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# Chemical Process Economics II CHEE 6369

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This 47 page Class Notes was uploaded by Beryl Skiles III on Saturday September 19, 2015. The Class Notes belongs to CHEE 6369 at University of Houston taught by Staff in Fall. Since its upload, it has received 72 views. For similar materials see /class/208281/chee-6369-university-of-houston in Chemical Engineering at University of Houston.

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Date Created: 09/19/15

CHEMICAL ENGINEERING 6369 Risk Analysis for Chemical and Petroleum Engineers PORTFOLIOS AND DIVERSITY Simple Portfolio Concepts Why diversify Consider Risk vs Return and concept of dominance with respect to either See hypothetical E V SD points in Figures a Pure cash position Fig 1 Riskfree gt Cash 0 Ecash Expected return on cash Bank interest Scash 0 Best Investments and AssetsA A w 0 V quotJ 0 E Dominated 3 Selection 0 a c Cash is a E Volatility Standard W quott Investments DeVIatIon SD J and Assets Fig 1 Use MeanVariance Rule see Hertz and Thomas 1983 p 116 o For same return take investments with lower variance 0 For same variance take investments with higher return See Montgomery amp Runge pp 249250 Eqns 635 638 Intro to Portfoliosdoc Page 1 21Mar01 Portfolios and Diversity b Now assume some fraction f of value in cash balance held in investmentX or Y Then what should we do with the l f Invest Ep fEcash Einvestment Expected return of cash amp investment S13p f Scash SDinvestment 0 SDinvestment Stndd Dev of cash investment Stndd Dev of investment Best Investments and Asset A nand 5 possible with portfolios of Cash Y uand a possible with portfolios of Cash X Mean Return E J L Volatility Standard YV rst nvestments Dev39atlon SD J and Assets Fig 2 See Fig 2 Hypothetical Ep v SDp plot Lines C X C Y Choices of X Yand f depend on returns volatility of stocks and risk averseness 0 Line btwn points represents some miX of cash stock some value of t 0 Line extension beyond X or Y represents leveraging the investment by borrowing assuming interest at the cash rate of return C O Complications arise when we hold a miX of investments Maybe stocks wells or whatever For simplicity here Assume holding 2 investments X and Y Random Variables gt 0 Ep fEX lt Ey SDp f2 SDX2 2f1 r R SDX SDy 1 D2 SDYZ 2 l f R f l correlation coefficient Intro to Portfoliosdoc Page 2 21Mar01 Portfolios and Diversity Perfect correlation R l gt SDp f SDX l f SDy Given 71 g R lt 1 EP is still weighted average but get reduction in portfolio SD 7 Uncorrelated 2 Variation in one will partly offset variation in the other and the farther R is from 1 the more this is true i Hypothetical 1 Ex By then E EX By is known amp SDX gt SDp lt SDy Note that SDp f2 SD 2f1 t R SDX SDy 1 D2 SDyz 2 f SDX 1 0 SDy2 2f1 t 1 R SDX SDy 2 weighted average SD2 positive number 2 lt weighted average SD iiHypothetical 2 EX 5 By and SDX 5 SDy See Figs 3 and 4 Plots for R 1 for l lt R lt1 and for R 1 Point Z R 1 gt f SDy SDX SDy Best Investments and AssetsA A W V LIJ g Combined investments with H X amp Y perfectly positively amp correlated R 1 g a Combined investments with X amp Y D imperfectly correlated 1 lt R lt 1 E Volatility Standard W quott Investments DeVIatIon SD J and Assets Fig 3 Intro to Portfoliosdoc Page 3 21Mar01 Portfolios and Diversity Fig 4 Investments and Asset Best Combined investments with X amp Y perfectly