Capital Investment Analysis for Engineering and Management 3rd Edition [3 ed.] 013143408X, 2004050537

Citation preview

'

\

' 'f ,·

I V

Tliird Edition

I

I I

/;. H ,

',

1

.r. o..111

----

i .1 ; 'I

. !l. C

j,I• 'I

rI . ..

( .CAPITAL : INVESTMENT ANALVsis FOR . ING ENGINEER AND--MANAGEMENT

·•

1, 1

't

I

- -

,

\..-'

,·

. ,.

'

.,

l II

.

I ,

1, \

. ...\

• I

. '•·

,"f

·.t

ff , ~~;: I/

' '

'

L

I

(; I (

' •!

' '

:

J-1..'

,

,

.,

, \

r ,

1

,'. i

I

:~

. f

l

. i

I

I

I

I / ..

. ;i

J

,

./ ), 1

JOHN R. CANADA / . WILLIAM G. SULLIVAN. / DENNIS J. KULONoJ· / JOHN A. WHITE / ,I I

/.

·,'

.

t

GLOSSA RY OF COMMO NLY o SYMBO LS AND ABBREV IATUSE IONs A$

ABC AC AHP

ANCF APV (or APW)

ATCF1 AW

H

/3 8 /C BOY BTCF(

BV1 Capex CE(= CME) CF

Cl CR C.R.

ch

d7 DB

El ·l e,,

E, EMY EOY

ERR EUAC EVA f FCF

FW C

Actual (innated. current ) dollars Acti vity-based cm.ting Annual cost ( method. or equivalent ) Analytic hierarchy process Annual net ca~h now Adjusted present value ( or worth l After-tax cash fl ow fo r period I... Annual worth (method. or equi valent ) Cost basis (for depreciatio n) Cost exponent factor (fur exponenti·•il ,-~ 0 ~ t·mg model) .

Benefil-co st ratio Beginning of year Before-tax cash flow for period /.: Book value at end of year /.: Capital ex penditures Certainty equivalent (= certain monetary equivalent) Cash flo w Consistenc y index (for AHP ) Capital recovery cost Consistenc y ratio (for AHP) Depreciatio n charge for year /.: Depreciation charges through year k Declining balance method of depreciatio n Expected value of I·I Equity financing cost rate Expenses (cash o utflows) for peri od k Expected monetary value End of year External rate of return Equivalent uni form annual cost (= AC) Economic value added Inflation rate Free cash flow Future worth (method, or e4uiva lent) Uniform period-by- period increase or decrease in amount Effective interest rate per interest period

Borrowed (debt) financing cost rate . h ·nnation included) C bined or nominal. intere!>t rate l wit I , • (witho ut inflation included) om . Real interest ra c . fl· . for period k to period n) Investment Index of price change (== /,/h) (m auon

i" i, i,

0

I,

IRR j

'),("Lamda" ) M MACRS MARR MIRR MY

h eriod ( eometric sen es) Internal rate of retun~ ., Percentage increase m amount ~ac . p Fraction of debt in total capitahzau on Number of compound ing periods per year Modified accelerated cost recovery system Minimum attractive rate of return Modified internal rate of return . . Market value (also called salvage value. 5 ) Number of compound ing periods (also. depreciabl e hfe)

N

MACRS property class Net cash flow Net operating profit after taxes NOPAT present value (or worth) NPV (or NPW) Net Probabi Iity of {·) Pr[· I Present worth (method. or equivalent ) PW Present worth-cos t (method, or equivalent ) PW-C Nominal interest rate per year(= annual percentag e rate)

N' NCF

r

Rk R$

RN RND RR

s (j

SL

TCk Tl U[·I V[·I

WACC WC

Revenues (cash inflows) for period k Real (uninflated , constant worth) dollars Random number Random normal deviate Rate of return Number of standard deviations (for standardiz ed normal · distributio n) Population (or estimated) standard deviation Straight-li ne method of depreciati on Effective (or marginal) income tax rate Tota\ (marginal) cost for year k Taxable income Utility of(· l Variance of(· l Weighted average cost of capital Working capital

PRE NTIC E HAL L INT ERN ATI ONA L IN IND UST RIA L AND SYS TEM S ENG l!~~ IEs W. J. Fabr ycky and J H Mize Ed·t RING · • • 1 ors ~\MOS ,.\ND SARt lllff • Mo11age111ent for £11gi neen

THIRD EDITION

AMRINI!.. RITCl·l l:Y. M OODIE , AND KM EC • Manu factur ing Orga ni· t · . I SaJet)' ,r. an d ASl',~IIL • l 11tf11llrw ~ ton and M Hea It II Mana gemen t. 5/E anagerne,. 8.\IJCOCI- • Mu1111ging Engin eering and Techn o logy. 3/E

'· 6/f:

8 AOIRU • £.,·,,ut System s Applic ations in Engin eering and Manu factur ing 8AN"- S (ARSO N NELSO N AND NICOL •

D isc rete-E vent System Simul ation

8 L,\NCl lr\RD • Logist ics Engin eering and Mana gemen t, 6/E

E

41

B LANCHARD AND FABRYC KY • System s Engin eering B t!SSH AND EsCHE NBAC H • The Econo mics

and Analy sis. 2/E Analy sis of Indus trial Projec ts . 2/E Bl l'Z..\COTT AN D SHANT HIKUM AR • Stoch ast ic Mode ls of Manu factur ing Svste C.-\t-A DA AND SULLI VAN • Econo mics and . ms Multi -Attrib ute Emlua tion of Ad,,an ced Mo1111fac111ring System s C .\NADA S ULLIV AN AND WHIT E• Capit al ln 11estm ent Analy sis for Engin eering and Mana gemen

t 2e

CHAN G Afl;D WYSK • An Introd uction to Autom ated Proce ss Plann ing CHAN G. WYSK , AND WANG • Comp uter Aided Manu factur ing

EBERTS • User Interfa ce Desig n

ELsAYEO AND BOUC HER • Analy sis and Contr ol f.\_BRY CKY AND B LANCH ARD• Ufe-C ycle

System s

2/E

of Produ ction S_vsrem s. 21£ Cost and Econo mic Analy sis fABRY CKY AND THuES EN• Econo mic Decis ion Analy sis, 3/E FlSHW lCK • Simula tion Model Desig n and Execu tion: Buildi ng Digita l World s FltANCIS. MCGIN NIS, AND WHIT E• Facili ty Layou t and Locat ion : An Analytic al Appro ach, 2/f. GIBSON • Modern Mana gemen t of the HighTechn ology Enter prise GRAED EL AND ALLEN BY • Indust rial Ecolo gy. 2/E HALL • Q11euing Metlw ds: For Sen•ic es nnd Manu factur in g H AMME R • Occup ationa l Safety Mana gemen t and Engin eering , 5/E H UTCHI NSON • An Integr ated Appro ach to Logis tics Mana gem ent IGNlZJ O AND CAVA LIER• Unear Progr ammin g KROEM ER . KROEM ER. AND KROE MER-E LBERT • Ergnn omics : How ro Desig n for Ease and Efficie11cy2/E K USIAK • lntel/igenr Manuf acturi ng System s . LANDE RS. BRO WN. FANT, MALST ROM , AND S C HMIT T• Electm nics Manu factur mg Process es LEE.'11 S • Reliab ility: Proba balisti c Model s and Statist ical Metho ds MUND ER AND DANN ER• Motio n and Time Study: Impro ving Produ ctivity. 71£ OSTW ALD• Engine ering Cost Estima ting, 3/E PINEDO• Scheduling: Theor y. Algor ithms. arid System s 2/E Put.AT • Fundamenta ls of Indust rial Ergon omics S KTUB. B ARD. AND GLOB ERSON • Project Mana gem ent: Engin eering Techn o logy a nd Implementatio n TAHA • Simulation Model ing and SIMN ET THUES EN AND FABRY CKY • Engin eering Econo my, 9/£ T tmNER . MIZE. CASE. AND NAZEM ETZ • Jnrrod 11ction to lnd11st rial and System s Engineering , 3/E WOLF F• S1ocl1a stic Modeling and the Theor y of Q11e11e s

Ca pi ta l Investment An al ys is for Engineering an d M an ag em en t John R. Cana da Norrh Carolina State University, Emeritlls

Willi am G. Sulli van Virginia Polyrechnic Institute and State University, Emerit us The University of Tennessee, Adjunct

Den nis J. Kulo nda Florida lnstitwe of Technology

John A. Whit e University of Arlwnsas

---PEAR SON

Prent ice Hall

Uppe r Sadd le River, NJ 07458

Library or Congress Cataloging-in-Publication Data

TABLE OF CONTENTS

· C Canada. John R. Capiial im·es~nt analysis for engineering and management / John R. anada. Wilham G. Sullivan. Dennis J. Kulooda. - [3rd cd.l .

p. cm.

