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IEEN 5329 Homework 6 8

Economics

IEEN 5329

Homework 6

8.3, 8.14, 8.19, 8.30, 8.33

PROBLEMS
Understanding [Incremental ROR the first $30,000 and 14% on the remain-
: . ing $70,000?
8.1 If alternative A has a rate of return of 10% g $70.0
and alternative B has a rate of return of 8.3 Why is an incremental analysis necessary
18%, what is known about the rate of re- when you are conducting a rate of return
turn on the increment between A and B if analysis for service alternatives?
the investment required in B ts (a) larger .
4 . (a) larg 8.4 If all of the incremental cash flows are
than that required for A and () smaller . .
negative, what 1s known about the rate of
than that required for A? . .
return on the incremental investment?
8.2 What is the overall rate of return on a 8.5 Incremental cash flow is calculated as cash
$100,000 investment that returns 20% on flow, — cash flow,, where B represents th

PROBLEMS 301
alternative with the larger initial invest- purchase new equipment. If $30,000 ts in-
ment. If the two cash flows were switched vested at 30%, $20,000 at 25% and the re-

wherein B represents the one with the maining $50,000 at 20% per year, what is
smaller imtial investment, which alterna- the overall rate of return on the entire
| tive should be selected if the incremental $100,000?
rate of return is 20% per year and the com-
pany ’s MARR is 15% per year? Explain. 8.9 A total of $50,000 was available for in-
vesting In a project to reduce insider theft
8.6 A food processing company ts considering In an appliance warehouse. Two alterna-
two types of moisture analyzers. The com- tives identified as Y and Z were under con-
pany expects an infrared model to yield a sideration. The overall rate of return on the
rate of return of 18% per year. A more ex- $50,000 was determined to be 40%, with
penstve microwave model will yield a rate the rate of return on the $20,000 increment
of return of 23% per year. If the company's between Y and Z at 15%. If Z is the higher
MARR ts 18% per year, can you deter- first-cost alternative, (a) what is the size of
mine which madel(s) should be purchased the investment required in Y and (/) what
solely on the basis of the rate of return in- is the rate of return on Y?
formation provided tf (a) either one or
both analyzers can be selected and (/) only 8.10 Prepare a tabulation of cash flow for the
one can be selected? Why or why nat? alternatives shown below.
. , . Machine A Machine B
8.7 For each of the following scenarios, state 0
whether an incremental investment analy- First cost, > — 15,000 25,000
sis would be required to select an alterna- an ee cost, S/ycar 00 «oon
tive and state why or why not. Assume that savage Vane. ”
; ", rarer Life, years 3 e
alternative Y requires a higher initial in-
vesiment than alternative X and that the
MARR is 20% per year. . . oe
5 eae BET Y 8.11 A chemical company is considering two
(a) X has a rate of return of 28% per . -

. | processes for making a cationic poly-
year, and Y has a rate of return of _ ee
20% per year mer. Process A will have a first cost of
VoL . r $100,000 and an annual operating cost

(b) X has a rate of return of 18% per .
ear and Y has a rate of return of of $60,000. Process B will have a first cost
y 30, ser ear of $165.000. If both processes will be ade-
| "7 ve year. ow quate for -1 years and the rate of return on
(c) X has a rate of return of 16% per Lo
“a | the increment between the alternatives is
year, and Y has a rate of return of e -
25%, what is the amount of the operating
19% per year. cost for process B’?
(d) Xhas arate of return of 30% per year. : Process Bs
and Y has a rate of return of 26% per .
year “Pe Incremental ROR Comparison
- ; Two Alternatives
(7) X has a rate of return of 21% per |
year, and Y has a rate of return of 8.12 When the rate of return on the incremental
22% per year. cash flow between two alternatives is ex-
actly equal to the MARR, which alterna-
8.8 A small construction company has tive should be selected—the one with the
$100,000 set aside in a sinking fund to higher or lower initial investment? Why?

