Engrecon Lecture Material

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    Engineering Economics

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    Topics

    Motivation

    Types of Costs

    Two Typical Scenarios for Analysis

    “Simple” Methods

    The Time Value of Money

    The Present Value Method

    The Proect Timeta!le  Accounting for Ta"es and #epreciation

     Accounting for $nflation

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    Motivation

    The o!ective is to introduce methods ofeconomic analysis for energy engineeringdecision ma%ing in a corporate& institutional or

    governmental setting' (egal& environmental& pu!lic relations& energy

    efficiency& safety and ethical considerationsare important& !ut the most importantconsideration for engineering designdecisions is economics)) “dollars and cents”'

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    More Motivation

    $f factors can !e valued in *& they should !eincluded in the economic analysis'

    The analysis methods here do not re+uire

    ta!les' The use of computer spreadsheets ,li%e E-CE(. will !e emphasi/ed'

     A spreadsheet is a computeri/ed accountant0sledger) ideal for economic analysis'

    Spreadsheets give greater fle"i!ilitythan ta!le)!ased methods'

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    Types of Costs

    There are usually two types of costs associatedwith an engineering proect& one-time costs&which include first costs and salvage costs& and

    annual costs ,or !enefits. that occur everyyear or severalyears of the

    proect'

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    1irst Costs

    First CostsFirst Costs or Initial CostsInitial Costs are the costsnecessary to implement a proect& including2

    3 Costs of new e+uipment

    3 Costs of shipping and installation

    3 Costs of renovations needed to installe+uipment

    3 Cost of engineering3 Cost of permits&  licenses& etc'

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    $tems that 4educe 1irst Cost

    Some costs of starting proects may !e offset !yimmediate savings2

    3 #educt gains from sale of replaced e+uipment

    3 #educt investment tax credits' These aregovernment ta" incentives to purchase certaine+uipment& and reduce first costs !y reducingta"es'

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      Salvage Value

    5e are attempting to estimate the total costof doing a proect' Cost is reduced if we can

    sell the e+uipment at end of proect'Salvage valueSalvage value is the money that can !eo!tained at the end of the proect !y sellinge+uipment' Salvage value is a !enefit ratherthan a cost'

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     Annual Costs or 6enefits

    Annual CostsAnnual Costs and BenefitsBenefits are costs and!enefits of the proect that accrue over two ormore years of the proect& including2

    #irect operating costs such as la!or&supervision& anitorial& supplies& maintenance&material& electricity& fuel& etc'

    $ndirect operating costs sometimes included&such as a portion of !uilding rent& a portion ofsecretarial e"penses& etc'

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     Annual Costs or 6enefits ,Cont0d.

    Sometimes include ta" costs or !enefits' $f theproect increases profits& it also increases ta"es&which are an additional cost' There is a ta"

    !enefit if proect reduces profits' #epreciation of e+uipment for ta" purposes is

    also a ta" !enefit'

    1inally& need to include savings or profits fromthe proect'

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    Two Analysis Scenarios

    New Project ) selecting from two or morealternative solutions' The o!ective in thisscenario is to find the lowest cost solution

    that accomplishes some o!ective'Example) 7our client& a school district is!uilding a new school' 7ou are designing theheating and cooling system' Should you

    select2 ,8. a gas !oiler plus an air conditioner&,9. an electric air)to)air heat pump& or ,:. aground)source heat pump;

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    Second Analysis Scenario

    Replacement Project ) a method foraccomplishing the goal is already in place& !uta new alternative solution can accomplish the

    goal more cheaply' #o the future savings fromthe new method ustify spending money now tocover the first costs;

    Example) Should 9 e"isting machines with an

    operator each !e replaced with a single newmachine with the same output and a singleoperator;

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    “Simple” Methods

    Simple Payback PeriodSimple Payback Period ,SPP.) The timere+uired for savings to offset first costs'

    Simple Return on InvestmentSimple Return on Investment (ROI) The

    simple percent return the proect pays over itslife'

    These methods are “simple” !ecause they do notconsider the

    time value of money time value of money '

    Simple methods are

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    Simple Pay!ac% Period

    SavingAnnual

    CostFirstSPP=

    For a replacement project:

    For comparing two projects A and B,where the frst cost o A is greater than

    B, but the annual costs o A are lowerthan B:

    BCostAnnualACostAnnual

    BCostFirstACostFirstSPP

    =

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    Simple 4eturn on $nvestment

    CostFirst

    ifetimeCostFirstSavingsAnnual

    !"#   

      −

    =

     $he simple rate o return oninvestment is:

    ietime is the lie o the project%

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    Simple Methods E"ample

    The Acme Threaded Products Corp' nowuses 9 machinists to operate its > screwmachines' Each screw machine costs

    *89&???@yr for electricity& maintenance andwasted materials' Each machinist costs*:&???@yr' 1ind SPP for replacing > oldmachines with 9 new machines B *?&???

    each that produce same output& cost*8>&???@yr each to operate& and can !e run!y only one machinist; The old machines can!e sold for *>??? each'

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    Solution

    1irst cost is 9 D *?&??? ) > D *>???& or2

     1irst cost *8?>&???'