.

Includes bibliographical references and index. . r. . . ISBN 0-13-143408-X I. Capital im'CSlmCD15-E>-aluauon. I. Sullivan, '>'llham G., 1942- 11. Kulonda. Dennis J. rn Title. HG4028.C4C3 2~ 658.15'242--0O th . be w h . e,rayment offixed ' ere n on w_h1le if production ca aci . expenses, and continued production Ill!) actual choices that should b p ty exists and no other alternative is available " · I e made m a d · · · •• va ue of M, but al so upon th d . ecJSJon situation depend upon not onlylhc e un erlymg si tuation and the range of alternatives Example 2-2 · April was an es . wh pec,ally busy month i N k at as the economy has deer ed S or u em Company. buJ business has tapered off somc0rder for 5,000 of a special •~ · alesman Herb Tarlock has arrived on the scene with ane-, tomer will furni sh the mat p\ uct D for rapid turnaround al a price of $ 5 00 each The cus· $ 10.17 per hour. The cost ena · La_ bor is eSlimated at 20 hours per hundred·. The labor rate u 163% of labor cost to co acbcounring depanmcnl has developed an overhead costing ra1eof Should Nukem accept thever oth fi xed and van·abl e overhead for the Heal Treat DepanmenL order? Solution Th $2 e labor cost for th e product Dis 20 hrs per hundred x $10 /7 perhoUr' . ·03 each. With a costin ,s $S.34 each. The account ratedof 163%, rhe overhead cosr is $3.31 per unit and the 10tal co~

ence of mm · d lo speak withng M'kepanmen1 wanrs to send poor Herb ro Siberia but has the prel· I e Jones first M 'k nance · out thar only supplies and main · Ieb . accou nrs (38.2% and '11 . • 1 e pomrs 36 fi usmess, as orher overhead .6 o vanable rates, respectively) would apply to the increment~ xrures needed· These dara ssuwould remain th e same. There would be $2 500 worth of spec1..~, . ggest incremental overhead cosrs per unit ~f Sup_ plies 38.2% x $2 .03 M amrenance 36.6% x $2.03 Special fixrures $2500 / 5000

=$0.775 0.742 = 0.50

Total incre and M = $5 00 mental Overhead/Unit = $ 2.0/ · -0-2.0J- 2 full y lo buy Herb a steak dinner -0l = $0.97, resulrin g in a dec,smn .. ro accept the conrracr and hope· •

•

2.7 Purposes of C Ost Accounf Staning with th . . rng-A Recapitulation e ongms of cost accounting • f cosr accounting we have identified 1 terns The '" ormation and three co ' d. three distinct uses for . se purposes are i rrespon mg purposes for cosr ace . S· Inventory valua . n_venrory valuation, cost managemem and ounrmg sy !ency is maintained b lion IS the leasr demanding reguiremen;_As roducr cos!Jng. in-process invenro etween the yardstick used ro measure costs flow~~g _as consis· inventories. and asi and 1he valuations of fini shed irems flowing into fin!s~r~ work· sonab/e allocations ong as all invenroriable costs are captured in the sysrem ean~OOds are made, lhis purpose is served. rea.

Sec. 2.7

Purposes of Cost Accounting-A Recapitulation

47

• th. · formation to manage costs can evolve into an elaborate system of Usmg 1s m • · h f res nsibility accounting and complex variance analysis that pmpomts I e source o pod · · n between budgeted costs and actual costs to operate the enterpnse, or any ev1a· 110 f ·1 There are two difficulties . . · th at the which must be overcome. one 1s any portion ·gn o '.must be quite elaborate. It is most effecuve . •,f respons1·b·1· 1 11y center system des, ·bT reports include and measure only those costs that are controllable at that respons1 1 1ty level. While responsibility for cost management hes at all levels wnhin the workforce, there needs to be a definition of boundaries that enables the foreman to commurucate relevant. timely, and accurate information to his manager and vice versa. It make~ no sense and serves no purpose for a department foreman to wrestle with a variance a machine depreciation overhead account, for example. Furthermore, a hi gh spend mg variance may force a foreman to dig through transactions to search fo r errors that might have gi_ven rise to an unfavorable variance that he must explai n to his manager. Finally, the most important shoncoming is that these systems all focus on after-thefact reporting. Managers are forced to explain history but with no specific tools to pre-

m

vent recurrence. This is one result of developing the cost control system as a by-product of the standard costing system. In contrast, systems designed expressly for cost management might base seiected control on cost reduction targets on the basis of observable physical changes. rather than abstract dollar amounts. Final_iy, cost accounting information often provides misleading information for product costing. Pricing studies. product profitabili ty studies, and spec ial anal yses (e.g., make vs. buy studies) are clouded by simplistic overhead assignment and allocations, which do not reflect the realities of cash flow. For this reason, many companies have begun to look for more sophisticated systems. There is often a drive to make the same system serve all three purposes. As Kaplan I explains, such a goal may miss the point, which is simply to perform all three functions well. Attempts to develop more sophisticated systems to overcome the deficiencies of cost accounting, panicularly in the area of product costing, are explained briefly next. They include multi base allocation systems and activity-based costing. Multibase Costing Systems

So far, we have described a simple cost accounting model in which costs are c~llected by cost category (overhead account) and by cost center. Some allocation ; en takes place to obtain cost center allocations for costs that are shared plantwide. tho; :xarnple, the heating and lighting charges may be allocated to each cost center on heat ~•s of the square footage it occupies. This may be inaccurate. For example, the ing t::~ng department probably receives a higher than justifiable allocation accordTher e square footage scheme, but few precise scientific alternatives are available. · hourse are other exampl es: Mamtenance costs may be allocated based on machine • power charges based upon connected wattages. pl ant management sa laries February' Kaplan, "One-6Cos, 1988) pp. . 61

6

Syste1n Isn,I Enough ... Han,ard 811smess . Reviell',

vol 66. no. I (January-

48

Cost Measurement and the Cost Accounting System

Chap. 2

based on volume of production, etc. Once all indirect costs are assigned to a cost center. lhe next task is to assign them 10 products passing through that center. This is a second stage allocation. In our simple costing model developed earlier, we allocated costs to products based upon their direct labor hours . In fact, accuracy might improve by using several bases and allocating costs on the basis of their best fit with a particular base to assign costs 10 products. For example, supervision costs may be assigned 10 products on the basis of their direct labor content; maintenance costs, on the basis of their machine hour content; material handling costs, on the basis of their weight; or material handling costs, on the basis of material costs or unit loads. These elaborate approaches anempt to remedy the shortco mings of their simpler counterparts by improving the precision with which cost assignments to products are made. The notion of flexibility in methods has great appeal as the cost of number crunching continues to decline in this digital era. A further refinement, Activity Based Costing, has emerged and is the subject of Chapter J 8. It provides for not only multiple bases. but also multiple drivers to further enhance lhe realism of standard cost information.

Chap. 2

49

Problems

REFERENCES Homgren. Charles T. . Srekant M. Datar, and George Foster. Cosr Accounting, a Managerial Emphasis. Upper Saddle River. NJ : Prentice Hall. 2003. Kaplan, Robert S. "One Cost System lsn't Enough." Harvard Business Review 66. no. t (JanuaryFebruary I 988): 6 H i6. o51 wald, Philip F. Eng ineering Cost Estimating, 3rd Edition. Englewood Cliffs, NJ : Prentice Hall, 1992. PROBLEMS 2-1. (Adapted, Ostwald) Nofziger Tool is developing their costing rates for the next budget

year. Develop vanable overhead and absorption costi ng overhead rates on the basis of direct labor dollars for the following production levels:

Labor costs

Number of units Variable overhead cost

Fixed overhead costs

2.8 Relevant Cost s in Economic Analyses

The focu s of this book is upon concepts and methods for the analysis of the economic consequences of decisions involving choices between two or more alternative means to create value. We use cost to measure the value of resources sacrificed or consumed in the process. For economic analyses, we should be concerned with the marginal costs of using resources for any alternative under consideration. What actually constitutes the appropriate margi nal cost depends on both the scale and timing of the alternative. To make valid comparisons, marginal costs must be

• incremental with respect to the decision at hand, • relevant to the decision, • incurred in the fu ture as a result of the decision, • a cash cost resulting from the decision, or • an opportunity foregone because of the decision. This defi nition avoids unquestioning use of nonnal accounting information such as book values and standard costs and focuses on the change in the value of assets affected by a parucular action or decision. Chapter 3 elaborates and ex tends these pri nci ples to deve lop examples of appropriate and inappropriate uses of cost in fonnation. It also explores approaches for esumatmg the future costs that are relevant to a decision. The basis for estimating may incl ude information from the accounting systems of a company or external sources of informati on or both.