8.13 Aconsulting engineering firm is trying to 8.16 The manager of a canned food processing
Jecide whether it should purchase Ford plant is trying to decide between two la-
Explorers or Toyota 4Runners for com- beling machines. Determine which should
pany principals. The models under consid- be selected on the basis of rate of return
cration would cost $29,000 for the Ford with a MARR of 20% per year.
und $32.000 for the Toyota. The annual
operating cost of the Explorer is expected _CMaachine A Machine B
to be $200 per year less than that of the First cost, $ —15.000 = — 25,000
4Runner. The trade-in values after 3 years Annual operating cost. $year = — 1,600 — 400)
are estimated to be 50% of first cost for the Salvage value. $ 3,000 4,000
Explorer and 60% for the Toyota. (a) What Life, years 2 4
is the rate of return relative to that of Ford. —
if the Toyota is selected? (4) If the firm’s
MARR is 18% per year, which make of 8.17 A solid waste recycling plant is cons:der-
vehicle should it buy? ing two types of storage bins. Determine
which should be selected on the basis of
8.14 A plastics company is considering two in- rate of return. Assume the MARR is 20%
jection molding processes. Process X will per year.
have a first cast of $600,000, annual costs Alternative P Alternative Q
of $200,000, and a salvage value of i
$100,000 after 5 years. Process Y will First cost, $ | ~ 18,000 735,000
have a first cost of $800.000, annual costs Anns Sheet 7.000 ~ 3.600
of $150,000, and a salvage value of Salvape : Ie. ; 1.000 2700
$230,000 after 5 years. (a) What is the rate Life, years 3 6
of return on the increment of investment
between the two? (4) Which process
should the company select on the basis of 8.18) ‘The incremental cash flow between alter-
a rate of return analysis, if the MARR Is natives J and K is estimated below. If the
20% per year? MARR is 20% per year, which alternative
should be selected on the basis of rate of
8.15 A company that manufactures amplified return? Assume K requires the extra
pressure transducers ts trying to decide be- $90,000 initial investment.
tween the machines shown below. Com-
pare them on the basis of rate of return, Incremental
und determine which should be selected if Year Cash Flow, $(K — J)
the company’s MARR ts 15% per year. 0 ~90,000
1-3 + [0,000
Variable Dual 4-9 + 20,000
Speed Speed 10 + 5,000
First cast. $ ~ 250.000  -225,000 Te
Annual operating cost. S/year — — 231,000 9 — 235,000 . oo,
Overhaul in year 3, $ _ ~ 26,000 8.19 A chemical company is considering two
Overhaul in year 4. $ ~ 39.000 _ processes for isolating DNA material. The
Salvage value, $ 50.000 10,000 incremental cash flow between two alter-
Life, years f o natives J and S is as shown. The company
oe uses a MARR of 50% per year. The rate of 

return on the incremental cash flow below Semiautomatic Automatic
is less than 50%, but the company CEO First cost. $ ~ 40.000 ~ 90.000
prefers the more expensive process. The Annual cost, $/year — 100,000 ~95.000
CEO believes she can negotiate the initial Salvage value, $ 5.000 7.000
cost of the more expensive process down- Life. years ? 4
ward. By how much would she have to a
reduce the first cost of S. the higher-cost
alternative, for it to have an incremental 8.23 The incremental cash flows for ulterna-
rate of return of exactly 50%? tives X and Y are shown below. Calculate