    Savings@yr is *:&??? ,la!or.& F > D *89&??? ) 9 D

    *8>&??? ,operation.& or2

    Savings@yr *&???@yr 

    SPP 1irst cost@,Savings@yr.

    *8?>&???@,*&[email protected] SPP ! "#$% yr  

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    1ollow)&??? and an annual savings of*&???@yr& the e"pected useful life of the

    e+uipment is > years' Acme Threaded ProductsCorp' re+uires a minimum simple return oninvestment& 4

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    Solution

    4&???@> yr.I@*8?>&???@yr 

    ROI ! '% ! '#%) ,per year.

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    Time Value of Money

    “5ould you prefer *8?? now or a year fromnow;” Most would prefer “cash up front”!ecause *8 today is worth more than *8

    some time in the future' 7ou could invest *8today and have more than *8 in a year'

     A proect with a life of several years has cashflows at various times' To consider dollar

    amounts at different times& we need to put allamounts on an equal basis taking the time

    value of money into account.

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    Present and 1uture Value

    Present *aluePresent *alue is the value now of an amount ofmoney 1 received n years in the future'

    Future *alueFuture *alue is value n years in the future of an

    amount of money P received now' $f we can earn interest rate i on investments& the

    relationship !etween P and 1 is2

    1 P,8 F i.n

    or  P 1@,8 F i.n

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    E"ample

    Problem) $f a savings !ond with a yield ofG matures with a value of *8??? in J years&what does it cost now;

    Solution) This is e+uivalent to as%ing what isthe present value P of 1 *8??? received n J years in the future at an interest rate of i G& so P 2

    1@,8 F i.n  *8???@,8 F?'?.J  +,'#-"

     A savings !ond with these terms would costthis amount today'

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    E"ample

    Problem) $f you invest *?? today at KGinterest& how much time is re+uired for theinvestment to !e worth *89??;

    Solution) Lere P *??& 1 *89??& i KG and n is the un%nown& so2

    1 P,8 F i.n  or 1@P ,8 F i.n 

    ln 1@P n ln,8 F $.or2 n Hln 1@PI@Hln,8 F i.I

    n  Hln 89??@??I@Hln,8 F ?'?K.I "' yr 

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    The Present Value Method

    Method determines the value in today’s dollars of a set of cash inflows and outflows at varioustimes from now into the future'

    Set up a ta!le ,spreadsheet. of all costs andsavings associated with the proect& ma%ingcosts negative and income@savings positive'

    Sum up all cash flows from each year to get thenet cas. flo/ ,NC1. for that year'

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    Present Value Method ,Cont0d.

    Convert each NC1 from all years n to presentvalue !y multiplying NC1 D 8@,8 F i.n' This processis called discounting  the NC1 to account for

    present value' Most large companies have a“discount rate” or “rate of return” i that they use forall proects'

    Add up discountedcash &ows or all'ears% $his is the

     present value o the

    investment%

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    Present Value Method ,Cont0d.

    Replacement pro0ects2 $f present value isgreater than /ero& then the accumulated&discounted savings e"ceed costs& and the

    investment should !e made'

    Osing a spreadsheet& i can !e adusted so thatP is e"actly /ero' The value of i for which P ?

    is the discounted rate of return' This meansthat the return on the proposed new investmentis the same as putting the money in the !an% atan interest rate of i'

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    The Proect Timeta!le

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    Proect Timeta!le ,Cont0d.

