Use a geometric gradient formula to compute thepresent

Compute the present value,P, for the following cashflows

Compute the present value,P, for the following cashflows.

Compute the present value,P, for the following cashflows.

Compute the present value,P, for the following cashflows.

Find the value ofQso that the present value is 0

Use a geometric gradient formula to compute thepresent value,P, for the following cash flows.

A stonecutter, assigned to carve the headstone for awell-known engineering economist, began with thefollowing design. He then started the equation as follows:P=G(P/G,i,6)He realized he had made a mistake. The equationshould have beenP=G(P/G,i,5)+G(P/A,i,5) The stonecutterdoesnot wantto discard the stoneandstart over. He asks you to help him with his problem.What one compound interest factor can be added tomake the equation correct?P=G(P/G,i,6)( ,i,)

A project has a net present worth of$14,000 as ofJanuary 1, 2015. If a 10% interest rate is used, whatwas the project NPW as of December 31, 2012?

The annual income from a rented house is $24,000.The annual expenses are $6000. If the house can besold for $245,000 at the end of 10 years, how muchcould you afford to pay for it now, if you considered9% to be a suitable interest rate?

Consider the following cash flow. At a 6% interestrate, what value ofPat the end of Year 1 is equivalentto the benefits at the end of Years 2 through 7?

How much would the owner of a building be justifiedin paying for a sprinkler system that will save $750a year in insurance premiums if the system has to bereplaced every 20 years and has a salvage value equalto 10% of its initial cost? Assume money is worth 7%.

A manufacturer is considering purchasingequipmentthat will have the following financial effects: Problems175If money is worth 6%, should he invest in theequipment?

In a present worth analysis of certain equipment,one alternative has a net present worth of+$420,based on a 6-year analysis period that equals theuseful life of the alternative. A 10% interest rate wasused in the computations.The alternative device is to be replaced at theend of the 6 years by an identical item with the samecost, benefits, and useful life. Using a 10% interestrate, computethe netpresentworth of the alternativeequipment for the 12-year analysis period

On February 1, the Miro Company needs to pur-chase some office equipment. The company is shortof cash and expects to be short for several months.The treasurer has said that he could pay for theequipment as follows:Date PaymentApril 1 $150June 1 300Aug. 1 450Oct. 1 600Dec. 1 750A local office supply firm will agree to sell theequipmentto Miro now and acceptpaymentaccord-ing to the treasurers schedule. If interest will becharged at 3% every 2 months, with compoundingonce every 2 months, how much office equipmentcan the Miro Company buy now?

A machine costs $980,000 to purchase and willprovide $200,000 a year in benefits. The companyplans to use the machine for 13 years and then willsell the machine for scrap, receiving $20,000. Thecompany interest rate is 12%. Should the machinebe purchased?

Annual maintenance costs for a particular sectionof highway pavement are $2000. The placementof a new surface would reduce the annual main-tenance cost to $500 per year for the first 5 yearsand to $1000 per year for the next 5 years. After10 years the annual maintenance would again be$2000. If maintenance costs are the only saving, what investment can be justified for the new sur-face? Assume interest at 4%.

A road building contractor has received a majorhighway construction contract that will require50,000 m3of crushed stone each year for 5 years.The stone can be obtained from a quarry for$5.80/m3. As an alternative, the contractor hasdecided to try to buy the quarry. He believes thatif he owned the quarry, the stone would cost himonly $4.30/m3. He thinks he could resell the quarryat the end of 5 years for $200,000. If the contrac-tor uses a 10% interest rate, how much would he bewilling to pay for the quarry?

IBP Inc. is considering establishing a new machineto automate a meatpacking process. The machinewill save $50,000 in labor annually. The machinecan be purchased for $200,000 today and willbe used for 10 years. It has a salvage value of$10,000 at the end of its useful life. The newmachine will require an annual maintenance costof $9000. The corporation has a minimum rate ofreturn of 10%. Do you recommend automating theprocess?

A firm has installed a manufacturing line for pack-aging materials. The firm plans to produce 50 tonsof packing peanuts at $5000 per ton annually for 5years, and then 80 tons of packing peanuts per yearat $5500 per ton for the next 5 years. What is thepresent worth of the expected income? The firmsminimum attractive rate of return is 18% per year.?