80%

100%

125%

$100,000 20,000 $60,000 $120.000

S125.000 25,000 S75.000 $120.000

St56,250 31.250 S93,750 $120.000

Production load

If l00% load is the best estimate of next year's volume. what costing rate should Nofzi ger use? Why? 2-2. (Adapted, Ostwald) An assembly area has floor space allocation as fo llows: Drop area Conveyor I Conveyor 2 Bench area

Total

300 100 ISO 800 1,350 square feet

Building service ove rhead costs are $ 8,000 fo r thts . area. Determine the overhead allocat" . ton ratio and overhead costs for each assembly production center. 2-3. (Adapted Ostwald) A · composed of four cost centers. Each month a budget is ' . company is . . . of certain costs. The company expects to prepared antt cipati ng th e pri· mary d1stnbut1on . 1.s reflected in the proJ·ected d. operate at 11 5% of budget vo 1ume .m March. and this trect 1abor hours.

-

Cosrcenter

Forging

--Machining

Finishing

Packi ng

Total

March, 2006 Direct Labor Hours (DLH)

Floor Space Square Feet

Nomtal

Nom1al

Maintenance

Kilowatt Hours

3,580

S.000

$13.000

8,300

10,032

20.000

$23.500

43.000

S,460

4.000

S 3.450

3.0S0

2,133

2,100

s

21.205

31,100

500

2.000

S40.4S0

56.350

Cost Measurement and the Cost Accounting System

50

Chap. 2

The referenced overhead ite ms are li sted at their nonnal ( I00'7c budget volume) levels Maintenance and energy consumption are treated i,1 the budget as purely variabl~ expenses. Suppose that the nonnal power bill is S 17.800 and nonnal building servi ces cost is $67.000. {a) Develop the March budget allowances for each cost center. {b) Develop the budgeted overhead costing rate for each cost center and a blanket overhead costing rate for the entire company. 2-4. (Ada pted. Ostwald ) Referring to Problem 2- 3, assume that a job is routed through Machining and Finishing. Machining is heavil) mechanized. with costly numerical control and other automatic equipment. Finishing has only a few simple tools. Obviously, overhead costs are hi gh in Machining and low in Finishing . Job l takes I labor hour in Macbining and IO hours in Finishing. Job 2 takes 9 labor hours in Machining and only 2 in Finishing. If a single blanket rate based on labor hours is applied to both jobs, then the overhead allocation would be the same in both cases ( I I hours for each job). What follows illustrates the previous discussion : Determine the overhead costs for jobs I and 2 by using department rates. Compare those with the overhead costs that would be computed using blanket rates. Discuss the importance of selecting the cor-

3

Relevant Costs and Revenues and Estimating

rect base.

2-5. (Adapted. Ostwald) Management is auempting to mai ntain an overhead rate of 175% for an assembled product. The .. problem" area is the machining process. Here, the overhead rate is 225% on the basis of $23,000 direct labor. Total direct dollars, excluding machining. is $89,000. Overhead charges. excluding machining, are $150.000. What overhead rate will the company achieve on the basis of this information? Use direct labor dollars as a base . 2-6. The machining center at Mills Corp. generates 400,000 direct labor hours annually and incurs tool maintenance costs of $800.000 annually. Part A 123 is broached at a standard rate of 0.4 direct labor hours per hundred parts. Overhead is simply assigned based on direct tabor hours . An industrial engineer recommends that the tool maintenance expenditures be allocated by machine group before assigning them to products. His studies show that broaching incurs 20% of the tooling maintenance expenditures and generates 20.000 of the direct labor hours. How will the overhead rate and product cost of A 123 change if the engineer's recommendations are followed? 2-7. In Example 2- I. Mike Jones plans to staff with 27 operators. If he produces exactly the April schedule, will he meet his direct labor budget? Should his direct labor budget allowance be based on that staff plan? Should his overhead budget allowances be based on that staff plan?

This chapter extends the cost c o ncepts in Cha pte r 2 and introduces numerous tec hniques useful in estimating for economic a na lyses.

3.1 Cost Concepts The word cos1 has many meanings in ma ny diffe re nt settings. The kinds of cost concepts that shou ld be used depe nd on the decision proble m at hand. There are two facets to estima ting fo r econo mic ana lyses: ( I ) determining the :propnate quantity lo estimate, a nd (2) making the estima te itself. Most estimates to made are costs and re venues (negati ve costs). For economic analyses, the a nal ys t sho uld be concerned with the marginal co st s·of using resources for the a lte rna ti ve. Wha t actua lly constitutes the a ppropri ate ;argrnal cost depends on both the scale a nd timing o f the a llerna ti ve. To de te rmine ts quantity, the term ·'cost" sho uld be de fin ed as fo llows: th The co, i of a reso urce is the decrease in wealth that res ul ts from commi11i ng is resource to a particulara lternati ve; that is. before any of the benefits of the alternative are calculated. · · · s unques ti o ning use o f norma l acco untrng · ·JO t·ormauo . n such This defirnttton av01d · the change mt · he v,1· Iue of as as book va Iues and one-ti· me costs a nd foc uses o n what 1s · llowmg · sccu·on d 1scusse, · rna · sets effected bYa paru·c ul ar actio n o r d ecisio n. The lo 0 · · ble 111 · ec 1 r cost . cone epts and issues useful fo r determ ining the ma rg ·ma l costs app 1tea 000 rruc analyses . 51

Relevant Costs and Revenues and Estimating

52

Chap. 3

3.1.1 Past Versus Future Costs Costs and other financial events that previously have occurred or have been presumed are tabulated and summarized within the accounting function of an organization. Past costs can be no more than a guide or source of information for the prediction of future costs. Specifically, the analyst should resist the temptation to rely unquestioningly on what may be described as the "actual cost" data from the accounting function . Even if the data are accurate, they will be at best recorded historical costs for similar circumstances. Future costs often differ significantly from the costs of similar activities in the past. The analyst should be prepared to adjust past costs to ~eflect probable changes by the time a proposed alternative is to be implemented, talcing mto ac~ount changes both in the prices of the resources and in the amount of each to be reqmred. Pnces of resources can be affected by innumerable factors such as chmate, geography, and labor regulations. . . . . In economic analyses, one is concerned with proJectmg what 1s expected to · the future as a result of alternative courses of acuon. Past costs often_serve h appen m d be be ed that the v1ewpomts of as a useful guide for such projections. It shoul remem r . . the accountant and of the economic analyst are generally very oppos1te--one is an historian and the other is a fortuneteller.

3.1.2 Joint Costs One of the difficulties in using accounting records is that some of the costs may

be recorded in a single category even though they are, in fact, joint (orcommo~) co;is for many different activities. This may be true for labor and material as :e t a\e~~ overhead cost items. These joint costs are often allocated to different pro uc s, vices, or projects by using more or less arbitrary formulas . al . t rested Any such formula should be scrutinized most carefully by the an Yst m e e in determining true marginal costs, that is, in the predictio~ of how to:! cos~: %r affected by the alternatives under consideration. To determine apphca e ~:salterany alternative, the analyst must both trace out each of the costs umque to . being native and determine the portion of joint costs that _is due to the alternat;::eadily examined. It is likely that the results will be very different from cost da available from the accounting function .

3 _1_ 3 Usual Accounting Classification of Production Costs

. . f nterprise keeps As described in Chapters I and 2, the accounung fun~t1on o an e ·n records of fh nings affecting the finances of the enterpnse. Accounu g records _o appe ormally are separated into three main categones: producuon costs n

1. direct labor, 2 _ direct material, and 3. overhead.