negatively correlated R 1 quotRisklessquot intercept 2 occurs where EZ SDY EX SDX EY I SDX SDY Mean Return E J Worst Investments and Assets Volatility Standard Deviation SD J Conclude Bene ts of diversi cation proven Applied Statistics and Probability for Engineers by Montgomery Extension What do we do when we hold gt2 investments Source Supplement Notes See amp Runge Wiley 1999 Section 67 pp 249250 Introduction to Portfolio Theory by HBS Prof Andre F Perold Harvard Business School Press Rev 9695 Risk Analysis and Its Applications by Hertz and Thomas 1983 Wiley pp 116120 Intro to Portfoliosdoc Page 4 21Mar01 Note on Present Value Demonstration Workbook John Joseph Crump 2001 This workbook has been prepared for use in class discussion for Prof Richard Dole39s course in Sales and Leasing given at the University of Houston Law Center Summer 2001 This Workbook contains the following tabs Title Block RE Opportunity Valuing a hypothetical real estate investment opportunity Compounding Illustrates how compounding works with several examples Inflation v Real Two examples comparing actual growth inflation and real gain Discrete Factor Tables Tables graphs examples and notes for four PV and FV tables Annuity PV Factor Plot Plots annuity PV factor v r and n PV with Periodic CF Example of an ordinary annuity roblem Actual amp PV CF Plot Graph from ordinary annuity problem IRR Plot Graph from ordinary annuity problem Martha39s Lease 21 Problem 21 from Keating CB Charlie39s Lease 231 Problem 231 from Keating CB Note on PVxs Title Block 8901 1 26 PV Example 2 Real Estate Investment Decision Interest Rate r 1r Discount Factor 11r US Government Securities Given Initial Investment Co Compute Future Value FV After One Year C1 Initial Investment Co Required to Receive Target FV Egg Future Value FV After One Year C1 Rebuilt Apartment House Initial Real Estate Investment CORE Initial Securities Investment Cos Total Initial Securities Investment Co Real Estate Value After One Year C1RE Return on Real Estate Investment rRE ORECORE 1 Securities Value After One Year C13 Return on Securities Investment rs C1sCos 1 Total Value After One Year C1 Return on Portfolio of Investments r C1C0 1 Present Value PV of Amount C1 Net Present Value NPV New Office Building Initial Real Estate Investment Co Total Value After One Year C1 Return on Real Estate Investment r Present Value PV of Amount C1 Net Present Value NPV 60 106 09433962 350000 371000 377358 400000 250000 100000 350000 293000 172000 106000 60000 399000 140000 376415 26415 350000 400000 142857 377358 27358 70 107 09345794 350000 374500 373832 400000 250000 100000 350000 293000 172000 107000 70000 400000 142857 373832 23832 350000 400000 142857 373832 23832 142857 1 142857 0875000 350000 400000 350000 400000 250000 100000 350000 293000 172000 114286 142857 407286 163673 356375 6375 350000 400000 142857 350000 0 172 1172 0853242 350000 410200 341297 400000 250000 100000 350000 293000 172000 117200 172000 410200 172000 350000 0 350000 400000 142857 341297 8703 Note on PVxs RE Opportunity 8901 226 Compounding and Comparison of Factors FV Factor FSPrAn comparison for n 1 Compare Discrete and Compare Discrete and Continuous FV Factors Annual Continuous Return Rates vs Continuous Compounding Annual vs Continuous Compounding 130 030 A n c E 125 PerfectMatch 11 g 025 D a 3 3 120 g 020 O x 5 5 E A E E 115 E 0 015 i l 395 O V 1 c 0 8 g 110 E 010 939 g g 105 393 005 U I 100 000 100 110 120 130 000 010 