prev

next

out of 75

View

212Download

0

Embed Size (px)

8/14/2019 Chapter 8x

1/75

02/19/10 1

CHAPTER 8

Rate of Return Analysis:Multiple Alternatives

M cGrawHill

ENGINEERING ECONOMY SixthEdition

Blank and

Tarquin

8/14/2019 Chapter 8x

2/75

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

8/14/2019 Chapter 8x

3/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 3

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

8/14/2019 Chapter 8x

4/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 4

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

8/14/2019 Chapter 8x

5/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 5

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.

8/14/2019 Chapter 8x

6/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 6

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

8/14/2019 Chapter 8x

7/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 7

8.1 Two Projects; A and B

A

$100

0 1 2 3 45

$120

B

$100

0 1 2 3 45

$201.14

8/14/2019 Chapter 8x

8/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 8

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!

8/14/2019 Chapter 8x

9/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 9

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?

8/14/2019 Chapter 8x

10/75

8/14/2019 Chapter 8x

11/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 11

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

8/14/2019 Chapter 8x

12/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 12

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%

8/14/2019 Chapter 8x

13/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 13

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%)

8/14/2019 Chapter 8x

14/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 14

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

8/14/2019 Chapter 8x

15/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 15

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

8/14/2019 Chapter 8x

16/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 16

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

8/14/2019 Chapter 8x

17/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 17

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)

8/14/2019 Chapter 8x

18/75

8/14/2019 Chapter 8x

19/75

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

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

8/14/2019 Chapter 8x

20/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 20

8.2 Example: A and B

For thisproblem, A issuperior to Bbased on PW

and on ROR! A is rankedfirst;

B is rankedsecond

8/14/2019 Chapter 8x

21/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 21

8.2 Example: A and B

Bothalternativeshave a PW > 0and have i*s

> MARR. Both arefeasiblealternativesinitially.

8/14/2019 Chapter 8x

22/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 22

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)

8/14/2019 Chapter 8x

23/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 23

8.2 Incremental Investment

LowestFirstCost

investment

NextHighest first

Costinvestment

TheIncrementalinvestment

A B (B-A)Find theROR of

thisinvestme

nt=

8/14/2019 Chapter 8x

24/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 24

8.2 Incremental Investment

B - A

The incremental Investment

8/14/2019 Chapter 8x

25/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 25

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

8/14/2019 Chapter 8x

26/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 26

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

8/14/2019 Chapter 8x

27/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 27

8.2 Explaining.continued

A B(B-A)

The investment (B-A) represents the year-

by-year difference between A and B

8/14/2019 Chapter 8x

28/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 28

8.2 Explainingcontinued

A B (B-A)

(B-A) is additional investment to move

from investing in A and moving on to investin B.

8/14/2019 Chapter 8x

29/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 29

8.2 The Incremental Investment

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

8/14/2019 Chapter 8x

30/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 30

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!

8/14/2019 Chapter 8x

31/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 31

8.2 Analysis

For this problem, NPV(10%) < 0

and, no ROR could be found!

8/14/2019 Chapter 8x

32/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 32

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!

8/14/2019 Chapter 8x

33/75

02/19/10 Authored by Don Smith, Texas A&M University 2004 33

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 ana