Chapter 8 Incremental Analysis 1

graphs can be used to solve multiple alternative and continuous-function alternatives as easily as two alternative problems.

The i m p o r t a n t s teps in incremental rate of r e t u r n analysis are: 1 1. Check to see that all the alternatives in the problem are identified. 3 ? 2. (Optional) Compute the mte of return for each alternative. If one or more

alternatives has ROR 2 MARR, reject any alternatives with ROR < MARR. i 3. Arrange the remaining alternat~ves In ascending order of Investment.

4. Make a two-alterative analysis of the first two alternatives.

5. Take the preferred alternative from Step 4, and the next alternative from the list in Step 3. Proceed with another two-alteratwe comparison.

6. Continue until all alternatives have been examined and the best of the multiple alternatives has been identified.

Decision Criteria for Increments oflnvestment: if ARORZ MARR, retain the higher-cost alternative.

if AROR < MARR, retain the lower-cost alternative.

Reject the other alternative used in the analysis.

Decision Criteria for Increments of Borrowing: If, AROR _< MARR, the increment is acceptable. I f , AROR > MARR, the increment is not acceptable

Benefit-cost graphs, being a plot of the PW of benefits vs. the PW of cost, can also be used in present worth analysis to graphically show the NPW for each alternative.

Problems Unless otherwise noted, all Cb. 8 problems should be solved by rate of return analysis.

8-1 A fm is considering moving its manufacturing plant from Chicago to a new location. The Industrial Engineering Depamnent was asked to identify the various alternatives together with the

Plant location First cost Uniform annual benefir Denver $300 thousand $ 52 thousand Dallas 550 137 San Antonio 450 117 Los Angeles 750 167 Cleveland 150 18 Atlanta 200 49

The annual benefits are expected to be constant over the eight-year analysis period. If the f m uses 10% annual interest in its economic analysis, where should the manufacturing plant be located? (Answer: Dallas) 8 2 In a particular situation, four mutually exclusive alternatives are being considered. Each of the alternatives costs $ 1300 and has no end-of-useful-life salvage value.

Useful life, Calculated rare of Alternorive Annual benefit in years return

A $100 at end of fmt year; increasing $30 per year thereafter 10 10.0%

B $10 at end of fust year; increasing $50 per year thereafter 10 8.8%

C Annual end of year benefit = $260 10 15.0% D S450 at end of first year; declining $50

per year thereafter LO 18.1%

8 3 A more detailed examination of the situation in Problem 8-2 reveals that there are two additional mutually exclusive alternatives to be considered. Both cost more than the $1300 for the four original

Annual end-OF . Useful lfe, in Calculated Alternative Cost years benefit years rate ofrehrrn

If tbe MARR remains at 8%, which one of the six alternatives should be selected? Neither Alt. E nor Fhas any end-of-useful-life salvage value. (Answer: Alt. F) 84 The owner ofa downtown parking lot has employed a civil engineering consulting f m to advise

3 18 Chapter 8 Incremental Analvsis r him whether or not it is economically feasible to consmct an office building on the site. Bill Samuels, a newly hired civil engineer, has been assigned to make the analysis. He has assembled the following data:

Alternative Sell parking lot Keep parking lot Build I-story building Build 2-story building Build 3-story building Build 4-story building Build 5-story building

Total investment* S 0

200,000 400,000 555,000 750,000 875,000

1,000,000

Total net annual revenue from property

'Includes the value of the land.

The analysis period is to be 15 years. For all alternatives, the propeny has an estimated resale (salvage) value at the end of 15 years equal to the present total investment. If the MARR is lo%, what recommendation should Bill make?

\ 8-5 An oil company plans to purchase a piece of vacant land on the comer of two busy streets for S70.000. The company has four different types of businesses that it installs on properties of this type.

Plan Cost of rmprovements*

A S 75,000 Conventional gas station with service facilities for lubrication, oil changes, etc.

B 230,000 Automatic carwash facility with gasoline pump island in front

C 30,000 Discount gas station (no service bays) D 130,000 Gas station with low-cost quick-carwash

facility *Cost of improvements docs not include the 570,000 cost of land.

In each case, the estimated useful life of the improvements is 15 years. The salvage value for each is estimated to be the S70,000 cost of the land. The net annual income, after paying all operating expenses, is projected as follows:

Plan Net annual income A S23,300 B 44,300 C 10,000 D 27,500

If the oil company expects a 10% rate of return on its invesrments, which plan (if any) should be selected?

