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# Cost Engineering and Analysis C E 406

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This 9 page Class Notes was uploaded by Charley Wintheiser DVM on Monday October 5, 2015. The Class Notes belongs to C E 406 at California State University - Long Beach taught by Jeremy Redman in Fall. Since its upload, it has received 61 views. For similar materials see /class/218764/c-e-406-california-state-university-long-beach in Civil Engineering at California State University - Long Beach.

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Date Created: 10/05/15

CE406 Chapter 5 092205 Present Worth Analysis Given alternatives how do we select the best List the alternatives Determine costs associated with each Engineering economy models time value of money interest rate etc Calculate the measure of worth When listing alternatives categorize each project as Mutually exclusive only 1 of the viable projects can be selected Independent more than one project can be selected Mutually exclusive You need to buy a new car Which brand do you chose Examine price yearly maintenance costs failure rates etc to chose the best When selecting between m alternatives always remember that Do Nothing DN is an option DN stick with current approach incurring no new costs revenues or savings Total of m 1 alternatives to evaluate Independent projects projects do not compete with one another Thus if there are m projects including DN there are 2m alternatives Back to engines if we had 3 models we have 23 or 8 alternatives DN A B C AB AC BC ABC Some options may be eliminated due to budgetary constraints We discuss independent projects at the end of the class Nature of alternative based on cash flow Revenue each alternative generates costs and revenue cash flow estimates and possibly savings Depend on which alternative selected Involve things like new systems products etc that require capital investments to generate revenue or savings Service each alternative has only cash flow estimates No revenue or savings are dependent on the alternative such as a safety improvement installing sprinklers evaluations based solely on cost estimates Present worth analysis of equallife alternatives We now refer to the present worth P as PW and we calculate it at the MARR for each alternative All future costs are transformed into equivalent dollars now If all alternatives are used for the same time period we have equalservice alternatives Page 1 of 9 CE406 Chapter 5 092205 Guidelines One alternative Calculate PW at the MARR lf PW 0 the MARR is met or exceeded and the alternative is financially viable Two or more alternatives Calculate PW of each alternative at the MARR Select the alternative with the largest PW value either most positive or least negative Ex PW1 1000 PW2 500 chose alternative 2 Wish to purchase a new water heater Our MARR is 10 Electric Gas Solar Price 2500 3500 6000 Annual operating costs 900 700 50 Salvage value 200 350 100 Life yrs 5 5 5 Pwe 2500 900PA 10 5 200PF 10 5 5788 ng 3500 700 PA 10 5 350PF 10 5 5936 Pws 6000 50PA105 100PF 105 5127 Go with electric However if the life of the unit was 10 years we could repeat the calculations and find that Pwe 7953 ng 7666 Pws 6268 Thus the lower operating costs of the solar unit offset the higher price only at longer times In this case the life for all the alternatives was equal What do we do if they are unequal PWAnaIysis of Differentlife Alternatives PW of alternatives must be compared over the same numbers of years and end at the same time If we don39t compare over equal periods then the shorterlived alternatives will Page 2 of 9 CE406 Chapter 5 092205 generally be favored as costs over longer periods will compound greater values How do we do this Compare alternatives over a period of time equal to the least common multiple LCM of their lives Compare alternatives using a study period of length n years This may not take into consideration the useful lives of the alternatives Called the planning horizon approach LCM Approach Extend cash flows for all alternatives to the same time period Given alternative with 2 year and 3 year lives the LCM would be a 6 year time period Assumptions in LCM approach service provided by the alternatives will be needed for the LCM of years or more selected alternative will be repeated over each life cycle of the LCM in exactly the same manner cash flow estimates will be the same in every life cycle Study Period Approach Chose a time horizon over which the analysis is conducted and only those cash flows which occur during that period are considered relevant Everything outside this period are ignored However estimated market value at the end of the period must be made a salvage value refund etc Useful when LCM yields an unrealistic evaluation period eg 5 year and 9 year would be an LCM of 45 years Page 3 of 9 CE406 Chapter 5 092205 Consider you want to open your own office You have 2 locations to chose from Location A Location B First cost 15000 18000 Annual lease cost yr 3500 3100 Deposit Return 1000 2000 Lease term yrs 6 9 If your MARR is 15lyr which is the best option based on a PW analysis An LCM approach With 6 and 9 yrs the LCM is 18 years 3 repeats ofA 2 repeats of B Draw diagram Note that the repeating uniform series runs for a full 18 years Thus for location A we can write Pwa 15000 15000PF156 15000PF15121000PF156 1000PF1512 1000PF1518 3500PA1518 Pwa 45036 For location B wa 18000 18000PF159 2000PF159 2000PF1518 3100PA1518 wa 41384 Many companies like to look at planning horizons Rather than look at costs over the life of a project the look at costs during periods If you chose a 5year study period then no cycle repeats are necessary Because the deposit return occurs after the study period we have to estimate a value For now we can just assume the same refund occurs at year 5 Pwa 15000 3500PA155 1000PF155 26236 wa 18000 3100PA155 2000PF155 27397 Thus if we use a 5 year planning horizon choosing option A is more acceptable Why are planning horizons used Maybe a companies long term future plans are uncertain but they know the short term very well so they plan for cash flows for only those shorter periods Page 4 of 9 CE406 Chapter 5 092205 Future Worth Analysis FW of an alternative can be determined directly from the cash flows by applying FP factor to the PW n value in FW analysis depends on the time period used to determine PW either the LCM of a specified study period Why would we care about future worth Consider you are a corporation One of your mandates is to maximize the future wealth