Sensitivity of Construction Contract Prices to Required Rate of Return and Retainage

Transcription

1 TRANSPORTATON RESEARCH RECORD Sensitivity of Constrution Contrat Pries to Required Rate of Return and Retainage f OAD FARD AND HLAL SAAD The fair and reasonable markup (FaRM) is the smallest markup that satisfies the required rate of return (RRR) ofthe ontrator for the partiular projet at hand or its general risk lass. The miroomputer-based FaRM priing model provides a systemati and effiient framework for analyzing the foreast ash flow stream of the projet and for estimating the minimum aeptable prie (MAP). The model utilizes a LOTUS spreadsheet. and an be implemented on most BM or BM-ompatible miroomputers. The omputerized model delivers speedy responses to a variety of what-if questions investigating the sensitivity of FaRM and MAP to the RRR of the ontrator and 1 the retainage poliy of the ageny. One the FaRM priing model has been implemented, ontrators should bid lower on projets that are more attrative, and should beome more ompetithe in other ways as well. This strategy should result in lower osts to agenies while satisfying the RRR of the ontrators. Conversely, ontrators an maintain their RRR on the less attrahve projets by submitting higher bid pries. An earlier artile reviewed onventional priing praties used in onstrution within the framework of basi priesetting models used in free-market eonomies (J). The ontrators' lak of finanial and managerial skills oupled with the intense ompetition inherent in ompetitive bidding were identified as the fators responsible for improper priing deisions by ontrators. The fair and reasonable markup (FaRM) priing model proposed a present-value approah to priing of onstrution ontrats (2). This approah was a ost-oriented priing tehnique in the sense that it attempted to ensure an adequate return on the investment of the ontrator. The FaRM priing model demonstrated that the markup was a funtion of the required rate of return RRR and the ash flow shedule of the projet. The miroomputer-based FaRM priing model provides a systemati and effiient framework for analyzing the foreast ash flow stream of the projet and for estimating the minimum aeptable prie (MAP). The omputerized model delivers speedy responses to a variety of what-if questions investigating the sensitivity of FaRM and MAP to the RRR of the ontrator and to the payment poliy of the ageny, that is, to retainage as speified in the ontrat douments. One the FaRM priing model has been implemented, Constrution Engineering and Management, Department of Civil Engineering, North Carolina State University, Raleigh, N.C ontrators should bid lower on projets that are more attrative, and should beome more ompetitive in other ways as well. This strategy should result in lower osts to agenies while satisfying the RRR of ontrators. Conversely, ontrators an maintain their RRR on the less-attrative projets by submitting higher bid pries. FaRM PRCNG MODEL The model onsidered several fators and eventually adopted the following definition for the markup that was onsidered fair and reasonable: The FaRM would be viewed as the smallest markup whih satisfies the required rate of return (RRR) of the ontrator for the partiular projet at hand or its general risk lass, where the RRR is the return investors expet the firm to earn on its projets. This is the return required to maintain the present market prie of a share of ommon stok of the firm (2, p ). The basi FaRM priing model was demonstrated with a manageably sized, hypothetial example projet-the University of llinois' nternational Friendship House (U-FH). The example projet assumed an RRR of 2 perent per period (month) inluding a premium for unertainties involved in the projet. The U-FH example projet assumed that there were no federal, state, or loal inome taxes and that inflationary pressures were negligible (2, p. 376). COMPUTERZED FaRM PRCNG MODEL The miroomputerized FaRM priing model is demonstrated by the same U-FH example projet so that results of the manual and omputerized models an be easily ompared without unneessary repetitions. The model uses LOTUS 1-2-3, Release 2.1 (Ll23-2), spreadsheet and an be implemented on most BM or BMompatible miroomputers with a minimum of 256K random-aess memory (RAM) (3). The row and olumn format of this popular spreadsheet ombined with maros, funtions, and the formula-writing apabilities of Ll23-2 provide an effiient framework for programming the FaRM priing model. The spreadsheet-based model is ost-effetive and should serve as a powerful and user-friendly eduational software that demonstrates versatility of spreadsheets as well.

