Chapter 6 - Annual Worth Analysis Click here for Streaming Audio To Accompany Presentation (optional)

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