of agement
any) d on figures
:1 0
SomeRelationshiPs BetweenDePreciatton and Accounting Economy Engineering
t '
Economy
amounts and affected by e such estimG that will be tions from
income tax
that this taxes makes it have some
Several
the
depreciation siriking-fund 4. There are in
transparentn$""il"*ff:*it i:"||;J:: A wordis not a crvstal' *:T;" and tt'nrrcht' mav""o the'll["d#'ii;"i"u is-u-sed' ;fi;; i" *t'rcrt it ;f and
;ili;ffi
tnJ"i'""-'t"nces
'ot*""
o[ return student of in order to bc
studies of economv * :lXffi;,"ti rhe examples on cash florv,"l'l';il;-on l"il'u"':
estimatesof the ettect omv studies is i"t'odJ""J (sucr ble fixed assets
'J:if$"-Tl
Tbs book deob
atdlc espects of [dbm::
econacco'nting TiF"l'*ll"o"'*""ri and I'jixl*: X"tli:nt'"'il th" p'"'"'.'i';;;;;"t' This -chapter deals ".'
Econoty.T::l of Engineering why shourdsrudenrs persons.respm;lt:j:i*m::,:ilHr-:?"il
of these reasonstrre
the accountsof an
Ii' .'["li'Jff jti:;ffi ;Iily*;l+"::: h",",.;y#:T:k"1",:"#:'1fi AboutDerccounri-nli assetsneeo^;:ril;;r preciarion fixed
of tion and retiremett ot re accountingfor a varietY ;;;:;;* "a"t"i"n"a in the PresentchaPter:
Cbpms f5 ry strdier Irrt b r
odc
r8
et
d
tl
reco,nl:l:i"?l it toneed 1. often isnecessar{ anses filJ::H;t:tJ}: This
studies' ]t*;;i;tto' economy tor Pr il i"i"i"a to the accounts
U"."^:'',Ji '"'"-it must U" modified by of an enterprise' i:";;.^';e accountsand t#J P" f'o* the gt; economy""d'"'' "orn" ti''"^#t{"; !:l:l:,tn%;[",'r"tlil?1""::l#]'iodi"' conversion Frequently to manto colleagues'
llnalgl8UnitedStatesSupremeCourtdecision,Towneo.Eimer,24Sv'S.418.
ch. t0
AND ENGINEERING ECONOMY DEPRECTATION
145
agement personnel, or to the general public. The follow-up (if any) of decisions based on economy studies must be based in part on ffgures from the accounts. 2. Economy studies for private enterprise require estimates of the amounts and dates of the outlays for income taxes that will be affected by a choice among proposed alternatives. In most cases, such estimates involve consideration of the depreciation methods that will be used for tax purposes. Although depreciation deductions from taxable income in any given year are not always equal to depreciation deductions from accounting income, it is necessary to understand depreciation accounting if one is to understand the income tax treatment of depreciation. In fact, the authors believe that this relationship between depreciation accounting and income taxes makes it essential that persons responsible for economy studies have some understanding of depreciation accounting. 3. Several approximate methods used by some analysts for computing the annual cost of capital recovery are related to two methods of depreciation accounting, namely, the straight-line method and the sinking-fund method. 4. There are in common use several methods of making so-called rate of return studies that depend on the depreciation accounts. The shrdent of engineering economy needs to understand these methods in order to be aware of their deficiencies. This book deals with depreciation accounting primarily in relation to cngineering economy; there are many aspects of the subject that are not lresented at all or that are discussed only briefly and superficially. Some o{:her aspects of depreciation accounting referred to later in the book !e as follows: Chapters 15 and 17 point out certain common errors made in economy studies for retirements and replacements-errors that are related in part to a misunderstanding of depreciation accounting. 2. Chapter 18 shows the relationship between depreciation accounting and one source of funds for investment in ftxed assets. It also discussesthe relationship between depreciation accounting and the provision of funds for the replacement of assets. 3. Chapter 21 discusses a common misuse of depreciation accounting in computing so-called payoff periods. A Classification of Reasons for Retirement. property units ar gencrally retired for one or more of the following reasons: L. The atsailnbiktu of improoed m.achines or structures for performing 'Research the same seroiie. and development work by sci,entistsanl engineers is continually leading to new and more economical ways of - doing existing jobs. If the prospective economies from new methods are sufficient, it will pay to replace old assets with new l.
146
OF PBOPOSED INVESTMENTS JUDGING THE ATTRACTIVENESS
Ch' 10
purposes or other inassetsto stand-by or to relegate the old ones This inferior uses' of senticerequirem'ents' service of in the amount and' tgpe 2. Changes o''a""*"t"-in the^amount cludes"'"t' "nu#"Jl'-i'''"t"u'"'
qu d T re ireJ'"
irise rrequentrv ir ;m"'""t'El'i?li:H:" *:ffit ^co o "i""iil t''="itt' f'o* "o"-**"mm* etitive, mp T:jm :l
.Ji*"11'i."il' a"" ^;h;;"; T,?Tft;;'tiq ^t""t1*t ff:,"J; rrom
s s 0
TD
resultof 3. changes '' ii-l'i*f,ng"-'nnchinl'wear ottt' "o"#"'"uJJ-i"""v'1t^:h" decreases sructures and and chines increase's'tiJ*"""""e costs that it pays ase and t'"' 6fi"" this to th" extent the quality ""d";"ii;;lliv-9f n"tf3-t*"""" may toreplace"'J;;;;;;""tin""p^ur"'ii*"ii""t"qt:^::"d"rservicc' make o"t'""o*osion' and' decay
wearin'g In somecircumstances metely economical' tttpit"ii"" 'utt'"' ihan retirement or structure' regarding the rnachine 4. Changesln iuUtl" requiremants 5. CasualtiPs' but in most are not mutually f:.I:tt::' old machine These reasonsfor retirement
aut^horitv ;* MaI"*r:;'+iH'T#"fft"":ilt':l i'' ";; fublicthemseloes' * structltres
601 50
E a
C O g
t
n
'l ::;ilili' *llo,::", ;:lT"#:''i:J"#T1lJIi:1*f iT*"":,Jli'"u"i "#i':ff f ,H,T"*ffi
fi'[':'i;t' i;;; than :111:li"-H1""Tl"lTlimachinf: the old
;:'"n"i'if"t"nli'1.'i'ill;mediate
costsof ;"il;;;""; (r/'#;?;;ir'"'-# obsolescence old u""tt lottg before for reduc . -^^r.:^+^ responsible .-r',"'..'",.',*r"r-""orroi.i"^t. i e retirments economical'
ff "*' iIi^t'::i'1q. ;?3S:l1 il1ll"i l"iJ ':'F' til*'m':#;:u":'""#:ll; iHf[1 high thecurrent
laDur """"' ti,l"i featuresthat reduced unlt and (B) had the prospect demand f"t :*.lJ:: "n ir,"t"ut"d ffi; r,,.,,pr rhan t'" ",rrr*t t'igtt
,'i:":;;';;"iir;Y,""::::-."ij.itJ",;J:',#'"J1: 8l::il:il"""ifi
human Property Units" Not all Dispersionfor Physical a ripe old Mortality live'to ai" v*tiJ^ni others die beings at tt'" 'o'nJng"'-so"" t; ;f"ry'J ht'-utt mortality experience of age. Neverth"t"", it'i""io'1ui". estimates- average satisfactory curves"t'i l"Uf"' that give to determine aqe' Thus a life insurance at anv
life and of the p"'"""iug" white native males zl of survivors
ffi;;;;-":"9'[t':]J':iif aiv individtralwhether iil,:":l*u1T:'lg:,"j,11'3:',]:i'l{ ;"L1-l-*"'p""ito
t. though n ""t'nlliil;i even
given number- or year)' he will survive any
retire' ,i",'v berore v*" l,lii'J;;; in'Tigure 10-1' This ":f t'j',Hl:t *;TJe"i":q'""fi:Y, ' ifft"ttut"a of '1"'fiitt''at'p"t'io" i' the
ment. This fact
Physicar Y;;;'' rrr'".t'i1il q':p"'tr "'" h:T::"iltff;:"i **" *rir
a mortality
or n!,,,",ho*, *;;ff :,.:{;***:t#,:T,Jl1'il":: y: ;}ili retirement experlen
andtspe-"l^:33:i"r:"#":K::i"IlJ6; in " 2. changestheamount inthe *;;;;" o' d""'"use in the ;::1":*:1"*t-;:'t'*:::::i:l':"lT lt''uito"^i""rtdes changes its p;"d;;;;
demand for
Ch' INVESTMENTS 10 OF PROPOSED THE JUDGING ATTRACTIVENESS or other inassetsto stand-by purposes or to relegate the old ones ferior uses'
l"'l':"' "^""*T:fnlt:*:#t,:'i:"""::" il o,,"'"i"lJffii',"i'11: product
,
:"g#;,,::nil':l'dll""l,ill'i";xJil*HTFi""'.fl",il:""' 960 M* ;*H^ 'hemseloei:s
Tlz:z:JilJ.dh:n ]r,i"';;r;;;' "o"oi"'";;J"e;;"y'-"t^:1" and structrir"'*Eu' ot't' chines
resultof
E i50
3 a t
d,
c,
that it pays aseandt""'oit""-thisincrease's*Jiiit""u''""costsanddecreases ol pofo'*"t'"" to the extent tiie quality ""a "a*Uiiily to renderservlce' of continuing make """t''tilui"uieitill capable to replace "1,,"o"J;;;;a decaymay In some"i,",,m,tui""i- *"u,i,,g-o,,., economical' irt"" merely retirementi-p"'TiiiJ'ltr'"' structure' tha regard'ing machineor in 4. Changes public requitements 5, Caw.alties'
""' are "": ',;;,h;;. for reasons for retirement l:e old machine These reasons retirement rhese T::li:y ff::'Tlan ltT *f;ff: Thus with,5 op"rute in combination new automatic ""r", ,tr, ,r...,r.rorated
= { l
,T"*l:;'i:J"#'li:"i,:::::::'lii**f,m1#::u":#li; fffi :"iJ;i"q#"::$,"i:i"l'::'il1;ur*;x3#:l HlllJ"#l':ff high current .r,i"the
tauur """'"' '1,1",^, featuresthat reduceo umt and (3) had the prospect *n io"'"ut"d demand f"t :* lJ:: r^.,,or rhen tr," ",rrrJ't ttigt' tl*il
fiJl':,i;i;-r"*"'' :1lTli"_H1"ffl"iTii machi|!, of the o-ld
::'"t"f
costs also are ;"il;;;";; (r,,#;;"r:;;r"'-# Obsolescence old assltstong before for ',fi"riii,'.:'iXl;me responsible reduc . -^r:^r^ --*,,.*or.''**"r"r-L"orroi-ri""t. no nt retireme is eco mical' diate
