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Engineering economy book mc graw hill higher education part 2
CHAPTER 10 Mak~ng Cholces The Method, MARR, and Multlple Attnbutes (b) What is the net present worth difference between the $200,000 now and the PW of the cost of the 80-20 D-E mix senes of cash flows necessary to finance the purchase? What does this number mean? (c) What is the Sullivans' after-tax WACC for this purchase? An engineer is working on a design project for a plastics manufacturing company that has an after-tax cost of equity capital of 6% per year for retained earnings that may be used to 100% equity finance the project An alternative financing strategv 1s to lssue $4 mill~onworth of 10-year pay bonds thatw~ll 8% per y c a r x t e r e s on a quarterly bas~sIf the effectwe tax rate IS 40%, wh~ch fund~ng source has the lower cost of cap~tal? - in debt capital to supplement $8 million in equity capital currently available The $10 million can be borrowed at 7.5% per year through the Charity Hospital Corporation Alternatively, 30-year trust bonds could be issued through the hospital's for-profit outpatient corporation, Charity Outreach, Inc The interest on the bonds is expected to be 9.75% per year, which is taxdeductible The bonds will be sold at a 2.5% d~scountfor rapid sale The effective tax rate of Charity Outreach is 32% Which form of debt financing is less expensive after taxes? obtaining sufficient equity capital will require the sale of common stock, as well as the commitment of corporate retained information earnings Use the follow~ng to determine the WACC for the implementation of HACCP Common stock: 100,000 shares Anticipated pnce = $32 per share Initial dividend = $1 I0 per share Dividend growth per share = 2% annually Retained earnings: same cost of capital as for common stock -< Tri-States Gas Processors expects to borrow $800,000 for field engineering improvements Two methods of debt fiwanting are poss~ble-borrow it all from a bank or issue debenture bonds The company will pay an effective 8% come pounded per year for years to d ~ bank The principal on the loan will be reduced un~formly over the years, with the remainder of each annual payment going toward interest The bond Issue will be 800 10-year bonds of $1000 each that require a 6% per year interest payment (a) Which method of financing is cheaper after an effective tax rate of 40% is considered? (b) What is the cheaper method using a before-tax analysis? Cost of Equity Capital ' 10.26 Common stocks issued by Henry Har- mon Builders paid stockholders $0.93 per share on an average price of $18.80 last year The company expects to grow rate the d~vidend at a maximum of 1.5% per year The stock volatihty of 1.19 is somewhat higher than that of other public firms in the construction industry, and other stocks in this market are paying an average of 4.95% per year dividend U.S Treasury bills are returning 4.5% Determine the company's cost of equity capital last year, using (a) the dividend method and (b) the CAPM 10.27 Government regulations from the U.S Department of Agriculture (USDA) require that a Fortune 500 corporation implement the HACCP (Hazards Analysis and Critical Control Points) food safety program in its beef processing plants in 21 states To finance the eaumment and personnel traming portions of this new program, Wholesome Chickens expects to use a D-E mix of 60%-40% to finance a $10 milhon effort for improved equipment, engineering, and quality control After-tax cost of debt capital for loans is known to be 9.5% per year However, > Charity Hospital, established in 1895 as a nonprofit corporation, pays no taxes on Income and receives no tax advantage for interest paid The board of directors has approved expanded cancer treatment equipment that will require $10 million 377 PROBLEMS - Last year a Japanese engineering materials corporation, Yarnachi Inc., purchased some U.S Treasu~y bonds that return an average of 4% per year Now, Euro bonds are being purchased with a realized average return of 3.9% per year The volatility factor of Yamachi stock last year was 1.10 and has increased this year to 1.18 Other publicly traded stocks ~nthis same business are paying an average of 5.1% dividends per year Detennine the cost of equity capital for each year, and explain why the increase or decrease seems to have occurred An engineering graduate plans to purchase a new car He has not decided how to pay the purchase price of $28,000 for the SUV he has selected He has the total available in a savings account, so paying cash is an option; however, this would deplete virtually all hls savings These funds return an average of 6% per year, compounded every months Perform a before-tax analysis to determine which of the three financing plans below has the lowest WACC 50%-50% Use $14,000 Plan 1: D-Eis from the sav~ngs account and borrow $14,000 at a rate of 7% per year, compounded monthly The difference between the payments and the savings would be deposited at 6% per year, compounded semiannually Plan 2: 100% equity Take $28,000 now from sav~ngs Plan 3: 100% debt Borrow $28,000 now from the credit union at an effective rate of 0.75% per month, and repay the loan at $581.28 per month for 60 months 10.30 OILogistics.com has a total of 1.53 million shares of common stock outstanding at a market price of $28 per share T h e before-tax cost of equity capital of common stock is 15% per year Stocks fund 50% of the company's capital projects The remaining capital is generated b y equipment trust bonds and short-term loans Thirty percent of the debt capital is from $5,000,000 worth of $10,000 6% per year 15-year bonds The remaining 70% of debt capital is from loans repaid at an effective 10.5% before taxes If the effective income tax rate is 35%, determme the we~ghted average cost of capital (a) before taxes and (b) after taxes 10.31 Three projects have been identified Capital w ~ l lbe developed 70% f r o m debt sources at an average rate of 7.0% per year and 30% from equity sources at 10.34% per year Set the MARR equal t o WACC and make the economic decis o n , ~f the projects are (a) ~ndependent and (b) mutually exclusive Annual Net Cash Initial Flow, Salvage Life, Project Investment, $ $/year Value, $ Years I -25,000 -30,000 -50.000 6,000 9,000 15,000 4,000 - 1,000 20,000 4 10 32 Shadowland, a manufacturer of airfreightable pet crates, has identified t w o 378 CHAPTER 10 projects that, though having a relatively high risk, are expected to move the company into new revenue markets Utilize a spreadsheet solutlon (a) to select any combmation of the projects ~fMARR = aftertax WACC and (b) to detem~ineif the same projects should be selected ~fthe nsk factors are enough to require an