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Flash back before we compare mutually exclusive alternatives

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Bank Loan vs. Investment Project Bank Customer Loan Repayment Company Project Investment Return Bank Loan Investment Project

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Payback Period Principle: How fast can I recover my initial investment? Method: Based on cumulative cash flow (or accounting profit) Screening Guideline: If the payback period is less than or equal to some specified payback period, the project would be considered for further analysis. Weakness: Does not consider the time value of money

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-100,000 -50,000 0 50,000 100,000 150,000 012 3 456 Years (n) 3.2 years Payback period $85,000 $15,000 $25,000 $35,000 $45,000 $35,000 0 123456 Years Annual cash flow Cumulative cash flow ($)

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Discounted Payback Period Principle: How fast can I recover my initial investment plus interest? Method: Based on cumulative discounted cash flow Screening Guideline: If the discounted payback period (DPP) is less than or equal to some specified payback period, the project would be considered for further analysis. Weakness: Cash flows occurring after DPP are ignored

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Example 5.2 Discounted Payback Period Calculation PeriodCash FlowCost of Funds (15%)* Cumulative Cash Flow 0-$85,0000 115,000-$85,000(0.15) = -$12,750-82,750 225,000-$82,750(0.15) = -12,413-70,163 335,000-$70,163(0.15) = -10,524-45,687 445,000-$45,687(0.15) =-6,853-7,540 545,000-$7,540(0.15) = -1,13136,329 635,000$36,329(0.15) = 5,44976,778 * Cost of funds = (Unrecovered beginning balance) X (interest rate)

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Net Present Worth Measure Principle: Compute the equivalent net surplus at n = 0 for a given interest rate of i. Decision Rule: Accept the project if the net surplus is positive. 2 3 4 5 0 1 Inflow Outflow 0 PW(i) inflow PW(i) outflow Net surplus PW(i) > 0

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Future Worth Criterion Given: Cash flows and MARR (i) Find: The net equivalent worth at the end of project life $75,000 $24,400 $27,340 $55,760 0 12 3 Project life

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Capitalized Equivalent Worth Principle: PW for a project with an annual receipt of A over infinite service life Equation: CE(i) = A(P/A, i, ) = A/i A 0 P = CE(i)

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Project Balance Concept N0123N0123N0123N0123 Beginning Balance Interest Payment Project Balance -$75,000 -$11,250 +$24,400 -$61,850 -$9,278 +$27,340 -$43,788 -$6,568 +$55,760 +$5,404 Net future worth, FW(15%) PW(15%) = $5,404 (P/F, 15%, 3) = $3,553

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Guideline for Selecting a MARR Real Return2% Inflation4% Risk premium0% Total expected return 6% Real Return2% Inflation4% Risk premium20 % Total expected return 26 % Risk-free real return Inflation Risk premium U.S. Treasury Bills Amazon.com Very safe Very risky

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Chapter 5 Present-Worth Analysis Loan versus Project Cash Flows Initial Project Screening Methods Present-Worth Analysis Methods to Compare Mutually Exclusive Alternatives

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Comparing Mutually Exclusive Alternatives Lecture No.16 Professor C. S. Park Fundamentals of Engineering Economics Copyright © 2005

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Comparing Mutually Exclusive Projects Mutually Exclusive Projects Alternative vs. Project Do-Nothing Alternative

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Revenue Projects Projects whose revenues depend on the choice of alternatives Service Projects Projects whose revenues do not depend on the choice of alternative

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Analysis Period The time span over which the economic effects of an investment will be evaluated (study period or planning horizon). Required Service Period The time span over which the service of an equipment (or investment) will be needed.

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Comparing Mutually Exclusive Projects Principle: Projects must be compared over an equal time span. Rule of Thumb: If the required service period is given, the analysis period should be the same as the required service period.

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Case 1: Analysis Period Equals Project Lives Compute the PW for each project over its life $450 $600 $500$1,400 $2,075 $2,110 0 $1,000$4,000 A B PW (10%) = $283 PW (10%) = $579 A B

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$1,000 $450 $600 $500 Project A $1,000 $600 $500 $450 $3,000 3,993 $4,000 $1,400 $2,075 $2,110 Project B Modified Project A Comparing projects requiring different levels of investment – Assume that the unused funds will be invested at MARR. PW(10%) A = $283 PW(10%) B = $579 This portion of investment will earn 10% return on investment.

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Case 2: Analysis Period Shorter than Project Lives Estimate the salvage value at the end of the required service period. Compute the PW for each project over the required service period.

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Example 5.6 - Comparison of unequal-lived service projects when the required service period is shorter than the individual project life Required Service Period = 2 years

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PW(15%)B = -$364,000 PW(15%)A = -$362,000

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Case 3: Analysis Period Longer than Project Lives Come up with replacement projects that match or exceed the required service period. Compute the PW for each project over the required service period.

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Example 5.7 - Comparison for Service Projects with Unequal Lives when the required service period is longer than the individual project life Required Service Period = 5 years Model A Model B $15,000 $12,500 $4,000 $4,500 $5,000 $5,500 $1,500 $5,000 $5,500 $6,000 $2,000 4 5 5 0 0 1 2 3 1 23 4

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Lease Model A to serve the remaining service life PW(15%)A = -$35.929 PW(15%)B = -$33,173

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Summary Present worth is an equivalence method of analysis in which a project’s cash flows are discounted to a lump sum amount at present time. The MARR or minimum attractive rate of return is the interest rate at which a firm can always earn or borrow money. MARR is generally dictated by management and is the rate at which NPW analysis should be conducted. Two measures of investment, the net future worth and the capitalized equivalent worth, are variations to the NPW criterion.

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The term mutually exclusive means that, when one of several alternatives that meet the same need is selected, the others will be rejected. Revenue projects are those for which the income generated depends on the choice of project. Service projects are those for which income remains the same, regardless of which project is selected. The analysis period (study period) is the time span over which the economic effects of an investment will be evaluated. The required service period is the time span over which the service of an equipment (or investment) will be needed.

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The analysis period should be chosen to cover the required service period. When not specified by management or company policy, the analysis period to use in a comparison of mutually exclusive projects may be chosen by an individual analyst.

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