Chapter 5 - Present Worth Analysis Click here for Streaming Audio To Accompany Presentation (optional)

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Chapter 5 - Present Worth Analysis 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

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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

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• Where we have been
• Equivalence concept
• Cash flows
• Compound interest factors

• Where we are going in this chapter
• Understanding economic criteria.
• Applying present worth techniques.
• Assumptions in solving economic analysis
  problems.

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Economic Decision Making Problems Fall Into Three
Categories

• Three criteria that apply to all of our analysis
  techniques
• For fixed input situations, maximize the benefits
  or other outputs.
• For fixed output situations, minimize the costs
  or other inputs.
• Where inputs and outputs vary, maximize
  benefits costs.
• First step is to decide which category applies.
• See the back inside cover of the text.

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Economic Criteria Restated Present Worth
Techniques
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Economic Criteria - Examples
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Applying Present Worth Techniques

• With PW analysis the analysis period used is a
  major consideration. Several cases
• Useful life of the alternative(s) equals the
  analysis period.
• Alternatives have useful lives different from the
  analysis period.
• The analysis period is infinite or long enough to
  be treated as infinite, n .

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Useful Lives Equal the Analysis Period

• Example 5-1 Require a project to last five
  years.
• The equipment and tooling will last five years.
• Calculate the PW or NPW over a five year span
  and junk the equipment at the end of the five
  years (salvage value 0).
• Two alternatives with cost of 1000 and useful
  live of 5 years. Assume i 7.

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Example 5-1 Fixed input, therefore maximize PW
of Benefits.

• Alternative A
• Find the PW of all cash flows related to benefits
  of Alternative A. Also include additional costs
  that come later.
• PW of Benefits 300 (P/A, 7, 5) 300 (4.100)
  1230

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Example 5-1 Fixed input, therefore maximize PW
of Benefits (contd)

• Alternative B - Here we have a combination of a
  uniform series (A 400) and a negative gradient
  (G 50). Decompose to use the factors available.
• PW of Benefits 400 (P/A, 7, 5) - 50 (P/G, 7,
  5)
• 400 (4.100) - 50 (7.647) 1257.65

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Example 5-1 Contd

• PWB Alternative A 1230.00
• PWB Alternative B 1257.65
• Since our criteria was to maximize PW of
  Benefits, Alternative B is preferred.
• Notice that each alternative provided the same
  total cash flow, but alternative B provided it
  sooner so that it was available sooner to the
  company to use.
• MONEY NOW IS BETTER THAN MONEY LATER

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More Examples

• Example 5-2 Two stage construction.
• Fixed output so Minimize PW of Cost
• Use PW factors to find PW of second stage costs
  and benefits at time 0.
• Example 5-3 Salvage value included
• Fixed output, so Minimize PW of Cost
• Use PW factors to find PW of salvage value.
• Operating maintenance costs were assumed equal.
• Example 5-4 Neither input nor output fixed
• Maximize (PWB - PWC) or Maximize NPW
• Salvage value treated as a negative cost ( a
  benefit)

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Useful Lives Different From the Analysis Period

• Consider (based on Example 5-3)
• Speedy Useful life 5 years. P 1500, S
  200, PWC 1357
• Allied Suppose useful life 10 years instead
  of 5 years. P 1600, Salvage value 325. PWC
  1435.
• If we have two alternatives with different useful
  lives, is it proper to compare PWB and/or PWC
  directly?
• Answer No, because we have 5 additional years of
  benefits for Allied that would be ignored
• Solution Require the project to last 10 years.
• For Speedy assume that you will purchase new
  equipment and tooling twice At the beginning of
  year one and six.
• Junk the equipment and tooling at the end of each
  five year period and replace with the same
  equipment.

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Useful Lives Different From the Analysis Period

• Calculate the PW or NPW over a 10 year span.
• Speedy PWC 2325
• Now Allied is the preferred choice since PWC is
  less than for Speedy

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Techniques for Dealing with Unequal Useful Lives

• Repeated Project Policy - We will assume the
  same costs and benefits and repeat a project all
  the way to the end of the analysis period. This
  is a major part of PW analysis.
• Least Common Multiple - Find useful life that
  coincides with multiple lives of each alternative
  under consideration e.g. If useful lives are 3
  years and 4 years, then the least common multiple
  is 12 years.

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Techniques for Dealing with Unequal Useful Lives

• Terminal year
• Sometimes the least common multiple method (LCM)
  creates an unrealistic useful life (e.g., 13
  years and 7 years LCM of 91 years).
• Instead, pick a terminal year and repeat all
  projects up until the terminal year.
• Truncate all costs and benefits after the
  terminal year
• (See Figure 5-1 on page 175 for an illustration)

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Infinite Analysis Period

• For n infinity, A i P
• Therefore
• P A / i
• i A / P
• When you have a very long analysis period, use
  the infinity assumption to simplify problems.
• Example 5-6 If we can resolve our desired task
  or service into an equivalent A, then we can use
  P A / i to simplify the process of finding P.

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Assumptions in Solving Economic Analysis Problems

• End-of-year (or period) convention (simplifies
  calculations)
• Viewpoint (generally the firm)
• Sunk costs (past has no bearing)
• Borrowed money (consider investing only)
• Effect of inflation (prices are not stable)
• Income taxes (must be considered for realism)