add~tional 2% per year for the investment to be made Estimated AfterInitial Tax Cash Flow Life, Investment $ Der Year $hear Years Proiect Wildlife (W) Reptlles (R) -250,000 - 125,000 48,000 30,000 PROBLEMS Malang Cholccs: The Method, MARR, and Multlple Attnbutes 10 Fmancing will be developed using a D-E mix of 60-40 with equity funds costing 7.5% per year Debt financing will be developed from $10,000 5% per year, paid quarterly, 10-year bonds The effective tax rate is 30% per year 10 33 The federal government imposes requirements upon Industry in many areas, such as employee safety, pollution control, env~ronmental protection, and noisecontrol One view of these regulahons is that their _ -c o m p l i a n c e tends-to decrease_tle return- on investment andlor increase the cost of capital to the corporation In many cases the economics of these regulated compliances cannot be evaluated as regular engineering economy alternatives Use your knowledge oi engineering economic al~alysis expla~n an engineer mght to how economically evaluate alternatives that define the ways in which the company will comply with imposed regulations Different D-E Mixes 10.34 Why is it financ~ally unhealthy for an individual to maintain a large percentage of debt financing over a long period of time, that is, to b e highly debt-leveraged? 10 35 Fairmont Industries pnmanly relies on 100% equity financing to fund plojects A good opportunity is available that will require $250,000 in capital The Fairmont owner can supply the money from personal investments that currently e m an average of 5% per year The annual net cash flow from the project is estimated at $30,000 for the next 15 years Alternatively, 60% of the required amount can be borrowed for 15 years at 9% per year If the MARR is the WACC, detemne whch plan, if either-is better;_ This is a before-tax analysis 10.36 Mrs McKay has different methods by which a $600,000 project can be funded, using debt and equity capital A net cash flow of $90,000 per year is estimated for years k analysis shows that it has a volatil~ty rat~ n g 1.05 and 1s paylng a prelruum of of 5% common stock div~dend.The U.S Treasury btlls are currently paytng 4% per year Is the venture financially attract ~ v e the MARR equals (a) the cost of if equity capltal and (b) the WACC? L 10 28 _Draw the gene@ shape of the three cost of capital curves (debt, equity, and -F-WACC),using theform of Figure 10-2 - := - Draw- them under the condttion that a - o~ n m r L - L ~ F - = ~ - ~ h- - h ~ h r ~ & a s b e e n P r ef~ e s ot e 1~ rg time for thepc%rporation Explain via b your graph and words the movement of ? c P the minimum WACC point under histor3 ically high leveraged D-E mixes Hlnt: High D-E mixes cause the debt cost to \j increase substantially Thls makes it k harder to obtain equity funds, so the cost & of equity capital also increases t 5; types and capacit~es c~awler of 10 41 D~fferent hoe$ are bang cons~deredfor use In a major excavation on a plpe-laylng project Several supervisors on sltnllar projects of the past have ldent~fied some of the attnbutes and the~r vlews of the Importance of an attnbute The lnfornlat~on has been shared wlth you Determ~ne the welghtedrankorder, usmg a to 100 scale we~ghts and the nom~al~zed - Attribute Comment _Truck versus hoe Vdally Important factor loading belght Type of top5011 Type of so11below tops011 Hoe cycle tune A Financing Plan, % Type of Financing Cost per Year, % Debt Equity 20 80 50 50 60 40 10 7.5 - Determine the rate of return for each plan, and identify the ones that are economically a c c e p t a b X f T a ) M A R R equals the cost of equity capital, (b) MARR equals the WACC, or ( c ) MARR is halfway between the cost of equity capital and the WACC 10.37 Mosaic Software has an opportunity to invest $10,000,000 in a new engineering remote-control system for offshore drilling platforms Financing for Mosaic will be split between common stock sales ($5,000,000) and a loan with an 8% per year interest rate Mosaic's share of the annual net cash flow is estimated to be $2.0 million for each of the next years Mosaic is about to initiate CAPM as its common stock evaluation model Recent 379 10.39 In a leveraged buyout of one company by another, the purchasing company usually obtains borrowed money and mserts as little of its own equity funds as possible into the purchase Explain some circumstances under which such a buyout may put the purchasing company at economicrisk Multiple-Attribute Evaluation 10.40 A committee of four people submitted the following statements about the attributes to he used in a weighted attribute method Use the statements to determine the normalized weights if scores are assigned between and 10 Attribute Comment Flextblllty The most Important factor 50% as important as uptlme One-half as nnportant as flexlb~llty As important as upume Tw~ce nnportant as safety as Safety Uphme Speed Rate of retum Match hoe trenchlng speed to plpe-laylng peed Usually only 10% of the problem One-half as Important as matchlng trenching and laylng speeds About 75% as important as sol1 type below topsoll As lmportant as attnbute number one 10 42 You graduated years ago, and you plan to purchase a new car For thiee different models you have evaluated the ~ n ~ t ~ a l cost and eshmated annual costs for fuel n -d maintenance -You-alsoevaluated t h e stylmg of each car In your role as a young englneenng professional L ~ s t some add~t~onal factors (tanglble and mtanglble) that mlght be used In your version of the we~ghtedattnbute method 10.43 (Note to z r t s ~ n ~ c t o ~ and the next This two problems may be assigned as a progressive exercise.) Johll, who works at Swatch, has decided to use the weighted attribute method to compare three systems for manufacturing a watchband The vice president and her assistant have evaluated each of three attributes in terms of importance to them, and John has placed an evaluation from to 100 ? 