Chapter 8x

8/14/2019 Chapter 8x

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02/19/10 1

CHAPTER 8

Rate of Return Analysis:Multiple Alternatives

M cGrawHill

ENGINEERING ECONOMY SixthEdition

Blank and

Tarquin


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02/19/10 Authored by Don Smith, Texas A&M University 2004 2

Learning Objectives

1. Why Incremental Analysis?

2. Incremental Cash Flows

3. Interpretation4. Incremental ROR by PW

5. Incremental ROR by AW

6. Multiple Alternatives


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Section 8.1Why Incremental Analysis is

Necessary

Assume we have two or moremutually exclusive alternative

Objective: Which, if any of thealternatives is preferred?

Prior Chapters: Use the PW or AWapproach

This chapter: We apply the RORapproach

Present Worth: Equal service livesmust apply


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8.1 Ranking Inconsistency

For some problems, PW and ROR mayrank the same problems differently.Why?

PW assumes reinvestment at theMARR or discount rate.

ROR assumes reinvestment at the i*

or i rate Two different reinvestment rateassumptions apply


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8.1 Review of Problem Types

INDEPENDENT AND MUTUALLY EXCLUSIVE ALTERNATIVES

INDEPENDENT - Selection of onealternative does not effect the selection of others. Example: select all projects with aROR> 20 %

MUTUALLY EXCLUSIVE - Selection on onealternative precludes the selection of others. Example: select the project with thehighest ROR.


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8.1 An Example Shows RankingInconsistency Problem

From Solomon {1956/59} Two Investments A and B Discount rate = 10%

Each investment requires $100 at t =0 A is a 1-year investment

B is a 5- year investment


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8.1 Two Projects; A and B

A

$100

0 1 2 3 45

$120

B

$100

0 1 2 3 45

$201.14


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8.1 Example Problem

i*A = 0.20 = 20%

i*B = 0.15 = 15% PW A(10%) = +$9.09

PB B(10%) = +24.89

Using ROR, A issuperior to B

Using PW, B issuperior to A

InconsistentRankings!


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8.1 Example Problem - Rankings

Using ROR Ranking

A is superior to B (20% > 15%)

Using a PW(10%) approach B is superior to A ($24.89 > $9.09)

The two methods do not rank thesame?


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8.1 Look at A and assumeReinvestment forward to t = 5

Find F 5 for Alt. A

$100

0 1 2 3 45

$120

F 5 = ?

F 5 = 120(F/P,10%,4)=$175.69


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8.1 ROR of A given reinvestment

-100 +120(F/P,10%,4)(P/F,i *A, 5) = 0

Solving for i* A

(P/F, i* A,5) = 0.569

i*A/reinvestment @10% = 0.1193

i*A/ c =10% = 11.93%


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8.1 Now Compare A to B

Compare revised A withreinvestment at 10% to B

i*

A/c = 10% = 11.93%

i* B = 15% as before

ROR Rankings:

B is superior to A (15% > 11.93%)


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8.1 Ranking Consistency

Now, PW(10%) and ROR with thereinvestment imposed on the 1-yearproject rank consistently.

B is superior to A with both methods


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8.1 Ranking Inconsistency

Occurs between ROR and PWbecause

Both methods have differentreinvestment rate assumptions

Two different cash flows may notgenerate funds at the same rate


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Section 8.2ROR for Mutual Exclusive

Projects Given Two or more alternatives

Rank the investments based upontheir initial time t = 0 investment

requirements

Summarize the investments in atabular format


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8.2 Tabular Format

t Alt. A Alt. B B - A

0 $ $

1 $ $2 $ $

N $ $Find the ROR of this investment

which is(B A)


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8.2 Example

Two Investments: A and B

A costs $30,000 at time t = 0

B costs $50,000 at time t = 0 MARR = 10%

Life is 4 years


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8.2 Example: A and B

For thisproblem, A issuperior to Bbased on PW

and on ROR! A is rankedfirst;

B is rankedsecond


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8.2 Example: A and B

Bothalternativeshave a PW > 0and have i*s

> MARR. Both arefeasiblealternativesinitially.


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8.2 Form the Difference (B A)

For mutually exclusive alternatives

One should focus on the differencesbetween the alternatives

Differences are illustrated best byforming what is called the incrementalinvestment (B-A)


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8.2 Incremental Investment

LowestFirstCost

investment

NextHighest first

Costinvestment

TheIncrementalinvestment

A B (B-A)Find theROR of

thisinvestme

nt=


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8.2 Incremental Investment

B - A

The incremental Investment


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8.2 The logic.

One would go with investment Ainitially because it is the leastexpensive alternative at time t = 0

And its present worth is > 0.

So, A is a feasible alternative to start


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8.2 Explaining the IncrementalInvestment

Now, is it worth it to the firm toconsider investing (-$50,000 (-$30,000) =

-$20,000 to get the cash flowsindicated in the (B-A) cash flow series?