zl'Y,""::::-""1i"ithiii"#'?,,X1: 8i::ifiil"ilil,T;;"'*l'-f
human Property Units'- Not all Dispersion lor Physical a ripe old Mortality live to Someai" Vu""-Joni others beings die at the '^-J"g"' ht'*utt mortality experience "t"ly'J age. Neverth"l"", ittl""io"iui"-t" insurance todeterminecurves"'di"ul",thatgivesatisfactoryestimatesofaverage at anv ag'e' Thus a life the p"'""''iug" of survivors healthy fife and of *t"'ui'i"'"lntug" of 100'000 or 65' can predict'*t?i """[a"'.'"" company ;;-'h; u["' of 27 -or 49 males20 v""^-"ia will survive white native to a-nyindividual whether t: '"y"Il:l-'""'p""t even though it is not possible number ot years' a mortality he will suivive any given t"'*-
before llii"';;; *""vFigure This i:mx"Pf *rTi"Je"l"1'""T'"1 inv""" 10-1'*he i' "il,:i}ljj' i*o'ttut"a fact of i"'i"itt''it'f""io"
ment. This
;;; ptp""v'"'''';t; lit", Physical
tiilT:d **" *iir lt"^T::"il retire-
n!,,,",ho*' l.: ;}ill
retirement experren
o m"t**:t"t.:*."1T;"::
ch. 10
ECONOMY AND ENGINEERING DEPRECIATION
147
r00 90
\ \ \
70
\i'*"i
\ \
.f1'1
remclnrl|g
.g 60
'6 E E 5 0
o o-
b 4 0
I\l't
1 E
c,
Percenfrelired I eochyeor -fl I
x
(t
lll
10
lrL N
il
3 o T'
(, .:
o
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-rflill
l0
h
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2 i
_ q ,
l o -
I hl
35
lL
l5
Age
30
10
45
Curve for Cer' Figure 10-1. Survivor Curve and Relirement'Frequency Cable tain TelephoneUnderground The reversed curve starting in the upper left-hand corner of the diagram is called a suroirsor curae. It shows the percentage of this type of particular group of cable studied, may be expected to plant that, in the be in serviceat any given number of years after its installation. For instance, 70% will be in service after 15 years of life. The lower stepped curve is a retirement frequency cltrDe. It shows the annual retirements expressedas a percentageof the original amount installed' Although the maximum number of retirements is at age 20, retirements are taking place from the Ist year of life to the 44th year. These curves are mathematically fitted ideal curves derived front a certain group of actual data involving several million dollars' worth of exchangeunderground cable. Curves of this type have been developed in connection with the requirements of depreciation accounting. Such curves may be developedfrom statisticalanalysisthat uses data involving exposuresto the risk of retirement and actual retirements of
Ch' INVESTMENTS 10 OF PROPOSED THE JUDGING ATTRACTIVENESS 148 all therefore refect retirements for units of various ages' The curves progress and the results of technological causes; they give *"igfi-io assetsto *"ff as to th-e tendency of industrial environmental change"s'* a series of such might be expected' deteriorate as they g"t.."fJ*' As average " period Jf y"*tt ofte' indicates that #J; ;;;; statistical analyses lengthening for "1"""' of assetsand fo"'o*" service lives are 'f'*ti"r"S other classes. in obtaining curves zuch as Figure Statistical analysis of the type used been "t which retirements actually have 10_1 can only reflect;;;; happens i' Chapter 17' it often maclp' For various ;";;";;;""tioned the date at which it would have that assetsare kept'* t-*tt"" beyond p a i d t o r e t i r e t h e m . t . f o l l o * s t h a t e c o r r o r n i c s e r v i c e l i v e s o f t ea a r e n lives that will be determined from shorter than the o'""'"g" '"'ui"" statistical analysisof retirements'z "Depreciation"' The meaningsof words The Various Meanings ol are used in a number of difierent develop out of tt "i' *"'- tt't"'-ty *o'd' word' In any use of the word' there meanings. Depreciatil-n-it ;"it a these various meanings' needsto be a clear difierentiation among Property' Professor J' C' BonIn his outstanding book, Voluation of the difierent technical meanings all bright 3 points orrt ii"i ,.rustantially attachedtothewotddepreciationarevariantsoffourbasicconcepts. These are: implies -that the value of one l. Dccnnesn rN Ver'uB' This concept a s s e t i s i n s o m e w a y c o m p u t e d a t t w o d i f i e r e n t d aise the depreciation t h e t s.Thevalueat earlier date later date subtracti from th" value at the may have been responsiblefor of regardless what combinationof causes used in everyday speech, this the value change. when depreciation is implied by most dictionary is the meaning g"''"tniif i-pti"a; it is also definitions. many meanings' As pointed Like depreciation, oalue is a word with important and useful of these out by ProfessorBonbright, the two- most word ire mnrket oalue and oalue s""'" of the meanings in the ";;;;#" iu value may apply ownnr. O"p'""iatio" in the senseof decrease to the values may be determined by to either of these'*o- "o"""pts of value. other appropriate way' actual market price, by appraisal, or in any concept of depreciation' 2. Arrlonrrzm cosr. This is the accounting From the viewpoint of which is being discussedin the present chapter' operating expense to be accounting, the cost of an asset is a prepaid
service of-ffndingaverage methods 2 For a concise of explanation the variousstatistical oiiir"iotio" (New York: The RonaldPress '# life, seeE. L. Grant;;d i;:i:N;rton, Jr.,Propertg "irr'n.Ui"v ilti"it"ylstatistical'Analgsis. of l.ndustrial1935 Co., f9B5), chap.v. )' station' Experiment, ( Ames,Io*",-n"il"ti" izs, lo*" nngineering Rethentents (Nei York'-McGraw-HillBook Co" Inc'' i;;;;;v e1. c. Bonbrten,;"t"':;;';i x. 1937),chaP.
ch. 10 apportioned
procedure. It apportioned in The of the Public
Deprccilh cct c othrr estinetcd
od retinl [r thc ycr.
b tlc ycr.
&L3tf,of,
G
ch. 10
DEPRECIATION AND ENGINEERING ECONOMY
149
apportioned among the years of its life by some more or less systematic procedure. It should be emphasized that it is cost, not value, that is apportioned in orthodox accounting. The accounting concept of depreciation is well described i' a report of the Committee on Terminology of thc American Institute of Certified Public Accountants as follows: a Depreciationaccountingis a systemof accountingwhich aims to distribute the cost or other basic value_oftangible capital assets, less salvage (if any), over the estimateduseful life of the unit (which may be a group of asseti) in a systematic and rational manner. It is a processof allocation,not of valuation. Depreciation for the year is the portion of the total chargeunder such a systemthat iiallocated to the year. Although the allocationmay properly take into account occurrences during the year, it is not intended to be Jmeasuiement of the efiect of all such occurrences. Although we shall use the common phrirse book oalue to describe the difference between tt-re cost of an asset and the total of the depreciation charges made to date against the rrsset,this difierence is more accuratelv described as unan'Lortized cost. 3. Drrrsn'NcE rN Ver.un BnrwnrN eN Exrsrrnc or,n Assnr aNp e Hvpornsrrcer, Nnw Asssr TarsN As A SreNoenn or covpenrsoN. This is the appraisal conccpt of deprecirrtion. Many appraisals of old assets are based on replacement cost. A replacement cosf appraisal should arlswer "what the question could one afford to pay for this asset in comparison with the most economical new one?" An upper limit on the value to its ow'er of an old asset may be determined by considering the cost of reproducing its service with the most economical new asset available for performing the same service. This most economical new substitute rrssetmay have many advantages over an existing old asset, such as lo.ger life expectancy, lower annrial disbursements for operation a'd maintenancc, i'creased ieceipts from sale of product or service. The deduction from the cost of the hypothetical new substitute asset should be a measure in mo'ey terms of ali of these disadvantages of the existing old asset. In the language of appraisal, this deduction is called clepreciation. Appraisal depreciatio', therefore, should mear.r the value inferiority at some particular date (th-e date of the appraisal) of one asset, the existing old one being apprirised, to ir'other urr"t, u hypothetical new one used as the basis of valuatio'. This concept implies iwo assets and the measurement of their values at one date. 4. Iupernno SrnvrcreslrNnss. As machi'es become older they are often unable to hold as close tolerances as when they were new. similarly, the st'e'gth of structures '''.y be impaired by the d"""y of timber mem+ Accounting Terminologg Builetin No. r: Reaiewand Resume (para.56), American Instituteof Certiffed PublicAccountants. lgEO.