2 94 nput Data As soon as the omputerized FaRM priing model is loaded, the software prompts the user to enter total ost of the projet, the initial retainage, and the required rate of return. The user may wish to enter the projet name,.d. number, and the user's name as well. The major input data onsist of the projet's umulativetotal-ost urve, ommonly known as the "S urve" or the progress report, whih is readily aessible. Figure 1, the modified umulative total estimated ost urve, shows the S urve for the hypothetial example projet U-FH. The term "modified" signifies that the vertial axis shows umulative ost as a perentage of the total estimated ost of the projet. Other information needed as input to the model inludes billing, payment, and rtainag poliies that ar usually speified in the ontrat (2, p ). Cash Flow Shedule A modified version of the umulative ash flow shedule for the U-FH example projet is presented in Table. The information depited in Figure 1 is diretly entered in this table under Column a by the user. Cash flow analysis is primarily onerned with the amount and timing of the atual funds transferred rather than osts inurred. Thus, Table 1 is based on the assumption that the management requires the ompany to have available at the end of eah time period suffiient funds for the projeted total inurred ost of the following period (2, p ). The umulative unallowables are also diret entries by the user. These are ost items, suh as home offie overhead (HOOH) expenses that may not be diretly hargeable to the owner under ertain ontrats suh as ost-plus-fee projets (2, p. 387). The Ul-FH example projet assumes that there are no unallowable osts so that the results an be ompared with those of the original manual FaRM priing model. Billing-poliy fator onstitutes the last input data that are diretly entered by the user under Column d. This fator enables the user to adjust ash nows if some of the inurred osts annot be inluded in ertain progress billings and other situations suh as front-end loading. Examples of suh expenses inlude ost of mobilization, haul roads, installing plants, and materials delivered to the site but not yet used in any ompleted work (2, p. 381). The model is based on a payment time lag of one period. The ontrator submits progress billings at the end of eah period. The owners or engineers have one period to proess, verify, and arrange the payment. Thus, the ontrator usually reeives the atual payment at the end of the following period (2, p. 382). Output Data The miroomputer-based FaRM priing model then generates the remaining part of the data presented in Table 1. The model automatially omputes the FaRM as a fum:tion of the TRANSPORTATON RESEARCH RECORD 1126 RRR and the ash flow shedule of the projet for eah run as presented in Table 2. The omputer then generates a list suh as the following one in whih the MAP is determined by adding FaRM and ost of bond to the total hargeable ost of the projet. Total hargeable ost of projet FaRM at 4.5 perent Contrat prie before bond premium Cost of bond Minimum aeptable prie (MAP) $72, 32,4 $752,4 5,275 $757,675 Assigning a new value to any one of the variables results in automati omputation of a new set of ash flow shedule, FaRM, and MAP. This feature provides speedy responses to a variety of what-if questions for performing sensitivity analysis. SENSTVTY ANALYSS The auray of the FaRM and MAP estimated by the model is, of ourse, a funtion of the auray of the input data. But, at the busy time period just prior to bidding on or negotiating a onstrution ontrat, only a limited amount of information is available. Thus, most of the input data to the model an best be desribed as random variables. The FaRM priing model assumes that all the values entered, for example, osts, ash flows, RRR, and so forth, are expeted values. nstead, RRR should inlude an allowane, that is, a premium, to ompensate for the unertainties involved in ash flow figures and other input data. Thus, the auray of the RRR is a key fator in the suess of the model. Estimating the RRR, however, is more an art than a siene, at least at the present state of knowledge. Therefore, the impats of varying RRR on FaRM and MAP should be of utmost interest to major parties involved in the onstrution proess. The omputerized FaRM priing model provides an effiient system for onduting suh sensitivity analyses. n fat, all data presented in the following setions are generated by the model. Sensitivity of FaRM and MAP to RRR Figure 2 shows the sensitivity of the fair and reasonable markup to the required rate of return for the U-FH example projet. The data onfirm that FaRM is quite sensitive to RRR. The passage of the urve through the origin serves as a spot hek for verifying the auray of the analysis. Reall that the basi U-FH example projet analyzed here assumes that there are no unallowable osts. That is, the example is based on the premise that every item of ost to the ontrator is inluded in the pool of the total estimated ost of the projet. Thus, if there were no time value of money and no unertainties involved in the projet, both unrealisti but implied by a zero RRR, then FaRM would indeed be zero as well.

