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CEE3000_HW5_solutions

# CEE3000_HW5_solutions - Name 50LW’°"’" CEE...

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Unformatted text preview: Name 50LW’°"’" CEE 3000: CIVIL ENGINEERING SYSTEMS Homework 5 Fall 2007 Assigned: 11/6/07 Due: 11/13/07 1. A large municipal water utility district is considering three large conduits. The ﬁrst involves construction of a steel pipeline at a cost of \$150 million. The pumping and other operating costs are expected to be \$1 million/year, increasing by 1% per year. The second involves construction of a reinforced concrete channel, at a cost of \$100 million, with operating costs of \$1.5 million starting at EOY 1 and increasing by \$150,000 per year thereafter. Alternatively, a gravity ﬂow canal can be constructed at a cost of \$200 million. The 0&M costs for the canal are expected to be \$0.75 million at EOY 1, increasing by \$200,000/year. Assuming the beneﬁts are the same for each and that each project begins operation at the same time, which conduit should be built at a discount rate of 6% if: (10 points) a. The projects are expected to last for 30 years? b. The projects are expected to last forever? 3) Alt. 1 r41) W: "0‘” -1= 0.0495 ”:— 1.01 P: 60,000 + \,OOO,OOO(C . 4 uﬁ/w’ 1.01 wt 1+ uh“ P if. \$3.01? 1S3 Al .7. P: 100 0000(1)“, 300 OLD (WA (9% 507+ 7-: §0,000(P/e‘ W 30‘ 1} m4: cox 0&6 AWE p Ogoooooo-msowok/A 69% 303+ 2.00 ooDUWCn (9% 1‘20 ‘ P:\$Q\$614Gl:N/:ZO or nr> 05 ,‘h F p, .go 000 000 +33% :31 mo DO? 000 gig. P’ #0090wa + A:1: 1 00(0 om ,3 15.93% 2&0 r“ o ow “2 0.9.61.1 0 com w 1 c on c» so 000 , Niel P '0 \u. .1.%>%:—- 1' [(66—57 P=\$2(p‘\$,os~:§,\$€w IP:[Cob/bbb/[email protected] ' J ewe 2. A sanitary sewer may be run in a pipe either through a cut or use a lift station and pipe to run the sewerage over land. The respective costs are shown below. Which design should an engineer select assuming least cost analysis? (5 points) Cut Lift Station Cost of pipe per foot \$2,500 \$500 Length of pipe 1,000 feet 1,500 feet Cost of lift station \$250,000 Annual 0&M \$500/year \$2,000/year Expected life 40 years 25 years Discount Rate 7% , . - | , m cm ~ x c ACUT .1 9,€(X.,OOO CA/r: I "ol‘iO/‘i Job I _, " ’1 A , as we , 0.3:?» - C‘s/t 15‘“ + " ,Cﬁ‘C-J ALAFT ' LOOO/DOO(A/P,“7 ”I J “" AUFT Tr ‘31 87,3“ CHOOSE w “r 5-; 10M School of Civil & Environmental Engineering 2 Georgia Institute of Technology 3. The beneﬁts and costs for ﬁve public works alternatives are shown below. Which alternative should be selected? Discount rate is 7%. (5 points) a. Based on the net annual worth method? b. Based on modiﬁed B/C analysis? Alternative E u E uivalent annual cost \$190,000 \$105,000 -_ \$180,000 \$90,000 \$145,000 \$100,000 uivalent annual benefit \$99,000 \$1 10,000 \$85,000 \$135,000 a) E’AW- =3 A= +85,000 " a: +qo,c>oc>< CH00<§€ B C : + qSIODD D = ~ 11,00o E 1 A EEO/ODD SALT. D :5 15/c< 1 .~ .1:> 00+ remake B/C :— li0,000—13S,oob:q B dominaﬁs E 5'95 gor_gg£ B/C _ \qg’QQC‘ " 1750,0913) __ .. 3 c: - 6 cibwﬂl‘éiﬁg C 6‘96 _. , W ' ”I ' ‘ 100/000 — Ci 0,. 000 B/C A'B = WW~ Cub? w[egocso ~ 570/005“ 8 d‘cxrv-KXLEZRS A CH (JOSE J6 W School of Civil & Environmental Engineering 3 Georgia Institute of Technology 4. A city-county-industry partnership has been formed to attract a professional sports team to the city. An engineer with a local consulting ﬁrm is assisting with the beneﬁt/cost analysis. The primary options are either to construct a domed arena holding 85,000 or a conventional stadium holding 70,000. The domed arena will cost \$300 million to construct and will have a useful life of 50 years. The maintenance and operations costs will be \$500,000 the ﬁrst year, increasing by \$50,000 per year thereafter. Every 10 years, except in year 50, an expenditure of \$1,000,000 will be required to remodel the interior of the dome. The conventional stadium will cost only \$100 million to construct and will also have a useful life of 50 years. The cost of operations and maintenance will be \$700,000 the ﬁrst year