020 030 Discrete Compounding FSP rA n Nominal Return Compounded Annually rA Note on PVxIs Compounding 8901 3 26 Discrete Compounding Comparison of Single Payment Future Value Factors with Different Compounding Plans Note on PVxIs Compounding 8901 4 26 2 2 1 4 I u E E E 21 g 3 w a g E g 5 E o E E a E I E E 3 o H w 3 0 I o o w Compounding z m E lt tn 0 E o o o a Equation for FSPJn 1 rAxn 1 rA1quot 1 n22n 1 n44n 1 rA12 quot 1 rA365365quot exprAgtltn x NA 1 2 4 12 365 as n 1 Xn NA 1 2 4 12 365 cc rA 0 FS1rAn 1000000 1000000 1000000 1000000 1000000 1000000 10000000 Increment 0000 0000 0000 0000 0000 1 FS1rAn 1010000 1010000 1010025 1010038 1010046 1010050 10100502 Increment 0002 0004 0005 0005 0005 2 FS1rAn 1020000 1020000 1020100 1020151 1020184 1020201 10202013 Increment 0010 0015 0018 0020 0020 3 FS1rAn 1030000 1030000 1030225 1030339 1030416 1030453 10304545 Increment 0022 0033 0040 0044 0044 4 FS1rAn 1040000 1040000 1040400 1040604 1040742 1040808 10408108 Increment 0038 0058 0071 0078 0078 5 FS1rAn 1050000 1050000 1050625 1050945 1051162 1051267 10512711 Increment 0060 0090 0111 0121 0121 6 FS1rAn 1060000 1060000 1060900 1061364 1061678 1061831 10618365 Increment 0085 0129 0158 0173 0173 7 FS1rAn 1070000 1070000 1071225 1071859 1072290 1072501 10725082 Increment 0114 0174 0214 0234 0234 8 FS1rAn 1080000 1080000 1081600 1082432 1083000 1083278 10832871 Increment 0148 0225 0278 0303 0304 9 FS1rAn 1090000 1090000 1092025 1093083 1093807 1094162 10941743 Increment 0186 0283 0349 0382 0383 10 FS1rAn 1100000 1100000 1102500 1103813 1104713 1105156 11051709 Increment 0227 0347 0428 0469 0470 11 FS1rAn 1110000 1110000 1113025 1114621 1115719 1116260 11162781 Increment 0273 0416 0515 0564 0566 12 FS1rAn 1120000 1120000 1123600 1125509 1126825 1127475 11274969 Increment 0321 0492 0609 0667 0669 13 FS1rAn 1130000 1130000 1134225 1136476 1138032 1138802 11388284 Increment 0374 0573 0711 0779 0781 14 FS1rAn 1140000 1140000 1144900 1147523 1149342 1150243 11502738 Increment 0430 0660 0819 0899 0901 15 FS1rAn 1150000 1150000 1155625 1158650 1160755 1161798 11618342 Increment 0489 0752 0935 1026 1029 16 FS1rAn 1160000 1160000 1166400 1169859 1172271 1173470 11735109 Increment 0552 0850 1058 1161 1165 17 FS1rAn 1170000 1170000 1177225 1181148 1183892 1185258 11853049 Increment 0618 0953 1187 1304 1308 18 FS1rAn 1180000 1180000 1188100 1192519 1195618 1197164 11972174 Increment 0686 1061 1324 1455 1459 19 FS1rAn 1190000 1190000 1199025 1203971 1207451 1209190 12092496 Increment 0758 1174 1466 1613 1618 20 FS1rAn 1200000 1200000 1210000 1215506 1219391 1221336 12214028 Increment 0833 1292 1616 1778 1784 21 FS1rAn 1210000 1210000 1221025 1227124 1231439 1233604 12336781 Increment 0911 1415 1772 1951 1957 22 FS1rAn 1220000 1220000 1232100 1238825 1243597 1245994 12460767 Increment 0992 1543 1934 2131 2137 23 FS1rAn 1230000 1230000 1243225 1250609 1255864 1258509 12586000 Increment 1075 1676 2103 2318 2325 24 FS1rAn 1240000 1240000 1254400 1262477 1268242 1271149 12712492 Increment 1161 1813 2278 2512 2520 25 FS1rAn 1250000 1250000 1265625 1274429 1280732 1283916 12840254 Increment 1250 1954 2459 2713 2722 Note on PVxIs Compounding 8901 526 Comparison of Effective Rates of Return with Different Compounding Freguencies Notes The Nominal Rate of Return with annual compounding is equivalent to the annual Effective Rate of Return Where rA is a Nominal Rate of Return compounded annually rx X1rAquotX X is the equivalent Effective Return