A wholesale company has signed a contract with asupplier to purchasegoods for $2,000,000 annually.The first purchase will be made now to be followedby 10 more. Determine the contracts present worthat a 7% interest rate

A new office building was constructed 5 years agoby a consulting engineering firm. At that time thefirm obtained a bank loan for $600,000 with a12% annual interest rate, compounded quarterly.The terms of the loan call for equal quarterly pay-ments to repay the loan in 10 years. The loanalso allows for its prepayment at any time withoutpenalty. As a result of internal changes in the firm,it is now proposed to refinance the loan throughan insurance company. The new loan would befor a 20-year term with an interest rate of 8% peryear, compounded quarterly. The new equal quar-terly payments would repay the loan in the 20-yearperiod. The insurance company requires the pay-ment of a 5% loan initiation charge (often describedas a 5-point loan fee), which will be added to thenew loan.(a)What is the balance due on the original mort-gage if 20 payments have been made in the lastfive years?(b)What is the difference between the equalquarterly paymentson the presentbankloan andthe proposed insurance company loan?

Argentina is considering constructing a bridgeacross the Rio de la Plata to connect its north-ern coast to the southern coast of Uruguay. Ifthis bridge is constructed, it will reduce the traveltime from Buenos Aires, Argentina, to So Paulo,Brazil, by over 10 hours, and there is the potentialto significantly improve the flow of manufacturedgoods between the two countries. The cost of thenew bridge, which will be the longest bridge in theworld, spanning over 50 miles, will be $700 mil-lion. The bridge will require an annual maintenanceof $10 million for repairs andupgrades and is esti-mated to last 80 years. It is estimated that 550,000vehicles will use the bridge during the first yearof operation, and an additional 50,000 vehicles peryear until the tenth year. These data are based ona toll charge of $90 per vehicle. The annual trafficfor the remainder of the life of the bridge will be1,000,000 vehicles per year. The Argentine govern-ment requires a minimum rate of return of 9% toproceed with the project.(a)Does this project provide sufficient revenues tooffset its costs?(b)What considerationsare there besideseconomicfactors in deciding whether to construct thebridge

A student has a job that leaves her with $500 permonth in disposable income. She decides that shewill use the money to buy a car. Before looking for a car, she arranges a 100% loan whose termsare $500 per month for 36 months at 18% annualinterest. What is the maximum car purchase pricethat she can afford with her loan?

Thestudentin Problem 5-23 findsa carshelikes andthe dealer offers to arrange financing. His terms are12% interest for 60 months and no down payment.The cars sticker price is $24,000. Can she affordto buy this car with her $500 monthly disposableincome?

Thestudentin Problem5-24 really wantsthis partic-ular car. She decides to try to negotiate a differentinterest rate. What is the highest interest rate thatshe can accept,given a 60-month term and $500 permonth payments?

We know a car can be had for 60 monthly paymentsof $399.The dealerhas set us a nominalinterest rateof 4.5% compounded daily. What is the purchaseprice?

Computethe presentvalue,P, for the following cashflows.

Ifi=10%, compute the present value,P,forthefollowing cash flows

Computethe presentvalue,P, for the following cashflows (assume series repeats forever).

By installing some elaborate inspection equipmenton its assembly line, the Robot Corp. can avoid hir- ing an extra workerwho would haveearned $36,000a year in wages and an additional $9500 a year inemployee benefits. The inspection equipment hasa 6-year useful life and no salvage value. Use anominal18% interest rate in yourcalculations. Howmuch can Robot afford to pay for the equipment ifthe wages and worker benefits were to have beenpaid(a)At the end of each year(b)MonthlyExplain why the answer in (b)islarger

Jerry Stans,a youngindustrial engineer,preparedaneconomic analysis for some equipment to replaceone production worker. The analysis showed thatthe present worth of benefits (of employing one lessproduction worker) just equaled the present worthof the equipment costs, assuming a 10- year usefullife for the equipment. It was decided not to buy theequipment.A short time later, the production workerswon a new 3-year union contract that granted theman immediate 40?c-per-hour wage increase, plus anadditional 25?c-per-hour wage increase in each ofthe two subsequent years. Assume that in each andevery future year,a 25?c-per-hour wageincreasewillbe granted.Jerry Stans has been asked to revise his ear-lier economic analysis. The present worth of ben-efits of replacing one production employee willnow increase. Assuming an interest rate of 8%, thejustifiable cost of the automation equipment (witha 10-year useful life) will increase by how much?Assume the plant operates a single 8-hour shift, 250days per year.