Sec. 3.1

Cost Concepts

53

Direct labor costs or direct materials costs are those la bor or materials costs that can be conveniently and economicall y charged to products or jobs on which the costs are incurred. By contrast, indirect labor cost and indirect materials cost are those costs that cannot be conveniently and economically charged to particular products or jobs on which the costs are incurred. Indirect labor and indirect material costs are part of the third category, overhead costs, which includes all production costs other than the costs of direct labor and direct material. Examples of other types of overhead costs are power, maintenance, depreciation, insurance, etc. O verhead costs are often referred to as "indirect costs" or "burden." 3.1.4 Fixed and Incremental Costs Fixed and incremental (also called variable or ma rginal) costs can best be defined with respect to changes in the alternatives (e.g ., equipment, methods, production levels, etc.) under consideration. As the names imply, fix ed costs re main constant, and incremental costs change (increment or vary) with respect to the change(s) under consideration. . O~e classical application of fixed and incremental (variable ) cost concepts is in cons1denng the effect of differing levels of production or facility utilization on total production cost. For example, space and equipment costs are often considered fixed com, while direct labor and direct material are often considered variable costs of producnon Such t · · · ca egonzat1ons are made difficult because no cost is fixed for a ll time. What may be ·d d r· . . cons1 ere 1xed over o ne penod may be a variable cost for another penod Th d'1 · · · e _stmct1on between fi xed and variable costs depends on the decision at hand and the time h · I . need. onzon re evant to them and should be reexamined for each analysis 0 tr costs / illuS ate th e problem, suppose a contractor has a backhoe for which the total macbi_or yedarl are the sum of depreciation, fuel , insurance, and operator wages If the ne 1s I e duri th h · . ng e year, t en the fuel and wages are the only variable (marginal) costs, smce the de · · · regardless of how preciauon a_n d msurance are fixed for that period of time slack periods on much the backhoe is used. Neglecting the effect of pricing during nd decision m k phnces a buSmess that can be obtained during other periods the a er s ould b ·1r ' greater tha th e wi mg to sell the services of the backhoe for any price n e cost of fuel d Yearly rental th an wages. If, however, the contractor were offered a on e machin · th • anct wages h h e at a pnce at essentially covered only the cost of fue l I • es ou dnotacce t F 1 should also 1·n I d P · or examp e, the relevant marginal costs over a year c u e the ins . . . not to be used f th . urance costs that could be elunmated 1f the backhoe were h or atumeO 1 s ould be cons1·d d . . ver an even onger term, even the depreciation expenses h ere var1able · th oe. This exampJ .11 smce e contractor may choose not to buy a new backth e I ustrates th I · · at may be cons1·d d e genera pnnc1ple that the proportion o f tota l costs c · ere Variabl d · ons1deration increases. e ecreases as the penod of time for the decision unde r lf one is maki :~:taJ (marginal) ~s~n ne;;;omic analysis of~ proposed cha nge, on ly the incre een alternatives need b be con sidered, s mce o nl y prospecti ve d ifferences e taken mto account.

54

Relevant Costs and Revenues and Estimating

Chap. 3

3. 1 .5 Long- and Short-Run Costs If an alternative system entails use of otherwise idle capacity, then the immediate opportunity costs and marginal costs will be low compared to the average costs. If, howe ver, the system is already operating near capacity , the opportunity ~osts of additional output are likely to be high compared to the average costs. In either case, the long-run marginal costs will tend to be less ~xtreme than_ the short-run marginal costs and will tend to somewhat approach, but not necessanly equal, the average costs. • h 1 · t d Long-run marginal costs also depend on the changes 1~ tee no ogy assoc1a e with shifts in level of production. In many industnes,_ marginal costs_decrease with increasing production over time as more efficient fac1lmes are_placed into operat10n. ln many other industries, both the long-run and short-run marginal costs may increase with increasing output as added resources become more scarce. _ _ _ Determination of long-run marginal costs rests on an adequate 1denuficat1on of the opportunities that will appear and disappear in the futu_re. Although some industries may have been characterized by particular cost trends in the past, these may well not apply in any particular situation projected into the future . Indeed, past trends may well be reversed by future events.

3.1.6 Opportunity Costs An opportunity (or alternative) cost is the value of that which is forego ne (prior to the calculation of any benefits) because limited resources are used in a particular alternative, thereby causing one to give up the opportunity or chance to use the resources for other possible income-producing or expense-reducing alternatives. It is the same as the shadow price of a resource in classical economics. The opportunity cost is the usual appropriate measure of the marginal cost of a resource for economic analyses of alternatives. While it can be equal to the price paid for a resource. it is often very different from that actual outlay . Indeed, the use of a resource normally entails an opportunity cost even if the resource were obtai ned without cost. As an example, suppose a particular project involves the use of firm-owned warehouse space that is presently vacant. The cost for the space that sho uld be charged to the project in question should be the income or savings that the best perceived alternative use of the space would bring to the firm . Thi s may be much more or much less than the average cost of the space that might be obtained from account· ing records. The opportunity cost of a resource is often fairly nebulous and hard to estimate. It may be the sacrifice of future earnings rather than present cash. In the most general sense, the cost of using a resource on one project is the cost of not having it availabl~ for the best alternative, whether that alternative is to sell the resource or to invest it productively in some other alternative that will bring future benefits. Extending the warehouse example, for instance, the opportunity cost of the space could be related 10 either the cash value that could be obtained from the outright sale of the space or th e value associated with some other productive use of the space over time.

Sec. 3_1

Cost Concepts

55

rn estimating opportunity costs. it is useful to distinguish between resources chat can be identically replaced, such _as loads of sand or pieces of steel,_ and those that are somehow unique, such as a specifi c piece of real estate. For 1dent1cally replaceable resources. for which there is a ready market, the opporturnty cost for the resource is merely the market cost of the replacement or, eq uivalently , the salvage price of the resource if it is already possessed and will no t be repl aced . For a resource that is somehow irreplaceable. the opportunity cost for the resource can be estimated as the cost of replacing the unique resource with the least undesirable substitute available. For example, suppose that the unique resource is an engineer who is especially talented at designing improved methods to reduce costs. The opportunity cost of using her on any project Xis her particular value on some alternative project(s) Y where she could make the best improvements with the time available. If, however, the assign ment of the especially talented engineer to this project X will cause one or more engineers to be hired to substitute for her on the project(s) she would have done otherwise, then the total cost of assigning her to project X is the net savings foregone plus the salaries of the substitute engineer(s). _ As another example, consider a student who cou ld earn $30,000 for working dunng a year and who chooses instead to go to school and spend $12,000 to do so. The tota_l cost of going to school for that year is $42,000: $ 12,000 cash outlay and $30,000 for mcome foregone. (Note: T his neglects the influence of income taxes and assumes that the student has no earning capability while in school.)

3.1:6.1 Opportunity cost in determ ination of interest rat es for economic analyses A · f . . . . .

th d . . · very important use o the opporturuty cost pnnc1ple cs en e . etermmatcon of the interest cost chargeable to a proposed capital investment proJect. The proper int · · of b erest cost is not Just the amount that would be paid for the use orrowed money but · h h . ex . · is rat er t e opportumty cost- the return foregone or pense mcurred becaus th · · · • • J)Ossibl . e e money cs envested en thcs project rather than in other ea 1tematcve proj·ects E h · funds · ven w en mternally owned funds rather than borrowed are used for invest' h · opponu . . . tog, I e enterest cost chargeable is determined by the same . mty cost pnnccple In cl · 1 · • 1s a measu f . · assica economics terminology , the opportunity cost re o the maxim b r· th , from an extr . . um ene it at, ,or any given situation. can be obtained a umt of capital. As an example su r· . !Unities su h ' ppose a crm always has avai lable certain investment oppor, c as expans· b This being th ion or onds purchases, that will earn a minimum of, say, Xo/o. • e case, the fi rm would b · · · earnmg less th X°' . e unwise to envest en other alternative projects an 7 0 T hus en · th may simply add in compuung e cost of various alternatives, the analyst of as the oppo . of the amount envested for each. Such a cost may be thought r1um ty cost ofn O1 · · · As anoth envesting en the readily available alternatives m0 er example co s ·d h · · ney to be obt . ' n c er t e enterest cost for investment in a car with acned from one f th , II . . , . o e ,o owmg three fmancing alternatives· (t) borrow d · (ii) an pay 14% per year: take out of sav i . (iii) . ngs account earnmg 5 % per year· cash m a "hot i ,, ' nveSt ment that you are confident would earn 30% per year.