380 CHAPTER 10 Malung Cho~cesThe Method,MARR, and Mult~ple Attnbutes on each alternative for the three attribUtes John's ratings are as follows: Alternatives Econonuc return > MARR H~gh throughput Low scrap rate 50 100 100 Attribute 70 60 40 100 30 50 Use the weights below to evaluate the altematives Are the results the same for the two persons' weights? Why? Importance Score VP Assistant VP Ecouonuc return > MARR Hlgh throughput Low scrap rate 20 80 100 100 80 20 - - - - 10.44 In Problem 10.43 the vice president and assistant vice president are not consistent in their weights of the three attributes Assume you are a consultant asked to asslst John What are some conclusions you can draw about the weighted attribute method as an altemative selection method, glven the altematlve ratings and results in Problem 10.431 Use the new alternative ratings below that you have developed yourself to select an altemative Using the same scores as the vice president and her assistant given in Problem 10.43,comment on anv d ~ f ferences in the alternative selected (c) What your new alternative ratings tell you about the selections based on the importance scores of the vice president and assistant vlce president? Attribute Ecunomlc return > MARR High throughput Low scrap rate Alternatives 30 70 I00 40 100 80 100 70 90 10.45 The watchband div~sion discussed in Problems 10.43 and 10.44 has just been fined $1 million for environmental pollution due to the poor quality of its discharge water Also, John has become the vice president, and there is no longer an assistant vlce president John always agreed with the im~ortance scores of the former assistant vice president and the alternative ratings he developed earlier (those present Initially in Problem 10.43) If he adds his own im~ortance score of 80 to the new factor of envlronmental cleanhness and awards alternatives 1,2, and rahngs of 80,50, and 20, respectively, for thls new factor, redo the evaluation to select the best alternative - For use an equal weighting of for each attnbute to choose the alternat~ve.Dld the weighting of attnbUtes change the selected alternative? The Athlete's Shop has evaluated two proposals for weight llfting and exercise equipment A present worth analysis at I = 15% of estimated incomes and costs resulted in PW, = $420,500 and PWB = $392,800 In addition to this economlc measure, three attnbutes were ~ndependently assigned a relatlve importance score from to 100 by the shop manager and the lead traner Importance Score Manager Trainer Attribute Econo~n~cs Durdb~llty Flex~b~l~ty Ma~nta~nab~l~ty + I00 35 20 20 381 EXTENDED EXERCISE 80 10 100 10 Separately, you have used the four attributes to rate the two equipment proposals on a scale of 0.0 to 1.0 The economlc attribute was rated uslng the PW values Proposal A Attribute Economics Durab~l~ty Flexlb~llty Malntalndb~l~ty Select the better proposal, using each of the following methods (a) Present worth (b) Weighted evaluations of the manager (c) Weighted evaluations of the lead trainer Proposal B 00 35 00 25 90 00 90 00 t i ~~*~ EXTENDED EXERCISE EMPHASIZING THE RIGHT THINGS A fundamental service provlded to the citizens of a city 1s police p$ecbon Increasing crime rates that Include injury to persons have been documented In the close-m suburbs In Belleville, a densely populated hlstonc area north of the cap~tal phase I of the effort, the pohce chief has made and prehmlnarily examlned In four proposals of ways 1x1 wh~ch pohce surve~llance protection may be proand v~ded the target residentlal areas In brief, they are placlng additional officers in In cars, on bicycles, on foot, or on horseback Each alternative has been evaluated separately to estimate annual costs Placing SIX new officers on bicycles 1s clearly the least expenslve optlon at an estimated $700,000 per year The next best is on foot with 10 new officers at $925,000 per year The other altematlves w ~ l cost shghtly more than the "on foot" option l Before entering phase 11, wh~ch a 3-month p~lot 1s study to test one or two of these approaches in the neighborhoods, a committee of five members (comprised of police staff and citizen-residents) has been asked to help determine and pnoritlze attributes that are important In this dec~slon them, as representatives of to the residents and police officers The five attributes agreed upon after months of discussion are hsted below, followed by each committee member's ordenng of the attnbutes from the most Important (a score of 1) to the least Important (a scale of 5) Committee Member Attribute A B C D E Abll~ty become 'close' to the cltlzenry to Annual cost Response tlme upon call or dlspatch Number of blocks ~n coverage area Sdfety of officers Tolais Sum - - 21 - 15 15 2 415 1 - -2 15 15 75 - - - - - 382 Malang Cho~ces Method, MARR, and Multiple Attributes The CHAPTER 10 Questions Develop weights that can be used in the weighted attribute method for each attr~bute The commlttee members have agreed that the simple average of their five ordered-attribute scores can be considered the indicator of how important each attribute is to them as a group One comnuttee member recommended, and obtained committee approval for, reducing the attributes considered in the final selection to only those that were listed as number by one or more commlttee members Select these attnbutes and recalculate the weights as requested in question A crimes prevention analyst in the Pollce Department applied the weighted attribute method to the ordered attributes in question The R, values obtained using Equation [10.11] are listed below Which two options should the police chief select for the pilot study? Alternative ( R, Car 62.5 I B~cycles 50.5 I Foot 47.2 1 Horse 35.4 CASE STUDY - 383 CHAPTER 11 11.I Replacement and Retkntlon Decisions BASICS OF THE REPLACEMENT STUDY The need for a replacement study can develop from several sources: Reduced performance Because of physical deterioration, the abillty to perform at an expected level of reliability (be~ng available and performing correctly when needed) or prod~icrivity(performing at a given level of quality and quantity) IS not present This usually results In increased costs of operation, higher scrap and rework costs, lost sales, reduced quality, diminished safety, and larger maintenance expenses Altered requirements New requirements of accuracy, speed, or other specifications cannot be met by the existing equipment or system Often the choice is between complete replacement or enhancement through retrofitting or augmentation Obsolescence International competition and rapidly changing technology make currently used systems and assets perform acceptably but less productively than equipment coming available The ever-decreasing development cycle time to bring new products to market is often the reason for premature replacement studies, that is, studies performed before the estimated useful or economic life is reached Replacement studies use some terminology that is new, yet closely related to terms In previous chapters Defender and chaZZenger are the names for two mutually exclusive alternatives The defender is the currently installed asset, and the challenger is the potential replacement A replacement study compares these two alternatives The challenger is the "best" challenger because it has been selected as the one best challenger to possibly replace the defender (This is the same terminology used earlier for incremental ROR and BIC analysis of two new alternatives.) AW values are used as the primary economic measure of comparisoll between