Two alternative courses of action have the followingschedules of disbursements. Based on a 6% interest rate, which alternativeshould be selected?

If produced by MethodA, a products initial capi-tal cost will be $100,000, its operating cost will be$20,000 per year, and its salvage value after 3 yearswill be $20,000. With MethodBthere is a first costof $150,000, an operating cost of $10,000 per year,and a $50,000 salvage value after its 3-year life.Based on a present worth analysis at a 15% interestrate, which method should be used?

Quintons refrigerator has just died. He can get abasic refrigerator or a more efficient refrigeratorwith an Energy Star designation. Quinton earns 4%compounded annually on his investments, he wantsto consider a 10-year planning horizon, and he willuse present worth analysis to determine the bestalternative. What is your recommendation?Contributed by Paul R. McCright, University ofSouth Florida

Walt Wallace Construction Enterprises is investigat-ing the purchaseof a new dump truck with a 10- yearlife. Interest is 9%. The cash flows for two likelymodels are as follows:AnnualFirst Operating Annual SalvageModel Cost Cost Income ValueA$50,000 $2000 $9,000 $10,000B80,000 1000 12,000 30,000(a)Using present worth analysis, which truckshould the firm buy, and why?(b)Before the construction company can close thedeal, the dealer sells out of ModelBand cannotget any more. What should the firm do now, andwhy?

Two different companies are offering a punch pressfor sale. CompanyAcharges $250,000 to deliver and install the device. CompanyAhas estimated thatthe machine will have maintenance and operatingcosts of $4000 a year and will provide an annualbenefit of $89,000. CompanyBcharges $205,000 todeliver and install the device. CompanyBhas esti-mated maintenance and operating costs of the pressat $4300 a year, with an annual benefit of $86,000.Both machines will last 5 years and can be sold for$15,000 for the scrap metal. Use an interest rate of12%. Which machine should your company buy?

A battery manufacturing plant has been ordered tocease discharging acidic waste liquids containingmercury into the city sewer system. As a result, thefirm must now adjust the pH and remove the mercuryfrom its waste liquids. Three firms have providedquotations on the necessary equipment. An analysisof the quotations provided the following table ofcosts.AnnualIncomeAnnual fromInstalled Operating Mercury SalvageBidder Cost Cost Recovery ValueFoxhill $ 35,000 $8000 $2000 $20,000InstrumentQuicksilver 40,000 7000 2200 0Almaden 100,000 2000 3500 0If the installation can be expected to last 20 yearsand money is worth 7%, which equipment should bepurchased?

A new tennis court complex is planned. Each of twoalternatives will last 18 years, and the interest rate is7%. Use present worth analysis to determine whichshould be selected.

In order to improve evacuation routes out of NewOrleans in the event of another major disaster suchas Hurricane Katrina, the Louisiana Department of Transportation (L-DoT) is planning to constructan additional bridge across the Mississippi River.L-DoT is considering two alternatives: a suspensionbridge and a cantilever bridge. The department usesan interest rate of 8% and plans a 50- year life foreither bridge. Which design has the most favorablenet present worth?

Teri is an IE at Smith Manufacturing in Sarasota. Shehas been studying process line G to determine if anautomated system would be preferred to the exist-ing labor-intensive system. If Smith wants to earn atleast15%and usesa 15-yearplanning horizon,whichalternative is preferred?

Telfono Mexico is expanding its facilities to serve anew manufacturing plant. The new plant will require2000 telephonelines this year,and another2000 linesafter expansion in 10 years. The plant will operate for30 years.Option 1Provide one cable now with capacity toserve 4000 lines. The cable will cost $200,000 andannual maintenance costs will be $15,000.Option 2Provide a cable with capacity to serve2000 lines now and a second cable to serve theother 2000 lines in 10 years. Each cable will cost$150,000 and will have an annual maintenance of$10,000.The telephone cables will last at least 30 years, andthe cost of removing the cables is offset by theirsalvage value.(a)Which alternative should be selected,assuming a10% interest rate?(b)Will your answer to (a) change if the demandfor additional lines occurs in 5 years instead of10 years?

