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Quiz and Tutorial
Copyright © 2006 Pearson Education Canada Inc. 4-2 Quiz Who was not here? Email me ASAP. Marks? Have to wait…. Problems: Too easy? Too hard? Print problem? Prefer handouts? Enough time? Quiz Review: Helpful? Skip? Other suggestion?
Copyright © 2006 Pearson Education Canada Inc. 4-3 Quiz Quiz schedule has to fit the course If you skip and Emailed me: marks moves to other quizzes If you have to skip more than 2 quizzes, I need a really good reason First one always too easy, will getting harder…. Informal quiz….handouts and white paper OK? Or some handouts will be enough?
Copyright © 2006 Pearson Education Canada Inc. 4-4 Tutorial and TA Everything covered? Quiz and practice problems? Anything else? More examples? Everything clear? Question time? Other Suggestions or comments: Email TA or to me
Engineering Economics in Canada Chapter 4 Comparison Methods Part 1
Copyright © 2006 Pearson Education Canada Inc. 4-6 4.1 Introduction An investment can be thought of as an exchange of resources now for an expected flow of benefits in the future. Not all investment opportunities should be taken –If the costs exceed benefits Not all investment opportunities can be taken –Due to physical or logical constraints Engineers frequently must evaluate costs and benefits of investments, as well as their feasibility
Copyright © 2006 Pearson Education Canada Inc. 4-7 Introduction (con’t) Chapter 4 deals with methods of comparing investment projects (henceforth ‘projects’). We start with a classification scheme that permits use of the appropriate comparison method Comparison Methods: –Present Worth –Annual Worth –Payback Period
Copyright © 2006 Pearson Education Canada Inc. 4-8 Assumptions of Comparison Methods: Costs and benefits are measurable in terms of money. –Chapter 13 deals with qualitative criteria. All cash flows are known with certainty. –Chapters 11 and 12 with uncertainty and risk. Cash flows are unaffected by inflation or deflation. –Chapter 9 deals with inflation. The effect of taxation is ignored –Chapter 8 deals with taxes.
Copyright © 2006 Pearson Education Canada Inc. 4-9 4.2 Relations Among Projects Independent: –Costs and benefits of one project do not depend on whether another is chosen Mutually Exclusive (ME): –a project is excluded if another is chosen Related, but not mutually exclusive: –Costs and benefits of one project depend on whether or not another is chosen –Or, a budget constraint limits the number of projects that can be done
Copyright © 2006 Pearson Education Canada Inc. 4-10 Relations Among Projects (con’t) Three-way classification scheme can be reduced to a two-way scheme Take related, but not mutually exclusive projects and organize them into mutually exclusive subsets: If there are n projects, then there will be 2 n mutually exclusive alternatives, including the “do nothing” alternative. This leaves: 1.Independent Projects (which are evaluated independently) 2.Mutually Exclusive Projects (which are ranked and the best is chosen).
Copyright © 2006 Pearson Education Canada Inc. 4-11 How to Treat Project Relationships
Copyright © 2006 Pearson Education Canada Inc. 4-12 Example 4-1 The AAM Company is considering opening three new marble quarries, call them T, L and M. a) What mutually exclusive alternatives are feasible with no budget constraint? ProjectFirst Cost T quarry$0.9 million L quarry$1.4 million M quarry$1.0 million
Copyright © 2006 Pearson Education Canada Inc. 4-13 Example 4-1: Answer Answer: M, L, LM, T, TM, TL, TLM, and no new quarry. All options can be generated through a table such as: #T?L?M?OptionCost 1NoNoNodo nothing0 2NoNoYesM1.0 M 3NoYesNoL1.4 M 4NoYesYesLM2.4 M 5YesNoNoT0.9 M 6YesNoYesTM1.9 M 7YesYesNoTL2.3 M 8YesYesYesTLM3.3 M
Copyright © 2006 Pearson Education Canada Inc. 4-14 Example 4-1 (con’t) Due to rich marble deposits at the L quarry, AAM could use mechanized cutter-loaders for that quarry (0.4M, but not for the other quarries). Now what mutually exclusive alternatives are available? Answer: Use C to denote the Cutter-loader. Alternatives are: M, L, LM, T, TM, TL, TLM, no new quarry LC, LMC, TLC, TLMC