the defender and challenger The term EUAC (equivalent uniform annual cost) may be used in lieu of AW, because often only costs are included in the evaluation; revenues generated by the defender or challenger are assumed to be equal Since the equivalence calculations for EUAC are exactly the same as for AW, we use the term AW Therefore, all values will be negative when only costs are involved Salvage value, of course, 1s an exception; it is a cash inflow and canies a plus sign Economic service life (ESL) for an alternative is the itrtmber of years at which the lowest AW of cost occurs The equivalency calculations to determine ESL establish the life n for the best challenger, and it also establishes the lowest cost life for the defender in a replacement study (The next section of this chapter explains how to find the ESL by hand and by computer for any new or currently installed asset ) Defender first cost is the initial investment amount P used for the defender The current market value (MV) is the correct estimate to use for P for the SECTION 11.1 Basics of the Replacement Study defender in a replacement study The fair market value may be obtaned from professional appraisers, resellers, or hquldators who know the value of used assets The eshmated salvage value at the end of 1year becomes the market value at the beginnlngof the next year, provided the estlmates remaln correct as the years pass It IS Incorrect to use the following as MV for the defender first cost bade-invalue that doesitotrep~esenra fairmarker valzre, or the depreciated book value taken from accounting records If the defender must be upgraded or augmented to make it equivalent to the challenger (In speed, capacity, etc ), this cost is added to the MV to obtan the estimate of defender first cost In the caseof asset augmentatlon for the defender altematlve, thls separate asset and its estlmates are lnclhded along with themstalled asset esbmates to form the complete defender alternative T h ~ alternative IS s then compared w ~ t h challenger via a replacement study the Challengerfirst cost IS the amouht of capital that must be recovered (amortized) when replacing a defender wlth a challenger T h s amount 1s almost always equal to P, the first cost of the challenger On occasion, an unreallsbcally high trade-in value may be offered for the defender compared to ~ t fsa r market value In this event, the rzet cash flow required for the challenger IS reduced, in and thls fact should be cons~dered the analysis The correct amount to recover and use in the economlc analysls for the challengerls its first cost minus the difference between the trade-ln value (TIV) and market valde (MV) of the defender In equahon form, this is P - (TlV - MV) T h ~amount represents s the actual cost to the company because a includes both the opportunity cost (I e , market value of the defender) and the out-of-pocket cost (I e first cost - trade-m) to acquire the challenger Of course, when the trade-in and market values are the same, the challenger Pvalue is usedm all computations The challenger first cost is the est~matedinitial investment necessary to acl quire and install it Sometimes, an analyst or manager w ~ l attempt to irzcrrnse this first cost by an amount equal to the unrecovered capital rema~ning the dein fender as shown on the accounting records for the asset This is observed most s often when the defender is working well and in the early stages of ~ t life, but technological obsolescence, or some other reason, has forced consideration of a replacement This unrecovered caoital amount is referred to as a sunk cost A sunk cost must not be added to the challenger's fist cost, because it will make the challenger appear to be more costly than it is Cdpital loss Sunk costs are capital losses and cannot he recovered in a replacement study Sunk costs are correctly handled in the corporation's income statement and by tax law allowances A replacement study is performed most objectively if the analyst takes the viewpoint of n corzsultant to the company or unit using the defender In this way, is the perspective taken is that neither alternat~ve currently owned, and the services provided by the defender could be purchased now with an "investment" that is equal to its first cost (market value) This is indeed correct because the market value will be a forgone opportunity of cash inflow lf the question Sec 174 CHAPTER 11 Replacement and Rerentlon Dec~s~ons SECTION 11.2 Economic Service Llfe "Replace now?" is answered with a no Therefore, the consultant's viewpoint is a convenient way to allow the economic evaluation to be performed without bias for either alternative This approach 1s also referred to as the outsider's viewpoint As ment~oned the introduction, a replacement study is an application of the in annual worth method As such, the fundamental assumptlons for a replacement study parallel those of an AW analysis If theplanning horizon is unlimited, that is, a study period 1s not specified, the assumptlons are as follows: are The servlces prov~ded needed for the indefinite future The challenger is the best challenger available now and m the future to replace the defender When this challenger replaces the defender (now or later), it wlll be repeated for succeeding life cycles Cost estimates for every life cycle of the challenger will be the same _ As expected, none of these assumptlons 1s precisely correct We discussed this prev~ouslyfor the AW method (and the PW method) When the intent of one or more of the assumpt~ons becomes incorrect, the estimates for the alternatives must be updated and a new replacement study conducted The replacement procedure discussed in Section 11.3 explains how to this When theplanning horizon is lirrzited to a specified study period, the nssziinptions above not hold The procedure of Section 11.5 discusses how to perform the replacement study in this case - ! ,, _% , I-& B g f C - 11.2 - - - - - - ECONOMIC SERVICE LIFE - - - - - Until now the Gt~mated noofan altername br asset has been stated In realfife - - - -best-life esiimaito use ~n-the ity, the - economicanalysisi notlmown~mtially =-'When a replacement s6dy orananalysis between new alternat~ves performed, is the best value for n should he determ~ned using current cost estimates The best life estimate is called the economic service life - - The economic service life (ESL) is the number of years IZ a t which the equivalent unifonn annual worth (AW) of costs is the minimum, considering the most current cost estimates over all possible years that the asset may provide a needed service The ESL is also referred to as the economic life or minimum cost life Once determined, the ESL should be the estimated life for the asset used in an engineering