A consulting engineer has been hired to advise atown how best to proceed with the construction ofa 200,000-m3water supply reservoir. Since only120,000 m3of storage will be required for the next25 years, an alternative to building the full capacitynow is to build the reservoir in two stages. Initially,the reservoir couldbe built with 120,000m3of capac-ity and then,25 years hence,the additional80,000m3of capacity could be added by increasing the heightof the reservoir. If interest is computed at 4%, whichconstruction plan is preferred

Use an 8-year analysis period and a 10% inter-est rate to determine which alternative should beselected:

A man had to have the muffler replaced on his2-year-old car. The repairman offered two alterna-tives. For $300 he would install a muffler guaranteedfor 2 years. But for $400 he would install a mufflerguaranteed for as long as you own the car. Assum-ing the presentownerexpectsto keepthe carfor about3 more years, which muffler would you advise him tohave installedif youthought20%wasa suitableinter-est rate and the less expensivemuffler would only last2 years?

An engineer has received two bids for an elevator tobe installed in a new building. Given a 10% interestrate, which bid should be accepted?

A weeklybusinessmagazineoffers a 1-yearsubscrip-tion for $58 and a 3-year subscription for $116. Ifyou thought you would read the magazine for at leastthe next 3 years, and consider 20% as a minimumrate of return, which way would you purchase themagazine:With three 1-year subscriptions or a single3-year subscription

A new alloy can be produced by ProcessA,whichcosts $200,000 to implement. The operating costwill be $10,000 per quarter with a salvage value of$25,000 after its 2-year life. ProcessBwill have afirst cost of $250,000, an operating cost of $15,000per quarter, and a $40,000 salvage value after its4- year life. The interest rate is 8% per year com-pounded quarterly. Using present value analysiswhich process should be selected.

Which process line should be built for a new chem-ical? The expected market for the chemical is 20years. A 9% rate is used to evaluate new processfacilities, which are compared with present worth.How much does the better choice save?

Which equipment is preferred if the firms interestrate is 9%? In PW terms how great is the difference?

North City must choose between two new snow-removal machines. The SuperBlower has a $70,000first cost,a 20-yearlife, and an $8000salvagevalue.At the end of 9 years, it will need a major overhaulcosting $19,000.Annualmaintenanceand operatingcosts are $9000. The Sno-Mover will cost $50,000,has an expected life of 10 years, and has no salvagevalue. The annual maintenance and operating costsare expected to be $12,000. Using a 12% interestrate, which machine should be chosen?

The Crockett Land Winery must replace its presentgrape-pressing equipment. The two alternatives arethe Quik-Skwish and the Stomp-Master. The annualoperating costs increase by 12% each year as themachines age. If the interest rate is 9%, which pressshould be chosen?

A small dam was constructed for $2 million. Theannual maintenance cost is $15,000. If interest is5%, computethe capitalizedcostofthe dam,includ-ing maintenance.

A depositor puts $25,000 in a savings accountthat pays 5% interest, compounded semiannually. Equal annual withdrawals are to be made fromthe account, beginning one year from now andcontinuing forever. What is the maximum annualwithdrawal? What amount of money deposited 50 years ago at8% interest would provide a perpetual payment of$10,000 a year beginning this year?

The presidentof the E. L. Echo Corporation thoughtit would be appropriate for his firm to endow achair in the Department of Industrial Engineeringof the local university. If the professor holding thechairwill receive $134,000per year,and the interestreceived on the endowment fund is expected to be8%, what lump sum of money will the Echo Corpo-ration need to provide to establish the endowmentfund?

Dr. Fog E. Professor is retiring and wants to endowa chair of engineering economics at his university.It is expected that he will need to cover an annualcost of $100,000 forever. What lump sum must hedonate to the university today if the endowmentwillearn 10% interest?

The local botanical society wants to ensure that thegardens in the town park are properly cared for.The group recently spent $100,000 to plant the gar-dens. The members want to set up a perpetual fundto provide $100,000 for future replantings of thegardens every 10 years. If interest is 5%, how muchmoney would be needed to forever pay the cost ofreplanting?

