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EGR 403 Capital Allocation Theory Dr. Phillip R. RosenkrantzPowerPoint Presentation

EGR 403 Capital Allocation Theory Dr. Phillip R. Rosenkrantz

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### 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

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

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

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

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 AnalysisEGR 403 - Cal Poly Pomona - SA8

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

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

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

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

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

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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