Copyright © 2006 Pearson Education Canada Inc. 4-15 Example 4-1 (con’t) Now suppose that they have decided to spend no more than $2.5 million in the first costs of the quarries. What mutually exclusive alternatives are feasible now? Answer: M, L, LM, T, TM, TL, LC, and no new quarry
Copyright © 2006 Pearson Education Canada Inc. 4-16 #T?L?M?C?OptionCost 1NoNoNoNonothing0 2NoNoYesNoM1.0 M 3NoYesNoNoL1.4 M 4NoYesNoYesLC1.8 M 5NoYesYesNoLM2.4 M 6NoYesYesYesLMC2.8 M 7YesNoNoNoT0.9 M 8YesNoYesNoTM1.9 M 9YesYesNoNoTL2.3 M 10YesYesNoYesTLC2.7 M 11YesYesYesNoTLM3.3 M 12YesYesYesYesTLMC3.7 M
Copyright © 2006 Pearson Education Canada Inc. 4-17 4.3 Minimum Acceptable Rate of Return (MARR) Investing in a project implies foregoing the opportunity to invest elsewhere. Hence, MARR is an opportunity cost. Any proposed investment must earn at least as much as elsewhere: MARR is sometimes called the “hurdle rate” Another view: any investment must earn at least enough to pay the “cost of capital” (e.g. interest on loans) MARR: Interest rate required to accept a project
Copyright © 2006 Pearson Education Canada Inc. 4-18 4.4 Present Worth and Annual Worth Comparisons The Present Worth (PW) and Annual Worth (AW) comparison methods are use a common basis upon which to evaluate projects (either PW or AW). With the Present Worth (PW) method, the analyst compares (say) two projects A and B by computing their present worths at the MARR With the Annual Worth (AW) method, two projects are compared by computing their annual worths at the MARR.
Copyright © 2006 Pearson Education Canada Inc. 4-19 Present Worth and Annual Worth Comparisons (con’t) We can also speak of Present Costs and Annual Costs. The sign convention we use is our choice, as long as we remain consistent. NOTE: “Annual” Worth does not necessarily mean time periods are one year (Think of it as “annuity” if this helps ).
Copyright © 2006 Pearson Education Canada Inc. 4-20 4.4.1 PW Comparisons for Independent Projects Consider the situation where we have n > 1 independent projects. We may invest in none (i.e., do nothing), 1, 2,… or up to n of the projects. To “do nothing” usually means that the money is invested elsewhere at a rate of return which is at least the MARR.
Copyright © 2006 Pearson Education Canada Inc. 4-21 PW Comparisons for Independent Projects (con’t) Decision Rule: –Select any project that has a PW 0 Observe: –Projects with a positive PW yield a rate of return > MARR –Projects with a zero PW yield exactly the MARR –Projects with a negative PW yield less than the MARR
Copyright © 2006 Pearson Education Canada Inc. 4-22 Example 4-2 A software genius is selling the rights to a new video game that he is developing right now. He has a contract under consideration. It offers $10 000 at the end of each year for the next 5 years, and then $20 000 per year for the next 10 years. The genius has to pay $50 000 for development and testing up front. His MARR is 9% per year. Should he take the contract? Base your analysis on a Present Worth analysis.
Copyright © 2006 Pearson Education Canada Inc. 4-23 Example 4-2: Answer PW = -50 000 + 10 000(P/A,9%,5) + 20 000(P/A,9%,10)(P/F,9%,5) = -50 000 + 10 000(3.8896) + 20 000(6.4176)(0.64993) = 72 316 Since the present worth is non-negative, (PW = $72 316), he should take the contract.
Copyright © 2006 Pearson Education Canada Inc. 4-24 4.4.2 PW Comparisons for Mutually Exclusive Projects Engineers are frequently asked to select the best of several mutually exclusive projects Decision Rule: Pick the project which has the greatest PW at the MARR Remark: For minimum cost problems, pick the project which has the smallest present cost at the MARR
Copyright © 2006 Pearson Education Canada Inc. 4-25 Example 4-3 A software genius is selling the rights to a new video game that he is developing now. He has two contracts under consideration. The first offers $10 000 at each year-end for the next 5 years, and then $20 000 per year for the next 10 years. The second offers 10 payments starting with $10 000 at the end of year 1, $13 000 at the end year 2, and so forth (G = $3000). The genius must invest $50 000 now for development and testing for either option. If his MARR is 9%, which (if either) contract should he choose?