150
OF INVESTMENTS Ch. 10 THE ATTRACTIVENESS PROPOSED JUDGING
ch. 10 (its assets), what it owners' equity in th balance sheet rules of irccounting same properties.
bers or the corrosion of metal members. Er.rgineershave sometimes used the word depreciation to refer to such imptriled functional efficiency. It should be emphasized thtrt this is not a value concept at all. Impaired serviceablenessmay result in decrease in value, but there are many other common reasons for decrease in value. Assets that are physically as good as new are not necessarily as vrrluable as when they were new. They may have higher operation and maintenance costs; they will nearly always have shorter life expectrurcy; service conditir-rnsmay have changed; more cconomicirl altemative mcthods may have become available. As the use of depreciation in the sense of impaired serviceablenesshas generally led to confusion in valuation matters, the word is not used in this sense elsewhere in this book. Concepts of Value.s As previously stated, the most useful economic concepts of value arc nwrket oulue and oalue to the ounnr. Market value properly refers to the price at which a property could actually be sold. For certain types of virluation this is not an appropriate concept to use. Often only one owner is in a position to make effective use of a given item of property; although continued possession of this property may be of great monetary importrrnce to its owner, the property might bring only a negligible price if sold to someone else. .{ence the concept of value to a specific owner is of great importance ir, the valuation of property. Value to the owner may be deftned as the money amount that would be just sufficicnt to compensate thc owner if he were to be deprived of the property. Generally speaking, this value will not be greater than the money amount for which the owner could soon replace the propelty with the best available substitute, with due allowance for the superiority or inferiority of that substitute. And, generally speakirrg, vrrlue to the owner will not be less than the market pricc for which the property could be sold. The concept of value to the owner may properly be applied to rr prospective owner as well trs to a present owner, The word oalue is also sometimes used in what rnight be called a neutral sense as any money amount that is associated with specific items of property for some given purpose. An example of this is the use of the phrase lnok aalue to describe the unamortized cost of property as shown by the books of account. The Balance sheet and Profit and Loss slatement. A'y presentatiorr of the elements of accounting must focus attention on two important types of statements obtained from the accounts. one of these, the bslance sheet, describesthe condition of an enterprise at a particular moment, for example, at the close of business on the final day of a fiscal year. Ther baltrnce sheet shows what the enterprise owns 5 For an authoritative thorough and discussion valueconcepts, Bonbright,op. of see cit.,chaps. 3,4, and 5.
The other
income statement,
shown by the books the enterprisehas
of time covered by
(A business fucal as it may start on profit and loss using the formal and Example l0-l
ing and the balane
simple case. This
which certain
adapted from another Gommon method of Ite accounts. Both It will be noted that mucressful even 6e enterprise was rith an enterprise f ffrst seemed to be
bd0r.h.
nfu of o0u eorgo Spelvln
Whan ho Jit lblin SEO
151 ;assets), what it owes (its liabilities), and shows the..value,,of the rrers'equity in the enterprise irs the excessot assets over liabilities. All auce shect valuations are arrived at using the formal arrd sysiematic :s of acconntiug and sometimes differ greaily fi.oni market value of th" re properties lhe other statement, the profit ancr ross staternent, arso cailecl the tme _statement, gives the i'co'res *'d expe'ses of a' enterprise ns ^*h"th", rvu by the books of account for a pcriod of time ancl states entc'prise has made a profit or ross .'d how 'ruch. The longest period lime covered by the -usual profit n.d loss stateme't is a fiscal yenr. business ffscal year docs ,roi arways coincide witlr the calenda. year, t may start or some date other than Ja'u.ry r. ) The ffgures in the fit and loss st.tement, Iike those i' the balance ,h""t, n.""d"t"rmined rg the_formal and systematic rules of accounting. ixample 10-1 illustrates the rerrrtio'ship betweeri depreciation account_ and the balance shec't and profft ,r'd loss strrtemerrt in on extremery ple case. This example is adapted from a' actuar i'vestment fro'.r cn certalrr conrpricating fact'rs have been omitted. Exampre 10-2 is pted from ir'other actual case that is relatively simple, illustrating a rmo. method of estimati'g year-by-yc-ar return cln investment fro'r accounts' Both cxanrpres dear with termi'ated business enterprises. 'ill bc noted that in Exampre r0-1 the e'terprise ffnaily tu'red o,r, ao b" rccessful even though the initial i'dicirtio' from the accounts was that enterprise was extremery profitablc. I' co.trast, Ex.mpre r0-2 dears ^profitable r an e.terprise that finaily turned out to be mucrr -u." than rst seemed to be from an analysis of the accoLurts.
10
DEPRECIATION ENGINEERING AND ECONOMY
EXAMPLE 1O-1. DEPRECIATION THE ACCOUNTS IN OF A MINIATURE GOLF COURSE actsof rhe case. Because miniature gorfcourses had seemedprofitabre number othercommunities his state, of in an individuar whomwe shail Georgespervinbuirtsuch a coursein his home city.He renteda vacant n a strategiccentral locationand spent $22,500 construct io 1is gott se' when he shut down for the winterat the end of his first season, he takenin $25,000 admission in fees and had paid out 97,500 various for ating expenses.At this time he refusedan offer of $42,500 from an sement syndicate his gorfcourseand rease. when he for startedopera"g"in in the springof his secondyear, the rocar interestin miniature : had decrined the pointwherehis receipts to barery covered operating his rrsements'He continued operations a few monthson tnis lnsatis_ for rry basisand then abandoned venture. his nancialstatementsfor the First year and rheir Rerationship to r Accounting.At the time of compretion the construction Depreciof of the gorf -pr"p"r"ot se' the barancesheet for this enterprise(if one hal o""n d havebeen as follows:
152
INVESTMENTSCh' 10 OF THE ATTRACTIVENESS PROPOSED JUDGING
ch. 10 (Later in this a depreciation entrY n hand, a dePreciation
Liabilitiesand Owner'sEquiU Assets Capital ' ' ' $22'500 $22'5OO G' Spelvin' Invested Goll Gourse that part of if spervin had not recognized At the close or his first season, he would have believed that ;;;;;"'had'expired' the service life of nis go-rf
overhis disbursements' receipts il";;;;"'"1 1i". his profitwas $17,500Y ni. o"r"n"e sheetbeforehis withdrawal Underrhis unreatisr,"''"i"ir"J,-'Ji] "profit" been: have would of "nVof this
flow for income tas.) 2. The proftt as ciation charge and
value and by the
use of straightJine Equlty life with no salvage andOwner's Liabilities Assete assumed a 2-Year lifte $22'500 Invested'C-apit3l -"'"" 17'500 $17'500 !' Spelvin' Cash ' course as dePreciatim' 22'5ooG $;;il'iilt$;dEarninss " "" GorrGourse $40'000 he had assumed6et $4o,ooo value, his profit 6gure golf course and decidedto a definition sai4 he estimated S-yearlife for his Actually as th'9'depreciationexpense 'in on"-tirin oi ni" Szz'so0outlay' a systematic and allocate $4,500, (fre sl:rr """ tn"t this is the" straisht-line and rational waYs to of the first vear's ";;;;il' golf coursewas The book valueof his methodof depreciat;;;;;il"ing') ffgures for 1nofit r e d u c e d b y $ 4 , 5 0 0 a s ' a r e s u | t o r n i s a c c o u n tsi,soo lessf o r t h i s d e p r e c i a t i o n ' & The valuatod i n g e n t r y than it would uy his accoJniti". and the figurefor piotii .no*n tt tte aepreCatUoo havebeenifnodepreciationhad'been-recognized'His.year.endbalance write-offwas: lh pordon of lhc to this depreciation sheet after giuing "!o-g;iiion erPc. Equity fqrocilfon and Liabilities Owner's As3ets
cash. Course
Golf Less
.
t?3:333 ^.--::^$17,soo FBoo3illl'ilffi1""1?X?llilr;: ut' i $22'5oo
4,soo 18'ooo $35,500 the year was:
$25,000 $7,500 4,500 12,000 $13,000 $35,500
tad
for ^';;;;;idi"n Allowance
."'
of thc fu the ycdr fttc bc tb
for His profit and loss statement
s R e c e i p t f r o m a d m i s s i o n" " " " " s Less ExPenses: Ooerating -'d'Jrri"tlnts ''''' for rent' taxes' upkeep'etc' ' on Depreciation golf course Profitfrom first year's operations
original $22'500 was 58oloof Spelvin's This profit shown by the books investment. simple exFinancial Statements' This Comment on the Foregoing accountpoints regarding depreciation ample illustrates ,"u"J i*iportint ing, as follows: on the th: $4'100 depreciation charge l. The operation of making no*' In eftect' the $4'500depreciation books of account'"uoi""J"o-li'n portion of a ftrst year of operation of a entry was ur, "llo""tio" to th" the o""o"'n' irad viewed as causing previous $22,500""'h flo* that the as the incurring of an expense' acquisition of "r, u""i '*t'"' than
ch. 10
DEPRECIATION AND ENGINEERING ECONOMY
153
( Later in this chapter, we shall see that even though the act of making a depreciation entry on the books does not in itself change the cash on hand, a depreciation entry in an income tax return infuences the cash flow for income taxes.) 2. The profit as shown by the books of account depends on the depreciation charge and therefore is infuenced by the estimated life and salvage value and by the depreciation accounting method selected. Thus Spelvin's use of straightJine deprecitrtion accounting and his assumption of a 5-year life with no salvage value gave him a profit figure of $13,000. If he had assumed a 2-year life and charged half of the 922,500 cost of the golf course as depreciation, his profit ffgure would have been only $6,250. If he had assumed that the golf course would always have I00% salvage value, his profit figure would have been 917,500. Although, as the quoted deffnition said, depreciation accounting requires the writing ofi of cost "in a systematic and rational manner," there are many difierent systematic and rational ways to write off cost, and these different ways give difierent figures for profit. 3. The valuation of assets on the balance sheet is similarly influenced by the depreciation charge. The so-called book value of an asset is merely that portion of the cost of the asset that has not been charged ofi as depreciation expense. The book value of the golf course was $18,000 at the end of the ffrst year because $4,500 of depreciation had been charged against the year's operations and deducted from the 922,500 cost of the course. If the depreciation charge had been less than $4,500, the book value would have been higher; if the depreciation charge had been more than $4,500, the book value would have been lower. The quoted deffnition of depreciation accounting pointed out that "it is a process of allocation and not of valuation." The valuation shown for a depreciable asset on the books of account is not infuenced by unpredicted fluctuations in market value. Thus the g18,000 book value for the golf course was not influenced by the fact that the syndicate's ofier, turned down by spelvin, indicated that the course had a market value of M2.500 on the year-end date when the balance sheet was prepared.
EXAMPLE1O-2. YEAR.BY.YEAR ESTIMATES RATESOF RETURN OF FROM AN INVESTMENT RENTALPROPERTY IN Facls of the case. Example 8-1 (page 10g)described investment an in rental property. The cash flow series from this investment was shown in Table8-1. The rate of returnon the investment was 1g.g%beforeincome taxes,as computed TableB-2 by appropriate in compound interest methods. Becausea propertycosting$109,000 was sold for a net $209,000 atter T yearsof ownership, actualrate of returnfrom the terminated the investment was considerably higherthan the rate of returnhad appeared be during to the periodof ownership.
