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
