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Chapter 5 - PresentWorth Analysis

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EGR 403 Capital Allocation Theory Dr. Phillip R. Rosenkrantz

Industrial & Manufacturing Engineering Department

Cal Poly Pomona
http://video.csupomona.edu/PRRosenkrant/EGR403Lecture-07.asxhttp://video.csupomona.edu/PRRosenkrant/EGR403Lecture-07.asxhttp://video.csupomona.edu/PRRosenkrant/EGR403Lecture-07.asxhttp://video.csupomona.edu/PRRosenkrant/EGR403Lecture-07.asx


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EGR 403 - Cal Poly Pomona - SA7 3

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

problems.

Where we have been:

Equivalence conceptCash flowsCompound interest factors


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Economic Decision MakingProblems Fall Into Three Categories

Three criteria that apply to all of our analysistechniques:

1. For fixed input situations, maximize the benefits or other

outputs.2. For fixed output situations, minimize the costs or other

inputs.3. 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

Maximize netpresent worth(NPW)

Neither capital nor$ benefits arefixed

Neither fixed

Minimize presentworth of costs

$ amount of benefit is fixed orfixed outcome

Fixed output

Maximize presentworth of benefits

Amount of capitalavailable fixed

Fixed inputCriterionSituation


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Economic Criteria - Examples

C

B

A

Alt

Maximize the profit - Thebiggest margin betweenbenefit & cost. MaximizePWB - PWC

Purchasingrental property

Neitherfixed

Negotiate for minimumcost/sq ft. Minimize input

20,000 sq ftbuilding needed

Fixedoutput

Purchase the most you canfor the money. Maximizeoutput.

$150,000budgeted forraw materials

Fixedinput

Criterion Example Situation


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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 LivesEqual the Analysis Period

1. Example 5-1: Require a project to last five years.2. The equipment and tooling will last five years.3. Calculate the PW or NPW over a five year span and junk the

equipment at the end of the five years (salvage value = 0).

4. Two alternatives with cost of $1000 and useful live of 5years. Assume i = 7%.

Year A B

0 -1000 -1000

1 300 400

2 300 350

3 300 300

4 300 250

5 300 200


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Example 5-1: Fixed input, thereforemaximize 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, thereforemaximize PW of Benefits (contd)

Alternative B - Here we have a combination of auniform 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 totalcash flow, but alternative B provided it sooner so thatit was available sooner to the company to use.

MONEY NOW IS BETTER THAN MONEYLATER


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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 DifferentFrom 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 itproper to compare PWB and/or PWC directly?

Answer: No, because we have 5 additional years of benefits forAllied that would be ignored

Solution: Require the project to last 10 years. For Speedy assume that you will purchase new equipment andtooling twice: At the beginning of year one and six.

Junk the equipment and tooling at the end of each five yearperiod 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 withUnequal Useful Lives

Repeated Project Policy - We will assume thesame costs and benefits and repeat a project allthe way to the end of the analysis period. This isa major part of PW analysis.

Least Common Multiple - Find useful life thatcoincides with multiple lives of each alternativeunder consideration: e.g. If useful lives are 3years and 4 years, then the least commonmultiple is 12 years.


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Techniques for Dealing withUnequal Useful Lives

Terminal year Sometimes the least common multiple method

(LCM) creates an unrealistic useful life (e.g., 13years and 7 years = LCM of 91 years).

Instead, pick a terminal year and repeat all projectsup until the terminal year.

Truncate all costs and benefits after the terminalyear (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, usethe infinity assumption to simplify problems.

Example 5-6: If we can resolve our desired task or service into an equivalent A, then we can useP = 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)

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