X% '

Relevant Costs and Revenues and Estimating

56

Chap. 3

Sec. 3.1

Cost Concepts

57

For financing alternative (i) the 14 % is a cash cos t rat her than a n opportuni ty cost and should present no conceptual difficulty. For (ii) the 5 % is an opportunity cost because that amount will be given up if the money is not left in savings. Similarly, for (iii) the 30% is the opportunity cost if one invests in the car rather than keeping the "hotshot investment." The wide range between the 5% and the 30 % is not highly unusual, for the opportunity cost of any resource (incl uding money) is very much a function of what alternati ve(s) is foregone . In economic studies, it is necessary to recognize the time value of money irrespective of how the money is obtained, whether it be through debt financing, through owners' capital supplied , or through reinvestment of earnings generated by the firm . Interest on project investments is a cost in the sense of an opportunity foregone, an economic sacrifice of a possible income that might have been obtained by investmenl

Often , sunk costs and opporlunily cost considerali on s occur logether. Fo r anolher example, consider the plight _o f Joe_and Joan Hapless, who bought a stock for $ fou_r years ago, only to see JI decline to $ I ,000 in value as of one year ago. Smee then, 11 has rebounded lo be worth $3,000 now. Joan now says "Sell th d 0 0 ' we· v e do• we ' ve Iost $7 ,000 .1" b UI J oe says, " No, by keepi ng it for the last year $2,000!" Who is righl ? The answe r is neither, based on the respective rat~o; :ie: stated. Both are guilty_ of cou nting those sunk costs -the$ I 0,000, the $ 1,000, and the $2,000 can all be considered "sun k" because they are all the result of the pas t. Only the $3,000 the stock 1_s now worth is rekvan t. It is the opportunity cost if the stock is kept now; so the dec1s1on should boil dow n to what is the best use of the $3 ,000--leave it m the stock or sell the stock and use the $3,000 elsewhere .

of chat same money elsewhere.

. A postponable cos; is a cost that can be avoided or delayed for some period of ume. As an exampl_e, the costs of cer1ai n types of maintenance or of personnel for ccrtarn planning functions may be postponable, while the cos1 of direct labor is unavoidable or not postponable if production is 10 continue .

As another illuslration of the opportunity cost principle, suppose a firm is considering replacing a n existing piece of equipment that originally cost $50,000, presently has an accounting book value of $20,000, and can be salvaged now for $5,000. For purposes of an eco nomic analysis of whether or not to replace the existing piece of equipment, the investment in that equipment should be considered as $5 ,000; for by keeping the equipmen t. the firm is givin g up the opportunity to obtain $5,000 from its disposal. This principle

3.1 .6.2 Opportunity cost in replacement analyses.

is elaborated upon in Chapter 9.

3.1.7 Sunk Costs Sunk costs are costs resulting from past decisions and are therefore irrelevant to the consideration of alternative courses of action. Thus, sunk costs should not be considered directly in economic analyses. A s an ex~ple, suppose J?,e Smdent finds a used bike he likes on a Saturday and pays $50 as a do_w n paym~nt, .which will be applied toward the $1 ,000 purch ase price but which will be forfeited if he decides not to take the bike. Over the weekend, Joe finds another bike that he c_ons1ders equally desirable for a purchase rice of $9 1O. For purposes of deciding which · a sunk cost p . . . bike to purchase • the $SO 1s and th us should not en1er into the dcc1SJon. The decision lhe 00 I-1 d . OOo · $50 $950 ' th fi · n s own to paymg $1 , mmus , or , ,or e 1rs1 bike versus $9 IO , th . · al ,or e second bike A classic example of a sunk cost occurs • th · th at the piece of equipment examin d . th m e replacement of asse ts. Suppose e m e last sect' · · · t $50.000, presently has an accounting book al ion , which ongmally cos for $5,000. For purposes of an economic : u~ of$ 20,000 and can be salvaged now However. the viewpoint is oflen take than ; sis, th e $50,000 is actually a sunk co st. the difference between the accounti n b at e sunk cost should be considered to be 0 value, which is called "book loss" ~ ook val ue and the present realizable salvage . or capital Jos .. A . sunk cost 1s $20,000 minus $S,OOO or s. . ccordmg to this viewpoint, the 5 should be considered in an econo~ic ~ •CJO?· Neither the $50,000 nor the $1 5 ,000 $IS ,OOO affects income taxes as d' alysis, except for the manner in which the • 1scussed m Chapter 7 .

W,000

3.1.8 Postponable Costs

3.1.9 Escapable Costs . Whe_n a reduction or elimination of business activity will result in certain coSIS being ehmmated (with perhaps o the rs increased), the net reduction in coSIS is conside'.ed the escapable cost. Escapable costs are related 10 declines in activity in a manner similar to the way variable costs a re related to increases in business acti vity . Th e escapable cost whe n a business ac ti vity is decreased from X2 to X 1 is frequ ently smaller than the variab le cos t th a t o riginally resulted when bus iness leve l was expanded from X, 10 X2. For example , it is usually a more difficull management task : reduce_labor and other costs and commitments during a contraction than to increase em dunng an expansion. It is important in estimating net escapable costs that the amount of eliminated costs be reduced by the amo unt of any additional costs that would be inc urred in related acti v ities as a result of the change.

3 .1.10 Replacement Costs . Replacement cost is, as the name implies, the cost of replacing an item . It is '.m~ortant to economic analyses because replacement cost rather than historical ori g:~a co st is the relevant cosl facto r for most economic decisions. For example, if a th~rekeepe r has bee n stocking an ite m costing $ 8, and selling tha t ite m for $ 12, and the pnce lo the sto rekeeper for replacing the item is suddenl y increased to$ I 4, then ar selling price should be raised to at least $ 14 before a ny additio nal units of that item e purchased.

3 -1-11 Cash Costs Versus Book Costs cosr CoS t s that invo lve pay me nts o f cas h or inc reases in lia bility a re call ed cash cos~ :e sting ui sh them from no ncas h (book) costs. Othe r common te rms for cas h out-of-pocket costs" or costs that are "cash fl o ws." Bo ok costs are costs tlrn1

~!

Relevant Costs and Revenues and Estimating

58

Chap. 3

do not involve cash payments, but . . . rather represent the amortization of p as t expenditures f~r items of lengtl.iy durab1hty . The most common examples of book costs are deprectallo~ and deplenon charges for the use of assets s uch as plant and equipment. In eco~om1c analyses; the only costs that need to be considered are cash fl ows or potenllal cash fl?ws. Dep_reciation, for example, is not a cash flow and is important only m the way 11 affects mcome taxes. which are cash flows.

3.2 Cost Factors In an economic analysis, a listing of main factors that may be relevant for projects under consideration is as follows : First cost, installed and ready to run (or net realizable value) Insurance and property tax The life period of the machine until displaced from the proposed job The salvage value at the date of displacement The degree and the panem of utilization ; that is, the percent of capacity at which the machine will operate on the intended job with allowances for possible future changes in utilization Routine maintenance and repair costs Major repair items or periodic overhauls Direct operating costs. including operating labor, fuel or power, scrap m aterial, and rework Indirect costs: indirect labor, tooling, supplies, floor space, inventory Fringe benefits Hazards and losses relative to equipment, material, and labor time Changes in sales volume or price resulting from the choice Changes in unit cost oflabor, power, supplies, etc. , resulting in changes in operating costs 3 -3 Cost Savings and Revenues

t Th~ benefits of capital investment alternatives are often realized by savings in coS S, whkh should reflect true incremental or marginal cost reductions Whenever a single project or mutually exclusive alternatives involve revenues as ~ell as costs, those mc~e~ental reve~ues and costs should be considered. Fortunately when muiuaII)' cxc us1ve alternatives are evaluat d ' d) for all alternatives d th e • many types of costs are often identical (fixe an us do not have to be estimated. 3.4 Introduction to Estimating Probably th e most difficult . . and ex n . • mine the estimates needed t pe sive pan of any economic analysis is to deter 0 complete the analysis . This chapter will attempt to

Sec. 3.6

Estimation Accuracy

59

provide a perspective and approac hes to estimating, wi_th emphasis on maki ng single-valued estimates for the trad111on~l_ a_ssumed-certam analyses . Part Three will cover estimating in terms of probab1ltt1es and other measures of vanab1ltty to reflect the risk inherent in predicting fu ture outcomes. Chapter 18 discusses how activity-based cost data are used in the estimati ng process. 3.5 Estimating: Difficulty and Perspective

The basic difficulty in estimating for economic evaluations is that forecasting of critical elements associated with the manufacture of a product or the delivery of a service is unavoidable. Another difficulty is that most prospective projects for which estimations are to be made are unique; that is, substantially similar projects have not been undertaken in the past under conditions that are the same as expected for the future . Hence, outcome data that can be used in estimating directly and without modification often do not exist. It may be possible, however, to gather data on certain past outcomes that are related to the outcomes being estimated and to adjust and project that data based on expected future conditions. Techniques for collecting and projecting estimation data and also for making pro babilistic estimates are founded in the field of statistics. Whenever an economic analysis is for a major new product or process, the estimating for that analysis should be an integral part of comprehensive planning procedures. Such comprehensive planning would require the active participation of at least the marketing, design engi neering, manufacturing, finance, and top man agement functions. It would generally incl ude the followin g features : l. a realistic master plan fo r product deve lopment, testing phase into production, and operation; 2. provision for working capital and facilities requirements;

3. integration with other company plans; 4. evaluation against company objectives for market position, sales volume. profit. and investment; S. provision of a sound basis for operating controls if the project is adopted. Obviously, such comprehensive planning is costly in time and effort, but when a new product or process has major implications for the future of a firm, it is generally anin sound cc . rule to devote a greater rather than a lesser amount of euort to comp lete plan. g, mcluding estimates fo r the economic analysis that is a partial result of the plan;he application of this rule. of course, is bounded by constraints of limited time sio a ent; however, fo llowing the rule will tend to minimize the chance of poor decibeenns ordlack of preparedness to implement projects once the decision to invest has ma e.