the incremental rate of return per month,
Incremental and determine which should be selected.
Year Cash Flow, $(S — J) using an AW-based rate of return analysis.
0 900.000 The MARR is 24% per year, compounded
400.000 monthly, and alternative Y requires the
2 600.000 larger initial investment.
3 $50,000
Incremental
Month Cash Flow, $(Y — X)
8.20 Alternative R has a first cost of $100,000, 0 ~ 62,000
annual M&O costs of $50,000, and a }-23 +4.000
$20.000 salvage value after 5 years. Alter- 24 + 10,000
native S has a first cost of $175,000 and a a
$40,000 salvage value after 5 years, but its
annual M&O costs are not known. Deter- 8.24 The incremental cash flow between alter-
mine the M&O costs for alternative S that natives Z| and Z2 is shown below (Z2 has
would yield an incremental rate of return the higher initial cost). Use an AW-based
of 20% per year. rate of return equation to determine the in-
cremental rate of return and which alterna-
8.21 The incremental cash flows for alterna- tive should be selected. if the MARR is
tives M and N are shown below. Deter- 17% per year. Let k = year | through 10.
mine which should be selected, using an
AW-based rate of return analysis. The Incremental
MARR is 12%. per year, and alternative N Year Cash Flow, $(22 — 21)
requires the larger initial investment. () — 40,000
I-10 9000 — S0OK
Incremental a
Year Cash Flow, $(N — M)
0) ~2? 000 8.25 Two roadway designs are under considera-
1-8 +4,000 tion for access to a permanent suspension
y + 12.000 bridge. Design 1A will cost $3 million to
a build and $100,000 per year to maintain.
Design 1B will cost $3.5 million to build
8.22 Determine which of the two machines and $40,000 per year to maintain. Use an
below should be selected. using an AW- AW-based rate of return equation to deter-
based rate of return analysis, if the MARR mine which design is preferred. Assume
is 18% per year. n = 10 years and the MARR ts 6% per year.

8.26 A manufacturing company is in need of 8.29 Mountain Pass Canning Company has de-
3000 square meters for expansion because termined that any one of five machines can
of a new 3-year contract it just won. The be used in one phase of its canning opera-
company is considering the purchase of tion. The costs of the machines are esti-
land for $50.000 and erecting a temporary mated below. and all machines have a
metal structure on it at a cost of $90 per 5-year life. If the minimum attractive rate
square meter. At the end of the 3-year pe- of return is 20% per year. determine the
riod. the company expects to be able to one machine that should be selected on the
sel] the land for $55.000 and the building basis of a rate of return analysis.
for $60,000. Alternatively. the company
can lease space for $3 per square meter
per month, payable at the beginning of on
each year. Use an AW-based rate of return Machine First Cost, $ Cost $ /year
equation to determine which alternative ts S$. $$
preferred. The MARR is 28%: per year. 1 ~ 31,000 — 18,000
2 — 28,000 — 19,500
8.27 Four mutually exclusive service alternatives 3 — 34,500 — 17.000
are under consideration for automating a 4 — 48,000 — 12,000
manufacturing operation. The alternatives 3 — 41,000 — 15.5)
were ranked in order of increasing initial
investment and then compared by incre-
mental investment rate of return analysis.
The rate of return on each increment of in- 8.30 An independent dirt contractor is trying to
vestment was less than the MARR, Which determine which size dump truck to buy.
alternative should be selected” The contractor knows that as the bed size
increases, the net income increases, but he
Multiple-Alternative Comparison is uncertain whether the incremental ex-
8.28 A metal plating company is considering penditure required for the larger trucks 1s
four different methods for recovering by- Justified. The cash flows associated with
product heavy metals from a manufactur- each size truck are estimated below. The
ing site's liquid waste. The investment contractor's MARR is 18% per year. and
costs und incomes associated with each all trucks are expected to have a useful life
method have been estimated. All methods of 9 years. (a) Determine which size truck
have an 8-year life. The MARR is 11% per should be purchased. (b) If two trucks of
year. (a) If the methods are independent, different size are to be purchased, what
because they can be implemented at dif- should be the size of the second truck”
ferent plants, which ones are acceptable?
(b) If the methods are mutually exclusive, Truck Initial Annual
determine which one method should be Bed Size, Invest- Operating Salvage Annual
selected, using a ROR evaluation. Cubic ment, Cost, Value, Income,
First Salvage Annual Meters $ $/year $ $/year
Method _Cost,$ Value, $_ Income, $/year 8 = 30,000 - 14,000 +2000 +26,500
A — 30.000 + 1.000 + 4,000 10 — 34.000  - 15.500 +2500 + 30,000
B — 36.000 + 2,000 + 5,000 15 — 38.000 — 18.000 +3000 + 33,5(X)
Cc — 41.000 +S) + 8.000 20 —48.000  —21.000 +350) + 40.SCK'
D — 34,000 — 2.000 + 10.500 25 —S7.000 —26.000 + 401K) +49.00K