Rate for period X where X is the actual number of compounding periods per year Since the continuous compounding factor exprc for an effective continuous return rate must equal FSPrA1 where the equivalent effective annual interest rate is rA we get exprc 1 rA and rc ln1rA Discrete Compounding 2 gt quoto a E E g gt 2 g E e gt g E 9 4 f quot3 E E g E s a E D i 3 w o E g E 2 E E 3 3 E a Z w 1 O 395 o o 63 Compoundlng w E lt E n w o E o o o a Equation for Fmquot rA 1 rA1 1 21 rA 2 2 41 a 4 121 mm 12 3651rA 365 365 ln1rA X NA 1 2 4 2 365 cc rA 0 Effective Return 00 00 00 00 00 00 00 Change 1 Effective Return 10 10 0997512 0996272 0995446 0995047 0995033 Increment 0249 0373 0455 0 495 0497 2 Effective Return 20 20 1 990099 1 985173 1981898 1 980316 1980263 39 0495 0741 0905 0 984 0987 3 Effective Return 30 30 2 977831 2966829 2959524 2956000 2955880 Increment 0739 1106 1349 1467 1471 4 Effective Return 40 40 3 960781 3941363 3928488 3922282 3 922071 Increment 0980 1466 1788 1943 1948 5 Effective Return 50 50 4939015 4908894 4888949 4879343 4879016 39 1220 1822 2221 2 413 2420 6 Effective Return 60 60 5 912603 5 869538 5841061 5 827356 5826891 Increment 1457 2174 2649 2 877 2885 7 Effective Return 70 70 6881609 6823410 6784974 6766492 6765865 Increment 1691 2523 3072 3336 3345 Note on PVxls Compounding 8901 6 26 8 Effective 80 80 7846097 7770619 7720836 7696916 7696104 6573 8206 9908 10715 107 Note on PVxIs Compounding 8901 7 26 Ilnflation and Real Interest Two Examples 1 lfinflation is expected to average d percent per year long term what rate or return r percent per year is required to realize a real gain of5 percent a er acounting for in ation d Target rm We knowthat 1 r 1 rm x 1 d a 1 r 11025 Therefore r 1025 500 500 Here 2 Our factory will require addition ofa new crane at time T lt 10 The cost today of such a crane is C If equipment costs are expected to grow at an average of d percent per year between now and time Tand the discount rate is r percent per year what is the PV cost of the crane ie how much should we invest now to assure that we can afford the crane at time T T 5 C 20000 CM In ated crane cost in Tyears C x 1 dT 2676451 d 600 r 1100 PV cost of crane sinking fund investment today inquot 1 rT 1588343 rm 472 Time year T 0 1 2 3 4 5 6 7 8 9 10 Inflation d 600 600 600 600 600 600 600 600 600 600 600 De ator 1 CIT 1 1060000 1123600 1191016 1262477 1338226 1418519 1503630 1593848 1689479 1790848 Discount Rate r 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 FV Factor 1 rT 1 1110000 1232100 1367631 1518070 1685058 1870415 2076160 2304538 2558037 2839421 Discount Factor 11 rT 1 0900901 0811622 0731191 0658731 0593451 0534641 0481658 0433926 0390925 0352184 Real Growth Factor Difference 0 0050000 0108500 0176615 0255593 0346833 0451895 0572530 0710690 0868558 1048573 Real Growth Rate rm 472 472 472 472 472 472 472 472 472 472 472 Real Growth Factor 1 rmT 1 1047170 1096565 1148289 1202454 1259173 1318568 1380765 1445896 1514098 1585518 Crane cost today C 20000 Inflated crane cost Cin 20000 2120000 2247200 2382032 2524954 2676451 2837038 3007261 3187696 3378958 3581695 Investment today 20000 1909910 1823878 1741721 1663265 1588343 1516796 1448472 1383226 1320918 1261418 Note on PVxls In ation v Real 8901 8 l 26 Growth Factors Total Growth v Real Growth and the Effect of Inflation Growth Factor 1 rquotn lnflation Factor 1 dquotn Real Growth Factor 1 rrealquotn OActual Growth Factor Inflation Factor Years Note