of your stockholders Thus you would like to predict the future value of projects at various future periods Most often used if an asset equipment building corporation is to be sold in the future before it39s expected life is reached In this way you can estimate whether it is better to sell it early or keep it for its end life salvage value Example Trump empire purchases a food store chain for 75 million 3 years ago There was a net loss of 10 million a year at the end of the first year of ownership net cash flow is increasing with an arithmetic gradient of 5 M per year starting in year 2 For large projects like this Trump has set the MARR at 25 per year from any sale If another firm offers 1595 million to buy the chain now is the MARR realized at this selling price What are we trying to determine exactly Given an interest rate of 25 on the money involved we want to know if we break even by selling now FW3 75 FP253 10 FP252 5FP251 1599 886 M Although we did make a profit on the sale we bought the store for 75 and had losses of 15 for a total of 90 M and we are selling for 1595 M we did NOT meet the minimum attractive rate of return that the investors expected for this transaction Let39s say we hold on to the chain for a total of 5 years what sale price in that year would be sufficient to meet the MARR FW5 75FP255 10FA2555AG255FA255 2468 M Thus we would need an offer of 2468 M in order to achieve a ROR of 25 on our money Page 5 of 9 CE406 Chapter 5 092205 Capitalized Cost Capitalized cost is the present worth of alternatives that will last forever Projects such as bridges damns irrigation systems railroads In addition to the initial construction cost these projects will have recurring annual maintenance upkeep etc costs 1z39 1 z391z39 lfwe take the limit as n gt infinity 1i 1 z391z39 1 1 1z39 PA P1imA P1imA I will I The present worth is redefined as the capitalized cost CC Ai Consider an endowment at a college to pay for tuition for needy students If the tuition is 20000 year how much money must be in the endowment if the college wants to fund 20 scholarships per year in perpetuity Assume an interest rate of 15 per year The annual amount is 2000020 400000 CC M 400000015 267 Million This value 267 Million is the exact amount needed such that the interest earned yearly is 400000 Public Sector alternatives are often analyzed in this manner Cash flows in CC calculations are either recurring periodic or nonrecurring In order to determine CC for infinite sequence of cash flows 1 Determine present worth of all nonrecurring amounts This is their CC value 2 Find the equivalent uniform annual worth A value through 1 life cycle of all recurring amounts Add to this all uniform amounts occuring in years 1 through infinity This is the AW AWi CC Add the CC values from 1 and 3 Ace Page 6 of 9 CE406 Chapter 5 092205 Example 525 City wants to attract professional football team Costs New Stadium 250 M Annual upkeep 800000 per year Replace artificial turf 950000 every 10 years Repaint 75000 every 5 years Capitalized cost at an interest rate of 8 per year Non recurring items construction CC1 250 M Recurring items turf repaint upkeep Annualize each of these items AW AturfAFin ArepaintAFin 800000 AW AturfAF810 ArepaintAF85 800000 AW 950000006903 75000017046 800000 878363 002 AWi 878363 008 1097 M Thus CC 250 1097 262 M This is the total capitalized cost or the present worth of the project that presumably will last forever We can also say that A CCi 262 M 8 209 M This value is the amount of money that the city will commit forever to operate and maintain the football stadium Thus when analyzing whether to build a stadium or not any benefits to the stadium sports revenue newjobs new businesses etc should generate at least 209 M per year in order to make the stadium worthwhile To summarize Capitalized costs are sum of Present worth of all single value payments now or in future CC Sum PW Annualized worths of all recurring payments annualized over their frequency then divided by i CC Sum AW i Can use the same technique for short term projects as well Present Worth of Bonds How is money raised for large capital projects like public projects that have infinite life spans Page 7 of 9 CE406 Chapter 5 092205 Bonds long term notes issued by corporations or government entities to finance major projects Borrower receives money now in return for a promise to pay the face value V at the stated maturity date How they work Bond has a face value say 50000 that matures on a stated date Between now and that stated date the bond pays regular interest based on it39s coupon rate On the maturity date the bond pays its face value V face value of the bond b bond coupon rate or the interest rate of the bond c number of payment periods per year l Bond interest or divident the amount paid c times per year face valuebond coupon rate number of payments per year Vbc Bonds are often sold at a discount so instead of being sold at the face value eg it might be sold at a 2 discount Our 50000 bond would sell for 49000 But dividend paid will still be based on it39s original 50000 value When dealing with bonds and calculations we have 2 interest rates the bond coupon rate and the market rate or MARR When dealing with projects the safe investment rate is usually set at the US Treasury bond rate for MARR determination 550 What is present worth of a 50000 municipal bond that has an interest rate of 4 per year payable quarterly The bond matures in 15 years and the market interest rate is 8 per year compounded quarterly 1 Determine l the interest per payment period I Vbc 500004lyr4 quartyr 500 per quarter 2 Construct cash flow diagram of interest payments and face value repayment 3 Establish the MARR MARR 8 The market rate is our base We should be able to beat it 4 Calculate PW of bond interest payments and face value at i MARR 1 bond PPquarterly and market interest CPquarterly effective i per pp 1 rmquotm 1 where r is nominal int rate per PP and m is of CPPP r for our case is 8 per year 4 quarters per year 2 quarter Page 8 of 9 CE406 Chapter 5 092205 effective i Iquarter 12l1quot1 1 2 PW of bond FPF2154 APA2154 50000 03048 500347609 3262045 This value tells us how much our investment is worth today Notice IT IS LESS THAN THE BOND Do not invest in bonds that don39t at least make more than what you initially pay In cases like this investors might now invest in the bond and as such the issuer would discount the bond The interest the bond pays is the same but the amount it is sold for decreases Page 9 of 9

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