A home builder must construct a sewage treatmentplant and deposit sufficient money in a perpet-ual trust fund to pay the $5000 per year operat-ing cost and to replace the treatment plant every40 years. The plant will cost $150,000, and futurereplacement plants will also cost $150,000 each.If the trust fund earns 8% interest, what is thebuilders capitalized cost to construct the plantand future replacements, and to pay the operatingcosts?

A man who likes cherry blossoms very much wantsan urn full of them put on his grave once each yearforever after he dies. In his will, he intends to leavea certain sum of money in trust at a local bankto pay the florists annual bill. How much moneyshould be left for this purpose? Make whateverassumptions you feel are justified by the facts pre-sented. State your assumptions, and compute asolution

An elderly lady decided to distribute most of herconsiderable wealth to charity and to keep forherselfonly enoughmoney to provide for her living.She feels that $1000 a month will amply providefor her needs. She will establish a trust fund at abank that pays 6% interest, compounded monthly.At the end of each month she will withdraw $1000.She has arranged that, upon her death, the balancein the account is to be paid to her niece, Susan. Ifshe opens the trust fund and deposits enoughmoneyto pay herself $1000 a month in interest as long asshe lives, how much will Susan receive when heraunt dies?

A trust fund is to be established for three purposes:(1) to provide $750,000 for the construction and$250,000 for the initial equipment of a small engi-neering laboratory; (2) to pay the $150,000 peryear laboratory operating cost; and (3) to pay for$100,000 of replacement equipment every 4 years,beginning 4 years from now.At 6% interest, how much money is requiredin the trust fund to provide for the laboratoryand equipment and its perpetual operation andequipment replacement?

We wantto donate a marble birdbath to the city parkas a memorial to cats. We also want to set up a per-petual care fund to cover future expenses forever.The initial cost of the bath is$5000. Routine annualoperating costs are $200 per year, but every fifthyear the cost will be $500 to cover major cleaningand maintenance as well as operation.(a)What is the capitalized cost of this project if theinterest rate is 8%?(b)How much is the present worth of this project ifit is to be demolished after 75 years? The final$500 payment in the 75thyear will cover theyears operating cost and the site reclamation

A local symphony association offers membershipsas follows:Continuing membership, per year $ 15Patron lifetime membership 375The patron membership has been based on the sym-phony associations belief that it can obtain a 4%rate of return on its investment. If you believed 4%to be an appropriate rate of return, would you bewilling to purchasethe patron membership? Explainwhy or why not

A city has developed a plan to provide for futuremunicipal water needs. The plan proposes an aqueduct that passes through 500 feet of tunnel ina nearby mountain. Two alternatives are being con- sidered. The first proposes to build a full-capacitytunnel now for $556,000. The second proposes tobuild a half-capacity tunnel now (cost=$402,000),which should be adequate for 20 years, and thento build a second parallel half-capacity tunnel. Themaintenance cost of the tunnel lining for the full- capacity tunnel is $40,000 every 10 years, and foreach half-capacity tunnel it is $32,000 every 10years.The friction losses in the half-capacity tunnelwill be greater than if the full-capacity tunnel werebuilt. The estimated additional pumping costs inthe single half-capacity tunnel will be $2000 peryear, and for the two half-capacity tunnels it willbe $4000 per year. Based on capitalized cost anda 7% interest rate, which alternative should beselected?

Use capitalized cost to determine which type ofroad surface is preferred on a particular section ofhighway. Use 12% interest rate

A new bridge project is being evaluated ati=5%.Recommend an alternative based on the capitalizedcost for each

A new stadium is being evaluated ati=6%.Recommend an alternative for the main structuralmaterial based on the capitalized cost for each

A rather wealthy man decides to arrange for hisdescendantsto be well educated.He wants each childto have $60,000 for his or her education. He plansto set up a perpetual trust fund so that six childrenwill receive this assistance in each generation.He estimates that there will be four generations percentury, spaced 25 years apart. He expects the trustto be able to obtain a 4% rate of return, and the firstrecipients to receive the money 10 years hence. Howmuch money should he now set aside in the trust?