     All operating costs and savings plus any ta" anddepreciation effects that occur at any time in7ear 8 are assumed to ta%e place on the final

    day of 7ear 8 & that is& one year after proectstart' Similarly& all costs or savings occurring inany year are considered to occur at the end ofthat year'

    The salvage value is a positive cash flow ta%enat the end of the final proect year'

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    Present Value E"ample

    2iven: CrimsonCorp lights its factory withfluorescent lights with a power !ill of *89&???@yrand a lamp replacement cost of *9??@year'

    CrimsonCorp is considering high pressuresodium lights that could !e operated for a powercost of *???@yr and a replacement cost of*9??@yr' The cost of removing the old fi"tures

    and installing new fi"tures is *:&???' The life ofthe new lamp fi"tures is estimated to !e at leastJ years'

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    Present Value E"ample

    Find) ,a. 1or a 8?G minimum rate of return&should lights !e replaced; ,!. 5hat is theactual rate of return on this investment;

    Solution) The 1irst Cost is *:&???' Theannual savings are the cost of operating oldlights less the cost of operating new lights' So&the annual savings are ,*89&??? F *9??. )

    ,*??? F *9??. *K??@yr' A spreadsheetsolution is used for this replacement  pro!lem'

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    Solution Spreadsheet  Part a

    7ear 8st Cost Savings NC1 #iscount P? ):??? ):??? 8 ):???

    8 K?? K?? ?'K?K8 J9':9 K?? K?? ?'J9> K::'K

    : K?? K?? ?'8: 989'> K?? K?? ?'J: 'K K?? K?? ?'9?K K?'J K?? K?? ?'> >8J'K

    K?? K?? ?'8:9 >K9':J K?? K?? ?'> >>J'K K?? K?? ?'>9>8 >?8':

    8? K?? K?? ?':J :?8'9

    Present Value $s2 9:KJJ

    #iscount 4ate $s2 ?'8

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    Solution& Part b

    The actual rate of return is the value of i thatcauses the present value to e"actly e+ual /ero'

    This is easily determined once the E"cel

    spreadsheet is set up !y using 2oal Seek'''

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    Ta"es

    Ta"es& local& stateand federal& are afact of life

    Ta"es are applied to profits& therefore2

    3 an e"pense that decreases profit also decreases

    ta"es owed !y the company'3 a cash inflow that increases profit also increases

    ta"es owed'

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    Ta"es ,Cont0d.

    To account for ta"es on the cash flow in aparticular year& add to the NC1 the +uantity2 )8D NC1 D ta" rate' The negative sign shows that

    a “F” cash flow has a “)” ta" effect' The federal corporate ta" rate varies over time

    ,with politics and circumstances.' Consult youraccountant for details

    The primary ta" effect descri!ed here affectsthe net cash flow any time there is any cashflow in a year)) positive or negative'

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    Ta"es ,Cont0d.

    $n addition to the primary ta" effect& in someyears there can !e a ta" effect from investmentta3 credits or depreciation'

    To encourage investment in some goods ,li%eenergy efficiency.& the government some)timeslegislates an investment ta" credit'

     An investment ta" credit is a specified

    percentage of the purchase price that can !esu!tracted directly from ta" !ill in the year of thepurchase ,7ear ? for our purposes.'

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    Ta" Credit vs. #eduction

     A ta" credit is an amount su!tracted directlyfrom the ta"es owed' The ta"payer0s ta"es arereduced !y the entire amount of a credit'

     A ta" deduction is an amount su!tracted fromincome' The company !enefits only !y the ta"rate times the deduction for a ta" deduction'

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    #epreciation

     A company cannot deduct the cost of capitalpurchases from its income as a “cost of doing!usiness'” The $4S regards capital purchases as

    investments rather than expenses' The company can “write off&” or depreciate 

    capital purchases over a num!er of years'

    #epending on type of e+uipment& a company can

    claim a depreciation deduction of a specifiedamount for a specified num!er of years& followinga “depreciation sc.edule'”

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    #epreciation ,Cont0d.

    The ta" effect of a depreciation deduction can !ecalculated as2

    ,)8. D 1irst Cost D #eprec' 4ate D Ta" 4ate

    Note that 1irst Cost is a negative +uantity& so thedepreciation effect is a positive cash flow'

    The most commonly used gov0t approveddepreciation schedule is the Accelerated Cost4ecovery System ,AC4S.2

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     AC4S #epreciation Schedule

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    #epreciation ,Cont0d.

