Chapter 8: Rate of Return Analysis: Multiple AlternativesA.Berrado/EGR2302/EGR2302_Ch08.pdf ·...

EGR2302-Engineering Economics

Al Akhawayn University

1

Chapter 8:

Rate of Return Analysis: Multiple

Alternatives

Session 24, 25

Dr Abdelaziz Berrado



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Topics to Be Covered in Today’s Lecture

Section8.1: Why Incremental Analysis is

Necessary?

Section8.2: Calculation of Incremental Cash Flows

For Analysis

Section8.3: Interpretation of Rate of Return on the

Extra Investment

Section8.4: ROR Evaluation by PW: Incremental

and Breakeven

Section8.5: ROR Evaluation Using AW

Section8.6: Incremental Analysis for the Analysis

of Multiple Alternatives



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Section 8.1: Why Incremental Analysis is Necessary?

• Assume we have two or more mutually exclusive alternatives

•Objective: Which, if any of the alternatives is preferred?

•Prior Chapters: Use the PW or AW approach

•This chapter: We apply the ROR approach

•Present Worth: Equal service lives must apply



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8.1 Ranking Inconsistency

• For some problems, PW and ROR may rank the same problems differently. Why?

•PW assumes reinvestment at the MARR or discount rate.

•ROR assumes reinvestment at the i* or i’ rate

•Two different reinvestment rate assumptions apply



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8.1 An Example – Shows Ranking

Inconsistency Problem

•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



6

8.1 Two Projects; A and B

• A

$100

0 1 2 3 4 5

$120

• B

$100

0 1 2 3 4 5

$201.14



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8.1 Example Problem

• i*A = 0.20 = 20%

• i*B = 0.15 = 15%

•PWA(10%) = +$9.09

•PBB(10%) = +24.89

•Using ROR, A is superior to B

•Using PW, B is superior to A

•Inconsistent 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 the same?



8

8.1 Look at A and assume Reinvestment

forward to t = 5

• Reinvest the $120 out to t = 5

$100

0 1 2 3 4 5

$120

•Assume the +$120 can be reinvested forward at the firm’s MARR rate of 10%/year out to the end of year 5.



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8.1 Look at A and assume Reinvestment

forward to t = 5

• Find F5 for Alt. A

$100

0 1 2 3 4 5

$120

F5 = ?

•F5 = 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 with reinvestment 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%)

•Now, PW(10%) and ROR with the reinvestment imposed on the 1-year project rank consistently.•B is superior to A with both methods



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8.1 Ranking Inconsistency…

• Occurs between ROR and PW because

•Both methods have different reinvestment rate assumptions

•Two different cash flows may not generate funds at the same rate



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Section 8.2: ROR for Mutually

Exclusive Projects

•Given Two or more alternatives

•Rank the investments based upon their initial time t = 0 investment requirements

•Summarize the investments in a tabular format



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8.2 Tabular Format

$$N

………

$$2

$$1

$$0

B - AAlt. BAlt. At

Find the ROR of this investment which is

(B – A)



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8.2 Ranking Rules

• Given two or more Mutually Exclusive investments

•Select the first investment to be the one with the lowest time t = 0 investment amount.

•The next investment is to be the one with the largest investment at time t = 0



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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 this problem, A is superior to B based on PW and on ROR!

•A is ranked first;

•B is ranked second

•Both alternatives have

a PW > 0 and have i*’s

> MARR.

•Both are feasible

alternatives initially.



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8.2 Form the Difference (B – A)

• For mutually exclusive alternatives…

•One should focus on the differences between the alternatives

•“Differences” are illustrated best by forming what is called the incremental investment (B-A)



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8.2 Incremental Investment

Lowest FirstCost

investment

Next Highest first

Costinvestment

The Incrementalinvestment

A B (B-A)

Find the ROR of this investment

=



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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 A initially because it is the least expensive alternative at time t = 0

•And it’s present worth is > 0.

•So, A is a feasible alternative to start



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8.2 Explaining the Incremental Investment

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

-$20,000 to get the cash flows indicated 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

(B-A) is “additional” investment to move from

investing in A and moving on to invest in B.



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8.2 The Incremental Investment

• Investing $20,000 at time t = 0 results in the following incremental investment



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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 to investment 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!

•The incremental investment shows a negative PW and no ROR is found•Thus, the increment is rejected.•Moving from A to B is not economically worth it•Stay with A!



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8.2 Another Example

•Cash Flows are shown on the next slide

• Two alternatives

•Semiautomatic machine vs.

•Automatic machine

•Assume a 6 year life for analysis



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8.2 Example

15,000-85,000-100,0005

21,000-74,000-95,0006

15,000-85,000-100,0004

50,000-85,000-135,0003

15,000-85,000-100,0002

15,000-85,000-100,0001

-$50,000-$90,000-$40,0000

(B-A)Auto

B

SemiAuto

A

Year



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8.2 Analysis

• Computed PW @ 18% shows that B has the lowest PW cost and would be preferred to A



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8.2 Incremental Cash Flow

21,000

15,000

15,000

50,000

15,000

15,000

-$50,000

(B-A)

6

5

4

3

2

1

0

•Question?

•Is it worth spending an additional $50,000 in the automatic machine in order to receive the incremental savings shown to the left?

•Compute the ROR of the incremental 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 @ Incremental ROR 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. Rates

NP

V(i

%)



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8.2: i* (B-A) = 35.95%

• The incremental i*(B-A) is greater than the firm’s

discount rate of 18%

•Since i*(B-A) > MARR, accept the increment 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 to the next most costly project

•If the i*incremental value is < MARR the increment

is not worth it. Go with to lower investment cash

flow



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8.3 Multiple Alternatives

• If Cost-Revenue Problem…

•Calculate the computed i*’s for each alternative in the set

•Discard those alternatives whose i* value is less than the MARR – they would lose anyway!