economy study, if only economics are considered When n years have passed, the ESL indicates that the asset should be replaced to,minimize overall costs To perform a replacement study correctly, it is important that the ESL of the challenger and ESL of the defender be determined, since their n values are usually not preestablished The ESL is determined by calculahng the tota1,AW of costs ~f the asset is in service 1year, years, years, a n a S o o n ~ t e ~ s t ~ t h e s & s c o n s i d ered useful Total AW of costs is the sum of capital recovery (CR), which is the AW of the initial investment and any salvage value, and the AW of the esfimated annual operating cost (AOC), that is, Total AW = -capital recovery - AW of annual operating costs = -CR - AW of AOC [ll.l] The ESL is the n value for the smallest total AW of costs (Remember: These AW values are cost estimates, so the AW values are negative numbers Therefore, $-200 is a lower cost than $-500.) F~gure 11-1 shows the characteristic shape of a total AW of cost curve The CR component of total AW decreases, while the AOC component increases, thus forming the concave shape The two AW components are calculated as follows Decreasing cost of capital recovery The capital recovery is the AW of investment; it decreases with each year of ownership Capital recovery is calculated by Equation [6.3], which is repeated here The salvage value S, CHAPTER 11 B Replacement and Retentton D e c ~ s ~ o n s SECTION 11 Economic Servlce Llfe Figure 11-1 Annual worth curves of cost elements that determine the economic service life Larger i tI i service life ~ : - ~ ~ which usually decreases with time, is the estimated market value (MV) in that year Capital rekovery = -P(A/P,i,n) + S(A/F,i,n) [11.2] Increasing cost of AW of AOC Since the AOC estimates usually ~ncrease over the years, the AW of AOC increases To calculate the AW of the AOC series for 1,2,3, years, determine the present worth of each AOC value with the P/F factor, then redistribute this P value over the years of ownership, using the A/P factor The complete equation for total AW of costs over k years is L- J [11.3] where P = initial investment or current market value S, = salvage value or market value after k years AOC, = annual operating cost for year j ( j= 1to k) The current MV is used for P when the asset is the defender, and the estimated future MV values are substituted for the S values in years 1,2,3, To determine ESL by computer, the PMT function (with embedded NPV functions as needed) is used repeatedly for each year to calculate capital recovery and the AW ofAOC Their sum is the total AW for k years of ownership The PMT function formats for the capital recovery and AOC components for each year k are as follows: Capital recovery for the challenger: PMT(z%,years,P,-MV-in-yeck) Capital recovery for the defender: PMT(i%,years,current-MV,-MV-in-year-k) AW of AOC: -PMT(i%,years,NPV(i%,year-1-A0C:year-k-AOC)+O) - When the spreadsheet IS developed, it is recommended that the PMT functions in year be developed using cell-reference format, then drag down the function thiough each column A final column summing the two PMT results displays total AW Augmenting the table with an Excel xy scatter plot graphically displays the cost curves in the general form of F~gure 11-1, and the ESL is easily identified Example 11.2 illustrates ESL determination by hand and by computer 393 CHAPTER 11 Replacement and Retention Decisrons SECTION 11.2 Econom~c Service Life It is reasonable to ask about the difference between the ESL analysis above and the AW analyses performed in prevlous chapters Previously we had an estirnnted life of rz years with associated other estimates: first cost in year 0, possibly a salvage value in year a, and an AOC that remained constant or varied each year For all previous analyses, the calculation of AW uslng these estimates determined the AW over n years T h s is also the economic service life when n is fixed In all previous cases, there were no year-by-year MV estimates applicable over the years Therefore, we call conclude the following: -When the expected life rrisknowrrfor the-challeng~r~r-ddexd-determine its AW over it years, using the first cost or current market value, estimated salvage value after 72 years, and AOC estimates This AW value is the correct one to use in the replacement study It is not difficult to estlmate a serles of marketlsalvage values for a new or current asset For example, an asset with a first cost of P can lose market value at 20% per year, so the market value senes for years 0, 1, 2, is P, 0.8P, 0.64P, , respecttvely (An overview of cost eshmation approaches and techniques is presented In Chapter 15 ) If lt is reasonable to predict the MV series on a year-by-year basis, it can be combmed with the AOC estimates to produce what is called the inargznal costs for the asset Marginal costs (MC) are year-by-year estimates of the costs to own and operate an asset for that year There are three components to each annual marginal cost estimate: Cost of ownership (loss in market value is the best estimate of this cost) Forgone interest on the market value at the beginning of the year AOC for each year 395 Compound Interest Factor Tables Compound Interest Factor Tables Compound Interest Factor Tables Compound Interest Factor Tables ~ompouna interest ractor lames 145 Compound Interest Factor Tables - Compound 111terest Factor Tables Compound Interest Factor Tables Compound Interest Factor Tables Compound Interest Factor Tables 749 754 Compound interest Factor Tables Compound Interest Factor Tables Absolute cell referencmg, 247 Accelerated Cost Recovery System (ACRS), 534 Accelerated wnte-off, 532, 578 rdtlos, 719-23 statements, 718-19 Acld-test ratlo, 720 - selection, 11, 603 nd altemat~ve nd annual worth, 586-88ash flow, 575-77,58692,606 debt versus equlty financing, 617-19 and depreclatlon, 532 internat~onal,603-5 and MARR, 353,586 rate or return, 588-91 and WACC, 356 After-tax replacement analysis, 595-99 A/G factor, 68 See also Grad~ents, anthmet~c Alternative deprec~ation system (ADS), 545 Altematlves attnbute-based ratlng, 368-69 and breakeven andlysls, 287 cash flow estlmate types, 220-21 defined, 9-10 and EVAT", 600-601 and incremental rdte-of-return, 588-90 dependent, 170-72,283,330 (see aLo Cap~tal budgeting) ~ n f i n ~ t e 228-31, 330 hfe, mutually exclus~ve,170,223-28, 348-51 and payback analysis, 186 revenue, 172 selection, 11 servlce, 172 in simulation, 678, 679 Amort~zat~on Deprec~at~on See Annual mcome, estimated, 10 Annual lnterest rate effectwe, 13LL36 nom~ndl, 130, 131 - - Annual operating costs (AOC), 10,220,391-92,451 and eshmahon, 9 In Excels spreadsheet, 702-3 Annual Percentage Rate (APR), 127-28 Annual Percentage