B-A


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8.2 Explaining.continued

A B(B-A)

The investment (B-A) represents the year-

by-year difference between A and B


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8.2 Explainingcontinued

A B (B-A)

(B-A) is additional investment to move

from investing in A and moving on to investin B.


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8.2 The Incremental Investment

Investing $20,000 at time t = oresults in the following incrementalinvestment


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8.2 Is it worth it?

Now the question is.

Is it worth spending an additional$20,000 to move from investment A toinvestment B?

Answer: Compute the ROR or PW of the incremental investment to see!


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8.2 Analysis

For this problem, NPV(10%) < 0

and, no ROR could be found!


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8.2 Analysis

The incremental investment shows anegative PW and no ROR is found

Thus, the increment is rejected.

Moving from A to B is noteconomically worth it

Stay with A!


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8.2 Another Example

Homework Problem 8.21 to illustrate

Cash Flows are shown on the nextslide

Two alternatives

Semiautomatic machine vs.

Automatic machine

Assume a 6 year life for analysis


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8.2 Example (Problem 8.21)

Year SemiAutoA

AutoB

(B-A)

0 -$40,000 -$90,000 -$50,000

1 -100,000 -85,000 15,000

2 -100,000 -85,000 15,000

3 -135,000 -85,000 50,000

4 -100,000 -85,000 15,000

5 -100,000 -85,000 15,000

6 -95,000 -74,000 21,000


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8.2 Analysis

Computed PW@ 18% showsthat B has the

lowest PW costand would bepreferred to A


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8.2 Incremental Cash Flow(B-A)

-$50,000

15,000

15,000

50,000

15,000

15,000

21,000

0

1

2

3

4

5

6

Question? Is it worth spending anadditional $50,000 in theautomatic machine inorder to receive theincremental savingsshown to the left?

Compute the ROR of theincremental Cash Flow


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8.2 Incremental ROR = 35.95%


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8.2 NPV Plot of A and B

A is equivalent to B @ IncrementalROR rate of 35.95%

NPV PLOT-INC. C.F.

-800000.00

-700000.00

-600000.00

-500000.00

-400000.00

-300000.00

-200000.00

-100000.00

0.00

0 . 0 0

0 . 1 0

0 . 2 0

0 . 3 0

0 . 4 0

0 . 5 0

0 . 6 0

0 . 7 0

0 . 8 0

0 . 9 0

1 . 0 0

1 . 1 0

1 . 2 0

1 . 3 0

1 . 4 0

1 . 5 0

1 . 6 0

1 . 7 0

1 . 8 0

1 . 9 0

2 . 0 0

Disc. Rate s

N P V ( i % )


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8.2 i* (B-A) = 35.95%

The incremental i* (B-A) is greater than

the firms discount rate of 18%

Since i* (B-A) > MARR, accept theincrement and go with Alternative B.

Same results as PW(18%) shows

B is clearly the winner


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Section 8.3 Interpretations of ROR

The i* incremental is the ROR of the

additional or incremental investment

required to move from one project tothe next most costly project

If the i* incremental value is < MARR the

increment is not worth it. Go with tolower investment cash flow


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8.3 Multiple Alternatives

If Cost-Revenue Problem

Calculate the computed i*s for eachalternative in the set

Discard those alternatives whose i*value is less than the MARR theywould lose anyway!


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8.3 Independent Projects

If dealing with independent projects,one does not compute incrementalinvestments among the candidate

projects Rule: Accept all projects whose ROR >MARR and stay within any budget

limitations


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8.3 The i* (B-A) value

Given two mutually exclusivealternatives, A and B.

The i* (B-A) value also representsthe interest rate at which the twoalternatives are economicallyequivalent.


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02/19/10 44

CHAPTER 8

Section 8.4ROR Using PW:

Incremental andBreakeven


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8.4 PW Approach Mutually ExclusiveCase

Given multiple alternatives

If unequal lives either establish

a common project life or, Apply the LCM of life approachfound in chapter 5


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Order (rank) the alternatives bytheir initial time t = 0 investmentcost

Start with the smallerinvestment alternative refer to

it a A The next highest investmentcost is called B


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Compute the incremental cash flow(B-A)

Given the MARR find the PW of (B-A)investment

If PW( MARR ) of (B-A) is >0; accept theincrement go with the higherinvestment cost alternative. Else, reject the increment and go withthe lower investment cost option


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8.4 ROR Case Unique i* (B-A)

Compose the incremental Cash Flow

Examine that cash flow for sighchanges and apply the Norstrom test(from Chapter 7)

If a unique i* (B-A) is indicated solvefor it and compare it to the MARR

If i* (B-A) > MARR, accept the incrementelse reject


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8.4 Setup A vs. B PW(15%) showsthat A has the

lowest PW Costand should win!

Note: No ROR forA (all negativesigns) and Bs

cannot bedetermined!


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8.4 PW analysis

We could stop because the PW(15%)has signaled that A is the winner!

Lowest PW cost

Proceed with a ROR analysis BUT.