A B C Installed cost $10,000 $1 5,000 $20,000 Uniform annual benefit 1,625 1,625 1,890 Useful life, in y e m 10 20 20

For each alternative, the salvage value at the end-of-useful-life is zero. At the end of ten years, Alt. A could be replaced by another A with identical cost and benefits. The MARR is 6%. If the analysis period is twenty years, which alternative should be selected?

8-7 Given the following four mutually exclusive alternatives: A B C D

First cost $75 $50 $50 $85 Uniform annual benefit 16 12 10 17 Useful life, in years 10 10 10 10 End-of-useful-life salvage value 0 0 0 0 Computed rate of return 16.8% 20.2% 15.1% 15.1%

If the MARR is 8%, which alternative should be selected? ( A w e r : A )

8-8 Consider the following three mutually exclusive alternatives:

A B C First cost $200 $300 $600 Uniform annual benefit 59.7 77.1 165.2 Useful life, in years 5 5 5 End-of-useful-life salvage value . 0 0 0 Computed rate of return 15% 9% 11.7%

For what range of values of MARR is Alt. C the preferred alternative? Put your answer in the following form: "Alt. C is preferred when % < MARR < %."

8-9 Consider four mutually exclusive alternatives that each have an 8-year useful life: A 6 C D

First cost $1000 $800 5600 $500 Uniform annual benefit 122 120 97 122 Salvage value 750 500 500 0

If the minimum attractive rate of return is 8%, which alternative should be selected?

r 320 Chapter 8 Incremental Analysis 8-1 0 Three mutually exclusive projects are being considered:

First cost $I000 $2000 $3000 Uniform annual benefit 150 150 0 Salvage value 1000 2700 5600 Useful life, in years 5 6 7

When each project reaches the end of its useful life, it would be sold for its salvage value and there would be no replacement. If 8% is the desired rate of return, which project should be selected?

8-1 1 Consider three mutually exclusive alternatives:

Year Buy X Buy Y Do nothing

Which alternative should be selected:

a. if the minimum attractive rate of return equals 6%?

b. ifMARR=9%? c. ifMARR- lo%?

d. ifMARR= 14%? (Answers: a. ,C b. Y; c. Y; d. Do nothing)

8-1 2 Consider the three alternatives:

Year A B Do nothing 0 -$lo0 -$I50 0 I +30 +43 0 2 +30 +43 0 3 +30 +43 0 4 +30 +43 0 5 +30 +43 0

Which alternative should be selected:

a. ifMARR = 6%?

6. ifMARR=8%? c. ifMARR= lo%?

Problems 321

A B Initial cost $10,700 $5,500 Uniform annual benefits 2,100 1,800 Salvage value at end of useful life 0 0 Useful life, in years 8 4

~t the end of four years, another B may be purchased with the same cost, benefits, and so forth. If the MARR is 1O0h, which alternative should be selected?

'- 8-14 Consider the following alternatives: A B C

lnitial cost $300 $600 $200 Uniform annual benefits 4 1 98 3 5

Each alternative has a ten-year useful life and no salvage value. If the MARR is 8%. which alternative should be selected?

I 8-1 5 Given the following: Year X Y

Over what range of values of MARR is Y the preferred alternative?

8-16 Consider four mutually exclusive alternatives: A B C D

Initial cost $770.00 $1406.30 $2563.30 0 Uniform annual benefit 420.00 420.00 420.00 0 Useful life, in years 2 4 8 0 Computed rate of return 6.0% 7.5% 6.4% 0

The analysis period is eight years. At the end of two years, four years, and six years, Alt. A will have an identical replacement. Alternative B will have a single identical replacement at the end of four years. Over what range of values of MARR is Alt. B the preferred alternative?

'uwaijo alw %s ue apl~oid 1sy) wAp8ma)la Vl!M SaA!l lyasn naq, JO pua aq le pa3eldal am 3 pue a wApusnly '2

.suamaqda~ le3!1uap! VIM saN[ 1 yasn i!aqjo pua aq le pa3eldaJ am3 pue g !ia~pm(y -1

2 isuo!len~~s %mmo[(o~ om) aq JO qma u! pam[as aq plnoqs '' aa!leuaqe q~!q,y, .popad s!sdleue a1!1rj~ uv pue *ale1 1saJalq %s ue 'nsdp quom ~uasaid asn

