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Annual Worth Analysis for Capital Allocation

This chapter covers the annual worth analysis method for evaluating the financial worth of capital allocation decisions. Topics include determining annual cash flow, resolving present costs to annual costs, and considering different analysis periods.

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Annual Worth Analysis for Capital Allocation

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  1. Chapter 6 - Annual Worth AnalysisClick here for Streaming Audio To Accompany Presentation (optional) EGR 403 Capital Allocation Theory Dr. Phillip R. Rosenkrantz Industrial & Manufacturing Engineering Department Cal Poly Pomona

  2. EGR 403 - The Big Picture • Framework:Accounting& Breakeven Analysis • “Time-value of money” concepts - Ch. 3, 4 • Analysis methods • Ch. 5 - Present Worth • Ch. 6 - Annual Worth • Ch. 7, 8 - Rate of Return (incremental analysis) • Ch. 9 - Benefit Cost Ratio & other techniques • Refining the analysis • Ch. 10, 11 - Depreciation & Taxes • Ch. 12 - Replacement Analysis EGR 403 - Cal Poly Pomona - SA8

  3. Annual Cash Flow CalculationsResolving a Present Cost to an Annual Cost • A is -PMT in EXCEL. • To duplicate the A/P factor, put the value for P in place of PV in the PMT fields: • PMT(rate, nper, pv, fv, type) • (fv and type are 0) • To duplicate the A/F factor, put the value for F in place of FV in: • PMT(rate, nper, pv, fv, type) • (pv and type are 0) • Simplest case is to convert the PV to an A-series (annual worth): • A = P(A/P, i, n) • Where there is salvage value: • A = F(A/F, i, n) See Examples 6 -1 & 2 EGR 403 - Cal Poly Pomona - SA8

  4. Annual Cash FlowFour Essential Points • EUAC = PWC(A/P, i, n) • EUAB = PWB(A/P, i, n) • EUAW = EUAB - EUAC • EUAW is • Decreased by a cost. • Increased by a benefit. • In MS Excel use “-PMT” to calculate EUAW (remember the minus sign) • For an irregular cash flow over the analysis period first determine the PW then convert to EUAW. EGR 403 - Cal Poly Pomona - SA8

  5. Situation Criterion Fixed input Amount of capital available fixed Maximize EUAB Fixed output $ amount of benefit is fixed Minimize EUAC Neither fixed Neither capital nor $ benefits are fixed Maximize EUAW Annual Cash Flow Analysis EGR 403 - Cal Poly Pomona - SA8

  6. Two More Examples of Resolving a PW to an EUAW These two examples further illustrate: • The equivalency of PW and EUAW. • Example 6-5 (Example 5-1) • Example 6-6 EUAW EGR 403 - Cal Poly Pomona - SA8

  7. Analysis Period Considerations • Analysis period equal to alternative lives. • Analysis period a common multiple of alternative lives. • Analysis period for a continuing requirement. • Some other period such as project life. EGR 403 - Cal Poly Pomona - SA8

  8. Analysis Period Equal to Alternative Lives. • Base the comparison on the life of the alternatives. • This is the case we have most often considered in our examples. • This is rarely the case in ‘real’ life organizations. EGR 403 - Cal Poly Pomona - SA8

  9. Analysis Period a Common Multiple of Alternative Lives. • When the lives of the equipment in the two alternatives varies, use a common multiple of the two lives. • Example 6-7 • However, calculations are simplified. You only need to use one useful life to get the EUAW. EGR 403 - Cal Poly Pomona - SA8

  10. Analysis Period for a Continuing Requirement. • Where the project will last forever (nothing does) use an infinite time period. • In most analyses organizations often use a representatively long time period to get a reasonable estimate. • Example 6-9: Alt A has infinite analysis period. Use A = P i EGR 403 - Cal Poly Pomona - SA8

  11. Some Other Period Such AsProject Life. • Most often physical equipment has a useful life that varies from the project life. • In this case use the project life as the analysis period. • This is the most common case in ‘real’ organizations. EGR 403 - Cal Poly Pomona - SA8

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