For the data in -16:(a)What are the expected savings per

Telephone poles exemplify items that have vary-ing useful lives. Telephone poles, once installed ina location, remain in useful service until one of avariety of events occur.(a)Name three reasons why a telephone pole mightbe removed from useful service at a particularlocation.(b)You are to estimate the total useful life oftelephone poles. If the pole is removed from anoriginal location while it is still serviceable, itwill be installed elsewhere. Estimate the opti-mistic life, most likely life, and pessimistic lifefor telephone poles. What percentage of all tele-phone poles would you expect to have a totaluseful life greater than your estimated optimisticlife?

The purchase of a used pickup for $9000 is beingconsidered. Records for other vehicles show that costs for oil, tires, and repairs about equal the costfor fuel.Fuel costs are $990 per year if the truck is driven10,000 miles. The salvage value after 5 years of usedropsabout8%permile. Find the equivalentuniformannualcost if the interest rate is 8%. How much doesthis change if the annual mileage is 15,000? 5000?

A heat exchanger is being installed as part of a plantmodernization program. It costs $80,000, includinginstallation, and is expected to reduce the overallplant fuel cost by $20,000 per year. Estimates ofthe useful life of the heat exchanger range froman optimistic 12 years to a pessimistic 4 years.The most likely value is 5 years. Assume the heatexchanger has no salvage value at the end of itsuseful life.(a)Determine the pessimistic, most likely, and opti-mistic rates of return.(b)Use the range of estimates to compute the meanlife and determine the estimated before-tax rateof return.

For the data in Problem 10-2 assume that the 5000,10,000,and 15,000mileage valuesare, respectively,pessimistic, most likely, and optimistic estimates.Use a weighted estimate to calculate the equivalentannual cost.

A new engineer is evaluating whether to usea higher-voltage transmission line. It will cost$250,000 more initially, but it will reduce transmis-sion losses. The optimistic, most likely, and pes-simistic projections for annual savings are $20,000,$15,000, and $8,000. The interest rate is 6%,and the transmission line should have a life of30 years.(a)What is the present worth for each estimatedvalue?(b)Use the range of estimates to compute the meanannual savings, and then determine the presentworth.(c)Does the answer to(b)match the present worthfor the most likely value? Why or why not?

A new 2-lane road is needed in a part of town that isgrowing. At some point the road will need 4- lanesto handle the anticipated traffic. If the citys opti-mistic estimate of growth is used, the expansion willbe needed in 4 years. For the most likely and pes-simistic estimates, the expansion will be neededin 8and 15 years, respectively. The expansion will cost$4.2 million. Use an interest rate of 8%.(a)What is the PW for each scenario, and what isthe range of values?(b)Use Equation 10-1 to find the mean value of theexpansions PW

When a pair of dice are tossed, the results may beany whole number from 2 through 12. In the gameof crapsone can win by tossingeither a 7 or an 11 onthe first roll. What is the probability of doing this?(Hint:There are 36 waysthat a pairof six-sided dicecan be tossed. What portion of them result in eithera 7 or an 11?

Over the last 10 years, the hurdle or discount ratefor projects from the firms research and develop- ment division has been 10% twice, 15% three times,and 20% the rest of the time. There is no recogniz-able pattern. Calculate the probability distributionfor next years discount rate.

The construction time for a bridge depends on theweather. The project is expected to take 250 days if he weather is dry and hot. If the weather is dampand cool, the project is expected to take 350 days.Otherwise, it is expected to take 300 days. Histori-cal data suggest that the probability of cool, dampweather is 30% and that of dry, hot weather is 20%.Find the projects probability distribution.

A new products sales and profits are uncertain.The marketing department has predicted that salesmight be as high as 10,000 units per year with aprobability of 10%. The most likely value is7000units annually.The pessimistic value is estimated tobe 5000 units annually with a probability of 20%.Manufacturing and marketing together have esti-mated the most likely unit profit to be $32. Thepessimistic value of $24 has a probability of 0.3, andthe optimistic value of $38 has a probability of 0.2.Construct the probability distributions for sales andunit profits

A road between Fairbanks and Nome, Alaska, willhave a most likely construction cost of $4 millionper mile. Doubling this cost is considered to have aprobability of 30%, and cutting it by 25% is con- sidered to have a probability of 10%. The statesinterest rate is 8%, and the road should last 40 years.What is the probability distribution of the equivalentannual construction cost per mile?