3 1 9 t a. " BO 8.3 L ii 7 r; 6 u "O 5 " w " 3 - f--. 2! B End-of-Period FGURE 1 Modified umulative total estimated ost urve. 1 TABLE 1 MODFED. CUMULATVE CASH FLOW SCHEDULE : End Cmltv. Less: of!total Cmltv.!Periodl Cost Unallo- 1 wables b j a : o : Cmltv. Chargeable Costs! Billing Cmltv. Poliy Bill Fator able d Cost e=.d oo oo o Less: 1.% f Cmltv. Payments before FaRM Due Revd. g h l : % of Total Cost ! ! ! l Cost l l in j72.oo j72.oo l! $1!! :',, 1 ' ' '- -'

4 12llll 11lllS,, :2 1lllS Q:!::. 9lllS Q. :> SlllS.Y. :2 7lllS :a 6lllS 5lllS " Q: 4lllS., D _ ii 3lllS 2lllS 1lllS Ollll O.OOlllS 2.lllS 4.lllS Required Rate of Return (p r p rlod) FGURE 2 Sensitivity of FaRM to RRR. 6.lllS TABLE 2 FaRM: A FUNCTON OF RRR AND CASH FLOW SCHEDULE Present Cash Outflows Cash nflows l End Value (Total Cost for the (Payments before FaRM of Fator Following period) as % Reeived) as % of Periodi at of Total-Cost of Projet Total Cost of Projet R = 2.%! j (j) = s(j) = l l(p/f,r%,j) a(j) - a(j-1) PV[(j)] h(j) - h(j-1) PV[s(j)] ! : : o : : : : o Sum of (j) Sum of s(j) NPV(R%,N' periods) = [1 + m(f)] Sum PV[s(j)] + Sum PV[(j)] = Sum PV[(j)] m(f) = = - 1 = Sum PV[s(j)] FaRM= 4.5%! l