154
JUDGING THE ATTRACTIVENESSOF PROPOSED INVESTMENTS Ch. 10
TABLE 1O-1 Accounting Figurestor Annual Prolits and Current Estimates of Rate of Return for Data of Example8-1
Erpensesfor Year
Book Value at Start ol Year
Year
Receipts tor Yeal
Repairs, Taxes, etc. $s,000 5,500 5,700 4,500 3,600 4,300
Depreciataon $3,400 3,400 3,400 3,400 3,400 3,400
Profits for Year
Apparent Rate of Return on lnvestment 6.'t% 8.6 8.7 10.2 11.5 11.2
1 2 3 4 5 6
$109,000 105,600 102,200 98,800 95,400 92,000
$15,000 18,000 18,000 18,000 18,000 18,000
$ 6,600 9,100 8,900 10 , 1 0 0 11,000 10,300
Table10-1 showsthe figuresfor annualprofitsas shownby the accounts lor of of this enterprise its first 6 yearsof operation.For purposes accountinvestment ing, the $109,000 was brokendown as follows: Land Buildings Furniture $15,000 80,000 14,000
no deIn accordance with the conventions accounting, prospective of in in crease(or increase) the value of land was considered the accounts. the buildingswere assumedto accounting, For purposesof depreciation life have a 4O-year with no terminalsalvagevalue, and the furniturewas value. Straight-line life to assumed havea 10-year with no terminalsalvage a at was chargedin the accounts $2,000 year for the buildings depreciation a a and at $1,400ayear for furniture, total of $3,400 year. The profitfigures columnof Table 1G-1are the years' for each year shownin the next-to-last positive charge. depreciation by cashflowsdiminished the $3,400 The table also showsthe book valueof the propertyat the start of each each year it was year. In the first year this was the investment $109,000; of in the booksof account. chargemade diminished the $3,400 by depreciation as The linal columnof the table showsthe profitfor each year expressed a percentage the start-oFyear bookvalue. This latterfiguremay be thought of computedby a of as a current estimateof rate of return on investment of to methodthat often is usedin relation the accounts an enterprise.o
TentativeGharacterof AccountingFigures for Prolit and for Rate lG-l and 10-2 is that both ol Return. An incidentalaspectof Examples
6 An alternate method, also frequently used, is to express the year's profft as a percentage of the average of the book values at the start and ffnish of the year. For example, the 5th year's profit, $11,000, would be divided by $93,700 (the average of 95,400 and $92,000) to obtain an apparent return of 11.7%.
ch. 10
DEPRECIATION AND ENGINEERINGECONOMY
155
examples illustratethe point that i'termediate judgmentsabout profitability and about rates of return may be consideraLry"ir, "rro.-i'fact, these examplesare extreme cases serectedto "*ph"ri" this point. ^deriberatery In Example r0-r the-rat-eof return appea."d to be 5g%at the e'd of the first year eve' though when the i'ves-t-mentwas terminated it turned out that there was not eve' a 0%retur'. In Exampre r0-2, the rates of return for the first three yearsappearedto be lesstt an g% "r"; ah"";l the over-all '#;." return o' the terminatedinvestmentturned out to be ipproximatery of coursethe true over-arlrate of retu'r obtained over the rife of an investmentca'not be k'ow' untir ownership has b"e' t"r-in"a"d. N",,r"._ theless,year-by-yearfigures for profit are cssentiar i' the co'duct of a busi'ess ( and in the collectio.,o? in"orrr" taxes ); it is 'ot practicabreto wait until the tennination of a businessenterprise to draw co.clusio's regarding its profftability. It is natural to cornpute year-by-yearrates of return by relating the-profit ffgures take'from th" o""ourrtr'to so.n" irr_ vestmentfigure also taken from the accounts. At this point in our discussiona clear disti'ctio' 'eeds to be made between the problem of .computing a si'gre ffgure for rate of return on an investmert basedon the fulr period of 1onr""q.r"n"", oJ-irr" investmeut and-the problem of estimating-y"ar-by-year ffguresfor rate of return. As explai'ed in chapter 8 (and-demonrir"t"d i""Tabr;--8;il Jo-po'na in_ terest methods are required to find the correct ffgure for rate of return over the life of an i'vestme't. The foregoing stJement "pfii", both to the calculationof rate of return from a iermi'ated past investmentand to the calculation of estimated rate of ,"*rr, from estimatesof cash flow for the_ entire period of service of a proposJ investment. It is rarely, if ever, of much i*p-turr"" to find the rate of return on a terminatedpast investment(such as the one in Exnmple r0-2). Although the rate of return may be of'historicaiint"r"rt, 'othing ca' be done about terminated investments. In contrast,the estimationof rate of return on a proposedinvestment is a .matter of great practical importance. A' important criterion of attractivenessof a proposed i'vestirent is the ,ingi" ng,rr"-iir", expresses -1, the prospective rate of return over the life of tf,""inrr"i_".i. needs t<r be emphasized that it is this over-ail ,"i" or ,f,.,r,';;';'rlg"iffcant for proposedinvestments, not estimates rates of return of the of -year-by-year type illustrated in Table l0_1. In the opinion of the authors of this book, there is serdom any valid reasonfor not using correct compound interest methods in anaryzingproposed investments'A great deai "i ;; and efiort often goes into making of estimates foieconomy ri"ai"r'l"r",ir" ;;';r;;;r"at]nu"r,*"nu. the
timeareneeded appty to methods of-computing ,:ljT flffit;ffrulor" thanareneeded *pp!, ",,i to of thevarious ""-n".,""!",',ii$r::.T:ilXj:.
Ch' INVESTMENTS 10 OF PROPOSED THE JUDGING ATTRACTIVENESS 156 p'ro:pTtive rates of methods of computinq However, several incorrect Although are in "g**oti ttsein-industry' on proposed i"t'"'t'n"'-'t' of rate of return ""gutt itt tft" iyp" of calculations l0-2' the these method, ull t'"u" ift"t'' l0-I ^another' and -in'Elimples on past i"";t;;;-iit'i'at"d these return Sometimes from one give results iit"iatn"t-greatly to cormethods tft* ih"y u'" Eood approximations under the methods are used itt ;; ["i*r ,o*"tii'rlr- - they are used '""r.r*, comporrnd inter"si methods; of several rect in prir"ipi". The' weaknesse-sthat they "* illusion 10-10 at the in'proui"ms lG-7 through methods "r" tri"r,r*a of these
""HtTl1:oT"lit"*u"""e
discussthe most "o*iott
-"thods of-Jepreciation accounting'
"approximate" we methods' must ffrst these
As of Depreciation Accounting' Comment on All MethodsGeneral it is the "r Jep'""iatiott accounting' brought out irr th" il;;;;n"ni"" that is rvritten ofi prospectit" ;;it"g" value' cost of tangible n"Jt', less viewed tfr"""ott"of capital assetsis on the books of ";il"H-efi^ect, of service of the upp-tiot'"a "-o"g the iears as a prepaid ""n""'i"tl"t" "in a systematicand rational manner"' are assets of writing ofi costthat obviously There nr" -"", a'i"'""t-'""tft"ds o"" another "svstematic."rvror"il"i--"tr'od' -b"i"g lhal. ;ifi"t"greatly i:oT "'"tio''ot'' li tft" United States the have been uduo""i"f,'"' in income tax b?"'-' i"fl""nced by changes methods ir, "o*-JJi'"-i"t" 1962' and uv."honJ"t-i" rgsl,.t954' laws and r."grrtutio;r,l"rti"rrt"rty in the iollowing discussion-' 1971 that will be ;;til; methods is as follows: accountin-g One way to classify depreciation write-off in the early years of 1. Methods that aim to give a .greater life than in the final Yearsot lrte the entire ;"'give a uniform write-ofi throughout 2. Methods th;;;; servicelife 3.Methodsthataimtogiveasmallerwrite.ofiintheearlyyearsof life than in the ffnal Years I n c l a s s ( 1 ) w e s h a l l d i s c u s s t h e d e c l i n i n g - b a l a n c e m e t h o d ' tIn e s u m methods' h method, and certain multifle-straight-line of-the-years-digits (3) we shall straight-iinemethod' In class class (2) *",r'ul'Ji'"t"''tr'"
T T h r e e p a p e r s b y o n e o f t h e a u t h o r s o f . t h i s b o o k t h a t t o g e t Stat-es'particularlvi cfrom c . her.giveahistor alpi u"itZa ;i d"pr""i"trn"i""'ift" t.re of the income il;;il;a
ttql$"'",Y1?1?:iji;"t""s
n-n'-llfll Autumn' tS6-A' ""?i;;';bR-svstem EngineeringEconomist, Tax Matters," E. L. Grant, The En' and other Relatq{In Spring'1972'pp' 200-210' ginniriie Economist' RelatedN'latters ..Some .and fiom Sixty Yearsof tr""illnt of Depreciation Papers' Lessons Ametican st"t"t';;"i' i' ct*t' Technicol U"rt"a for lnt'omeT"- P";;;';'in" inntuertors'conferenceand conaention' iiita-eitt| rnstitute of narrifi"Elni^i-rr, 1973,PP.45-54'
E' Restudied," socie-ty-rax feolgciation
rhe L' Grant'
ch.10
DEPRECIATIONAND ENGINEERING ECONOMY
157
discuss the sinking-fund method. Because of its historical the straight-line method is discussed ffrst'
importance,
straighhLine Depreciation Accounting. In the straight-line method, the full service life of the asset is estimated. The prospective net salvage value at the end of the life is also estimated and expressed as a percentage of first cost. The annual depreciation rate to be applied to the first cost of the asset being written ofi is computed as follows: StraightJine rate : Consider a machine tool with a first cost of $35,000, an estimated life of 20 years, and an estimated net salvage value of $3,500. The salvage percentage is $3,500 -i- $35,000 = 0.10 ot IiO%.