You recently had an auto accident that was yourfault. If you have another accident or receive aanother moving violation within the next 3 years,you will become part of the assigned risk pool,and you will pay an extra $600 per year for insur-ance. If the probability of anaccident or movingviolation is 20% per year, what is the probabil-ity distribution of your extra insurance paymentsover the next 4 years? Assume that insuranceis pur-chased annually and that violations register at theend of the yearjust in time to affect next yearsinsurance premium.

Al took a midterm examination in physics andreceived a score of 65. The mean was 60 and thestandard deviation was 20. Bill received a score of14 in mathematics, where the exam mean was 12and the standard deviation was 4. Which studentranked higher in his class? Explain.

For the data in Problem 10-10, construct the proba-bility distribution for the annual profit. Assume thatthe sales and unit profits are statistically indepen-dent.

A projecthasa life of10 years,andno salvagevalue.The firm uses an interest rate of 12% to evaluateengineering projects. The project has an uncertainfirst cost and net revenue.First CostPNetRevenueP$300,000 0.2 $ 70,000 0.3400,000 0.5 90,000 0.5600,000 0.3 100,000 0.2(a)What is the joint probability distribution for firstcost and net revenue?(b)Define optimistic, most likely, and pessimisticscenarios by using both optimistic, both mostlikely, and both pessimistic estimates. What isthe present worth for each scenario?

A robot has just been installed at a cost of $81,000.It will have no salvage value at the end of its usefullife.SavingsUsefulper Year Probability Life (years) Probability$18,000 0.2 121/620,000 0.752/322,000 0.141/6(a)What is the joint probability distribution forsavings per year and useful life?(b)Define optimistic, most likely, and pessimisticscenarios by using both optimistic, both mostlikely, and both pessimistic estimates. What isthe rate of return for each scenario?

Modifying an assembly line has a first cost of$80,000, and its salvage value is $0. The firmsinterest rate is 9%. The savings shown in the tabledepend on whether the assembly line runs one, two,or three shifts, and on whether the product is madefor 3 or 5 years.Shifts/ Savings/Useful Lifedayear Probability (years) Probability1 $15,000 0.3 3 0.62 30,000 0.5 5 0.43 45,000 0.2 (a)Give the joint probability distribution for sav-ings per year and the useful life.(b)Define optimistic, most likely, and pessimisticscenarios by using both optimistic, both mostlikely, and both pessimistic estimates. Use a lifeof 4 years as the most likely value. What is thepresent worth for each scenario?

Two instructors announced that they grade on thecurve, that is, give a fixed percentage of each of thevarious letter grades to each of their classes. Theircurves are as follows:Grade InstructorAInstructorBA 10% 15%B15 15C45 30D15 20F15 20If a random student came to you and said thathis object was to enroll in the class in whichhe could expect the higher grade point aver-age, which instructor would you recommend?

For the data in Problem 10-8, compute the expectedvalue for the next years discount rate.

For the data in Problem 10-9, compute the projectsexpected completion time.

Forthe datain Problem10-11 calculatethe expectedvalue of the equivalent annual construction cost permile.

A man wants to decide whether to invest $1000 ina friends speculative venture. He will do so if hethinks he can get his money back in one year. Hebelieves the probabilities of the various outcomes atthe end of one year are as follows:

The MSU football team has 10 games scheduledfornext season. The business manager wishes to esti-mate how much money the team can be expected tohave left over after paying the seasons expenses,including any postseason bowl game expenses.From records for the past season and estimates byinformed people, the business manager has assem-bled the following data:Prob- SituationabilitySituation Net IncomeRegular seasonRegular seasonWin 3 games 0.10 Win 5 or $250,000Win 4 games 0.15 fewerWin 5 games 0.20 gamesWin 6 games 0.15 Win 6 to 8 400,000Win 7 games 0.15 gamesWin 8 games 0.10Win 9 games 0.07 Win 9 or 10 600,000Win 10 games 0.03 gamesPostseasonPostseason AdditionalBowl game 0.10 Bowl game income of$100,000What is the expected net income for the team nextseason

In the New Jersey and Nevada gaming casinos,craps is a popular gambling game. One of the manybets available is the Hard-way 8. A $1 bet in thisfashion will win the player $4 if in the game thepair of dice come up 4 and 4 before one of the otherwaysof totaling 8. For a $1 bet, what is the expectedresult

A man went to Atlantic City with $500 and placed100 bets of $5 each, one after another, on the samenumberon the roulette wheel. There are 38 numberson the wheel, and the gaming casino pays 35 timesthe amount bet if the ball drops into the bettorsnumbered slot in the roulette wheel. In addition, thebettor receives back the original $5 bet. Estimate how much money the man is expectedto win or losein Atlantic City.