Copyright © 2006 Pearson Education Canada Inc. 4-26 Example 4-3: Answer Contract 1: PW(C1) = 72 316(as before) Contract 2: PW(C2) = -50 000 +10 000(P/A,9%,10) + 3000(A/G,9%,10)(P/A,9%,10) = -50 000(P/A,9%,10)[10 000 + 3000(A/G,9%,10)] = -50 000 + 6.418 [ 10 000 + 3000(3.798) ] = 87 295 The genius should choose the second contract as it has the higher PW.
Copyright © 2006 Pearson Education Canada Inc. 4-27 4.4.3 AW Comparisons AW comparisons are essentially the same as PW comparisons, except that all costs and benefits are transformed into a uniform series at the MARR. AW comparisons may lead to amounts which are easier to conceptualize than PW amounts. Sometimes there is no clear justification for using one method over the other except computational ease. Remember that “Annual Worth” may also be for periods different than a year (e.g. months).
Copyright © 2006 Pearson Education Canada Inc. 4-28 4.4.4 Comparison of Alternatives with Unequal Lives Projects must be compared over the same time period so that we properly take into account the full costs and benefits of each. –E.g. Compare two pieces of testing equipment for printed circuit boards. –One has a small first cost and a service life of 5 years, the other has a larger first cost and a service life of 7 years. –The need for the equipment continues indefinitely.
Copyright © 2006 Pearson Education Canada Inc. 4-29 Comparison of Alternatives with Unequal Lives (con’t) If the service lives of alternative projects are unequal, we can transform them into equal lives with one of two methods: Repeated Lives Approach: Repeat the service lives of each alternative over the least common multiple of the service lives (e.g., 35 years for the testing equipment) Study Period Approach: Adopt a study period for comparison. Note that we need a salvage value for the assets at the end of the study period.
Copyright © 2006 Pearson Education Canada Inc. 4-30 Example 4-6 Sam is buying a refrigerator. He has two choices. A used one, at $475, should last about 3 years. A new one will cost $1250 and has an expected service life of 8 years. Sam will need a refrigerator for only 3 more years. At that time, he expects that the new refrigerator will have a resale value of $1000. Interest is at 8% per year. Which should Sam choose? Use a Present Worth comparison and the study period method
Copyright © 2006 Pearson Education Canada Inc. 4-31 Example 4-6: Answer PW (used) = 475 PW (new) = 1250 - 1000(P/F,8%,3) = 1250 - 1000(0.793 83) = 456.17 The new refrigerator has the smallest present worth of costs, and is thus preferable.
Copyright © 2006 Pearson Education Canada Inc. 4-32 4.5 Payback Period Payback period: The number of years for the first cost of an investment to be recovered. If annual benefits are constant: If annual benefits are not constant, the payback period is computed by accumulating each year’s savings until the first cost is recovered. Commonly used, easy to understand, but ignores interest (This is the only place in this course where we ignore the time value of money!)
Copyright © 2006 Pearson Education Canada Inc. 4-33 Payback Period (con’t) Companies often set a “hurdle” payback period (e.g., 2 years). Projects that have a payback period greater then the hurdle are not considered viable. The best project of several mutually exclusive ones is the project with the shortest payback period.
Copyright © 2006 Pearson Education Canada Inc. 4-34 Example 4-8 Two independent investment opportunities are shown below. What is the payback period for each? If you require a 3 year payback period, should none, either or both be purchased? Machine AMachine B First cost$15 000$20 000 Revenues (annual)900011 000 Annual costs60008000 Scrap value10002000 Service life5 years10 years
Copyright © 2006 Pearson Education Canada Inc. 4-35 Example 4-8: Answer Machine A: First cost = $15 000 Annual net benefits = 9 000 - 6 000 = $3 000 Payback period = (15 000)/(3 000) = 5 years Machine B: First cost= $20 000 Annual net benefits= $11 000 - 8 000 = $3 000 Payback period = (20 000)/(3 000) = 6.7 years (or, 7 years if you assume cash flows occur at year- end). Therefore you should not invest in either (paybacks too long).
Copyright © 2006 Pearson Education Canada Inc. 4-36 Summary Relations Among Projects Minumum Acceptable Rate of Return (MARR) Present Worth and Annual Worth Comparisons –Comparsions for Independent Projects –Comparisons for Mutually Exclusive Projects –Comparsons of projects with unequal service lives Payback period comparisons
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