8.31 An engincer at Anode Metals is consider- which should be selected (a) if they are
ing the projects below, all of which can be independent and () if they are mutually
considered to last indefinitely. If the com- exclusive.
pany s MARR is 15% per year, determine
Annual Alternative's Rate
First Cost, $ Income, $/year of Return, %
A — 20,000 + 3.000 IS
B — 10,000 + 2,000 2()
Cc ~ 15,000 + 2.800 18.7
D ~ 70,000 + 10.000 14.3
E — 50,000 + 6,000 |2
$.32 Only one of four different machines is to chine. All machines are assumed to have
be purchased for a certain production a 0-year life. Which machine, if any,
process. An engincer performed the fol- should the company select if its MARR is
lowing analyses to select the best ma- (a) 12% per year and (6) 20% per year?
Machine
1 2 3 4
Initial cost, $ — 44.000 — 60.000 —72.000 —98,000
Annual cost, $/year — 70.000 — 64,000 — 61.000 — 58.000
Annual savings, $/year +80,000 + 80,000 +80.000 + 82,000
ROR, % 18.6 23.4 23.1 20.8
Machines compared J tol 3toa 2 4to3
| Incremental investment, $ —16.000 — 12.000 — 26.000
Incremental cash flow, $/year + 6,000 + 3.00) + 5.0000
ROR on increment, % 35.7 21.4 14.)
8.33 The four alternatives described below are (b) It the proposals are mutually exctu-
being evaluated. sive, which one should be sclected
(a) If the proposals are independent. when the MARR ts 9& per year?
which should be selected when the {c) If the proposals are mutually exclu-
MARR its 16% per year? sive, which one should be selected
when the MARR its 12% per year?
Incremental Rate
of Return, %, When
Compared with
Initial Alternative
Alternative Investment, $ Rate of Return, % A B C
A — 40,000 29
B — 75.000 IS I
Cc — 100.000 lo 7 20
D — 200.000 14 10 13 12

8.34 A rate of return analysis was initiated for (c) What alternative should be selected
the infinite-life alternatives below. if they are mutually exclusive and the
(¢) Fill in the blanks in the incremental MARR is 16%’
rule of return column on the tncre- (¢} What alternative should be selected
mental cash flow portion of the if they are mutually exclusive and
table. the MARR is 11%?
(2) How much revenue is associated (e) Select the two best alternatives at a
with each alternative? MARR of 19%.
Incremental Rate of Return, %,
on Incremental Cash Flow When
Alternative’s Alternative’s Compared with Alternative
Alternative Investment, $ Rate of Return, % E F G H
E — 20,000 20) —
F — 30,000 35 —
G — 40,000 2 — L1.7
H — 80,000 30 11.7 —
8.35 Arate of return analysis was initiated for (b) What alternative should be selected if
the infinite-life alternatives below. they are independent and the MARR
(a) Fill in the blanks in the alternative’s is 21% per year?
rate of return column and _ incre- (c) What alternative should be selected
mental rate of return columns of the if they are mutually exclusive and the
table. MARR 1s 24% per year?
Incremental Rate of Return, %,
on Incremental Cash Flow When
Alternatives Alternatives Compared with Alternative
Alternative Investment, $ Rate of Return, % E F G H
E — 10,000 25 — 20
F — 35,000 20) — mI
G — 30,000 4 _
H — 60.000 30) —
we Ee STE
FE REVIEW PROBLEMS
8.36 Alternative | requires an initial investment on the $10,000 increment?
of $20,000 and will yield a rate of return (a) tis greater than 20% per year.
of 15% per year. Alternative C, which re- (b) Itis exactly 20% per year.
quires a $30,000 investment, will yield (c) Itis between 15% and 20% per year.
20% per year. Which of the following (d) [tis less than [5% per year.
stalements Is true about the rate of return