For the data in Problems 10-2 and 10-4, assume thatthe optimistic probability is 20%, the most likely is50%, and the pessimistic is 30%.(a)What is the expected value of the equivalentuniform annual cost?(b)Compute the expected value for the number ofmiles, and the corresponding equivalent uni- form annual cost.(c)Do the answers to (a)and(b) match? Why orwhy not?

For the data in Problem 10-3, assume that the opti-mistic probability is 15%, the most likely is 80%,and the pessimistic is 5%.(a)What is the expected value of the rate of return?(b)Compute the expected value for the life, and thecorresponding rate of return.(c)Do the answers to (a)and(b) match? Why orwhy not?

For the data in Problem 10-5, assume that the opti-mistic probability is 20%, the most likely is 50%,and the pessimistic is 30%.(a)What is the expectedvalue of the presentworth?(b)Compute the expected value for annualsavings,and the corresponding present worth.(c)Do the answers to (a)and(b) match? Why orwhy not?

For the data in Problem 10-10, calculate theexpected value of sales and unit profits. For the datain Problem 10-14, calculate the expected value ofannual profit. Are these results consistent?

Assume that the pessimistic and optimistic esti-mates in Problem 10-6 have 40% and 20% proba- bilities, respectively.(a)What is the expected PW the expansion costs?(b)What is the expected number of years until theexpansion?(c)What is PW of the expansion cost using theexpected number of years until the expansion?(d)Do your answers to (a)and(c) match? If not,why not?

The energy efficiency project described in Problem10-18 has a first cost of $150,000,a life of 10 years,and no salvage value. Assume that the interest rateis 8%. (a)What is the equivalent uniform annual worth forthe expected annual savings?(b)Compute the equivalent uniform annual worthfor the pessimistic, most likely, and optimisticestimates of the annual savings. What is theexpected value of the equivalent uniform annualworth?(c)Do the answers to (a)and(b) match? Why orwhy not?

An industrial parkis beingplannedfora tract oflandnear the river. To prevent flood damage to the indus- trial buildings that will be built on this low-lyingland, an earthen embankment can be constructed.The height of the embankment will be determinedby an economic analysis of the costs and benefits.The following data have been gathered.Embankment HeightAbove Roadway(m) Initial Cost2.0$100,0002.5165,0003.0300,0003.5400,0004.0550,000AverageFrequencyFlood That Flood LevelLevelAbove WillExceedRoadway (m) Height in Col. 12.0 Once in 3 years2.5 Once in 8 years3.0 Once in 25 years3.5 Once in 50 years4.0 Once in 100 yearsThe embankment can be expected to last 50 yearsand will require no maintenance. Whenever theflood water flows over the embankment, $300,000of damageoccurs.Should the embankmentbebuilt?If so, to which of the five heights above the road-way? A 12% rate of return is required.

If your interest rate is 8%, what is the expectedvalue of the present worth of the extra insurancepayments in Problem 10-12?

Should the project in Problem 10-15 be undertakenif the firm uses an expected value of present worthto evaluate engineering projects?(a)Compute the PW for each combination offirst cost and revenue and the correspondingexpected worth.(b)What are the expected first cost, expected netrevenue,and correspondingpresentworth oftheexpected values? (c)Do the answers for (a)and(b) match? Why orwhy not?

A new engineer is evaluating whether to use alarger-diameter pipe for a water line. It will cost$350,000 more initially, but it will reduce pump-ing costs. The optimistic, most likely, and pes- simistic projections for annual savings are $30,000,$20,000, and $5000, with respective probabilitiesof 20%, 50%, and 30%. The interest rate is 68%, and the water line should have a life of40 years.(a)What is the PW for each estimated value? Whatis the expected PW?(b)Compute the expected annual savings andexpected PW.(c)Do the answers for the expected PW match?Why or why not?

An energy efficiency project has a first cost of$300,000, a life of 10 years, and no salvage value.Assume that the interest rate is 9%. The most likelyvalue for annual savings is $60,000. The optimisticvalue for annualsavings is $80,000 with a probabil-ity of 0.2. The pessimistic value is $40,000 with aprobability of 0.3.(a)What is the expected annual savings and theexpected PW?(b)Compute the PW for the pessimistic, mostlikely, and optimistic estimates of the annualsavings. What is the expected PW?(c)Do the answers for the expected PW match?Why or why not?