:~g;

3-6 Estim · at,on Accuracy ~:tt::a:~:i\~orecasts. by their nature, are evaluati ons of incomplete evidence indi e future may hold . They may be based on empirical observati ons of

Relevant Costs and Revenues and Estimating 60

Chap. 3

only somewbat similar or analogous situations, adjusted on the basis of the kind of personal hunch that grows out of the accumulation of the experiences. Or they may be inferences drawn from various kinds of available objective data, such as trade statistics, results experienced in analogous situations. or personal observations. Regardless of the estimate source, the estimate user should have specific recognition that the estimate will be in error to some extent. Even the use of formalized estimation techniques will not, in itself, eliminate error, although it will hopefully reduce error somewhat, or will at least provide specific recognition of the anticipated degree of error. The level of detail and accuracy of an estimate should depend on the following :

sec. 3.7

Sources of Data

61

3.7 Sources of Data The variety of sources from which estimating information can be obt ame · d 1·s too great . . for complete e_numerat1on . The _followmg four major sources, which are ordered roughly according to decreasing importance, are described in subsequent sections: I. accounting records ; 2. other sources within the firm;

3. sources outside the firm; 4. research and development.

3.7.1 Accounting Records

1. the estimability of that which is to be estimated; 2. methods or techniques employed; J. qualifications of estimator(s); 4. time and effort available and justified by the importance of the study;

5. sensitivity of study results to the particular estimate. As estimates differ from conceptual to more detailed, the cost of preparing the estimate increases . As one might expect, the more expensive detailed estimates, which are usually associated with the final design of a system, are also more accurate. Toe general relationship between phase of design (conceptual, preliminary. and fi nal) and its typical estimation accuracy versus cost of the estimate as a percentage of total project cost is shown in Fig. 3- 1.

Conceptual design

It should be emphasized again that, although data available from the records of the accounting function are a prime source of information for economic analyses. these data are_ very often not suitable for direct, unadjusted use. The data generated by the accountmg funcuon are often mherently misleading for economic analyses, not only because they are based on past results, but also because of the fo llowing limitations. First, the acco unting system is rigidly categorized. These categories for a given firm may be perfectly ap propriate for o perating decisions and financi al summaries. but ~ely are they full y appropriate to the needs of economic analyses for longer-term dectsJOns. . Another limitation of acco unting data for obtaining estimates is the misstatements •m_bedded_ by convention into acco unting practice. These underestimates are based phtlosophtcally on the idea that management should avoid overstating the value of its assets and should therefore assess them very conservatively. This leads to such practices as nm changing the stated value of one 's resources as they appreciate due to rising market pnces and depreciating assets over a much shorter life than actually expected. As a result of such accounting customs, the analyst should always be careful about treating such resources as cheaply (or, sometimes, as expensively!) as they might be represented . The_final limitations of accounting data are their illusory precision and implied authontat,veness. Although it is customary to present data to the nearest dollar or the nearest cent, the records are not nearly that accurate in general. h In summary, acco unting records are a good source of historical data, but they ave hmttations when used in making estimates for economic analyses. Further, accounting records rarely directl y conta in the variab le costs, especially opportunity COS ts, appropriate for economic analyses.

3.7.2 Other Sources within the Firm

25

Accuracy (! %) Figur, .l-1

50

Estimation accurac~ versus cost of the estimate. (general relauonship)

The usual firm has a large number of people and records that may be excellent sources of estimates or information from which estimates can be made. Colleagues. supe_rvisors, and workers can provide insights or suggest sources that can be obtained readily . . Examples of records chat ex ist in most firms are sales. production. inventory. qualtty, purchasing, industrial engineering, and personnel. Table 3-1 provides a list of

62

Relevant Costs and Revenues arid Estimating TABLE 3-1

Chap. 3

Types and Sources of Cost Estimating Data

Description of darn

Sources

Gener.ii design specifications

Product engineering and/or sales department

Quanl fl)· and rate of producti on

Request for es1irnate or sales department

Assembly or layout drawings

Product engineering or sales department or

General tooling plans and list of proposed sul,a,;semblies of produc,

Produc1 engineerin g or manufacturing engineering

customer 's contact person

Detail drawings and bill of material

Product engineering or sales depanmenl

Test and in spection procedures and equipment

Quali ty ronlrol or produ~t engineering or sales department

Machine tool and equipment requirements

Manufacturing engineering or vendors of materials

Packaging and/or transportation requirements

Sales department, shipping department, er product engineering (government specifications)

Manufacturing routings and operation sheelS

Manufacturing engineering or methods engineering Manufacturing engineering or material vendors

Detail tool, gau ge, machine. and equipment requirements Operation analysis and workplace studies Standard time data Material release data Subcontractor cost and delivery data Area and building requirements Historical records of previous cost estimates (for comparison purposes. etc.)

Methods engineering SpeciaJ charts, tables. time studies. and technical books and magazines Manufacturing engineering and/or purchasing depanment or materials vendors Manufacturing engineering and/or purchasing department or customer Manufacturing engineering, plan! layout. or plam engineer Manufacturing engineering, cos1department. or saJes departmenl

the types of data that might be needed for cost-estimating purposes, together with typical sources (mostly intrafirm) for the data.

3.7.3 Sources Outside the Firm There are in~umerable sources outside the firm that can provide information helpful for esHmatmg. The mam problem is to determine which sources are potentially most fruitful for panicular needs. Publish_ed information such as technical directories, trade journals, U.S. gove_m ment pubhcat1ons, and comprehensive reference books offer a wealth of information to the knowledgeable or persistent searcher. Personal contacts are excel! . . . ent potential sources. Vendors salespersons profes1 s1ona acquaintances, customers, banks, government agencies. chambers of co~merce,

Sec. 3.7

Sources of Data

63

and even competitors are often willing to furnish needed information if the requesi is serious and tactful. Probably the most valuable estimating sources outside the firm, which are available and updated continuously, are cost indexes. Cost indexes provide a means for converting past costs to present costs through the use of dimensionless numbers called indexes, to reHect relative costs for two or more points in time. ' There are many cost indexes, and they cover almost every area of interest. Some are based on national averages; others are very specialized. Indicative values of indexes from the Engineering News-Record are shown in Table 3-2. The Bureau of Labor Statistics of the U.S. Department of Labor publishes extensive data on price changes of many types of products and earnings of workers in almost every industry. Some of these data are components of many cost indexes, and others are useful in constructing highly specialized indexes. Cost indexes are limited in their accuracy and, like all statistical devices, must be used with caution. Most indexes are based on data combined in more or less arbitrary fashion. A cost index, like cost data themselves, normally will reHect only average changes, and an average often has little meaning when applied to a specific case. Under favorable conditions a ±10% accuracy is the most that can be expected in projecting a cost index over a 4- or 5-year period.

TABLE 3-2

Typical Engineering Indexes•

Year

Ma1erials price index.

Skilled labor index.

[975 1976 1977 1978 1979

862 97 1 1077 1177 1303

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 19.92 1993 1994

--

Building index

Construction cost index

1921 206 1 2208 2350 2487

1378 1504 1620 1750 1826

2128 2322 2513 2693 2886

1449 1480 1547 1641 1632

2670 2902 3244 3507 3691

19 15 2014 21 92 2352 2412

3159 3384 3721 4006 4 11 8

1604 1612 1648 1693 !677

3765 3808 3937 4061 4153

2406 2447 25 18 2586 2612

4151 423 1 4359 4484 4574

1708 1693 1738 1846 2109

4283 4387 4536 4665 4764

2673 27 15 2799 29 15 3 11 6

4691 4772 4-927 5 106 5381

COSl

•Tnese inde . lhe M x values are from the March 28, 1994 issue of Engineering News-Record. pubhshed by cGraw-Hill Publishing Company. The base year is 1913, with an index value of 100.