Y~eld (APY), 127-28 Annual worth advantages, 218,254 after-tax analysis, 8 of annual operating costs, 391 and BIC analys~s, 321-23,326,333 and breakeven analys~s, 451 221-23 and cap~tal-recovery-plus-~nterest, components, 221-23 computer solutions, 225,227-28,230-31 equivalent unlfonn, 221,229 evaluat1on%y;2183? and EVAm', 0 and future worth, 218 and incremental rate of return, 588-91 projects, 228-31 of ~nfin~te-hfe and mflahon, 218,485-86 and present worth, 218 and rate of return, 248,291-92 and replacement analysis, 388,390,392-96, 404-10 and censltivlty analys~s, 623 when to use, 350 (table) AOC See Annual operating costs NP factor, 58-59,221 APR, 127-28 APY, 127-28 Anthmet~c gradlents See Grad~ents, arithmetic Assetc See also Book value, Deplet~on, Depreciat~on; Llfe, Salvagc value ln balance sheet, 717 capital recovery, 22 ieplacement studles, 220 (see also Replacement analys~s) retum on, 721 sunk cost, 389 Attnbutes evaluating multiple, 369-71 ~dent~fy~ug, 365-66 we~ghting, 366-69 Average See Expected value Average cost per unit, 448 Average tax rate, 57 1-72 - 758 - INDEX INDEX - - B Balance sheet baslc equation, 717 and busmess ratios, 719 categories, 717 Base amount defined, 69 and slufted graments, 103, 108 - - - _ _ Bas~s, unadjusted, 532 BIC See Benefit/cost ratlo -_ - - Before-ia~rigeof return - andiifkr-€ax;354;589 - - - - ~ - ~ - - c - ~ - ~ a -_ c-_ a t l o ~ - ~ ~ - _l d -= = I - = Bell-shipeacu~e-SeeNomal d~stnbutlon Benefit and cost mfference, 319-21 Benefitlcostratlo _ _ _ calcuJakon, 19-24 convent~onal, 319-20 Incremental analysls, 324-27 mod~fied, 320 for three or more altematlves, 327-33 for two alternatives, 324-27 when to use, 350 (table) Benefits dlrect versus implled, 327 ~npubhc projects, 315,320,327,333 p, 360,361 Bonds and debt financing, 352,357-59.363-64 and mflat~on, 492-93 merest computation, 194 - payment penods, 194 present worth, 194-95 for pubhc sector projects, 315 rate of return, 261-63 types, 194-95, 315 Book depreciation, 532,534,600 Book value by dechnmg-balance method, 539 defined, 532 by double dechnlng balance method, 539 and EVAn', 600 by MACRS, 541,543 versrls market value, 533 stra~ght method, 535 llne sum-of-year->s method, 555 Borrowed money SeeDeht capital Bottom-up approach, 497-99 Breakeven analysis See also PW vs r graph, Sensltivlty analys~s, SOLVER and annual worth, 220 dverage cost per unlt, 448 description 442 fixed costs, 444-48 453 and make-buy decls~ons, and payback, 185,448-50 and rate or return, 287, 291,591 ver\rrs sensltlv~ty analys~s, 442, 622-23 slngle project, -50,459 spreadsheet apphcat~on, 455-58 three or more alternat~ves, 431 two alteniat~ves, 451-54,459 variable, 451 Breakeven polnt, 444,628-29 Budgeting See Capital budgetmg Bundlea, 424,426 _ I I c c See External rate of return Canada, deprecldhon and taxes, Cap~tal cost of (see Cost of cap~tal) cost of ~nvested, 600-601 debt verslrs equlty, 29,352 hmlted, 353,424-36 unrecovered, 389 worllng, 720 Capltal asset pnclng model (CAPM), Capltal budgeting descnptlon, 422,424-26 equal life projects, 426-28 llnear progrdmmlng, 432-36 mutually exclus~ve bundles, 426 and net cash flow, 436 present-worth use, relnvesunent assumption, 425-27 spreadsheet solut~on, 433-36 unequal llfe projects, 428-32 Cap~tal cost ~naltemat~ve evluat~on, 179-85 and present wonh, 179 and publlc projecls, 314-15,331 Caprtal expense deduction, 533-34 Capital financing See also Cost of cap~tal debt, 29,352 debt versus equlty, 382-83.617-19 equlty, 29-30,352,617-19 m~xed (debt and equ~ty), 355-57, 362-64 Capital gans defined, 58 short-term and long-term, 582-83 taxes for, 583-85 Capital Investment, and alterndt~ve evaluahon, 172 Cap~tal losses defined, 582 taxes for, 582-83 Capltal recovery, 220-23 See olro A/€' factor, Depreclat~on de~reaslng cost of, 391-92 defined, 221 and EVATM, 603 and mflatlon, 485-86 and replacement analys~s, 395,403,407 Cap~tal recovery factor and equivalent annual worth, 221 and random smgle amounts, 98 Capital recovery for assets See Depreclatlon CAPM See Capltal asset pnclng model Carry-back and carry-forward, 575 Case stud~es alternative descnption, annual worth, 236-37 breaheven analys~s, 464-67 compound Interest, 4647,90-91 cost estlniatlon, 525-29 debt ve~srrs equlty financmg, 382-83,617-19 house findncmg, 162-64 Independent project select~on, 440-41 multlple Interest rates, 310-11 pdybackana!ysls, Z&l5 puhllc project, 4 rdtes of retum, 273-75 replacement analysls, 420-21 sale of business, 309-10 sensltlvtty analys~s, 525-27 Cdsh flow See also D~screte cash flow, Grdd~ents, anthmetlc, Payment penod actual versus mcremental, 591 after tax, 575-77 and EVATM, 600-603 beyond study penod, 175 contlnuous, 151 as contlnuous vanable, 664-66 convent~onal senes, 248,249 defined, 11 dlagram, conventional gradlent, 70 d~agrammng, 32-34,3941.70 d~scounted,168,632 estlmatmg, 11.30-34,220-21,315-16 759 future, mcremental, 279-82.291-92 after tax, 590-94 Inflow and outflow, 30-31,244 net, 31, 98,574-75 In Excel*, 702-3 and payback penod, 8 nonconvenuonal 249-55 and NPV Cunctlon, 198 penodlc, 180-82 posltlve net, and ROR, 255 - - - - - and public sector projects, 315-16 - - recurring and nonrecumng, 180 and replacement analysls, 403,595-99: ~~~ -revenue versus service, 172 series factors, 71-73 serles w ~ t h slngle amounts, 98-103 before tax, 575-77 zero, 111, 198,700,708 Cash flow after taxes (CFAT), 575-77,586-92.606 and EVAT", 600403 Cash flow before taxes (CFBT), 575-77,606, 63940 Cash-flow diagrams, 32-34,3941 paltlt~oned, 70 Cell references, 703 absolute, 247 slgn, 247,705-6 Cenalnty, 656,658,667 CFAT See Cash flow after taxes CFBT See Cash flow before taxes - Challenger - -In multiple-alterndt~ve evaluahon 293, 327 In replacement analysa, 388,389,391,404,410 Chats In Excel", 701-3 Class llfe, 545 Common stock, 352,359 Companson types, selection of, 348-5 Composite rate of relurn (CRR), 25541,283 Compound amount factors slngle payment (FP), 50 un~form senes (FIA), 60 Compound Interest, 18-22,38-39,699-715 See also Co~npoundmg Compound~ng annual, 130-36,151 contmuous, 149-5 doubllng tlme, 18-22, 35 frequency, 128, 135,136 ~nterpenod,1 and snnple interest, 17-22 760 INDEX Compounding penod and apparent savmgs, 193 of asset ownersh~p.221 d~rect, 496-99.5056.507 estlmatlng, 496-99 EUAW (see Annual worth, equivalent unlfom) fixed,444-45.450 continuous, 149-51 - - defined, 128 annual rate, 132 (table) and effect~ve monthly, 141 (table) number per year, 130 and payment penod 9 Computers, uses, 26-28, See also Spreadsheets Conshuct~on costs, change In, 71 Construct~on stage, 191 Contingent projects, 424 Contlnuons compoondmg, 149-51 Conudcts, types, 18 Convent~onal benefittcost ratlo, 319-20 Conventional cash Row senes, 249,261 Conventional gradlent, 