rate straightJine = W:ff
= +.sn
With this straight-line depreciation rate, the depreciation charge every first cost)' of year will be $I,575 (i.e',4.5% the $35,000 The same $1,575may be computed without the use of the 4'5%frgwe, as follows: StraightJine depreciation charge
=@" a i s
first cost minus estimatedsalvagevalue
s35.000 - $3.500 = - $31,500 = Q i , D , D ^, P4/ =------n Z0 Prior to 19M. it was common in the manufacturing industries of the United States for cost to be written ofi in a much shorter period than full service life. For example, the cost of machinery often was written ofi by a uniform annual "h"tg" during the first I0 years of its life. At the expiration of this period the machinery was carried on the books of ac"fully depreciated." It was not uncommon for the full service count as lives of machines so written ofi to be 20 or 25 years or even longer. Al"straightthough in pre-1934 days, this method of write-off was described as line;; we thull r"" that the method is more accurately described as a special case of multiple-straight-line depreciation accounting' A change in policy of the U. S. Treasury Department in 1934 and thereafter was intended to force the writing off of cost for tax purposes over the full service life. With the straight-line method applied over full service life, the ffnal years of life receive exactly the same depreciation charges as the initial years of life. Declining-Baladce Depreciation Accountang. It is common for assets to be used for stand-by or other inferior uses during the final years of
INVESTi'ENTS Ch' 10 OF PROPOSED THE ATTRACTIVENESS JUDGING 158 greater in to income often is much The contribution of assets their lives' these reasons and for f* fttul y""tt' ofi years of fit""tit"i"itt-the to the early ll""riv it-sensible write
ch. 10
brought"*;;-bhal1:t ",.,- y"u" of life than in the later otherreasons i" tft" "u'ty *"*"i"piify the costof assets
For example, life, both with salvage value ol declining-balare
In the achral depreciation reb compute a rab
t"t'|.,", *avs. makin more gthis .raYl1 of "t TlU"Tl J::: purposes in the X::.";ftil.:lT
t#;";;;a'
tax -m"tnoa'to assets authorized foi it'come t:ttll::d for tax- purposes *": taxof these liberalized acquired new 'bv the *o'" tlt"t' *o" of th'"" ;;;;;;' having lives *ut the so-called
permitted by intended to
in the ffrst brtr
*.r'izcd ",-d
ii1" '"r in Davers 1954"' Inl'""it* declini"g-balance-method.'. ilffi;;," a grven depreciation depreciation accounting'
In any de"ti"i"g-iat"nce
"#;;;i" ,fo':lll[:.i::-";l}i;"liif"i; *,'ff; is rate appried toan i'""pptied asset #**xffi',:::" ff::Iffi?:i Jft"?"" v"ui it o'to($35'000) ti'" n*t
d;G;;"*tio" "t'u'gJii = 0'10 $35,000, thatcost crrarqS"tJ'blotg"'000 t|'soo)= 0'10 In - $3'150) = g3,500. the'"""J'r""1th3 l;-tt" ir'i'a v""' it it o'ioi$sr'5oo = (31,500) $3,150'
it' taxpurposes tr'"'ijiitli"il* as2W+ 1"sti*atJiil;;;;) ril';;'is
in 6e ln qtrrj
b|tc
tbn
hr r-
rorincome i-?;'ill i"1,tr?"'-i;.1*ii"1l*-*t*"," authorized method is computed rlte th" in 1954' d"p'""iutiol1
rtas an estimated zero salvage foi an "r.",iLi rate that would u"-ullo*"d permissible declinlife. In "'o*p"aiog the and ttre givei^eisat-"i"a value disregarded' uot"" t"'*""i'"t"iu"i" 'is ing-balance rate, any prospec^t]ye^ we *1rig1r computed g35,000
the double straight-line
estimated,"fu"g"";i,;".'Th" rate for 20 vears will ;i ;i}il ihe^applic#;; is 20M - 20 :'if asset at ihe end of the 20th year' lead to a book uuio" oi $n'255 a"d f representsthe decliningof 1" F; If P represe*' ttt"-n"i cost of r years th" boot value at the end ."t" "*n'""JJ;'";;;d' balance 'hu so-called j-fj"' At this p"t"ii1 o"' di'""oio-:' obviously will be-P-(i textbookmethodoicomputingadeclining.balanceraterequiresabrief make the book value ;;i; i r' a""'"J ?i"i *il salvage mention. Assume;;; "q""it" an estimated terminal at the end of "" n-vT"'iii" "-"*fy value,L.Then L=p(r_f)" and
#il";1";ir"t the for consider, exampfe, a $3'500 life ;"u " io-y"*-estimated and for this 4'5%straight-liie'i"i"'"ittit the rate p"r*irrili"'-d""lining-bulance
f=lis rarely if a declining-balance rate-However, this method of setting Small difierences with "ero sal"ag-eu"lt":' rate' ever used. lt "a""ot t" used u g'"ut aln"'l"tt"" in the computed in estimated salvage t"i"""*"t"
ch. 10
DEPRECIATIONAND ENGINEERING ECONOMY
159
For example, consider two $1,@0 assets each with a Z}-year estimated Iife, both with small prospective salvage values. Asset X has an estimated salvage value of $50; asset Y has an estimated salvage value of $1. The declining-balance percentage computed for X is l3.gl% and for y is 2g.2M. In the actual use of the declining-balance method, it is better to select a depreciation rate that seems appropriate, all things considered, than to compute rl rate from the textbook formula. The declining-balance rates permitted by the 1954 tax laws and regulations in the united States are intended to permit a write-ofi of about two-thirds of the cost of an asset in the ffrst half of the estimated life.
used in actual accounting practice before that date. The digits correspondingto the uumber of yearsof estimatedIife are added togJther. For example,considerour $35,000 machine tool with its estimatedlife of zo years. th-e sum of the digits from I to 20 is 210. The depreciation charge for the ffrst year is 2012L0 the depreciablecost (i.e., of the first cost of minus the estimatedsalvagevalue). This is 20/210($95,000 $g,500) = 20/2r0(ffir,500) - $3,000.In the second year the charge is rg/2r0 ($31,500)- $2,850. In the third year it is t8/2I0($31,500) = .t'd EZ,ZOO. so on. The chargedecreases $f50 (i.e., by Ll2L0 of $91,500)each year by until it is $150in the 20th year. This method writes ofi about three-fourths of the depreciable cost in the first half of the estimated life.
sum-of'the-Years-Digits Depreciation Accounting. This method, authorizedin the United statesby the lg54 tax law, apparentlywas never
sinking-Fund Depreciation Accounting. This method visualizesan imaginary sinking fund establishedby uniform end-of-year annual depositsthroughoutthe life of an asset. Thesedepositsare assumed draw to interestat somestatedrate, such as B%, or B%, 4%, and are just sufficientso that the fund will equal the cost of the assetminus its estimatedsalvage value at the end of its estimatedlife. The amount chargedas depreciation expensein any year consistsof the sinking-fund deposit plus the interest on the imaginary accumulatedfund. The book value at iny time is the first cost of the assetminus the amount accumulated the imaginary fund in up to date. The sinking-fund method is arso known as the pr'esent-worth ^worth method; the book value at any time is equar to the present of the uniform annual cost .of capital recovery for the reriaining years of life plus the presentworth of the prospectivesalvagevalue. Fo,t example,assumethat our $35,000machine tool is to be depreciated _ 6% sinking-fund method. The annuar sinking-fund d-eposit is 9r:!: ($3Spsg-- $3,500) (AlF,6%,20) ($3r,500)(0.02218) = ="$856.2.This wiil also be the depreciation charge in the ffrst year. In the second year the depreciatio-n chargewill be g8b6.2+ $856.240.06) $907.6. In the third = yeaf it will be $856.2+ ($S5O.Z g902.6)(0.06)= + $962.0. And so on.
