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# Civil Engr Systems CEE 3000

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This 0 page Class Notes was uploaded by Coty Von on Monday November 2, 2015. The Class Notes belongs to CEE 3000 at Georgia Institute of Technology - Main Campus taught by Adjo Amekudzi in Fall. Since its upload, it has received 31 views. For similar materials see /class/234177/cee-3000-georgia-institute-of-technology-main-campus in Civil and Environmental Engineering at Georgia Institute of Technology - Main Campus.

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Date Created: 11/02/15

Name ANSWER KEY Date CEE 3000A CIVIL ENGINEERING SYSTEMS HOMEWORK 3 Engineering Economy Spring 2011 Assigned 2171 lDue 3111 Problem 1 Draw a cash ow diagram when appropriate and solve each problem 2 pts each a How many years will it take for 15000 to reach 40000 if the annual interest rate is 5 i5 11000 40 000 0 n n ln40000l5000ln1005 ln2667lnl05 09810049 2002 or 21 years b If 700 is invested today what will it be worth after 10 years at an annual interest rate of 10 i10 P 7 0 0 10 F 700FP 10 10 70025937 1816 c What is the present value of a uniform stream of costs of 15000 that begins in year 5 and occurs each year for the neXt 10 years at an annual discount rate of 4 P 15000PA 4 11PF 4 4 P z 7 i4 P 150008760508548 A 15000 P 112327 0 5 15 d You plan to buy a used car and will have a monthly payment of 450 per month for three years What is the present value if the nominal annual interest rate is 16 P imon1612 1333 7 T A 450 0 1 P 450 PA 1333 36 36 P 450 285695 12856 What is the capitalized value of an annualized cash stream of 1200 at an annual interest rate of 6 39D 9 i6 P 7 T A 1200 0 1 P Ai for nin nity P 1200006 20000 f What amount should you invest today if you want to draw 1500year from an account for 25 years with an annual interest rate of 5 50 I o A 1500 P 1500140939 P 1500PA 5 25 P T 0 1 25 P 21 14085 g If an 8 nominal interest rate is compounded quarterly what is the effective annual interest rate iquarter 0084 002 ie 1002 L 1 824 h A company charges 2 interest per month on credit purchases What is the equivalent nominal annual interest rate inom imomh m 002l2 24 annually A company charges 2 interest compounded monthly on credit purchases What is the effective annual interest rate V ieff l02 1 268 annually Problem 2 5 points A small town wants to acquire an electric generator facility for half a million dollars It will cost approximately 4500year to maintain the facility The facility has an expected useful life of about 50 years The annual interest rate is 6 5 points a What is the present worth of the capital and maintenance costs of the facility Start by drawing a cash ow diagram P i6 500000 A 439500 0 b 1 50 P 500000 4500PA 6 50 500000 45001576l9 57092855 or 570929 b What is the EUAC equivalent uniform annual cost of the facility over its useful life 570929 i6 A 0 1 50 A 570929AP 6 50 570929006344 36220yr Problem 3 5 points A city concerned about the impacts of climate change is considering two options for bridge design In the rst option the bridge will cost 25000000 and the annual maintenance costs will be 50000 The second option will cost 20000000 and incur maintenance of 40000 per year but will require a retro t of 15000000 in year 20 if rainfall intensity increases Assume i5 annual and the eXpected life of both bridges is 75 years a What is the equivalent present worth of options one and two assuming that a retro t is not 57 0 needed Be sure to draw a cash ow diagram for each option Option 1 P 25000000 50000PA 5 75 25 i5 P 25000000 5000019485 A 501000 P 25974250 0 1 75 Option 2 P 20000000 40000PA 5 75 P 20000000 4000019485 20 A 40 000 I5 P 20779400 v 0 1 75 What is the equivalent annual worth of option 2 if the retro t is needed 20M A 40000 i5 T 15M 0 1 20 75 P 20000000 40000PA 5 75 15000000PF 5 20 P 20000000 4000019485 1500000003769 P 20000000 779400 5653500 26432900 A 26432900 AP 5 75 A 26432900 005132 A 1356536yr A option 1 25974250 005132 1332999yr Which design option would you recommend knowing that it is uncertain whether the retro t will be needed Why Answers will vary 7 need to compare EUAW or PW for all alternatives and weigh higher costs vs risk Problem 4 5 points A local consultant is evaluating two competing proposals The interest rate is 7 per year and all annual payments occur at the end of the year Which of the two proposals is better Start by drawing a cash ow diagram for each project Proposal A Initial cost 100000 Operations and maintenance costs 1200 per year Salvage value None at EOY 16 Proposal B Initial Cost 150000 Operations and maintenance costs 1000 per year Salvage value 5000 at EOY 16 A i7 A 1200 01 16 Annual Worth ofA 100000NP 7 16 1200 100000010586 1200 11786 Present Worth ofA 