8.37 The rate of return tor alternative X is rate of return for the lower first-cost
18% per year and for alternative Y 1s alternative.
17% per year, with Y requiring a larger initial (6b) The rate of return on the increment 1s
investment. [f a company has a minimum less than the rate of return for the
attractive rate of return of 16% per year, lower first-cost alternative.
(a) The company should select alterna- (c) The higher first-cost alternative may
live X. be the better of the two allernatives.
(b) The company should select alterna- () None of the above.
tive Y.
(c) The company should conduct an in- 8.40 The incremental cash flow between two
cremental analysis between X and Y alternatives is shown below.
to select the economically better
an hould sel he d Year Incremental Cash Flow, $
ce company should select the do- Tn
“ nothing alternative: 0 ~ 20,000
1-10) + 3,000
8.38 When one is conducting an ROR analysis 10 +a)
of mutually exclusive service projects, TT
(a) All the projects must be compared The equation(s) that can be used to cor-
against the do-nothing alternative. rectly solve for the incremental rate of re-
(bh) More than one project may be selected. turn is (are)
(c) An incremental investment analysis (a) O = —20,000 + 3000(A/P.i,10) +
Is Necessary to identify the best one. 400( P/Fi,10)
(¢) The project with the highest incre- (b) O = —20.000 + 3000(A/P.i,10) +
mental ROR should be selected. AQO(A/F..10)
8.39 When one is comparing two mutually ex- (e) 0 = ~ 20,0014 / Pi10) + 3000 +
clusive alternatives by the ROR method, if | 400( P/F 1.10) |
oo .; , (7) O = —20,000 + 3000(P/AU,10) +
the rate of return on the alternative with 400( PIF.i.10)
the higher first cost is less than that of the a”
lower first-cost alternative, Questions 8.41 through 8.43 are based on the fol-
(a) The rate of return on the increment lowimg. The five alternatives are being evaluated
between the two ts greater than the by the rate of return methad.
Incremental Rate
of Return, %, When
Compared with
Initial Alternative Alternative
Alternative Investment, $ Rate of Return, % A B Cc D E
A — 25.000 9.6 — 28.9 19.7 36.7 25:5
B — 35.000 15.4 — 1S 39.8 24.7
Cc — 40,000 13.4 — 49.4 28.0
D — 60.000 25.4 — —-0.4A
E — 75,000 20.2 —

8.41 Ifthe alternatives are independent and the (a) B
MARR 1s 18% per year, the one(s) that (6) D
should be selected is (are) (c) E
{a) Only D (d) None of them
a one 5 me dE 8.43 If the alternatives are mutually exclusive
te nyo and the MARR ts 25% per year. the alter-
(7d) OnlyE _
native to select is
(a) A
8.42 If the alternatives are mutually exclusive (b) D
and the MARR ts 15% per year, the alter- (c) E
native to select 1s (¢) None of them
i Po ; =
EXTENDED EXERCISE
INCREMENTAL ROR ANALYSIS WHEN ESTIMATED
ALTERNATIVE LIVES ARE UNCERTAIN
Make-to-Specs is a software system under development by ABC Corporation. It
will be able to translate digital versions of three-dimensional computer madels,
containing a wide variety of part shapes with machined and highly finished (ultra-
smooth) surtaces, The product of the system is the numerically controlled (NC)
machine code for the part’s manufacturing. Additionally, Make-to-Specs will build
the code for super-fine finishing of surfaces with continuous control of the finish-
ing machines. There are two alternative computers that can provide the server
function for the software interfaces and shared database updates on the manufac-
turing floor while Make-to-Specs is operating in parallel mode. The server first cost
and estimated contribution to annual net cash flow are summarized below.
Server 1 Server 2
First cost, $ $100,000 $200.000
Net cash flow. $/year $35.000 $50,000 year 1. plus $5000 per year
for years 2, 3, and 4 (gradient).
$70,000 maximum for years 5 on, even if
the server is replaced.
Life, years 3or4 Sor 8
The life estimates were developed by two different individuals: a design engi-
neer and a manufacturing manager. They have asked that at this stage of the proj-
ect. all analyses be performed using both life estimates for each system.
Questions
Use computer analysis to answer the following:
1. Ifthe MARR = 12%, which server should be selected? Use the PW or AW
method to make the selection.