ROR must be performed on the

incremental investment

8 4 I t l C h Fl Fig


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8.4 Incremental Cash Flow Fig.8-2


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8.4 Inc. Cash Flow Results

Inc. PV(18%)and is

negative.Thus, reject

theincrement

and go withA!

i* (B-A) is lessthan theMARR of

18%.Reject

incrementand go with

A!


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8.4 So-called Breakeven ROR

Recall, the incremental i* (B-A) is theinterest rate at which the twoalternatives are economically

equivalent. This special interest rate is called:

Breakeven Interest Rate

Fisherian Intersection Rate


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8.4 Breakeven Rate Illustrated

For Example 8.3 the NPV Plot is:NPV PLOT-INC. C.F.

-50000.00

-45000.00

-40000.00

-35000.00

-30000.00

-25000.00

-20000.00

-15000.00

-10000.00

-5000.00

0.00

0 . 0 0 0 . 1 0 0 . 2 0 0 . 3 0 0 . 4 0 0 . 5 0 0 . 6 0 0 . 7 0 0 . 8 0 0 . 9 0 1 . 0 0 1 . 1 0 1 . 2 0 1 . 3 0 1 . 4 0 1 . 5 0 1 . 6 0 1 . 7 0 1 . 8 0 1 . 9 0 2 . 0 0

Disc. Rate s

N P V ( i % )

i*(B-A) rate;Alternativesare identical at this rate.


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8.4 Conclusions i* (B-A) = 12.65%

For MARR < 12.65% extra investmentis justified. Go with B

For MARR > 12.65%, the extrainvestment is not justified: Go with A

If MARR = 12.65%, both options areeconomically equivalent.

Recall: MARR = 18%


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02/19/10 57

CHAPTER 8

Section 8.5ROR Evaluation Using

Annual Worth


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8.5 ROR Using AW

ROR approach requires comparisonover an equal-service life

When the lives are equal or unequalset up the AW relationship for the cashflows of each alternative

Then solve 0 = AW B AW A for the i*value


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8.5 ROR Using Annual Worth

See Example 8.5

Manual approach

It is best to avoid this approach andstay with either the PW or ROR overthe total life of the project or the LCMlife


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02/19/10 60

Section 8.6

Incremental RORAnalysis of Multiple,

Mutually ExclusiveAlternatives


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8.6 Criteria

Select the one alternative that:

Requires the largest investment

And indicates that the extrainvestment over another acceptablealternative is justified


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8.6 Ranking Rules - Ordering

1. Order the alternatives fromsmallest to largest initial investment

2. Compute the cash flows for eachalternative (assume or create equallives)

3. If the alternatives are revenue-costalternatives do the following


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8.6 Revenue-Cost Problems

4. Compute the i* value for allalternatives in the considered set.

If any alternative has an i* < MARRdrop it from further consideration

The candidate set will be thosealternatives with computed i* values >MARR. Call this the FEASIBLE set


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8.6 Revenue-Cost - Approach

Calculate i* for the first alternative

The first alternative is called theDEFENDER

The second (next higher investmentcost) alternative is called theCHALLENGER

Compute the incremental cash flow as

(Challenger Defender)


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8.6 Revenue-Cost

4. Compute i* Challenger Defender

If i* Challenger Defender > MARR drop the

defender and the challenger wins thecurrent round.

5. If i* Challenger Defender < MARR, drop thechallenger and the defender moves onto the next comparison round


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8.6 Revenue-Cost

6. This process continues until thereare no more challengers remaining.

The alternative that remains after allalternatives have been evaluated isthe final winner.


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8.6 Potential Problems

See Example 8.6 for the potentialproblems that can occur using RoR

Pitfalls often exist when one uses theROR approach for the analysis of alternatives


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8.6 Cost Problems

Remember Cost problems do not have computed

RoRs since there are more costamounts that revenue amounts(salvage values may exist)

Thus there are no feasible i*s foreach alternative


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8.6 Cost Problems - Rules

Rank the alternatives according totheir investment requirements (low tohigh)

For the first round compare:

Challenger Defender Cash Flow

Compute i*

Challenger Defender

If i* Challenger Defender > MARR,Challenger wins; else Defender wins


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8.6 Cost Problems

The current winner now becomes thedefender for the next round.

Compare the current defender to thenext challenger and compute i* Challenger Defender

The winner becomes the currentchampion and moves to the next roundas the defender

Repeat until all alternatives havebeen compared.

Section 8.7


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Section 8.7Spreadsheet Applications

Use the E-solve software for PW-AW,and ROR Analysis

Study and evaluate example 8.8

Create your own spreadsheet fromscratch and employ the built infinancial functions.


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Chapter 8 Summary

PW and AW methods are preferredmethods for evaluating alternatives

ROR can be used but care must betaken

If ROR, must perform an incrementalanalysis

Two at a time (paired comparison) isrequired

ENGINEERING ECONOMY Sixth


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End of Chapter 8 SlideSet

Mc

GrawHill

ENGINEERING ECONOMY Edition

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Chapter 8x