160
Ch' INVESTMENTS 10 OF PROPOSED THE JUDGING ATTRACTIVENESS without year-by-yearcalcuThe book value at any age can be computed imaginarv sinking fund and subtractlations by finding the airorint in the instance, the sinkin^g-fundat the ing this amount fro- ih" first cost. For = (FlA'6%''12) = $856'2(16'870) end of 12 years will amo"nt to $856'2 $ L 4 , 4 4 4 . T h e b o o k v a l u e a t t h i s t i m e i s t hcomputingthe 'presentL 4 ' 4 4 4 : e r e f o r e $ 3 5 0 0 0 - $ wofth checkedby $20,556.This book t;il;;r;e a t d a t e 1 2 0 f t h e " r r . r r r u l " o r t ' o f c a p i t a l r e c o v e r y f o r t h e r e m a i ncapital e a r s ing8y value' The annual plus the present *o*f' of the terriinal salvage (AlP'6%'201+ffi'500(0'06): ($31'500) costis ($35,000 $3'500) recovery
ch. 10
Compariran
FC (Assd
and. capital'i"-o-u-"ty -terli11l^ worthsof remaining present + = gg]500(P1F,616,8) $2' s56'2(g'?10) $3' 500 * (PlA,6%,8) $2,e56.2 this book (Th" i"t"t"tt : + (0.6274) $18,358 gz,rrjo $20,554' 1abl.e1.in
of = Thesum the + + (0.08718)$3,500(0;11:-62fia: $210'0 $2'956'2' value is t^*:*"
Year 0 1 2 3 4 5 6 7 8 I 10
Declining Balance
for this calculation to check are not carried to "'1o"gi' 'ignificant fig"'"' to the nearestdollar.) :r always greatt than they Book values with the sinking-fund method are The difierence is greater for longwould be with tfr" rtr"ilfrt-line method. high interest rates than for sho"rtlived ones,and is greater with liveJ assets meiirod has sometimesbeen dethan with low ones. The straightline method in which the i'scribed as the limiti.,g-caseof ihe sinking-fund terest rate has been assumedto be 0%' -certain industries a few ertrro"gr, th" ,irrkir,!_f"nd method was used in actual accounting to ago, it has cea"sed be of much importancein decades of the use of so-called i.'i, "*ptuir,"d here primarily beJause ;;;;;. economy studies in a ii.rt ing-f,roa depreciation in certain engineering *arrn"t explained later in this chapter' An|||ustrationo|DepreciationchargesandBookVa|uesbyVarious Methods.Tablel0-2showsthey"",-by-y"n'write-ofisthatwouldbe methods that have been made for our g35,000machine toof by the four the declin"*pi"i""a. rh" tubi" also shows end-of-yearbook-values..In values have bee' ini-b"I"n"" and the 6%sinking-fundmetirods' the book the figures showr.r rounded ofi to the nearestdoll"arfor listing in the table; made consisteut in the table for yearly depreciationchargeshave been with the ftguresshown for book value' "systematic" ways of writing ofi cost can differ greatly It is evident that fromoneanother.Commentontherationalbasisofachoiceamongthe difierent methods is deferred until later in the chapter' SomeotherMethodsofDepreciationAccounting.Sometypesof specificunits of outcan be identiffedwith the production_of capital assets be charged in proportion to units depreciationcan p,rt. Fo, such assets, ^of units' to productionprovided if is reasonable estimatelife in production with exhaustiblenatural associated The method has been used for assets the quantity of resourceswhere the factor limiting the life the of assetsis
11 12 13 14 15 16 17 18 19
n
$3,s00 3,150 2,835 2,551 2,297 2,067 1,860 1,674 1,506 1,356 1,221 1,098 998 890 801 720 649 584 525 473
the natural preciated at so
nine tipPle rniglrt
quentlY the lreciation chargd
in Ed sitable
It is possibb b 'ftigbt liqo arc estimated
6e amtd more rhrn Fc
r yc.rh
ch.10
DEPRECIATIONAND ENGINEERING ECONOMY
161
f $
TABLE 1O-2 Comparisonof DepreciationCharges and Book Values by Four Methods of DepreciationAccounting (Asset firstcostof has $35.,000, estimated of 20years, life and
estimated salvage value of SS,bOO.t Depreciation Charge for year Declining Balance Years Digits Straight Line 6o/" Sinking Fund
End-ol-Year Book Value
Declining Balance
Year
Years Digits
Straight Sinking Line Fund
6%
1 2 3 4 5 6 7 8, I t0 11 12 13 14 15 16 17 18 19 20
$3,500 $3,000 $ 1 , 5 7 5 3,150 2,850 1,575 2,835 2,700 1,575 2,551 2,550 1,575 2,297 2,400 1,575 'l,575 2,067 2,250 1,860 2,100 1,575 1,674 1,950 1,575 1,506 1,800 1,575 1,356 1,650 1 , 5 7 5 1,221 1,500 1 , 5 7 5 1,098 1,350 1,575 998 1,200 1 , 5 7 5 890 1,0s0 1,575 801 9OO 1 , 5 7 5 720 1,575 750 649 boo 1,575 584 450 1,575 525 3oo 1,575 473 150 1,575
$ 856 908 962 1,020 1,081 1,146 1,215 1,287 1,365 1,447 1,533 1,626 1,723 1,827 1,936 2,052 2,175 2,306 2,444 2,591
$35,000 $35,000 $35,000 $35,000 3 1 , 5 0 0 32,000 33,425 34,144 28,350 2 9 , 1 5 0 31,850 33,236 2 5 , 5 1 5 26,450 30,275 32,274 22,964 23,900 28,700 31,254 20,667 21,500 27,125 30,173 18,600 19,250 25,550 29,027 16,740 17,1 50 23,975 27,812 15,066 15,200 22,400 26,525 13,560 13,400 20,825 25,160 12,204 1 1 , 7 5 0 19,250 23,713 10,983 10,250 17,675 22,180 9,885 8,900 1 6 , 1 0 0 20,554 8,897 7,700 14,525 18,831 8,007 6,650 12,950 17,004 7,206 5,750 1't,375 15,068 6,486 5,000 9,800 1 3 , 0 1 6 5,837 4,490 8,225 r0,841 5,253 3,950 6,650 8,535 4,728 3,650 5,075 6,091 4,255 3,500 3,500 3,500
It is possibleto use d-epreciation accounting methods where two or more straight lines are neededto show trr" J*ii* in book-valuefrom first cost 'such to estimated salvage value. " ,"t"-" -ay be describ"d;; " multiple, straight-line method. under trr" u"ii"i" states rg54 tax law, murtipre_ straightJine methodsmpy be used for i"* purpor", subject to the restriction that the amount written ofi "t "nf ti-" a,in"g the ffrst two-thirds of rrfe is not more than wouid have,been p"t-i,"a ,rnder the a""r*lg-tarance method. For examnle,our $g5,000^;;;;e tool might be written off at $2,250a year for the ffrst t0 ,;;;;;rd;; On* " year for the ffnal t0 years.
or **;iil;; nnding any :ii:;: il:::ff"1T;;:i""*""gu""""'" the
the natural resourcein question. Thus the-cost of a sawmi' might be de_ preciatedat so much p_er thousandboa.Ji""t sawed,or the cost of a coar mine tipple might be depreciated at so much per ton of coal mined. Fre_ quently the.unit-of-production method i, ured for motor vehicres with de_ preciationchargedin proportion to miresof operation. The method is rarery
162JUDG|NGTHEATTRAGT|VENESSoFPRoPosED|NVESTMENTSch.l0 Aspecialcaseofthemultiple-straightJinemethodistheoneinwhich salvagevalue, if any ) is written ofi on the eniire ftrst cost ( less estim^ated As previously a straight-line basis in some period shorter than the life' states before 1934' stated,"this was the common situation in the United for l0 years whenan assetwith a Zl-year life was written ofi at l0% ayear multiple-straightJine and 0%for the remainini 15 years, this was really a method with one of the straight-line rates as 0%' Under the 1954tax law iri the United States,it is permissible to switch any time from the declining-balancemethod to the straightJine-method at book value before an assetis retired. For example,Table 10-2 shows the at the of our machine tool by the declining-b"l"tt"" method to be $8,897 7 years still errd of 13 years, If the estimated remaining life on this date is value is still $g,5oo,a straight-line write-off of and the estimated salvage $8'897 $3'500 = $771a year could be used for the ffnal 7 years' for Estimates of Service Life and Salvage Vatue for Tax Returns, studies. certain types of assets, Business Accounting, and tol Economy the scrap such as automobiles,may h"lr" several owners before reaching "lif"" for accounting purposesordinarily is the heap. For each owner, ih" life "*p"cted period of service to the owner himself. In general, service of years lapsing from an for accounting purposesis viewed as the number uses to asset'sacquisition to its final disposal, regardlessof the different years' since 1934, the which the assetmay have been put during these income foi"loing view of slrvice life has governed the administration of tax laws in the United States. Estimatesof terminal salvagevalue used for accountingand tax purposesshouldbe consistentwith estimatedlives, For example,if automobiles ir" ,"g.rt"tty purchasednew and disposedof at the end of 3 years, the with the estimated3-yearlife should used in connection percentage salvage for ialvage percentage 3-year-oldautomobiles. be an"eJtimated Where sufficientdata-are available,various types of statistical studies such studies may be made to estimateaverageservicelives. In many cases of the lype illustrated in Figure l0-1. Statistical lead to survivor curves studies made year after year for a particular class of assetsoften indicate that the averagerealized life has been changing' "guideIn 1962the United StatesTreasury Department made .available assets.In 1971,the Treasury of line lives" for many broad classes business approval of congress, established an Department, with the subsequent "aslet depreciation to range" (generallyabbreviated ADR) systemfor assets the of 31, 1970. For many classes assets placed in- serviceafter-December from approximately 20%shorter to iDR systempermitted the use of lives longer than the 1962 guideline lives.s The use of both guideline lives 20%
sThe o{ffcial document establishing the guideline lives was Revenue Procedu 62-21, fSO2. the official documents setting up thl epn system were Treasury Decision 7128 and Revenue Procedure 7t-25, both 1971.
ch.10
and the ADR
keeping and these relatively mated lives for An economy somewhat for the asset @
the economy ing purposes and that usually is often relates oly b stand-by or o$cr regardedon the of the eoonomy ln some cascs than the eapected necessaryto esti than termiml such residuel is discussedin
ch. 10
DEPRECIATIONAND ENGINEERING ECONOMY
163
and the ADR system was subject to a variety of restrictions about record keeping and other matters. In many cases, taxpayers who elected to use theie relatively short lives for tax purposes used considerably longer estimated lives for the same assetsin their own business accounting. An economy study rel_ative to acquiring a proposed asset involves a somewhat difierent viewpoint from the keeping of the depreciation accounts for the asset once it is acquired. It may be reasonable to assume a life in the economy study that difiers both from the life used for business accounting purposes and the life used for tax purposes. It is the economic life that usually is relevant in the economy study. Moreover, an economy study often relates only to the primary or initial type of service of an asset; possible stand-by or other inferior service during the ffnal years of life is often disregarded on the grounds of having a negligible infuence on the conclusions of the economy study. In some cases an economy study may relate to an even shorter period than the expected economic lives of the various proposed assets; if so, it is necessary to estimate residual values at the end of the study period rather than terminal salvage values at the end of the eConomic lives. The use of such residual values in economy studies was illustrated in Example 9-1 and is discussed in Chapter 13.