2. Use incremental ROR analysis to decide between the servers at MARR =
12%.
3. Use any method of economic analysis to display on the spreadsheet the
value of the incremental ROR between server 2 with a life estimate of
5 years and a life estimate of 8 years.
a |
CASE STUDY 1
SO MANY OPTIONS. CAN A NEW ENGINEERING GRADUATE HELP
HIS FATHER?’
Background Options
“[T don’t know whether to sell it, expand it, lease it, or Over the next few weeks, Mr. Kettler outlined five
what. But I don’t think we can keep doing the same options, including his favorite of selling in 5 years. John
thing for many more years. What I really want to do 1s summarized all the estimates over a 10-year horizon.
to keep it for 5 more years, then sell it for a bundle,” The options and estimates were given to Elmer, and he
Elmer Kettler said to his wife Janise, their son, John agreed with them.
Kettler, and new daughter-in-law, Suzanne Gestory. aS = Option #1: Remove rebuild. Stop operating the rebuild
they were gathered around the dinner table. Eimer was shop and concentrate on selling wholesale parts. The
sharing thoughts on Gulf Coast Wholesale Auto Parts, removal of the rebuild operations and the switch to an
a company he has owned and operated for 25 years —ai_ parts house” is expected to cost $750,000 in the
on the southern outskirts of Houston, Texas. The busi- first year. Overall revenues will drop to $1 million the
ness has excellent contracts for parts supply with sev- first year with an expected 4% increase per year there-
eral national retailers operating in the area—NAPA, after. Expenses are projected at $0.8 million the first
AutoZone, O'Reilly, and Advance. Additionally, year, increasing 6% per year thereafter.
Gulf Coast operates a rebuild shop serving these same . ; ;
. | ps . | , P e Option #2: Contract rebuild operations. To get the re-
retailers for major automobile components, such ;
| Lk . ve. build shop ready for an operations contractor to take
as carburetors, transmissions, and air conditioning
| over will cost $400,000 immediately. If expenses stay
compressors. . ane
. 7 ts , the same for 5 years, they will average $1.4 million
At his home after dinner, John decided to help his vats
. La Laure a | per year, but they can be expected to rise to $2 million
father with an important and difficult decision: What to .
Lak: , , . per year in year 6 and thereafter. Elmer thinks rev-
do with his business? John graduated just last year with .
oo. | . . . oo, enues under a contract arrangement can be $1.4 mil-
an engineering degree from a major state university in ; ;
. , lion the first year and rise 5% per year for the duration
Texas, where he completed a course in engineering
_ i, of a [0-year contract.
economy. Part of his job at Energcon Industries is to
perform basic rate of return and present worth analyses Option #3: Maintain status quo and sell out after 5 years.
on energy management proposals. (Elmer’s personal favorite.) There is no cost now, but the
‘Based upon a study by Mr. Alan C. Stewart. Consultant. Communications and High Tech Solutions Engineering.
Accenture LLP.