For the data in Problem 10-16:(a)What are the expected savings per year, life,and correspondingrate of return for the expectedvalues?(b)Compute the rate of return for each combinationof savingsper year and life. What is the expectedrate of return?(c)Do the answers for (a)and(b) match? Why orwhy not?

For the data in Problem 10-17:(a)What are the expected savings per year, life, andcorresponding present worth for the expectedvalues?(b)Compute the presentworth for eachcombinationof savingsper year and life. What is the expectedpresent worth?(c)Do the answers for (a)and(b) match? Why orwhy not?

The tree in Figure P10-40 has probabilities aftereach chance node and PW values for each terminalnode. What decision should be made? What is theexpected value?D1Pick APick B0.40.6HLC2900050000.40.6HHLLC1400010,000Pick A1Pick A2D2C30.412,0000.68100

The tree in Figure P10-41 has probabilities aftereachchance node and PW values for each terminal node.What decision should be made? What is the expectedvalue?Pick YPick XPick ZC10.20.50.30.40.60.30.7MHHLLLHC2C315,000Pick Z1Pick Z2D2C4C50.210,0000.87,0000.98,0000.14,000

A decision has been made to perform certain repairson the outlet works of a small dam. For a partic- ular 36-inch gate valve, there are three availablealternatives:A.Leave the valve as it is.B.Repair the valve.C.Replace the valve.If the valve is left as it is, the probability of afailure of the valve seats, over the life of the project,is 60%; the probability of failure of the valve stem is50%; and of failure of the valve body is 40%.If the valve is repaired, the probability of afailure of the seats,over the life of the project, is 40%;of failure of the stem is 30%; and of failure of thebody is 20%. If the valve is replaced, the probabilityof a failure of the seats, over the life of the project, is30%; of failure of the stem is 20%; and of failure ofthe body is 10%.The present worth of cost of future repairs andservice disruption of a failure of the seats is $10,000;the present worth of cost of a failure of the stem is$20,000; the present worth of cost of a failure of thebody is $30,000. The cost of repairing the valve nowis $10,000; and of replacing it is $20,000. If the crite-rion is to minimize expected costs, which alternativeis best?

A factory building is located in an area subject tooccasional flooding by a nearby river. You have beenbroughtin as a consultantto determine whetherflood-proofingof the building is economicallyjustified.Thealternatives are as follows:A.Do nothing. Damage in a moderate flood is$10,000 and in a severe flood, $25,000.B.Alter the factory building at a cost of $15,000to withstand moderate flooding without damageand to withstand severe flooding with $10,000damages. C.Alter the factory building at a cost of $20,000 towithstand a severe flood without damage.In any year the probability of flooding is as follows:0.70, no flooding of the river; 0.20, moderate flood-ing; and 0.10, severe flooding. If interest is 15%and a 15-year analysis period is used, what do yourecommend?

Five years ago a dam was constructed to impoundirrigation water and to provide flood protection forthe area below the dam. Last winter a 100-year floodcaused extensive damage both to the dam and to thesurrounding area. This was not surprising, since thedam was designed for a 50-year flood.The cost to repair the dam now will be $250,000.Damage in the valley below amounts to $750,000.If the spillway is redesigned at a cost of$250,000and the dam is repaired for another $250,000, thedam may be expected to withstand a 100-year floodwithout sustaining damage. However, the storagecapacity of the dam will not be increased andthe probability of damage to the surrounding areabelow the dam will be unchanged. A second damcan be constructed up the river from the exist-ing dam for $1 million. The capacity of the sec-ond dam would be more than adequate to providethe desired flood protection. If the second dam isbuilt, redesign of the existing dam spillway will notbe necessary, but the $250,000 of repairs must bedone.The development in the area below the dam isexpected to be complete in 10 years. A new 100-year flood in the meantime would cause a $1 millionloss. After 10 years the loss would be $2 million. Inaddition, there would be $250,000 of spillway dam-age if the spillway is not redesigned. A 50-year floodis also likely to cause about $200,000 of damage,but the spillway would be adequate. Similarly, a25-year flood would cause about $50,000 of damage. There are three alternatives: (1) repair the exist-ing dam for $250,000 but make no other alterations,(2) repair the existing dam ($250,000) and redesignthe spillway to take a100-year flood ($250,000),and (3) repair the existing dam ($250,000) andbuild the second dam ($1 million). Based on anexpected annual cash flow analysis, and a 7% inter-est rate, which alternative should be selected? Drawa decision tree to clearly describe the problem