I 'a~eds asnoqarem paauaJJo sJa1am .bs OOOL q!m 's! se anqq -E

I .a3eds asnoqaiem due %quai area3 pue asnoqarem man aq Lng .Z

1 'slalam .bs oooz 01 pa3npa~ aq plnom ajeds p?,waX~ ap 'uw UI 'a~eds aqjleq duedm03 uosuqoy atp areal pue asnoqmm mau aw Lna I :sa~!letualle aaq %m~ap!sucn n '~aaq%na lue~d

aid^ aql 'de13 wo~ .dlanlua amds asnoqanw %uyua~ asea3 ppo3 aiL~ '1aqun.J quom e OOO~$ aq I plnow lual djquom aql ase3 q3!qm u! 'ualam .bs oooz 01 a3eds palua~ aql Bq~npjo uo!ldo aq seq 1 11 .qmom e OOLZ$ JOJ a3eds asnoqareMjo sJalam .bs OOOL saz!l!ln pue nu Lpu-d ?ILL

.wuom e ooszs JOJ asnoqaiem Mau allljleq asealol paqo seq dueduo3 uosuqol au.aurpnq) le peds asnoqamm aql ([e paau IOU saop Inq 'asnoqaiem ay Lnq p[nos pue alqe[!eAe qse~ papaau aql seq a&

.smad airy JO pua aql w ooo'oo9$ JO anleA alesale aAeq plnom asnoqarem aql lev pa]euysa s! 11 -]saJa)u! uopaseq ~uaur/(ed /(lq)uom lenba 4x!s u! pled Sqaq a3uepq aqa ql!w luamded umop 000'001 $e an pagosolla) au '000'0~fl JOJ ales JOJ s! uo!1=0&03 ald~ aql 01 ~oop Ixau asnoqamm slam -bs 000'01 mau y 81-8

-s!sd[eue rumaijo ale1 ql!m 4u1paa3o~d aJoJaq a%ueq3 n%!s an0 01 MOD qSe3 e u~1ojsue4 01 %01 JO qw 1saalF leualxa ue asn 'a1e!idoidde aiaw i,pamjas aq plnoqs aA!leuaIle q3!4M '%s I JO mvpq e uo pasea .anleA a8e~les ou pue aj!I [yasn mL-(-ua~ e seq aA!leualle qzea

SPI OSZ OSP snad s luanbasqns JO qm m lgauaq pnq 059 OSZ OSZ smad s ~snj JO q3ea m lgauaq pnmy StOZS OOOlS 0051J as03 le!l!ul 3 B V

s!sA/euV /eluauarJul 8 JW7PY3 ZZE A

Problems 323 20 A problem often discussed in the engineering economy literamre is the "oil-well pump

pmhlern":z Pump 1 is a small pump; Pump 2 is a larger pump that costs more, will produce slightly more oil, and will produce it more rapidly. If the MARR is 2096, which pump should be selected? Assume any temporary external investment of money earns 10% per year.

Pump I Pump 2 Year ($000~) (6000s)

0 -S 100 -61 10 I +70 +l I5

8-21 Three mutually exclusive alternatives are being studied. If the MARR is 12%. which alternative should be selected?

Year A B C 0 -$20,000 -$20,000 -$20,000 I +10,000 . +10,000 +5,000 2 +5,000 +10,000 +5,000 3 +10,000 + 10,000 +5,000 4 +6,000 0 +15.000

8-22 The South End bookstore has an annual profit of $170,000. The owner is considering opening a second bookstore on the north side of the campus. He'can lease an existing building for five yean with ao option to continue the lease for a second five year period. If he opens the second bookstore he expects the existing store will lose some business that will he gained by the new "The North End" bookstore. It will take $500,000 of store fixtures and inventory to open The North End. He believes that the two stores will have a combined profit of $260,000 a year after paying all the expenses of both stores.

The owner's economic analysis is basedon a five year period. He will beable torecover this $500,000 investment at the end of five years by selling the store fixtures and inventory. The owner will not open The North End unless he can expect a 15% rate of return. What should he do? Show computations to justify your decision.

< 8-23 A paper mill is considering two types of pollution control equipment. Neunalizarion Precipitation

Initial cost $700,000 $500,000 Annual chemical cost 40,000 110,000 Salvage value 175,000 125,000 Useful life 5 years 5 years

1 3 'Oneofthernore interertine.exchangesofopinion aboutthis problem is In Pmf. Manin Wohl's "CommonMisunderrtandinas

About the lnrrnal Rate of~eturn ind ~ e t ~ n c x n t Value ~conornic Analysis Methods:" and the asociated discussion by Rofssron W i n h v . Leavenwonh. Steiner. and Beremann. oublished in Evaluatin~ Tmm~ortarionPro~oraI~. Transoonarion

- , t kcarch Record ;3 1. Transpm~~on Research g a d , wkhugton. D C

r 324 Chapter 8 Incremental Analysis The f i wants a 12% rate of return on any avoidable increments of invesbnent. Which equipment should be purchased?