current trend of negative net profit will probably con- Case Study Exercises
tinue. Projections are $1.25 million per year for ex-
penses and $1.15 million per year in revenue. Elmer Help John with the analysis by doing the following:
had an appraisal last year, and the report indicated Gulf I. Develop the actual cash flow series and incre-
Coast Wholesale Auto Parts is worth a net $2 million. mental cash flow series (in $1000 units) for all
Elmer’s wish is to self out completely after 5 more five options in preparation for an incremental
years at this price, and to make a deal that the ROR analysis.
new owner pay $500,000 per year at the end of year 5 2. Discuss the possibility of multiple rate of return
(sale time) and the same amount for the next 3 years. values for all the actual and incremental cash
Option #4: Trade-out. Elmer has a close friend in the flow sertes. Find any multiple rates in the range
antique auto parts business who is making a “killing,” of 0 to 100%.
so he says, with e-commerce. Although the possibility 3. IfJohn’s father insists that he make 25% per year
is risky. it is enticing to Elmer to consider a whole new or more on the selected option over the next
line of parts, but still in the basic business that he 10 years, what should he do? Use all the meth-
already understands. The trade-out would cost an esti- ods of economic analysis you have learned so far
mated $1 million for Elmer immediately. The 10-year (PW, AW, ROR) so John’s father can understand
horizon of annual expenses and revenues is consider- the recommendation in one way or another.
ably higher than for his current business. Expenses 4, Prepare plots of the PW vs. i for each of the five
are estimated at $3 million per year and revenues at options. Estimate the breakeven rate of return
$3.5 million each year. between options.
. 5. What is the minimum amount that must be re-
Option #5: Lease arrangement. Gulf Coast could 4. | .
. ceived in each of years 5 through 8 for option #3
be leased to some turnkey company with Elmer re- | ,
_ . . (the one Elmer wants) to be best economically”
maiming the owner and bearing part of the expenses ,; .
a4: . Given this amount, what does the sale price have
tor building. delivery trucks, insurance, etc. The
. ; . . lays to be, assuming the same payment arrangement
first-cut estimates for this option are $1.5 million to . Loe,
. , as presented in the description?
get the business ready now, with annual expenses al
$500,000 per year and revenues at $1 million per year
for a 10-year contract.
a
* (Mra
CASE STUDY 2
PW ANALYSIS WHEN MULTIPLE INTEREST RATES ARE PRESENT’
Background signs. They recall that a PW or AW equation should be
. set up to solve for a rate of return. It seems that the two
Two engineering economy students, Jane and Bob, | ,
. investment plans should have identical ROR value(s).
could not agree on what evaluation tool should be ,
. i, It may be that the two plans are equivalent and should
used to select one of the following investment plans.
os . both be acceptable.
The cash flow series are identical except for their
“Contributed by Dr. Tep Sastri (former Associate Professor, Industrial Engineering, Texas A&M University).

Year Plan A Plan B Case Study Exercises
0 $+ 1900 $— 1900 Given their discussion, the following are some ques-
| 500 +300 tions Jane and Bob need to answer. Help them develop
2 — 8000 + 8000
2 +6500 ~ 6500 the answers.
4 +40) — 400 1. By simply inspecting the two cash flow patterns,
SSS determine which ts the preferred plan. In other
words, if someone is offering the two plans,
which one do you think might obtain a higher
Up to this point in class, the professor has dis- rate of return?
cussed the present worth and annual worth methods 2. Which plan is the better choice if the MARR is
at a given MARR for evaluating alternatives. He (a) 15% per year and (6) 50% per year? Two ap-
explained the composite rate of return method during proaches should be taken here: First, evaluate
the last class. The two students remember that the pro- the two options using PW analysis at the MARR,
fessor said, “The calculation of the composite rate of ignoring the multiple roots, whether they exist or
return is often computationally involved. If an actual not. Second, determine the internal rate of return
ROR is not necessary, it 1s strongly recommended that of the two plans. Do the two cash flow series
the PW or AW at MARR be used to decide on project have the same ROR values?
acceptability.” 3. Perform an incremental ROR analysis of the two
Bob admitted that it is not very clear to him why plans. Are there still multiple roots to the incre-
the simplistic “PW at MARR” is strongly recom- mental cash flow series that limit Bob‘’s and
mended. Bob is unsure how to determine if a rate of Jane’s ability to make a definitive choice? Ef so,
return Is “not necessary.” He said to Jane, “Since the what are they?
composite ROR technique always yields a unique 4. The students want to know if the composite ROR
ROR value and every student has a calculator or a analysis will consistently yield a logical and
computer with a spreadsheet system on it, who cares unique decision as the MARR value changes. To
about the computation problem? I would always per- answer this question, find out which plan should
form the composite ROR method.” Jane was more be accepted if any end-of-year released cash flows
cautious and suggested that a good analysis starts (excess project funds) earn at the following three
with a simple, common-sense approach. She sug- reinvestment rates. The MARR rates change also.
gested that Bob inspect the cash Hows and see if he (a) Reinvestment rate is 15% per year; MARR
could pick the better plan just through observation of is 15% per year.
the cash flows. Jane also proposed that they try every (6) Reinvestment ts at 45% per year. MARR its
methad they had learned so far, She said, “If we ex- 15% per year.
periment with them, | think we may understand the (c) Reinvestment rate and MARR are both
real reason that the PW (or AW) at the MARR method 50% per year.
1s recommended over the composite rate of return (7d) Explain your findings about these three dif-
method.” ferent rate combinations to Bob and Jane.

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