Smith, "Engineering Economy: Analysis of Capital Expenditures", 3rd ed. Iowa State University Press. 1979
-----------------------
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Yes
Yes
No
Yes
No
No
No
Discard this alt..
Consider next higher alt.
Keep "Current Best" unchanged
The "Current Best" is the final selection.
Accept the higher Alt. as "Current Best"
Calculate Incremental RoR ((B/(C) based on incremental cash flows
Calculate incremental cash flows
Compare the "Current Best" with the next higher alternative.
Accept this alternative as
"Current Best"
Calculate RoR (B/C) of the lowest alternative
Rank alternatives according to the size of investments
Is there
any more higher alts?
If
Inc. RoR(MARR?
((B/(C(1)
If
RoR(MARR?
(B/C(1)
[pic]
No
................
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