increasing by \$75,000 per year (higher costs due to more people needed to operate the conventional stadium). Periodic costs for repainting and resurfacing for the stadium are estimated at \$250,000 every 4 years, ending at EOY 48. Revenue from the domed arena is expected to be greater than that from the conventional stadium by \$400,000 the ﬁrst year, increasing by \$100,000/year through year 15 (due to the fact that more events can be hosted with an indoor stadium). The extra revenue from the dome is expected to remain constant at the level found at EOY 15 up to EOY 50. Assuming that the salvage value of the domed stadium is \$5 million and of the conventional stadium is \$3 million, determine which structure should be built. You may choose the NPV approach or conduct a B/ C analysis. The annual interest rate is 7%. (5 points) STADNM “risk/Yum 123--.io 2; 3on4» 5., tz's‘t"%~'tz---qsso Pome : 500,320+ SCOﬁoCMP/Aﬂcyuﬁo‘b + \$09605 12/31,-w/of.d>+ LOCO/000 ( Km; [4%] 1559+ LOOOJCBOCN p/F; .7 0/“, 203+ '10“), 00% WFf‘ro/D 50.7; l 000, DOD C P/ 1L, ”I 0/0, ‘45} ' ’30:.ng (re/(r; “70/0, go") I W’Lﬁ' never/rue ot‘ :. qommm P/Aﬁ' two , + {£13,060 (”WC/11,“) Dr’o/ 1:; 3+“ L100,000 + 1,400, 00 0):] WM (WA ,7 9%, as 3 (WP, 7%, 63+ 5, seqewc mega/0;; 0) prev : is mess 53a NPVDOME = 319.9030“ 1323033342: 2 3‘: 1% be?» a o NPVSTA‘DNM: IOOIOOOIQCD "i’ ’70 0, DOC) ( P/A [’1 ‘70] SO>+75,OOD([email protected],’?W¢I \$30)"? 250300 (WA , 3' . “”0, ‘1’)— 3, coat-Li) (We, '2 “/0. Se) Ce“ 2 (l +o.e721“’—\ = 0.3” NPVgTAplUM2 ‘ﬁ napsz, (008 C H 0053‘? CTATJI 1 UM School of Civil & Environmental Engineering 4 Georgia Institute of Technology 5. The Georgia Department of Transportation (GDOT) has adopted a policy of promoting the construction of toll roads to meet the state’s mobility needs where private investors are willing to invest in a road. Clearly, such investors will not be willing to invest unless they are guaranteed some return on their investment, that is, their initial loan will earn “interest.” The investors have established a requirement of a 10% return (or interest) on their initial investment. Given this requirement, examine the following situation. GDOT has identiﬁed a potential toll road between Atlanta and Athens. The expected cost of construction, or in other words, the initial investment required from the investors, is \$85,000,000, with a repayment schedule over 25 years. The annual operations and maintenance costs, which must also be covered by the toll revenues, are expected to be \$2,500,000 per year, increasing by \$100,000 per year. The Governor has let it be known that the toll will be \$1.00 per vehicle using this road (ignore the fact that a longer distance traveler should pay more than a shorter distance traveler). The GDOT planning folks have predicted that there will be 55,000 vehicles per day using the road on Monday through Friday (there are 260 weekdays per year). On Saturdays and Sundays, there will be 20,000 vehicles per weekend day (there are 105 weekend days per year). Given these data, will the private investors be interested in this toll road. . ..in other words, will the return on investment (or interest) be 10% or greater? Hint: you should set this problem up similar to a problem where you want to determine a toll per vehicle. In this case, you know the toll, but not the interest rate. So, you simply set up the equation and substitute in an interest rate to see if you meet the investment criterion. (5 points) Acosr ': €\$,wO/wDCA I'E/ L'1, 25> + 115001006 + ‘w’DmLP/E‘IL"ZSDCNPLL’Z'S): A REV :- (a (,ooyrssbmx 2am :0,c>uox1b\$3= S (Lo/Ll-DDIOOD/gr . (:9 L. ’— [Op/o A605,. 2: ﬂ tunic/0’41)» < (La/‘iOD/OQQ .' . Bevemm? C os+s Trﬂ L: (1% Aces—r -= a {4,01%};th <Kb/4OO/DC‘Q wnar— gee see is. aimed? we Amy, w. ag—eriw‘m Closer +0 reverting : , (w \-.J _ ”. . as L, increasee ,“Therﬁ-tmtirme L came, 1% eitna+et3>lD°/o Cacwatlﬂ around 1%0/0>.'.lﬂbfs+ W; School of Civil & Environmental Engineering 5 Georgia Institute of Technology ...
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