Distinction Belween Single-Asset and Multiple-Asset Depreciation Accounting. Assumea group of assetsthat have the mortality distribution shownin Figure 10-1. Although the averageservicelife of theseassets is 20 years, retirements occur all the way from the ftrst to the 45th year' For the sake of simplicity in the following illustration, assumethat the expected salvage value is zero and that each asset,when retired, actually has a zero salvagevalue. Assumethat straight-line depreciation is to be used; the 20-year averageservicelife and zero salvagevalue requires a 5%depreciation rate. Now assumethat each assethas its own account and that the depreciation on each assetis computed separately. ( This is referred to as singleasset or item depreciation accounting. Approximately half of the assets ) will be retired before they are 20 years old. Every such asset will have somebook value when retired; with no realized salvagevalue, the books "loss" for each retirement. The half of the assets of account will show a that survive for more than 20 years will be fully written ofi at age 20; no further depreciation chargeswill be made against them during their period of service from years 20 to 45. In contrast. assumethat one account is used to include the investment in all of these assets; each year the depreciation charge is made against the group of assetsrather than against the individual assetand the book value at any time applies to the group with no identifiable separateffgure applicable to each asset, With the assetsconsidered in a group and with the fact of mortality dispersion recognized, it will be evident that the retire-' "premature" in the sensethat they ments at ages short of 20 years are not
164JuDGINGTHEATTRAGT|VENESSoFPRoPosEDlNvEsTMENTsch.l0 life. If a are inconsistent with the estimate of a 2}-yeat aoerage service of the numbers must be less set of unequal numbers are averaged, some of this point than the uu:"rug" and others must be greater. The recognition "loss on disposal" the in multiple-arrit d"pr"ciation accounting eliminates multiple-asset ent.y ,rride, .ror^uf circumstances. However, in traditional life' accounting, depreciation charges continue beyond the average service Internal Revenue SerIn the luog,r"g" used in publications of the U. S. acvice, a distin;tio; is made among three general types of multiple-asset counts. as follows: l. Croup accounts' Examples of such accounts would be passenger automobiles, punch presses' office desks' 2. Clnssified' accounts' Some examples are transportation equipment' machinery, furniture and fixtures. ml3. Composite sccounts. As an example, transportatiol equipment' and fixtur-es might be included in a single "rtl"Jry, and furniture account, particularly
ch. 10 -that investments in where this is not 0 reason to forecast much more or relevant in any
invest in the lan&
element of cash f,ow Many economy sale of a new prdd to the investment b
outlay for worlchrg clude inventoriesof
also include the over accounts there may also be en
in the manufacturing industries, the most common practice use of item is to use classlffed accounts for income tax purposes. Often, the accounts is limited to such assetsas buildings and structures' is in In this book the most important use of depreciation accounting of connection with the calculation of cash flow for income taxes. In most our examples and problems illustrating such calculations, our computations ^of depreciation are made as if item accounts were to be of the tax^aspects used. This aisumption of single-assetaccounting is made chiefly for reasons the of simplicity-to avoid the need to devote space to an explanation of multiple-asset accounting. In many studies, ,r,r-"rir$ tlchnical details of particularly those relative to proposed new assets, it makes no difierence i"hethe, single-assetor multiple-asset accounting is assumed. in An economy study fo, a proposed retirement is one type of study taxes with single-asset accountwhich the timing of cash flow for income ing may difier greatly from the timing with multiple-asset accounting. "loss on disposal" Oiten tire criticaipoini in this type of study is whether a discussed in Chapter 17. will be allowable Jor tax purposes. This topic is
The working books of account. ing funds should had a prospective is, it usually is
the accounts
liquidated. This
on certain aspocB made in
ACCOUnts.It is a conventionof accountingthat land is carried on the books at its original cost regardlessof changesin its market value. No depreciationor appreciationon land is shown in the books of account' Of co,rrs", if land is ftnally sold at a price above or below its original "gain" or "loss" assignedto the year of the sale is shown on the cost, a to pu{poses, is not necessary make an estimate it books. But for accounting future sale price of land' of the In the absenceof any basis for a different forecast, some economy studiesmay follow the lead of orthodox accountingand assume-in efiect
Ghargesin the certain Typesof AssetsNot Subiectto Depreciation
ch. 10 -that
DEPRECIATIONAND ENGINEERING ECONOMY
165
investments in land will have 100% salvage values. But cases occur good where this is not an appropriate assumption. Sometimes there is for reason to forecast that at-the end of a study period land will be sold less than its original cost. If so, this forecast is much more or much relevant in any analysis tg guide the decision on whether or not to invest in the land; the estimated future sale price of the land is one element of cash fow to include in the economy study' Many economy studies relate to the investment in plant to permit the sale of a new product or expanded sale of an existing product. In addition to the investment in physical plant, such a proiect usually requires an outlay for working funds. The working fund investment will usually incl.rde inventories of materials, work in process, and ffnished goods. It will also include the excess of accounts receivable associated with the project over accounts payable similarly associated. For certain types of product there may also-be an inventory of returnable containers to be considered. The working fund investment is not subiect to depreciation on the books of account. For purposes of an economy study an outlay for woiking funds should ordinarily be treated as if it were an investment that had a prospective 100%salvage value at the end of the study period. That is, it uiualiy is reasonable to expect that when a product is discontinued the accounts receivable will be collected and the inventories will be liquidated. This treatment was illustrated in Example 8-3. Comments on certain aspects of the estimation of working fund requirements are made in Chapter 15.
of Estimates CashFlow for IncomeTaxesBasedon Economy-Study in and CertainSimpliliedAssumptions.Manyof the examples problems in of Chapters6, 7, and 8 included estimates the difierences cash fow
for income taxes that would be caused by a choice among stated alternatives. In those studies applicable to competitive industry, these estimates were made under the following simpliffed assumptionsi 1. The same estimated lives and salvage values used in the economy study will also be used for tax purposes and will be acceptable to the taxing authorities. 2. StraightJine item depreciation accounting will be used for tax purposes. 3. Throughout the period of the economy study, the effective tax rate on an increment of taxable income will be 50%' 4. Except for capital items, receipts and disbursements before taxes in any year apply to the calculation of the taxable income for that year. (Capital items include first costs and salvage values of depreciable plant. They also include assets such as land and working capital that are not subiect to depreciation charges in computing taxable income. ) 5. Recovery of investments in nondepreciable assets such as land and working capital does not give rise to any tax consequences'
$il
166
OF PROPOSED INVESTMENTS JUDGING THE ATTRACTIVENESS
Ch' 10
*"t-:1'"n""*1""'il":fr: "T#;;;";i;"'*,:I":"1:::'*JT"*ff,i'; Giuen *:j"lTJil'"T,i:,T"I"il""J4ft ,"i:'1,it'"-il:H:'Ii'fr ':J"l-":*,::1"*,i*:::,'iJ[1Xl:follows:ln f
aoouL tus '"'"t", "F^----j^^*^"1 A reasonable questlon trir.rnres in investpurposes "oo"gtt for practical they give results tf'"i "t" lood ment evaluation'
*d tf total Boththe absolute amount i':'T
,il:l "H#:.TJ':J',ilr"";'T;;$111i::,1::,':fi'iil"T,'1"*ff t-, of the ammn
we La^E 4 -^":-;.";;e good at all. In Chapter ro
ff
"*"J'::'o,o",sometrmes9":"^l':"llif i::::i:'"%5:"*"9::i
The spdb by year arc: l, and 13, f{lQG wilt be.t;nr;niicd
[trTi:111";"'LH';l:,'lqy":-,*:;*:;li:"*""'.J:":S,ilX':n the sim'J#:t::: influencethe amount and -timing ."f -,:1".]X::t;}l."*""Tt"iL
::;ffi cash ffi:f [1TJ:'i'r'i#*{:":*1;;;T*';lti',:H:il: in estimated disbursements ;;tr;;; ;il,H'il"il'#il
t"ITt
taxes. for income taxes'
tia"''o'r'' $""ffi"T;'"' .I; th"'YY:T*::.::: :ht:il;
tax consequences of
The
res ll,flD,(IID frr oooomlLg ttccoffi
^i-,;il"Ji:S1: :'"i;i*''fi rhis ,"ff;"IT:ffi x,;l?""','",1::ln':,1"iffi ;iit;-,ate, regurated. Tti;TiT?'if* ;:-;t,""1
,"p* lt "* discusseduntil Chapter 20'
t:1"i^ of The treatment prospective -ii:o3:. T :"::il""".t[*t,i:l ^u," "r"iil
lccmnd
frrr
froo llc
H ;H "";i"l}ir"y::*'-':1'"T:"*:"'T,uil: *f H"':H"l:iJHffi made the *re'" ror iffi**
Tax of !i1e1^:i-T::*: verification Income Ditfereyes
lL Erfu Lt'tLi cd
r)
f';,."fft'"'ltl|;tti;1'ti" two examPles: ::ift"* in these
;i;-;f;-"o*Pu'"d
First cost Life . . Terminal salvage value ' '' n^tt"f before-tax disbursements
PlanA $0 10 years $0 $9,200
PlanB
PlanG
E;r
ldt
$15,000 $25,000 10years 10 years $5,000 $0 $4,050 $5,100
the reference to production methods; These were alternatives with not be influenced p'od""t o-l'ni""^would receipts from the of" lf th" estirtt"'"fore' the difierence in by the choice u,,'o"i ;h";;;;i*'' in estimated tax o-tt ttt" difierences mated income .u*""a"i'"";;";"iy ir,"o*" each year are as follows: deductions. rh" d"d.,lffij;;;.;;j" PlanC B Plan PlanA $1,s00 $2,000 $o dePreciation 4,050 Straight-line 5,100 9,200 :" " " "
Befoie-taxdisbursements .. Total deductions " $9,200 $6,600 $6,050
than deductions from taxable income BecausePlan B has $2'600 less of $1'300' annual.i"corne tax disbursements Plan A, it will inuoluJ h;;;;t figure given in the stategf3& was the income tax 50%of.$2,600.ff i'
*T*t"l"*?i:*""9-o:,
tax disbursementsof $1'575' Plan A, it will iouofvlftigit"' annual.i""o*" stateincome tax figure given in the of 5O1o $3,150' ffti, Of,'fZ?was the ment of ExamPle il2'
than income from taxable g3,rs0lessdeductions
ch. t0
DEPRECIATIONAND ENGINEERING ECONOMY
167
Explanation of the Method of Estimating Each Year's Income Taxes Given in Example 8-3. The third paragraph of Example B-3 ended as follows: The speciffc estimatesof net positive before-tax cash fow from operations year by year are: l, $100,000;2, $300,000;3, $400,000;4 through 11, $500,000; 12 and 13, $400,000; f4, $300,000; and 15, $200,000. These positive cash flows will be diminished by yearly disbursementsfor income taxes estimated to be 50% of the amount that each year's figure exceeds $100,000. The depreciable investment in plant and equipment in this example was $1,500,000made over a period of two years. The depreciation charge for accounting and tax purposes would not start until date 0 when the construction would be completed and the plant put in service. Because the estimated life was 15 years with no terminal salvage value, the annual straight-line depreciation is $1,500,000+ 15 = $100,000. It is this $100,000 deduction from taxable income that was referred to in the second sentence quoted from the statement of Example &-3. The reader will note that Example 8-3 difiers from Examples &-l and 6-2 in that the choice between the alternatives (accepting the project or rejecting it) involves differences in annual receipts. Moreover, because the estimated before-tax positive cash flow varies from year to year, the estimated disbursements for income taxes also vary from year to year. According to the conventions of accounting and income taxation, the $300,000 outlay for land and the $200,000 outlay for working capital are nondepreciable and therefore have no infuence on estimated disbursements for income taxes during the lS-year operating period of the project. Because it is assumed that these investments will be rec.overed without increase or decrease at the end of the l5-year operating period, the cash flow incident to their recovery at date 15 has no influence on income taxes in the 15th year, the terminal date of the project.
d a
L
le
:d ritx 's:
Some Economy-Study MethodsThat Appear to Tie Annual Capital RecoveryCosts to the Depreciation Accounts. One of the topicspresentedin Chapter 6 was the conversionof a ffrst cost, P, into an equivalent uniform annual ffgure over a Iife or study period. To make this conversion, it is necessaryto have a stipulated minimum attractive rate of return or interest rate, f *, an estimated life or study period, n, and an estimatedsalvagevalue, L, at the end of the life or study period. Throughout this book, we use the following equation to compute this annpal cost of capital recovery with a return: CR = (P - L)(A/P,io,n) + Li"
an
}0,
tean 75, te-
This equation, which involves the use pf the capital recovery factor, obviously is independent of the depreciat(on accounts. In some economy studies that use the method of annual costs, various
168
are ftgures are used' The figures and interest lrgures combinations of depreciation r - r-t^-^-+ ;" intended to serve the same purpose o interest
OF PROPOSED INVESTMENTS JUDGING THE ATTRACTIVENESS
Ch' 10
ch. 10 tion charge. If
the manner depreciation first year to
il;ffi;;;""iutio"
,om"ti-", 1.