5 Farid and Saadi Computations of FaRM as presented in Table 2 indiate that FaRM is not a linear funtion ofrrr. Figure 2 shows a linear relationship beause of a to 5 perent range for RRR and beause this small example projet will be substantially omplete by the end of the sixth period. Figure 3 shows the sensitivity of FaRM to a wider range of RRR. The plot onfirms that the general relationship is onvex and not linear. That is, the marginal inrease in FaRM beomes larger as RRR inreases. However, a linear assumption may be an aeptable approximation as long as the RRR is limited to perhaps 2 perent per period and ash flow duration is shorter than some 2 periods. Figure 4 shows the sensitivity of the MAP to the RRR. The shape of the relationship is, of ourse, similar to that of Figure 2. The MAP varies from $725,63 for zero RRR to $88,477 for an RRR of 5. perent per period. Sensitivity of FaRM and MAP to Retainage Figure 5 shows the sensitivity of FaRM to retainage for the U-lFH example projet. This plot indiates that FaRM is sensitive to retainage but not as sensitive as it was to RRR. FaRM still inreases from 4. perent at no retainage to 5. perent at 2 perent retainage-a 25 perent inrease, whih is not negligible. Figure 6 shows the effet of varying retainage on the MAP. As retainage grows from to 2 perent, MAP inreases from $754,124 to $761,371. FaRM and MAP are not, in general, linear funtions of retainage. Again, Figures 5 and 6 show linear relationships simply beause they are based on a 2. perent RRR and a six-period duration. Figure 7 shows the sensitivity of MAP to the same zero to 2 perent range of retainage but with an RRR of 1 perent. This plot also onfirms that the general relationship is not linear but onvex. n other words, the inremental inrease in MAP grows with inreasing retainage. Again, a linear assumption might be aeptable as long as the ash flow stream extends no more than, say, 12 periods and RRR is no larger than some 2 perent per period. SUMMARY AND CONCLUSONS The miroomputer-based FaRM priing mod! automatially omputes FaRM as a funtion ofrrr and the ash flow shedule of the projet based on a present-value analysis. The MAP is determined by adding FaRM and ost of bond to the total hargeable ost of the projet. Assigning a rtew value to any one of the variables results in automati omputation of a new set of ash flow shedule, FaRM, and MAP data. This feature provides speedy responses to a variety of what-if questions for performing sensitivity analysis. The model uses LOTUS 1-2-3, Release 2.1, spreadsheet and an be implemented on most BM or BM-ompatible miroomputers with a minimum of 256K RAM. The row and olumn format of this spreadsheet ombined with its maros, funtions, and formula-writing apabilities provide an effiient framework for programming the FaRM priing model. The spreadsheet-based model is ost-effetive and should serve as powerful and user-friendly eduational software. FaRM and MAP are quite sensitive to RRR but the general relationships are onvex and not linear. That is, the marginal inreases in FaRM and MAP beome larger as RRR inreases. FaRM and MAP are not as sensitive to retainage as they are to RRR. FaRM and MAP are not, in general, linear funtions of retain age. n fat, the inremental inreases in both FaRM and MAP grow with inreasing retainage % 3% :::!! <'. 25% a. :J :::!! 2% : i:: 15%., <'. " "U 1% i:: 5% %.% 2. % 4. % 6. % 8. % 1. % Required Role of Return (per period) FGURE 3 Sensitivity of FaRM to large RRR.

6 $82,, $81 "O " : " $8 J: $79 t:. u $78 ;: $77 jj a. $76 u < $75 E E " $74 Si $73 $72.llS 2.llS 4.llS 6.llS FGURE 4 Sensitivity of MAP to RRR. 5.5% 5.4% 5.3% - 5.2% - a:: 5.1% - u. 5.% - a. 4.9% :J 4.6% t 4.7% 4.6%,, U "O U ". 4.5% : 4.4% U 4.3% 4.2%. a:: " "O 4.1% : 4.% '- 3.9% a u. 3.8% 3.7% 3.6% Required Rate of Return (per period) 3.5% -+---,-,--,-r-r-.-,,--..-r-.--r-.% 2.% 4.% 6.% 6.% 1.% 1 2.% 1 4.% 1 6.% 1 6.% 2.% FGURES $765 $ $763 $762 - ". $761 t. $76 " u $759 $756 :a " $757 a. $756 " u $755 < E $754 ". $753 $752 $751 - Retain age Sensitivity of FaRM to retainage $ ,---,-.% 2. % 4.% 6.% 8.% 1.% 1 2.% 14.% 1 6.% 18.% 2.% Retalnage FGURE 6 Sensitivity of MAP to retainage.

7 Farid and Saadi 99 $ (RRR = 1 %) (/). :::i: $3.5 $3.4 OJ (J $3.3 a. OJ.a a. OJ (J (J <( E :..!:: :::i: $3.2 $3.1 $3. $2.9 $2.8, -..% 2.% 4.% 6.% 8.% 1.% 1 2.% 1 4.% 1 6.% 1 8.% 2.% Retain age FGURE 7 Sensitivity of MAP to retainage at RRR = 1 perent. REFERENCES 1. F. Farid and L. T. Boyer. Constrution Priing Praties and Objetive of the Firm. Pro., CB W-65 3rd nternational Symposium on Organization and Management of Constrution, Dublin, reland, July 6-8, F. Farid and L. T. Boyer. Fair and Reasonable Markup (FaRM) Priing Model. Journal of Constrution Engineering and Management, ASCE, Vol. ll, No. 4, De. 1985, p LOTUS Referene Manual. Release 2 Lotus Development Corporation, Cambridge, Mass., Publiation of this paper sponsored by Committee on Constrution Management.