6 Convertible bonds, 195 Corporat~ons financ~al worth, 600601 - - - leveraged, 6 Cost, first, 10 Cost, hfe-cycle, 190-93 Cost-capac~ty equations, 503-5 Cost centers, 508-10 Cost components, 496-98 Cost depletion See Depleuon Cost dnvers, 512-16 Cost estlmatlon approaches, 497-99 cost-capac~ty method, 503-5 and cost mdexes, 499-503 factor method, 505-7 and ~nflat~on, 14-15 unlt method, 499 Cosl mdexes, 499-503 Cost of capttal mlx, 355-57, 36264 and debt-equ~ty for debt financing, 357-59 defined, 28-30.351-52 for equlty financ~ng, 359-62 ver srrs MARR, 28, 351-54 we~ghted average, 29-30,355-57 Cost-of-goods-sold, 508,510,718-19 statement, 718-19 caprtal, 600601 Cost of ~nvested Cost pool, 512-16 Costs See also Capital cost: Incremental costs, Opportunity cost, Total cost relat~on and altemat~ve evaluation, 172 and annual worth, 221 761 INDEX ~nd~rect, 505-7,508-16.719 of lnvested cap~tal, 351-54,580 I~fe-cycle,190-93 marginal, 394 operaung, 71-73 per~od~c, 180 ~npubllc pro~ects, 315 slgn convenhon, 235 sunk, 389 vanable, 44445,451,454 Coupon rate, 194 - CRR See€omposlte rate of return Cumulative cash flow s ~ g test, 250 n Cumulat~ve d~stnbnt~on, 66 Current assets, 717 720 Current hab~ltt~es, Current rdt~o, 720 D DB funct~on, 537.7034 DDB funct~on, 53740, 704 D~str~buuon normal, 688-91 standard normal, 688-91 tnangular, 663,66546 un~fom, 663,664,670 Distnbuhon esumates, Div~dends, 194.35940 m mult~ple alternative evaluatton, 293,327 tn replacement analys~s, 388-89,391,595-99 Deflauon, 473-74 Delpbl method, 6 Dependent projects, 424 cost, 54647,548 percentage, 547-48 Depreclahon See also Rate of depreciation; Recaptured deprenatton; Replacement analys~s accelerated, 532 alternative system, 545 In switching, 5 and taxes, 578 book, 532,534,600 balance, 533,53637,711-12 Doubhng tune, 35 cllrdngbalance;537 40 - E Economtc eqmvalence See Equivalence Economtc service Me (ESL), 388,391-97,402 Economic value added, 220,600603,606 530,534-35.575-76 Effective lnterest rate annual, 130-35 for any tlme period, 136-38 of bonds, 196 penods, 132 (table), 13638 and compound~ng for continuous compoundmg, 149-5 present worth, 560 recovery penod for, 541,54546,549,562 not used, 534 rate of, 533 recovery rate, 533 stra~ght line, 533,535-36,549 Debenture bonds, 195 Debt capital, 352,357-59 Debt-equ~ty mtx, 355-57,36244 Debt financing, 29,352 on balance sheet, 717 Excel@ funct~ons, 710-13 ght hne alternauve, 4 costs of, 357-59 and ~nflatlon, 479-80 leverag~ng, 36344 Debt ratlo, 720-21 es' rule, 249-50.251.253 stages, prehmary and detaled, 190, 193 -to-cost approach, 497-99 ent-hfe alternatives, 174-77, 197-99 Dec~slon mak~ng attnbutes, 365-69 under certainty, 658,667 englneenng economy role 7-9 gu~del~ne, 35 under nsk, 658-59,66066 under uncerta~nty, 659 Dec~s~on 635-36 trees, Decl~nlng balance depreclatlon,533,536-37 ~nExcel@, 703-4.711-12 Decreasing grad~ents, 108-10 69, Dollars, today versus future, 472-73 Do-nothmg alternative, 11, 170, 173 325 and BIC analys~s, and independent projects, 425,426 and rate of return, 282-83,292-93.295 Double dechtng balance, 537,54345 m Excel@,540,704 defined, 127-28.153 flow chart, 165 533,555-57,711 -of-year dlg~ts, chmg methods, 557-62.711-12 lrect benefits, 327-28 D~rect costs, 49699,505-7 D~sbenefits, 315,319-20 D~sbursements, 31,244 D~scount rate, 316, 333 D~scounted-cash-flow 168,633 Discounted payback analysis, 185-89 Discrete cash flows compound Interest factors (tables), 727-55 dlscrete compoundmg, 147, 150 Dlsposal stage, 191 and nominal rate, 571,595 Effectlve tax rate, 571,595 Efficiency rattos, 719 - End-of-penod conventton, 31-32 EngIneenng economy defined, role m dec~s~on-makmg, 7-9 study approach, 9-11 ternnology and symbols, 23 uses, 6-9 Equal-serv~cealternatives, 172-74, 282,297-300.592 Equ~ty financmg, 29-30,352 cost of, 359-52 Equ~valence,15-17,20-22,243 compoondmgpenod greater than payment penod, compounding penod less than payment penod, - INDEX Equivalent annual cost See Annual worth Equivalent annual worth See Annual worth Equivalent umform annual cost, 388 See also INDEX FV functfon, 704-5 - Annual worth Equllralent nmform annual worth See Annual worth Error dlstnbut~onSee Normal d~stnbuhon E S L See Econornlc servlce l ~ f e E-solve, 28 and random slngle amounts, 102-3 and shlfted unlfor~nsenes, 111 and smgle payment factors, 52-53 E 23,26 FIA factor, 60 See also Unlform senes, amount factor FIG factor, 69 See also Gradients, anthmet~c Income eltlmated annual, 10 In Excel@ spreadsheet, 702 gross and net, 570 taxable, 570 583 lncome statement baslc equation, 718 categones 718 ratios, 721 Income tax and annual worth, 220 average tax rate, 571-72 and cao~tal a n s and losses 581-83 s and cash flow, 575-77,58692,606 corporate, 571 (table) defined, 570 and deprec~at~on, 530,534-35,575-76 recaptured, 577,582 effechve rates, 571,595 and lndlvldual taxpayers, 573-74 ~nternatlonal,603-5 negative, 575-76 present worth of, 578-81 and rate of return, 588-95 rates, 570-72 and replacement studles, 595-99 tax savlngs, 575-76 Incremental benefitlcost dnalysls for three or more alternatlves, 327-33 for two alternrlt~ves, 324-27 Incremental cdsh flow, 279-82,1191-92.588-91 Incremental costs - - - aFd bTn&t/cTst aidiis~s, 32C33definltlon, 282 and rate-of-return, 283-97 Incremental rate of return for multlple alternatlves, 292-97,588-91 for two alten~atlves, 283-92,588-91 unequal hves, 349,432 Independent altematlves, 17672,283 331 See also Capltal budgeting Indexing, mcorne taxes 571 - and uncertamty, (see also Uncearunty) EUAC See Annual worth EUAW See Annual worth, equivalent unlfom Evaluallon crrtena, 11, 348-51 Evaluat~onmethod, 348-51 EVA See Econorn~c value added Excele See also Spreadsheets, specrficfunct~ons after-tax AW and PW, 587-88 baslcs, 697-701 and breakeven analysrs, 455-58 charts, 703 and depreclatlon, 533,535,53740,542,544-45, 558,56061 dlsplay~ng entnes, 39 embedding funchons, 703 error messages7715 funct~ons llstmg, 13-15 ~ntrodnctlon, 26-29 and linear programmmg, 433-36 random number generahon, 696 and rate of return, 254,296 and replacement value, 402-3 and slmulatlon, 683-86 spreadsheet layout, 701-3 Expected value computation, 632 and dec~s~ons under nsk, 659 and dec~slon trees, defined, 671 ln slmulatlon, 678, 684,685 Expenses, 570,718 Sec also Cost eshmahon, Costs External rate of return, 256 See also Rate of return Extta lnvestrnent, 282-83.292-9s base amount, 69, 103 tables, 51-52.727-55 unlforrn-senes, 5&58,60-63,8&81 Factory cost, 510,718 Fmanc~al worth of c o r p ~ r a h ~600-601 n~, F~nancmgSee Debt financmg, Equlty financing F~n~te-hfe altemahves, 183 Fust cost, 10,388-89,451 See also Iu~hal lnveshnent and depreclahon, 532,541,581 and estlmahon, 496-98 m Excel@spreadsheet, 702 and senslhvlty analysis, 