An open-pit mine must fund an account now to payfor maintenance of a tailingpond in perpetuity (afterthe mine shuts down in 30 years). The costs untilshutdown are part of the mines operating costs. Themaintenance costs begin in 30 years at $300,000annually. How much must be deposited now if thefund will earn 5% interest?

A firm wants to sponsor a new engineering lab at alocal university. This requires $2.5M to construct thelab, $1.2M to equip it, and $600,000 every 5 yearsfor new equipment. What is the required endowmentif the university will earn 6% interest on the funds?

A firm is considering three mutually exclusive alter-natives as part of a production improvement program.The alternatives are:ABCInstalled cost $10,000 $15,000 $20,000Uniform annual 1,625 1,530 1,890benefitUseful life,10 20 20in yearsThe salvage value at the end of the useful life ofeach alternative is zero. At the end of 10 years,AlternativeAcould be replaced with anotherAwithidentical cost and benefits. The maximum attractiverate of return is 6%. Which alternative should beselected

A steam boiler is needed as part of the design of anew plant. The boiler can be fired by natural gas, fueloil, or coal. A decisionmust be made on which fuel touse. An analysis of the costs shows that the installedcost, with all controls, would be least for natural gasat $30,000; for fuel oil it would be $55,000; and forcoalit would be$180,000.If naturalgas is usedratherthan fuel oil, the annual fuel cost will increase by$7500. If coal is used rather than fuel oil, the annualfuel cost will be $15,000 per year less. Assuming 8%interest, a 20-year analysis period, and no salvagevalue, which is the most economical installation?

Austin General Hospital is evaluating new officeequipment offered by three companies. In each casethe interest rate is 15% and the useful life of theequipment is 4 years. Use NPW analysis to deter-mine the company from which you should purchasethe equipment.

The following costs are associatedwith three tomato-peeling machines being considered for use in a can-ning plant. If the canning company uses an interestrate of 12%, which is the best alternative? Use NPWto make your decision. (Note:Consider the leastcommon multiple as the study period.)

A railroad branch line to a landfill site is to be con-structed. It is expected that the railroad line will beused for 15 years, after which the landfill site will beclosed and the land turned back to agricultural use.The railroad track and ties will be removed at that time. In building the railroad line, either treated oruntreated wood ties may be used. Treated ties havean installed cost of $6 and a 10-year life; untreatedties are $4.50 with a 6-year life. If at the end of 15years the ties then in place have a remaining usefullife of 4 years or more, they will be used by the rail-road elsewhere and have an estimated salvage valueof $3 each. Any ties that are removed at the end oftheir service life, or too close to the end of their ser-vice life to be used elsewhere, can be sold for 50?ceach.Determine the most economicalplan for the ini-tial railroad ties and their replacement for the 15-yearperiod. Make a present worth analysis assuming 8%interest

A building contractor obtained bids for some asphaltpaving, based on a specification. Three pavingsubcontractors quoted the following prices and termsof payment:Paving Co. Price Payment ScheduleQuick $85,000 50% payable immediately25% payable in 6 months25% payable at the endof one yearTartan 82,000 Payable immediatelyFaultless 84,000 25% payable immediately75% payable in 6 monthsThe building contractor uses a 12% nominal interestrate, compounded monthly, in this type of bidanalysis. Which paving subcontractor should beawarded the paving job?

Given the following data, use present worth analysisto find the best alternative,A,B,orC.ABCInitial cost$10,000 15,000 $12,000Annual benefit 6,000 10,000 5,000Salvage value 1,0002,000 3,000Useful life 2 years 3 years 4 yearsUse an analysis period of 12 years and 10% interest.

Consider the following four alternatives. Three aredo something and one is do nothing. AB C DCost$0 $50 $30 $40Net annual benefit 0 12 4.5 6Useful life, in years510 10At the end of the 5-year useful life ofB, a replace-ment is not made. If a 10-year analysis period and a10% interest rate are selected, which is the preferredalternative?