Relevant Costs and Reven ues and Estimating

64

Chap. 3

3.7.4 Research and Development If the information is not published and can not be o btained by consulting someone wbo knows, the only alternative m ay be to undenake research to generate it. Classic examples are developing a pil ot pla nt and unden ak.ing a test market program. These activities are usuall y expensive and may not always be successful ; thus. this final step is taken only when there are very impon an t decisions to be made and when the sources mentioned above are known to be inadequate.

3.8 Quantitative Estimating Techniques An estimate. or forecast, is useful if it redu ces the uncenai nty surrounding a revenue or cost element. In do ing this, a decisio n should result that creates increased value relative to the cost of making the estim ate . This section describes three groups of e st1· mating techniques that have proven 10 be very useful in preparing estimates for economic anal ys is. They are ( I) time-series techmques, (2) subJect1ve techmques, and (3) cost engineering techniques . . . . When revenue and/or cost elements are a function of time, such as umt sales per quaner, they are often referred 10 as a time series. Time-series data should be collected for the element under study and then carefully e~amined for underlymg patterns. For example, a sudden increase in sales may be explamed.by mcrnased government spending or a vendor filling its distribution. pi_p eline. We_will examme the use_of regresswn for estimating causal relationships w_1thin_ume-senes data and exponenual smoothmg for estimating future extensions to h1stoncal data patterns. Frequently. the next stage of estimating is to apply expen judgment to the results of time-series techniques. Examples of subjective estimating approaches to be examined are the Delphi technique and technology forecasting . A highly effective estimating strategy is to couple a time-series technique, based on past data, with a sub· jective technique that introduces human judgment in anempting to discover hoW future revenue and cost elements will differ from those of the past. Cost engineering techniques identify and utilize various revenue/cost drivers to compute estimates. They include models for estimating capital, material, labor, and many other factors of production . These models may utilize correlation and regression analysis. or they may be as simple as extensions of ratios of relevant cost iudexes. For example, capital costs _can often be ~ccurately estimated by knowing the weight of a parucular structure. Similarly, operating costs such as that for fuel can be co mputed from forecasts of k1lowatt-hours generated by an electric power station.

3.8.1 Time-Series Techniques 1 Two relatively simple yet ext e I f ·· I . · f • . r me Y use ul . techniques for obtaining imll 3 ume-senes_ orecasts o e1ements being estimated are d . . . . . . ) Jin· ear regression analysis and (2) . escnbed m this secuon. ( I · exponential smoothing. i_ Section

3.8. I is adapted from J. R. Canada and W . . . ft Evalua11on of Adranced Manufacturing Svsrems (E · G._Sullivan, Economic and Muluatrr~bll d by penni ssion of the publisher. · nglewood Cliffs. NJ: Prentice Hall, 1989). Repn ntc

Sec. 3.8

Quantitative Estimating Techniques

65

3.8.1.1 Correlation and Regression Analysis. Sometimes it is possible to correlate an element, such as revenue for a product line. with one or more economic indices. such as construction contracts awarded. disposable personal income, etc. Correlati on concerns the explainable assoc iation between variables. When an index can be found to which an element to be estimated is highl y correlated. bu! with a time lag, fonnal correlation analysis may be highl y usefu l. [n cases in which the lag is insufficient for longer-term forecasts, correlation of an element to be estimated with the available index still leaves the esti mator with the need to predict the future value(s) of the index itself Regression is a statistical method of fitti ng a line thro ugh data to minimize squared error. It is exact ; however, graphing might be used to provide a satisfactory approximation. With linear regression, approximated model coefficients can be used to obtain an estimate of a revenue/cost element. In linear regression involving one independent vari able x and one dependent variable y, the relationship that is used to fit n data poin ts ( I ~ i 11) is

y =a+ bx.

(3- 1)

A mathematical statement of expressions used to estimate a and bin the si mple linear regression equation 3- 1 is as follows:

b =

ix;y; - xi y; ;- 1

(3 -2)

Ix?-,tf x, i= I

a=

i= l

1= 1

y- bx.

(3-3)

Here, x and y are averages of the indepe nde nt vari able and dependent vari able . respectively, for the II data points. Example 3-1 A ~urable goods manufacturer has found personal disposable income in its market region in a given quaner to be strongly related to sales in the fo llowing quarter. These data are li st ed and summarized in Table 3-3. Because a plot of these data indicates an approximately linear relationship between the dependent variable (on the y-ax is) and the independent variable (on the X·axis), linear regression is used to fit an equalion to the data. The data and calculations summarized in Table 3-3 are utilized below to determine the linear regression equation :

f xf f x;' - xf x, =

x ,y; Y; b = ~•-~ '-- -''-"-,._,_

i=J

2,626.8 17 - 250.6(9,788) 1,41 6.926 - 250.6(5.0 12)

; .. J

173.944.2 = 160,918 .8 = I.OBI. a =

y - bx =

489.4 - 1.08 1(25 0.6)

= 2 185 .

Relevant Costs and Reven ues and Esti mating

66

Cha p. 3

sec. 3.8

Quantitative Est im ating T echn iques

fi7

,,.$,~f

Thus. y = 21 8.5 + 1.081,.

figure 3-2 sho~'S lhc: plOlted data and the calculated regression line. As an example of how the regression equation is used. suppose that disposable income for the previous quaner is 310 (or S310 x Hf). Then our forecast or estimate of sales (in thousands of dollar.;) for the cur. rent quaner. j· . is

;- = 218.5 + 1.081(310) = 553.6 (or S553.6 x 10

TABLE 3-3

Dmpoint.i (period)

x,

360 260

= 400

360

500 580 560 9

505

10

480 602

118 211 190 75 263 3:;.,

30.680

13.924

119.240 76.000 27.000 131.500 193.720

368

206.080

73.441 36. 100 5,625 69. 169 111.556 135.424 93.025 44,100 149,769 72.900 4 7,524 116,964 29.929 136.900 28.900 42.025 I 14.92 1 80.089

305

154.o->..5 100,800

232.974 145.800 90.470 20 1.780 85, 116

342

-t91

173

660

370 170 205 339 283

360 4 10 680 594 9,788

244.200 61.200 84.050 230.520 168.102

2.626.81 7

5,012

i.Y,

i x; = 5,0 11

,ix,

,=l

n

20 - -

·

i >,

y =.i=L= 9,788 =4894 n 20 · Kry. y, = actual quarterly sales (SIO') for period ;

x, = disposable iocomr (SI 06 } in prrceding pcnod

f"

400

"

300

~

·

I,xf= l,416,926 x, y, = 2.626,8 17

• !.()SJ

X

.0S1

•

/·

"/.

.--:·. / "

• y· •

/

/

a= 2185

200

100

200 300 400 500 Disposable income in precedine quan er. .r (mi ll ions of doll arsf

Figure 3-2

Ploncd poi ms and regression line fo r E.umpll' 3 . 1_

The correlation coeffi ciem is a

111

f h

-

\·arfa.bles only if che variables 1·. ca:,., ure o t e strength of the relationship between two which meas ures the de ,. /1re ~mea rly rdared. In Example 3- 1. the co rrel::i.t.ion t·odfil'icnt r. grcc O strength. can be determined as follows:

(3 -1 )

where

-(i,;)(i _,,) 111 I x',-(i f..., _. ., -(r .,.)',,, _

50 = i,.,,_,., i= I

,= I

i

/

= 218.5

I

(- 1 5 r $ I ).

= 9,788

i=l

-= £ L = 5.0 12 - 150 6

-'

1.416,9 26

.

600

1 300

,: 14.641

121

2JO

540

Tc " :: ""'.... :; 'i5 02- :;" "' -0

-


211

The Tax Reform Act of 1986 and Its Depreciation Provisions

s,c.7.2 TABLE 7.3 MACRS PropertY Classes and Permissible Methods for

Calculating Depreciation Rates

MACRS property class and depredation method

Step 2

Ascertain MACRS property class (e.g., 3-year. 5-year, etc.) for recovery property (Table 7_3).

3-year. 200'¼ declinin g balance 5.ycar. 200% declining balance

Step3

ADR guideline period 4 years or less

More than 4 years to less than iO years

Special n,les Includes some r.._-.,oorses. Exdud

Solution From Eq. 7-20, we have ATCF = ($10,000 - $4,000 - $2,000)(1 - 0.4) + $2,000 = $4,400.

I

2004

Toe same result can be obt2ined with Eq. 7-21 (or 7-24): ATCF?llOI = ($10,000 - $4,000)(1 - 0.4) + 0.4($2,000) = $4,400. . . , d't1 0 f td to [he after-la! cash 1 Equation 7-21 clearly shows that deprec1auon contnbutes a ere 1

>

.:0 I

>

flow in operating year k.