629 F~scal year, 716 Rxed assets, 717 Rxed costs, 444-45,451 F~xed-mcome mnveshnent, 492-93 See also Bonds Rxed percentage method See Declmmug balance depreclahou F P factor, 50 See also Slngle payment factors analysls Future worth See also Sens~hvlty from annual worth, 218 calculahou, 69 and effechve lnterest rate, 130 evaluahon by, 177-79 IU Excel", 704-5 and mflahon, 48&84,486 of shifted senes, 94-96,98 when to use, 177,350 (table) r annual senes, 60 m Half-year couvenhon, 533,542,545 fighly leveraged corporations, 6 rn Hurdle rate See M ~ n ~ m uattractive rate of return Hypennflahon, 473,484 23.26 See also Effechve Interest rate, Interest mte, Internal rate of return 1' See Composite rate of return I*, 243-48 See also MARR, Rate of return IF funchon, m Excel", 705 Implemeutatlon stage, 191 763 costmg, 512-16 Ind~rect o s t s and act~v~ty-based ~ allocation vanance, 510-11 charge, 510 In cost of goods sold statement, 719 and factor method, 505-7 rates, 508-10 Infinlte hfe, 179,228-31,314,331 764 INDEX INDEX Inflahon assumption m PW and AW, 175,218 and capital recovery, 485-86 defin~hon,14,473 and future worth, 480-84 high, 484,486 Impact, 14,472-73 and lnterest rates, 473 and MARR, 473,482-84 and present worth, 473-80 and sensltlvlty analysis, 622 Imtlal investment See also F ~ scost t defined, 220 larger, 279,281,287,293 lower, 295-97 In replacement analys~s, 388-89,4034 In spreadsheet analys~s, 197 Installation costs, 389 IiEtaUE6nt fiiiaiicin~,24-fZ2 Intang~ble factors, See also Mult~ple attnbute evaluanon, Noneconomic factors Integer hnear programm~ng, 432-36 Interest accrued, In Excel@ (see IPMT funchon) from bonds, 194 compound, 1&22,38-39,4647 continuous compounding, 149-51 defined, 12 mterpenod, 14749 rate (see Interest rate(s)) simple, 17-18, 35, 36-37 Interest penod, 12, 14 Interest rate(s) See also Effectlve lnterest rate and breakeveu analys~s, 451 defin~hon, 12-13 estimat~on, 35 m Excel? 710-11 expressions, 129 ln8atlon-adjusted,473 ~nflahon free (real), 473,480-84,486 lnterpolat~on, 6&65 market, 473 mult~ple,310-11 nomlnal verms effectwe, 12629 for publlc sector, 316 and nsk, 36041 and senslhvlty analys~s, 622 unknown, 74-77 on unrecovered balance (ROR), 240-42 varylng over trine, 151-53 - Interest tables discrete compounding, 727-55 mterpolation, 63-65, 133 Internal rate of return, 255 See also Rate of return International aspects after taxes, 603-5 contracts, 18 cost estlmatlon, 498 deflation, 473-74 depreciation, 532,53&36,603-5 design and manufacturing, hyperinflation, 484 Interperiod interest, 14749 Interpoiahon, ln interest rate tables, 6345, 133 Inventory turnover ratio, 721-22 cost Invested cap~tal, of, 600601 Investment(s) See also Initial investment _ Ap extra, 282-83,292-95 fixed-mncome, 492-93 net, 256-60 permanent, 228-3 safe, 194-95 Investment opportunity, 353 IPMT function, IRR function, 75-77,245,706-7 Incremental after-tax, 592-93 L Land, 533 Lang factors, 505 Least common multlple, 174-75, 177 and annual worth, 218,226 in evaluahon methods, 349-50 - and future worth 177 and Incrementalcash flow, 279-81.291 a n d Incremental rate of return, 283,291-92, 590-91 projects, 432 and ~ndependent In spreadsheet analysls, 197 Leveraging, 6 L~abll~t~es, 717 L~fe fin~te, 183 lnfinlte or very long, 179,228,314,331 mnumum cost, 391 recovery (tax), 535 m simulat~on, 696 unknown, 77-78 useful, 10,545 L~fe cycle, and annual worth, 218 L~fe-cycle costs, 190-93 L~kert scale, Linear programming, 432-36 Llves common multlple, 174-75 equal, 172-74,279-80.426-28 and Independent projects, 425 perpetual, 179,225, 314 and rate of return, 279-81 unequal, 280-81,297,333,349, Loan payment, 20-22 I m See Compounding penod, number per yea Accelerated Cost MACRS (Mod~fied Recovery System), 4 In CFAT example, 576-77 computer use, 544-45 deprec~at~on 4 rates, PW of, deprec~at~on, 557 recovery penod, 541,54546,562 stra~ght alternative (ADS), 545, hne 546 (table) sw~tchmg, U S ,requ~red, 534,544 Maintenance and operatlng (MBO) costs, 320,570 See also Annual operatlng costs, L~fe-cycle costs Make-or-buy dec~s~ons, 220,453 See also Breakeven analysls Marginal costs, 395-97 Marg~nal rates, 571 tax Market interest rate See Interest rate(s) Market value 533 and deprec~atlon, In ESL analysls, 394 eshmatlng, 395-97 and PW, different l ~ f alternatlves, 175 e In replacement analys~s, 388-90 as salvage value, 220,389 MARR See M ~ n ~ m uattractlve m rate of return Mater~alsSee Duect cob& Mean See Expected value Mean squared deviation, 674 765 Measure of worth, 9,11,678 Median, 672-73 Mexlco, deprec~at~ou taxes, 604 and Mlnlmum attractlve rate of return after-tax, 353,586,591,603 in alternative evaluanon, 172-73, 174-75, 177-79,223-24 and bonds, 195-96 and caprtal budgeting, 425-32 defin~tlon, 28 establlshmg, 28-30,24243,351-54 as hurdle rate, 28 and ~ndependent projects, 425-32 lnflatlon-adjusted,473,482-84 and rate of return, 28243,284, 287,291,293 In sensltlvlty analys~s, 623 before tax, 589 and WACC, 29-30,36162 _ ~ y n l m u m l ~ f e asset See Econom~c cost of servlce 11fe MIRR funct~on, 261,707 M&O costs See Annual operatlng costs, Mantenance and operating costs Mode, 664,672-73 Mod~fiedbenefitlcost ratlo, 320 Money financ~al unlts, 11 and ~nflat~on, 1615,472-73 hme value of, 677-86 Monte Carlo s~mulat~on, Mortgage bonds, 194 Most l~kely estimate, 629-31 Mult~ple alternatlves benefitlcost analysls for, 324-33 Incremental rate of return, 283-97 mdependent, 170-72,283,331 (see also Cap~tal budgetmg) mutually exclus~ve,170,223, 348-51 Mult~ple attnbute evaluahon, 365-72 Mult~ple of return See a150 Net ~nvestment rate procedure defin~t~on, 248 delerm~nlng, 250-52 presence of, 249-50 removing, 255 M u n ~ ~ ~bonds, 194,315,492-93 pal Mutually exclus~ve alternahves, 170 and annual worth, 223-28 evaluat~onmethod selechon, 348-51 and present worth, 172-77 - - - 766 INDEX N n, 23,26, 103-5 See also Interpolation In Interest rate tables, Least common mult~ple, Payback andlysip, Study penod Natural resources See Depletlon Net cd~h flow, 31,436,574-75 Net lncome (NI);570 Net Imestment procedure 256-61 Net operatlng profit after taxes (NOPAT), 570 on, Net present value See NPV f ~ ~ n c ~ lPre\ent worth Net profit after taxes (NPAT), 570, 602-6 Net worth 717 Nomlnal ~ntelest rate, 126, 128 annual, 130, 131 130, 131 any payment per~od, of bonds, 196-97 and effecuve rates, 133 (table), 138 Nonconvent~onal cash flow senes, 249-55 Noneconoinlc factors, 10 Nonrecumng cash flows, 180 Nonsunple cash flow senes, 249-55 No-return (c~mple) payback, 8 Nom~al d~stnbuhon,663,687-91 Norstram's cntenon, 250,593 Notat~on factols, 51, 58, 61, 67.72 for NPER fnnct~on, 707-8 and annual worth, 230-31 and unknown 11, 77-78 NPV funcuon, 708 afler-tax,587, 588 for anthmet~c grad~ents, 69