A cost analysis is to be made to determine what,if anything, should be done in a situation offer-ing three do-something and one do-nothingalternatives. Estimates of the cost and benefits are asfollows.Uniform End-of- UsefulAnnual Useful-Life LifeAlternatives Cost Benefit Salvage Value (years)1 $500 $135 $ 0 52 600 100 250 53 700 100 180 1040000Use a 10-year analysis period for the four mutuallyexclusive alternatives. At the end of 5 years, Alterna-tives 1 and 2 may be replaced with identical alterna-tives (with the same cost, benefits, salvage value, anduseful life).(a)If an 8% interest rate is used, which alternativeshould be selected?(b)If a 12% interest rate is used, which alternativeshould be selected?

ConsiderAE, five mutually exclusive alternatives:ABCDEInitial cost$600 $600 $600 $600 $600Uniform annual benefitsFor first 5 years 100 100 100 150 150For last 5 years 50 100 110 0 50The interest rate is 10%. If all the alternatives havea 10-year useful life, and no salvage value, whichalternative should be selected?

An investor has carefully studied a number of com-panies and their common stock. From his analy- sis, he has decided that the stocks of six firms arethe best of the many he has examined. They rep- resent about the same amount of risk, and so hewould like to determine one single stock in whichto invest. He plans to keep the stock for 4 yearsand requires a 10% minimum attractive rate ofreturn.

Six mutually exclusive alternatives,AF,arebeingexamined. For an 8% interest rate, which alternativeshould be selected? Each alternative has a 6-yearuseful life.

The management of an electronics manufacturingfirm believes it is desirable to automate its produc- tion facility. The automated equipment would havea 10-year life with no salvage value at the end of10 years. The plant engineering department has sur-veyed the plant and has suggested there are eightmutually exclusive alternatives. If the firm expectsa 10% rate of return, which plan, if any, should it adopt

A corporate bond has a face value of $1000 withmaturity date 20 years from today. The bond paysinterest semiannually at a rate of 8% per year basedon the face value. The interest rate paid on sim-ilar corporate bonds has decreased to a currentrate of 6%. Determine the market value of thebond

Calculate the present worth of a 4.5%, $5000 bondwith interest paid semiannually. The bond maturesin 10 years, and the investor wants to make 8% peryear compounded quarterly on the investment.

An investor is considering buying a 20-yearcorporate bond. The bond has a face value of $1000and pays 6% interest per year in two semiannualpayments. Thus the purchaser of the bond willreceive $30 every 6 months in addition to$1000 atthe end of 20 years, along with the last $30 interestpayment. If the investor wants to receive 8% inter-est,compoundedsemiannually,how muchwould heor she be willing to pay for thebond?

You bought a $1000 corporate bond for $900 threeyears ago. It is paying $30 in interest at the end ofevery 6 months, and it matures in 4 more years.(a)Compute its coupon rate.(b)Compute its current value, assuming the marketinterest rate for such investments is 5% per year,compounded semiannually.

A 6% coupon rate bond has a face value of $1000,pays interest semiannually, and will mature in 10years. If the current market rate is 8% interest com-pounded semiannually, what is the bonds price?

A Treasury bond with a face value of $5000 anda coupon rate of 6% payable semiannually wasbought by Kirt when the markets nominal rate was8%. The bond matures 20 years from now. What didKirt pay for the bond?

A zero-couponbond (couponrate=0%) with a facevalue of $10,000 and maturity date in 5 years isbeing considered for purchase by Pam. The currentmarket interest rate is a nominal 10%, compoundedquarterly. How much should she pay for the bond?

A city government wants to raise $3 million by issu-ing bonds. By ballot proposition, the bonds couponinterest rate was set at 8% per year with semiannualpayments.However,market interest rates have risento a nominal 9% interest rate. If the bonds mature in20 years, how much will the city raise from issuing$3M in bonds

Kal Tech, a manufacturing company, needs to raise$2 million to finance an expansion project. Thebonds will have a coupon interest rate of 12%,payable quarterly, and 20 years to maturity. Whatwill the face value of the bonds have to be, ifthe bonds are to have an interest rate of 12% peryear, payable quarterly, and a maturity date of 20years? The current market interest rate is a nominalsemiannual rate of 16% compounded quarterly.

Assume monthly car payments of $500 per monthfor 4 years and an interest rate of 0.5% per month.What initial principal or PW will this repay?

Assume annual car payments of $6000 for 4 yearsand an interest rate of 6% per year. What initialprincipal or PW will this repay?