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8.3 Independent Projects

• If dealing with independent projects, one does not compute incremental investments 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 exclusive alternatives,

A and B.

•The i* (B-A) value also represents the

interest rate at which the two alternatives

are economically equivalent.



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8.4 ROR Using PW: Incremental

and Breakeven– Mutually Exclusive Case

• Selection between multiple mutually exclusive alternatives by the IROR method.

•If unequal lives – either establish a common project life or,

•Apply the LCM of life approach found in chapter 5



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8.4 PW Approach – Mutually

Exclusive Case

• Order (rank) the alternatives by their initial time t = 0 investment cost

• Start with the smaller investment alternative – refer to it as “A”

•The next highest investment cost is called “B”



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8.4 PW Approach – Mutually

Exclusive Case

• 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 the increment – go with the higher investment cost alternative.

•Else, reject the increment and go with the 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 sign changes and

apply the Norstrom test (from Chapter 7)

•If a unique i* (B-A) is indicated – solve for it

and compare it to the MARR

•If i* (B-A) > MARR, accept the increment else

reject



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8.4 Example 8.3 Bell/GTE

•10 year project (merger)

•New equipment is required

•Two vendors

•MARR = 15%

•Which vendor should be selected

•Cost or Service Problem



43

8.4 Setup A vs. BPW(15%) shows that A has the

lowest PW Cost and should win!

•Note: No ROR for A (all negative signs) and B’s cannot be determined!



44

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



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8.4 Incremental Cash Flow Fig. 8-2



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8.4 Inc. Cash Flow Results

Inc. PV(15%) and is

negative. Thus, reject the increment and go with A!

i* (B-A) is less

than the

MARR of

15%.

Reject

increment

and go with

A!



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8.4 So-called Breakeven ROR

• Recall, the incremental i*(B-A) is the interest rate at which the two alternatives 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. Rates

NP

V(i

%)

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



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

• For MARR < 12.65% extra investment is justified. Go with B

•For MARR > 12.65%, the extra investment is not justified: Go with A

•If MARR = 12.65%, both options are economically equivalent.

Recall: MARR = 15%



50

8.5 ROR Evaluation Using Annual

Worth based relation

• ROR approach requires comparison over an equal-service life

•When the lives are equal or unequal (Must use LCM), set up the AW relationship for the cash flows of each alternative

•Then solve 0 = AWB – AWA for the i* value



51

8.5 ROR Using Annual Worth

• See Example 8.5

•Manual approach

•It is best to avoid this approach and stay with either the PW or ROR over the total life of the project or the LCM life



52

8.6 Incremental ROR Analysis of Multiple,

Mutually Exclusive Alternatives: Criteria

•Select the one alternative that:

•Requires the largest investment

•And indicates that the extra investment over another acceptable alternative is justified



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8.6 Comparing Alternatives

• A given alternative should not be compared with one alternative for which the incremental investment is not justified

•If a given alternative looses out in a comparison, that alternative is dropped from further consideration.



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8.6 Ranking Rules - Ordering

1. Order the alternatives from smallest to largest initial investment

2. Compute the cash flows for each alternative (assume or create equal lives)

3. If the alternatives are revenue-cost alternatives do the following…



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8.6 Revenue-Cost Problems

4. Compute the i* value for all alternatives in the considered set.

•If any alternative has an i* < MARR drop it from further consideration

•The candidate set will be those alternatives with computed i* values > MARR.

•Call this the FEASIBLE set



56

8.6 Revenue-Cost - Approach

• Calculate i* for the first alternative

•The first alternative is called the DEFENDER

•The second (next higher investment cost) alternative is called the CHALLENGER

•Compute the incremental cash flow as

•(Challenger – Defender)



57

8.6 Revenue-Cost

4. Compute i*Challenger – Defender

•If i*Challenger – Defender > MARR drop the defender and the challenger wins the current round.

5. If i* Challenger – Defender < MARR, drop the challenger and the defender moves on to the next comparison round



58

8.6 Revenue-Cost

• At each round, a winner is determined

•Either be the current Defender or the current challenger

•The winner of a given round moves to the next round and becomes the current DEFENDER and is compared to the next challenger



59

8.6 Revenue-Cost

6. This process continues until there are no more challengers remaining.

•The alternative that remains after all alternatives have been evaluated is the final winner.



60

8.6 Potential Problems

• See Example 8.6 for the potential problems that can occur using ROR

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



61

8.6 Cost Problems

• Remember

•Cost problems do not have computed ROR’ssince there are more cost amounts than revenue amounts (salvage values may exist)

•Thus there are no feasible i*’s for each alternative



62

8.6 Cost Problems - Rules

• Rank the alternatives according to their investment requirements (low to high)

•For the first round compare:

•Challenger – Defender Cash Flow

•Compute i*Challenger – Defender

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



63

8.6 Cost Problems

• The current winner now becomes the defender for the next round.

•Compare the current defender to the next challenger and compute i* Challenger – Defender

•The winner becomes the current champion and moves to the next round as the defender

•Repeat until all alternatives have been compared.



64

Chapter 8 Summary

•PW and AW methods are preferred methods for evaluating alternatives

•ROR can be used but care must be taken

•If ROR, must perform an incremental analysis

•Two at a time (paired comparison) is required



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Assignments and Announcements

� Homework7 (Chapter8 due April 26th)

� Assignments due at the beginning of next

class:

� Online Quizzes for chapter 8 Due

� Read Chapter 14

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