Plus
:"J:1,:'"ffili":::i:'H#F;';;;;; follows:
are used are as
that l":::i*:"-retum methods rhree
g. Slt;tght fine dJpreciation plus average interest results in some cases and misleading These methods give satisfactory results in others' on First Cost' This is a Sinking-Fund Depreciation-Plus.lnterest the same annual cost of ;"thod that - gives correct compound t"i;;"" intert""tnld provided the assumed capital recovery "' ";;^;;;;irt*r minimum attractive stipulated esl rate on the sinkin! f;;;;q"al.to.the plus i' '"r"tt"a to as interest ii" il"*'"a rate of return. S"#'i'";' "*,}'XXli:;"ed factor 'is alwavs equal in chapter 4,. thJ capital recovery way of plus the- interest rate. An alternate to the sinking f"od'-i;;i;, rate i is therefJ' lupituf recovery at interest writing our basic "n;;; fore:
;' ;i;';dii. lil
interest on ffrst cost Sinking-fund depreciation plus
on a"f,""i"tio" ilus interest first cost
depreciationPlc This annuitY times referred b
same root as applied to tbe
particularly If the intrt interest rate m method obvioudY
calculation ufi6
rate is used to sinking fund will then apIE r
tiinHngitd lnbrrrto Totrl
+ cR = (p - L )(A /F ,i o ,,r ) ( P L) :ft"!
+ "1( A/F,io,n) pio
Som Pru. Plr hbrtc
io cry
Gooooary l|rlfu rAtfil|ff
depreciation plus interest on In efiect, the method of sinking-fund example will help htt", fori.rla.- A n^rrmerical first cost is based ;ffi; this method and the conventional to show the relationship between. an estimated in assetwith " fi"i cost of $22'000' method. Let us """*" We shall use "ui*"t"a 'ulu"g" value of $2'000' life of l0 years, "J';; of iog' By the conventional method a minimum attractiie?tl" oi-'"t""' that is used throughout this book: + $2'000(0'10) Qft= ($22,000 $2,000)(A/P'IM'10) -
cb--
rbd
fil
= + +'$2'000(0'10)$3'255 $200 $3'455 '16275) = $eo,ooo(0
-"tnoa u"l*":ililf, l;: ffii;tt;" .;; in"identical ::":il-:1*'*nidepreciation as result, follows: an #;';;ri-r""*,!,
;iiJffi,];
tl:333 = ll^--ll1/i 'i*'nl- $20'o0o(o'062tu' depreciation. Sinkins-fund = 2,200 Pi = $22,000(0'10)
l^'ii*i-""ii i;#t",=;, return with recovery a 107o cost annual of capital Total
= $3,455
Assumingthe use of a !0% interest.,rat" 1" .:?-:n-"rtt:*,::::::,ti;:
for so-called sinking-fund depreciaIt should be noted that the ffgure full "upry'l recovery cg.t 'is not the tion in the foregoing ;i"t't*tio"*ot if the sinking-fund ir," uootr depreciationcharge .d,;;il;J^H-i" the depreciaii i, *"r"ty the onnuitg portion of method shourd u" ,rr"J,
ch. 10
DEPRECIATION AND ENGINEERING ECONOMY
169
tion charge. If we should calculate year-by-year depreciation charges in the manner illustrated in Table lG-2, we would see that the sinking-fund depreciation charge for our $22,000 asset would vary from $1,255 in the first year to $2,959 in the l0th year; in our calculation of sinking-fund depreciation plus interest on -first cost, only the $1,255 ffgure was used. This annuity portion of the sinking-fund depreciatio4 charge is sometimes referred to as amortizationo (The verb qmortize comes from the "to same root as mortal and literally means make dead or destroy." It is applied to the provision for extinguishment of a debt or other obligation, particularly through periodic payments into a sinking fund. ) If the interest rate used on the amortization fund differs from the interest rate on first cost, the capital recovery cost obtained by this method obviously will differ from the one obtained by a conventional calculation using only one interest rate. For example, assume that a l0% rate is used to compute interest on ffrst rcost and a 3% rate is used in the sinking fund calculation. The capital recovery cost for our $22,000 asset will then appear to be: Sinking-fund = depreciation ($22,000 $2,000XA/F,gyo,1Ot = $20,000(0.08723) = $1,745 - 2,200 Interest first cost = $22,000(0.10) on Total = $3,945
SomePros and Conson the Methodof Sinking-Fund Depreciation Plus Intereston First Cost. Although this method not beencommon has
in economy studies in competitive industry, it has been widely used in economy studies for regulated public utilities and for governments.In such studiesit is usual to assumethe sameinterest rate on ffrst cost and on the sinking fund. Where used in this manner with a single interest rate, the method gives exactly the same annual cost figure as the method employing the capital recovery factor, which is used throughout this book. The choice between these two methodsof computing annual cost must therefore be based on other grounds than the correctnessof the results given by the two methods. If sinking-fund depreciation accounting were actually to be used in the accounts,the use in economy studies of sinking-fund depreciation plus interest on ffrst cost would serve the purpose of helping to reconcile economystudieswith the accountsof the enterprise. But this method of depreciation accounting,once used by a few regulated public utilities, has largely been abandoned.This method is subject to the objection that it gives an unrealistically high proportion of the total write ofi in the ffnal -''' years of the life of an asset.
0For some'reasonthis word is often mispronounced. The correct division into sylIables is a-mor-ti-za-tion, with the second and fourth syllables accented. The common nrispronunciation assumesthe ffrst syllable is am and accents the am.
17O
INVESTMENTSCh. 10 OF THE ATTRACTIVENESS PROPOSED JUDGING
ch. 10
Or sinking-fund depreciation plus interest on first cost might tie an economy study to the ffnancial policies of an enterprise if an actual sinking fund were to be established to recover an investment ( less salvage, if any) in a fixed asset at the end of its life. But such sinking funds are rarely used. In most cases, therefore, this method should be viewed as a compound interest conversion unrelated to the accounts or to the establishment of any actual fund. Viewed in this way, the method of sinking-fund depreciation plus interest on first cost does not seem to the authors to have any advantage over the conventional method of computing the annual cost of capital recovery with a return illustrated throughout this book. Often the method using sinking-fund depreciation is harder to explain than the conventional method because critics may make such comments "We "There are not actually using will be no actual sinking fund" or as this method of depreciation accounting." It is hard to give a satisfactory answer to these comments. Valid objections may be raised to this method where two interest rates are used. A discussion of these obiections follows the explanation of the method of straight-line depreciation plus interest on ffrst cost because this latter method is really a special case of the analysis using two interest rates.
Objection to
We have computed recovery with a l0l
ment, The conventid us a figure of $3,451 depreciation plus l0I tion plus l0% interest of $3,945. And us $4,200. The usual objectitc omy study is to iudgo yield at leasta m assetis $22,000 duced disbursements) plus the final $2,000 S22.000investment If we should
annual Capital recoveqf clusion that the asset
should compare the
the incorrect because it would not
Depreciation PlusIntereston First Gost. If thismethod StraighhLine asset would be were used,the annualcapitalrecoverycostof our $22,000 as computed followsr
depreciation Straight-line
The reader may conclusionsobtainablc by the Hoskold sinking fund bearing r
calculation using two same one that we method.
=-=--
$22,000-
$2,000
$20,000 =-i-
=$2,000
2,200 = $4,200
Interest first cost = Pi* = $22,000(0.10) on Total
Except in the special case of a salvagevalue of 100%(or more), this method invariably gives too high a figure for equivalent annual cost. The $4,200 a year that the method indicates is needed to recover our return is in fact sufficient to permit proposed$22,000 investmentwith a 10% recovery with a return of about 14.5%. It has been pointed out that the straight-line method of depreciation accountingmay be thought of as a limiting caseof the sinking-fund method in which the interest rate on the sinking fund has been assumedto be 0%. Similarly, straightJine depreciation plus interest on ftrst cost may be viewed as a special case of sinking-funjlePreciation plus interest on first cost in which the sinking-fund interesf rate is 0%.
Consider the $3,800 annual receipfr of 3% depreciation and proposed $22,000 flow that it will cause
on our investment.
it at 3% and (with tf,c back at the end of permit us to do this, less than 10%." The error here b asset,are to bG $22,000 of.tuo investments,6c asset,yielding IZ.L\
DEPRECIATIONAND ENGINEERII,IGECONOMY
171
objection to Annual cost calculations using Two Interest Rates.
we have computed three different figures for the annual cost of capital recovery with a l0% return for our proposed $22,000investment in equipment. The conventional method using the capital recovery factor gave us a ffgure of $3,455;this same figure was obtained with 10%sinking-fund depreciation plus 10%interest on ffrst cost. But 3%sinking-fund depreciation plus l0% interest on ffrst cost gave us an annual capital recovery cost of $3,945. And straight-line depreciation plus interest on ftrst cost gave us $4,200. The usual objective of comparing equivalent annual costs in an eco...