Assume annual car payments of $6000 for 4 yearsand an interest rate of 6.168% per year. What initialprincipal or PW will this repay?

Why do the values in Problems 5-94, 5-95, and 5-96differ?

Assumemortgage payments of $1000per month for30 years and an interest rate of 0.5% per month.What initial principal or PW will this repay?

Assume annual mortgage payments of $12,000 for30 years and an interest rate of 6% per year. Whatinitial principal or PW will this repay?

Assume annual mortgage payments of $12,000 for30 years and an interest rate of 6.168% per year.What initial principal or PW will this repay?

Why do the values in Problems 5-98, 5-99, and5-100 differ?

A construction project has the following end-ofmonth costs. Calculate the PW at a nominal interestrate of 18%.January $ 30,000 May $520,000February 50,000 June 460,000March 110,000 July 275,000April 430,000 August 95,000

A factory has averaged the following monthly heat-ing and cooling costs over the last 5 years. Calculatethe PW at a nominal interest rate of 12%.January $25,000 July $29,000February 19,000 August 33,000March 15,000 September 19,000April 9,000 October 8,000May 12,000 November 16,000June 18,000 December 28,000

Ding Bell Imports requires a return of 15% on allprojects. If Ding is planning an overseas develop- ment project with these cash flows, what is theprojects net present value?

Maverick Enterprises is planning a new product.Annual sales, unit costs, and unit revenues are astabulated; the first cost of R&D and setting up theassembly line is $42,000. Ifiis 10%, what is thePW?

Northern Engineering is analyzing a miningproject. Annual production, unit costs, and unitrevenues are in the table. The first cost of the minesetup is $8 million. Ifiis 15%, what is the PW?

Bayviews growth is constrained by mountains onone side and the bay on the other. A bridge acrossthe bay is planned, but which plan is best? It canbe built with a single deck to meet the needs of thenext 20 years, or it can be built with two decks tomeet the needs of the next 50 years. The piers canalso be built to support two decks, but with onlyone deck being built now.Building it all now will cost$160M,and leav-ing the top deck for later will save $40M. Building that top deck later will cost $70M including thecost of traffic disruption. A single-deck bridgewill cost $100M now and $115M in 20 years.Deck maintenance is $1.4M per year per deck.Pier maintenance is $1.2M per year per bridge.If the interest rate is 5%, which design should bebuilt?If the two-deck bridge is built immediately,then dedicated lanes for buses, carpools, and bicy-cles can be added. To economically evaluate thisuse, estimate the cost of the underutilized capacityfor the bridge

Florida Power and Light has committed to build-ing a solar power plant. JoAnne,an IE working forFPL, has been tasked with evaluating the three cur-rent designs. FPL uses an interest rate of 10% anda 20-year horizon.Design 1: Flat Solar PanelsA field of flat solar panels angled to bestcatch the sun will yield 2.6 MW of power andwill cost $87 million initially with first-year oper-ating costs at $2 million, growing$250,000 annu-ally. It will produce electricity worth $6.9 millionthe first year and will increase by 8% each yearthereafter.Design 2: Mechanized Solar PanelsA field of mechanized solar panels rotatesfrom side to side so that they are alwayspositionedparallel to the suns rays, maximizing the produc-tion of electricity. This design will yield 3.1 MWof power and will cost $101 million initially withfirst-year operating costs at $2.3 million, grow-ing $300,000 annually. It will produce electricityworth $8.8 million the first year and will increase8% each year thereafter.Design 3: Solar Collector FieldThis design uses a field of mirrors to focusthe suns raysonto a boiler mountedin a tower. Theboiler then produces steam and generates electric-ity the same way a coal-fired plant operates. This system will yield 3.3 MW of power and will cost$91 million initially with first-year operating costsat $3 million, growing$350,000 annually. It willproduceelectricity worth $9.7 million the first yearand will increase 8% each year thereafter.

Your grandparents are asking you for advice onwhen they should start collecting social securitypayments. If they wait until age 66, they will col-lect $2000 per month; but if they start collecting atage 62, they will collect $1600 per month. Assumethey live to be85, andsimplify by assumingannualpayments.(a)When do the higher payments catch up in totaldollars received with the lower payment thatstarts earlier?(b)If their interest rate is 6%, which plan has ahigher PW?