11786 PA 7 1611786 94466 111338 B i7 150000 I A 11000 5000 0 1 16 Annual Worth ofB 150000AP 7 16 1000 5000 AF 7 16 15000010586 1000 7 5000003586 1669970 or 16700 Present Worth ofB 16700 PA 7 16 16700 94466 157758 Proposal A is the better option because it is less expensive over its life time Name ANSWER KEY Date CEE 3000A CIVIL ENGINEERING SYSTEMS HOMEWORK 4 Engineering Economy Spring 2011 Assigned 3 811Due 3 1511 Reminders about rounding answers 0 For nal answer round time period to re ect interestpayments occurring at end of time period 0 For nal answer keep two decimal places for any rate 0 For preliminary steps keep four decimal places for rates and factors 0 Round all monetary values to the nearest dollar Problem 1 You must draw a cash ow diagram for each problem and solve 2 pts each a Find the present value of a project cash flow that starts at EOYl with a value of 20000 and increases by 4 an The expected life of the project is 10 years and the discount rate is 7 lo 0 7 m m a W ex 0029 P 1 7 1a 039 P 3 040 W c 120quot 3032 m we 0272 a as b Find the present value of a project cash ow that starts at EOYl with a value 0f5000 and increases each year thereafter by a value of per year The expected life of the project is to all intents and purposes in nite and the discountrate ME I 7 y Wquot l V J l 39 o as P 395quot 2 Jquot a 2 W 5 M a 2 I v 0 7 a 7 7mm 24 macer F W23 4 70 2 0 Find the futle value of a project cash ow that starts at EOYl with a value of 5000 and increases each year thereafter a value of 0 The expected life of the project is 30 years and the discount rate is 7 A 3 T CKCl 15 m c3 ulv ulovuuuu JMLV lo I IV 33 J P4 19quot I 325 14 w 7 ml 3 vQy 441 r W quot at 68 a a 3 pto 97 W New fatWV pm MSG31 r393 WW3 397 um i i 3amp3 t a Q3 0 d Find the present value of a project cash ow that starts at EOYS with a value of 5000 and increase each year thereafter by a per year cted life of the project is 30 years and the discount rate is 5 r I xv JV Q u wi uxv unuvvuns K r gt Au with tar quotVI 3i has 3 a m h u an 6 Find the present value of a project cash ow that occurs every 2 years starting at EOYS with a value of 5000 and increases thereafter by a value of 1000 every 2 years The expected life of the project is 30 years and the discount rate is 5 Problem 2 10 points A Your firm is designing a new 2 mile bridge for a river crossingi and you ve been asked to explore financing options The initial capital costs will amount to 32wmillion Annualquot operatigiismaiid 395 maintenancecostswillwsta N 39 I nd increasebvmld in subsequent years Every gleam the bridge will need to be resurfaced at a cost of15 million The bridge will be funded with a combination of state and local funds andOra tbi39 You re developing funding scenarios for the bridge i and are considering the following three scenarios among others it i a w r 1 What toll would be required to recover construction costs assuming a 30 year payback period and 4 annual interest rate l A T r at M v i lt3 q r x mi of f it 39 is f J COIN reamrv 2 What toll would be required to recover assuming a 75 v ekarwlife and 4 annual interest rate at 3 What toll would be required to recover all costs en perpetuity with a 4 annual interest rate J C V L 3 ll Problem 3 10 points 5 t Your county wants to biiild a new wastewater treatment plant and the mayor wants to know what the 39 quot 39fco st is of the proposed facility so that he can explore nancing options As the county engineer you have been asked to estimate construction and operations and maintenance costs and then determine the capitalized cost You estimate that the facility and new collection pipes will cost 15 million to construct Annual 0ampM costs will be 15 0000 and a major rehabilitation 1000000 must occur every 5 years aggrvtlie rst 10 years of operation What is the capitalized cost of the treatment plant assuming the nominalinterest rate is 8 Vet a UFvm 34 k M i v v 139 at Q 441217 C Am L Q I 2 x I l A w k m v t i quot i 47an i M r a t a t t it A ay V by i rs it if X k i j r i 3 39 quoti 1 E a t 3w 31 1quot SUBJECT JRDV PQ o S 1 EV DATE RKDVVNQ Cgt quotguKD DATE H 755 QCxquot 17x H 1515 Krv quot39Y tV39eLv y WWW HM n 9 v lt Clb lquot r4 O may YLL in am 71 0 03 15 3 Md my 9 1 r oo 3 a W 3 3mg UM v 52 awwhcyzz L W J 2o m 20 3 I gm Maggir Lo lt5 ilkm km Q E w Ah If 9L1 A Y39WJV V39MVNJQ quotm C CVQ l Fm 3 11 WM mo C Kim 0 3 2o w ox PW 17 0C J gtltlt qin t 3 i i ov xx L1fJ1 D w39 izltgtltgtlt 30 w 0 5 2 quot i 0 33 C f w La i Ah m we X1 L Wadi H xv cc 4 0133 V N quot 400 0 90 PlM mm 540 gogxw CV C3 Lqu a quot 8x014 339 4398 C quot1 1 L20 Eu L N W 43 w 400 out gmoo o A 5 1 91ng quot3 3 5 f Chm baa 5Q 3 1 r0 rvx 0 xx o ryi ct yak fgrardfslt7u 3 0 n 421 mu ix gt can hWW I r kOo mm LDP3 ZM 39K CVK Cr bw mwx 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