. ( savings) is td1 in The ATCF attributable to depreciation a tax_ . tax 5h'18 Id.' "deprec1at1on d year k. This is often referre to as a )f nd a reve· After income taxes, an expense becomes (l - t k a nue becomes (1 - tlRk·

+

::E

earsisbe~!

Example 7-15 d eciable life of five Y ' Suppose that an asset, with a cost basis of $100,000 and a epr depreciated with alremale MACRS as follows: 2()()7 2006 2005 2004 Year 00o s20,o(J(J · ()()9 wha11slb< Depreciation S10,000 szo.OOo $20. ucaon , I f1d 40% during 2()()4--2 %per year ' ded t If the f1rm'seffect1ve income tax rate remains conS ant atwhen t,(ARR"" IO c·ation 1 chedule is d PW of after-tax savings resulting frorn epre c1a11on s d 10 thlS depre income taxes)? Solution Toe PW of tax credits (savings) ue ()(J0(0,82 (,A)., . 2009

L

PW(I090) = b

2004

4 0.4d;(Li0f'"' S ,000(0.

9091)+

$8

'

- 528,948 + $4,000(0,5645)-

0[1)1

fSJ , · uesl 0 ,e ~ . 6 after-taJI. cost of eq Equation 1 5 We use Equation 7-13 to find the WACC. The annual and ta 0.38 rrorn 0.50. Borrowed capital, before income taxes. costs I0% per year

sec.1.5

General Procedure for

(b) The 1,efore-tax

o=

·c Analyses for Projects 229 M king After-Tax Econom1 a

!RR is computed from column A :

-$180,000 + $

' """· 7-7. By each of the listed methods. calculate the BV O a ig . ated safvage value I 5 y~· · II $1 800 and had an eSt1m •od ·s of 4 years if the item ongma Y coSI • ACRS recovery pen licabl< The ADR guideline penod 1s 8 years. and th e M , Table 7.4 al' aPP ,¢ · 005 d MACRS rates in 'th half·) a. The machine was purchased m 2 • an • R riod of g years, w• th b. Alternative MACRS is to be utilized over e AD pe used f

R$(01

" = A$,(PIF, JO%, n) $2J,600(p;f 10 _ _ _ _ _ (PIF,5%,n) 23,328(P/F: $19,637 25,194(P/F lQo/,' )- 19,278 0 3 ' • ) = 18,928

(a) pJll = A() 1(P/A, i,, 3)

pJOI =

(I)

A$,= A$ 1(FIP. 8%,n _ I)

10:•~):

Solution

261

sec. B.7 Manipulating Series that Inflate (Escalate) at RDGI

PWciO)

-=o~.9-52_4_ _ __:__:,::,c>___ 0.90?0 $18,702 J7 85 0.8638 .4

No1e fro IPUrchasin · rncotllrnn(I ----$52,537 Preseni g llOwer) of tha ). that even though h e Worths 0 f t salary · er A$ al llllr. both wa is going down s ary is going u E~ ys of expressing the (~pproximately 10% _!'g~t 8% per Year), the R$ •• lllpl, 8-4 sa ary are the same o = 2% per Year) Th "'ilry Q • except for . · e sPe .. Contra.,, . minor round-off . nd1ng - , Wish ing ihe Powe,. As es to retire i • is e next 25 surne that th n the Year 2030 . 0c 'Pecied to . Years. Ma e expected i . With persona] . curs at increas ry Plans to . nflation rate . savings of $50() llluch Wi\itlte end of 2eOOby 6,5% per invest in a 6.0% tn the economy Will ,000 in 20()5 he, 101 6. If M Year between per Year savin average 3 5% or ,h lnisexa al salary h ary PUts asid 2005 and 2030 A gs account, and h. durknow' catculatilllpJc dernon:ve to be in 2 e I 0% of her sal . ssume that th er salary . Ir Wed ons are b trates the fl 0()5 to make h _ary for retire e first depo , • ea1 in ac ased on a . ex1b1lity of er rcurcment mem PUrpos s11 tua1 doll • Piece of . c a spreadshe ' t plan a te·111·t es, how ars th in,orrn . e • even . . • y • e cash flow at,on (the 2 in instance , : relationships. OOs salary) ti . s 11, Which . ll are strai ght f ,,\\ We do ,I orw,1rct. A 1101 Yet

spre,1ct,h s ee1

262

Effect of Inflation on Before-Tax and After-Tax Economic Studies

263

Se g,

where

. . th be inning of year N + I or. equiv• pN is the present value of a perpetuny at e g

alently. the end of year N, . ear-end payments, . ·n year N + I assuming Y A is an annual cash flow starting t ' f the invested amount, . as a percentage o i is the nominal cost of capital per year. and

rcentage of the annual amount. . unted to p should then be disco . for The terminal value, previously calculatedh apsre~~nt value of the proiecuons P/F. 1· N) and added tot e . · · n target. the present as Po= PN ( ' ' . the NPW of the acquisiuo . T ble J0-9. . ·u·a1 N years (here, 6) to deterrmne f •TCF results m a h t e 1m . these to four relevan t co mponents o /'\ App Iymg g is the growth rate of A per year. as a pe

Acquisition

Table 10-9 Analysis of Terminal Value o

Componen1 NOPAT d !!,WC

Capex Total

Year 6 value $407.00 $120.00 -S JS.00 - $100.00

$409.00

'For exampIC, g -- (427.35 -

f the Ajax Pool Company P

Year 7 value

(i-g)

$427.35 $120.00 -$ 18.90

0.05 0 0.05

- $100.00

0

$428.45

407)/407 = 0.05: :.

0.10 1 0.15 0.10 0.15

' $4,274

$800 -5189

-$667 $4.218

.

-0.15 - 0.05 :O. iO•

I-

-

Po

si.848 346 -S82 -5288 si.823

335

sec. 10.s

Summary

. bl _ the present worth of the terminal value is $ 1,823,000. f b d A5 5hown m Ta e 10 9' . . al value assumes that the organization generates returns orever, ase h This1the ermm , 'tal expenditures. The present worth of the after-tax influx of new capt . . 00 ,cas upon over the 6-year plannino" horizon developed tn Table I0-8 ts $1,223,0 flow . J , or a' • 'al f $3 046 000. This generates an NPW of $46,000 relative to combined tot o , • . . · · . ones h · pnce · of $3 ,000 ,000 · This appears to be a margmally asking . . . viable . propos1Uon, . . owever, that can be only a tentative conclusion, as sens1Uvt1y testmg, n sk analysts, and analysisof business fit or strategic fit have not yet been considered. The problem exercises leave tha1 important task to the readers. 10.8 Summary

At this point, after-tax present worth computations should be a routine matter. However, th~detennination of the appropriate cash flows to include will always require careful thought. The analysis is se ldom a single event, but rather an evolution of th o~ghl as our understanding of a proposed investment becomes clearer as more details emerge throughout the project life cycle. . This chapter has enlarged the investment framework from the consideration of mvestment in indiv'd h. • . • 1 al a.,"ee1lhe entire b · u mac Th mes. or projects to one that considers prospects. which lh eimpact . usmess. · e not10n of cash flow after taxes has expanded to mclude of work· tures 10 . tng capita1changes, as well as undefined future capital expendisustam an ong · b . . acquisitio fb . omg usmess venture. This enlargement progressed to the zonmay hnave aUmajor Smesses, · wherein tenninal values after an abbreviated planning horiEqual! . impact on the valuation results. intangibles y dimponant, the chapter deve loped a framework for consideration of ,,_ an tdent1ficaf f . . ""0Ugh a quai-t . ion ° n sks tn investment analysis. These are pursued ronmen1a1 entiit_ative analysis of fit with value chain factors stakeholders, and envilh ies m the bus· · ' ecompany. mess envtronment and fit with the strategic direction of Finally h ourr ' t ese enlarge tned in Ch ments allow us to expand the systems analysis framework Capit I . apter l and Ch t 5 a Investment A . ap er • A further amplification. now di splayed as the UJlda1e nalys1s Wo k h · · · fu s needed lo inco r s eet m Figure I0-1, shows that process with the rther Steps to be rporate the new concepts added in this chapter and a preview of presented in the remainder of the text.

°

SYSTEM I SPEc ANALYs1s STEPS: IFypRO %ai"' IECT OBJECTIVE 1 Us1 be ac DEFJNE Al C0111p/ished? By when? Ind, TERNATi VES A

,., i'