    #epending on what the government decides isthe lifetime of a type of capital e+uipment& a :& & or 8?)year depreciation schedule is followed'

    1ote4 the fact that an item has !een depreciated8??G for ta" purposes has no relation to itsactual value or salvage value'

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    Ta" and #epreciation E"ample

    2iven) Previously& CrimsonCorp wasconsidering an investment with a first cost of*:&??? and annual savings of *K??@yr'

     Assume that CrimsonCorp is entitled to a Ginvestment ta" credit on the first cost& that paysa :>G ta" on profits& and that the federal gov0tclassifies the lighting e+uipment in the “)year”

    property class'

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    Ta" and #epreciation E"ample

    Find) ,a. the present value of the investmentassuming a 8?G discount rate& and ,!. theactual rate of return for the investment'

    Solution) Again& a computer spreadsheetsolution is recommended' The G investmentcredit is the only 7ear ? ta" effect& there is aprimary ta" effect for 7ears 8 ) 8?& and the )

    year class depreciation schedule is followed in7ears 8 ) '''

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    Measures of $nflation

    Prices tend to increase over time  due to inflation in money0s value'

     Although some goods inflate faster 

    than others ,li%e health care andeducation.& the average rate of inflation isreflected !y the Consumer Price Inde3 ,CP$.'

    The ratio of the CP$ for one year to that ofanother is inversely proportional to the ratio ofthe !uying power of a dollar for the same twoyears'

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    $nflation@CP$ E"ample

    2iven) The average CP$ ,!ased on 8KJ9)J> 8??. for 8K? was :J'J and the CP$ for 8KK8 was8:'9' Low much could a dollar !uy in 8KK8

    compared to 8K?' Sol5n) The ratio of !uying power is inversely

    proportional to the ratio of CP$2

    CP$)8K?@CP$)8KK8 :J'J@8:'9 ?'9J

    Therefore& the 8KK8 dollar is worth only 9J'G ofthe 8K? dollar for the average consumerpurchase'

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    $nflation

    There is a simple relationship !etween thepurchasing power of a dollar now compared tothe value of a dollar n years in the future

    assuming that the inflation rate is $2*now  *future@,8 F $.n

    Note that i is used for interest rate& $ for inflation

    rate'

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    E"ample

    2iven) $f it costs you *8&???@year to live now&how much will it cost in 8? years if the inflationrate is >'G;

    Sol5n) *1uture  *Now D ,8 F $.n

    so *8&??? D ,8 F ?'?>.8?  *9:&:??

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    E"ample

    2iven) 1or medical care& the 8K? CP$ was :>'?and the 8KK8 CP$ was 8'

    Find) the average inflation rate for medical care

    over the 98 year period' Sol5n) *:> in 8K? *8 in 8KK9& so

    *8 *:> D ,8 F $.98 

    ln,8@:>. 98 ln,8 F $.e"pH,8@98. ln,8@:>.I 8 F $

    $ e"pH,8@98. ln,8@:>.I ) 8 ?'?J8 J'8G

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    $nflation

    Note that a dollar in the future is worth less thana dollar now for two different reasons2

    ,8. 7ou could invest your dollar today and have

    more than a dollar at the future time& so it ta%esmore than a dollar in the future to have thepresent value of a dollar today ,time value ofmoney.'

    ,9. 7our dollar in the future won0t !e a!le to !uy asmuch as it could today !ecause of inflation'

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     Accounting for $nflation

    ,8. $nflate all costs and savings using theavaila!le information& so that net cash flow!efore ta"es is accurate for the year in

    +uestion' (ac%ing !etter information& use theaverage inflation rate'

    ,9. Calculate NC1AT the usual way'

    ,:. Calculate the present value discount factorthe same as !efore& using discount rate i'

    P* 6iscount ! "7(" 8 in

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     Accounting for $nflation ,Cont0d.

    ,>. Calculate an inflation discount factor usinginflation rate $2

    Inflation 6iscount ! "7(" 8 In

    ,. Calculate an overall discount factor2

    Overall 6isc# ! Inflation 6isc# 9 P* 6isc#

    ,. The Present Value for a year is the NC1ATtimes the overall discount factor'

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    $nflation E"ample

    2iven4  Acme A"les needs a heat treating ovenfor its account with #eutschmo!ile AQ' Anelectric oven and natural)gas fired oven are

    considered' 1or !oth options assume a ta" rateof :>G& )year depreciation& a 8?)year life& no ta"credits& salvage value of 8?G of first cost&discount rate of 8?G& inflation rate of >G&

    electricity inflation rate of G& and natural gasinflation rate of G& All costs of the two ovensare identical e"cept for the following2

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    $nflation E"ample ,Cont0d.

    Electric Oven) 1irst cost is *89&???& electricitycost is *:&???@yr& maintenance cost is*???@yr'

    as Oven) 1irst cost is *8J&???& fuel cost is*8?&???@yr& maintenance cost is *K???@yr'

    Find4 which option should Acme select;

    Sol5n4  Ose spreadsheet solution method& asfollows2