8-24 A stockbroker has proposed two investments in low-rated corporate bonds paying high interest rates and selling below their stated value (in other words. junk bonds). Both bonds are rated as equally risky. Which, if any, of the bonds should you buy if your MARR is 25%?

Annual Current market Stated value inreresr price, including Bond

Bond payment buying commissron maturily3 Gen Dev %I000 5 94 $480 15 years

WR 1000 140 630 15

8-25 Three mutually exclusive alternatives are being considered.

Initial investment $50,000 $22,000 $15,000 Annual net income 5,093 2,077 1,643 Computed rate of return 8% 7% 9%

Each alternative has a 20-year useful life with no salvage value. If the minimum attractive rate of return is 7%, which alternative should be selected?

8-26 A f i is considering five alternatives. 1 2 3 4 5

Initial cost $100.00 $130.00 $200.00 $330.00 Do nothing

Uniform annual net income 26.38 38.78 47.48 9 1.55

Computed rate of return 10% 15% 6% 12%

Each alternative has a five-year useful life. The f i ' s minimum attractive rate of return is 8%. Which alternative should be selected?

'AI rnilfurlty the bondholder recetves the l z t Interest payment plus the bond stated value

Problems 325 Alternatives

Initial Cost $2000 5000 4000 3000 A M U ~ Benefit 800 500 400 1,300 Salvage Value 2000 1500 1,400 3,000 Life in Years 5 6 7 4 MARR Required 6% 6% 6% 6%

Find the best alternative using incremental ROR analysis.

' 8-28 Our cat Fred's summer kitty-cottage needs a new roof. He's considering the two proposals below and feels a I5 year analysis period is in line with his remaining lives. Which

, roof should he choose if his MARR = 12%? What is the actual value of the ROR on the ,, incremental cost? (There is no salvage value for old roofs.)

Thatch Slate First Cost $20 00 $40.00 A M U ~ Upkeep 5 00 2.00 Serv~ce L ~ f e 3 years 5 years

8-29 Don Garlits is a landscaper. He is considering the purchase of a new commercial lawn mower. Two machines are being considered, the Atlas and the Zippy. The table shown below provides all the necessary information for the two machines. The minimum amactive rate of return is 8%.

a. Determine the rate of return on the Atlas mower (to the nearest lo/.). 6. Does the rate of return on the Zippy mower exceed the MARR? c. Use incremental rate of return analysis to decide which machine to purchase.

Initial cost

Atlas Zippy

$6,700 5 16,900 Annual operation and maintenance $1,500 $ 1,200

cost

A M U ~ ~ benefit $4,000 $ 4,500 Salvage value $1,000 $ 3,500

Useful life 3 6

8-30 QZY, Inc. is evaluating new widget machines offered by three companies. The machines have the following characteristics:

- - . . - ~- . . 4 Company B Company C F = r .. :.. .- 5 1 5.000 $25,000 $20,000 \#.i:.--,u(t;? i .,TCL .- : 1,600 400 900 % - l-L, - ,r.t 8,000 13,000 9,000

:,A ;: , L -1 3,000 6,000 4,500

bCx:& = 15 %. Using rate of return analysis, from which company, if any, should you purchase the widget machine?

8-31 The Croc Co. is considering a new milling machine. They have narrowed the choices down to three alternatives:

Alternative

, First cost Annual benefit

Delure Regular Economy S220,OOO S125,OOO $75,000

79,000 43,000 28,000 Maintenance & operating costs 38,000 13,000 8,000 Salvage value 16,000 6,900 3,000

All machines have a life of ten years. Using incremental rate of return analysis, which alternative, if any, should the company choose? MARR = 15%.

8-32 Wayward A f i i g h t , Inc. has asked you to recommend a new automatic parcel sorter. You have obtained the following bids:

SHIP-R SORT-Of U-SORT-M First cost S184.000 $235,000 $180,000 Salvage value 38,300 44,000 14,400 Annual benefit 75,300 89,000 68,000 Yearly maintenance and

operating cost 2 1,000 2 1,000 12,000 Useful life, in years 7 7 7

Using an MARR of 15% and a rate of return analysis, which alternative, if any, should be selected?

a 8-33 Build a spreadsheet to fmd the EAC of each roof in 8-28. Use the GOAL SEEK tool of Excel to fmd the IRR of the incremental investment.

5 8-34 Build a spreadsheet to find the EAW of each lawnmower in 8-29. Use the GOAL SEEK tool of Excel to find the IRR of the incremental investment.