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

EGR Cal Poly Pomona - SA82 EGR 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 Replacement Analysis

EGR Cal Poly Pomona - SA83 Annual Cash Flow Calculations Resolving a Present Cost to an Annual Cost 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) 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) See Examples & 2

EGR Cal Poly Pomona - SA84 Annual Cash Flow Four 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 Cal Poly Pomona - SA85 Annual Cash Flow Analysis Maximize EUAW Neither capital nor $ benefits are fixed Neither fixed Minimize EUAC$ amount of benefit is fixed Fixed output Maximize EUABAmount of capital available fixed Fixed input CriterionSituation

EGR Cal Poly Pomona - SA86 These two examples further illustrate: The equivalency of PW and EUAW. Example 6-5 (Example 5-1) Example 6-6 EUAW Two More Examples of Resolving a PW to an EUAW

EGR Cal Poly Pomona - SA87 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 Cal Poly Pomona - SA88 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 Cal Poly Pomona - SA89 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 Cal Poly Pomona - SA810 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 Cal Poly Pomona - SA811 Some Other Period Such As Project 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.