In Problems 10-17 and 10-39, how much is it worthto the firm to be able to extend the products lifeby 3 years, at a cost of $50,000, at the end of theproducts initial useful lif

An engineer decided to make a careful analysis ofthe cost of fire insurance for his $200,000 home.From a fire rating bureau he found the follow-ing risk of fire loss in any year.Outcome ProbabilityNo fire loss 0.986$ 10,000 fire loss 0.01040,000 fire loss 0.003200,000 fire loss 0.001(a)Compute his expected fire loss in any year.(b)He finds that the expectedfire loss in any yearisless than the $550 annual cost of fire insurance.In fact, an insurance agent explains that thisis always true. Nevertheless, the engineer buysfire insurance. Explain why this is or is not alogical decision.

For the data in Problems 10-8 and 10-20, computethe standard deviation of the interest rate.

For the data in Problems 10-11 and 10-22, computethe standard deviation of the equivalent annual costper mile

For the datain Problem10-36,computethe standarddeviation of the present worth.

For the datain Problem10-37,computethe standarddeviation of the present worth.

The GrahamTelephoneCompanymayinvestin newswitching equipment. There are three possible out- comes, having net present worth of $6570, $8590,and $9730. The outcomes have probabilities of 0.3,0.5, and 0.2, respectively. Calculate the expectedreturn and risk measured by the standard deviationassociated with this proposal.

A new machine will cost $25,000. The machine isexpected to last 4 years and have no salvage value.If the interest rate is 12%, determine the return andthe risk associated with the purchase.P0.3 0.4 0.3Annual savings $7000 $8500 $9500

A new products chief uncertainty is its annualnet revenue. So far, $35,000 has been spent ondevelopment, but an additional $30,000 is requiredto finish development. The firms interest rate is10%.(a)What is the expected PW for deciding whetherto proceed?(b)Find theP(loss) and the standard deviation forproceeding.StateBad OK GreatProbability0.3 0.5 0.2Net revenue$15,000 $15,000 $20,000Life, in years5 5 10

(a)In Problem 10-53, how much is it worth to thefirm to terminate the product after 1 year if thenet revenues are negative?(b)How much does the ability to terminateearly change theP(loss) and the standarddeviation?

What is your risk associated with Problem10-34?

Measure the risk for Problems 10-15 and 10-35using theP(loss), range of PW values, and stan-dard deviation of the PWs.

(a)In Problems 10-17 and 10-39, describe the riskusing theP(loss) and standard deviation of thePWs.(b)How much do the answers change if thepossible life extension in Problem 10-44 isallowed?

A firm wants to select one new research anddevelopment project. The following table summa-rizes six possibilities. Considering expected returnand risk, which projects are good candidates?The firm believes it can earn 5% on a risk-freeinvestment in government securities (labeled asProjectF).Project IRR StandardDeviation1 15.8% 6.5%2 12.04.13 10.46.34 12.15.15 14.28.06 18.5 10.0F5.00.0

A firm is choosing a new product. The following table summarizes six new potential products.Considering expected return and risk, which prod-ucts are good candidates? The firm believes it canearn 4% on a risk-free investment in governmentsecurities (labeled as ProductF).Product IRR StandardDeviation1 10.4% 3.2%29.8 2.336.0 1.64 12.1 3.65 12.2 8.06 13.8 6.5F4.0 0.0

A projects first cost is $25,000, and it has nosalvage value. The interest rate for evaluation is7%. The projects life is from a discrete uni-form distribution that takes on the values 7,8, 9, and 10. The annual benefit is normallydistributed with a mean of $4400 and a stan-dard deviation of $1000. Using Excels RANDfunction, simulate 25 iterations. What are theexpectedvalue and standarddeviation of the presentworth?

A factorys power bill is $55,000 a year. The firstcost of a small geothermal power plant is normallydistributed with a mean of $150,000 and a stan-dard deviation of $50,000. The power plant has nosalvage value. The interest rate for evaluation is8%. The projects life is from a discrete uni- form distribution that takes on the values 3, 4, 5,6, and 7. (The life is relatively short due to cor- rosion.) The annual operating cost is expected tobe about $10,000 per year. Using Excels RANDfunction, simulate 25 iterations. What are theexpectedvalue and standarddeviation of the presentworth?