on PVxls In ation v Real 8901 926 Sample Tables for Four Present and Future Value Factors with Discrete Compounding FXYJn Notation P Present value the value now today 5quot Future value at the end ofthe nth time period R R2 Uniform ie repeated each period endof year amount Can be positive revenue or negative cost Rh Uniform beginningof year amount r Return discount interest or hurdle rate or the opportunity cost of capital in per time period Note that these tables assume that r r r2 constant In practical capital budgeting a single discount rate is usually applied but it is not required See RA BREALEYAND C MEYERS PRINCIPLES OF CORPORATE FINANCE at 242246 6th ed 2000 n Number of periods for discrete periodic factors Most commonly n is in units ofyears but it can be in anytime units or it can be continuous nym Present Value Factor for using X to compute Y given r and n Note on PV gtlti5 7 Discrete FactorTabieS 890171026 Note 8901 7 11 ISingle Payment Future Value Factors with Discrete Compounding FPS Here S PFPSM P1 rquot and FPSquot is the Future Value of100 today given r and n Use the value now P to compute the Jture value S ifthat present value is invested for n time periods eaming interest or a return of r per period Sn 0 1 3 4 5 6 7 1nr11 T p As shown this table assumes that payment in P and payment out 8 are made at the ends of periods 0 and h respectively Example 100 invested at 7 interest per year for4 years is worth 1001007 100 X 13108 13108 at the end ofthe fourth year N019 The Rule of 17s or 725 Roughly speaking FPSquot 2 in the range of 6 5 r11 and 6 3 n 11v1nere r n 17 Alternatively dividing 72 by the interest rate r gives the approximate number of periods n needed for FPSquot to be about 2 and vice versa erlod the opportunltv cost of capital in 1 per time period n 1 n n n n 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 30 1 1000 1 02000 1 03000 1 04000 1 05000 1 0E000 1 07000 1 00000 1 09000 1 10000 1 11000 1 12000 1 13000 1 14000 1 15000 1 1E000 1 17000 1 10000 1 19000 1 20000 1 21000 1 22000 1 2300 1 24000 1 25000 1 3000 2 102010 104040 10E090 1001E0 1 10250 1 123E0 1 14490 1 1EE40 1 10010 121000 123210 125440 127E90 1299E0 132250 1345E0 13E090 139240 141E10 144000 14E410 140040 151290 1537E0 15E250 1 E9000 3 1 03030 1 0E121 1 09273 1 1240E 1 157E3 1 19102 1 22504 1 25971 1 29503 1 33100 1 3E7E3 1 40493 1 44290 1 40154 1 52000 1 5E090 1 E01E1 1 E4303 160516 172000 177156 101505 106007 190662 195313 219700 4 1040E0 100243 1 12551 1 1E90E 121551 12E240 131000 13E049 141150 14E410 151007 157352 1 E3047 1E009E 1 6901 101066 107309 193070 200536 2 07360 216359 221533 2 20007 2 36621 246161 2 05610 5 105101 1 10400 1 15927 121EE5 127E20 3023 140255 4E933 1530E2 1 E1051 1 E05 7E234 106266 192561 2 01136 210036 219265 2 20776 2 30E35 2 40032 2 59374 2 1 2 01531 2 931E3 3 0517E 3 71293 6 10E152 1 12E1E 1 19405 12E532 134010 141052 150073 150E07 1 E7710 17715E 107061 197302 200195 219697 2 3130E 2 43E40 2 5E51E 2 E9955 2 0397E 2 90590 313043 3 29730 3 4E203 3 E3522 3 01470 4 02E01 7 1 07214 1 140E9 1 22907 1 31593 1 40710 1 503E3 1 E0570 1 71302 1 02004 196072 2 076 21060 2 352E1 2 50227 2 EE002 2 02E22 3 00124 310547 3 37932 3 50310 3 79750 4 02271 4 25920 4 507E7 4 7E037 E 27405 3 1 0020E 1 171EE 1 2EE77 1 3E057 1 4774E 1 59305 1 71019 1 05093 199256 216359 2 30454 2 4759E 2 E5044 2 05259 3 05902 3 27041 3 51145 3 7500E 4 02139 4 29902 4 59497 4 90771 5 23091 5 50951 5 9E04E 015731 9 1 093E9 1 19509 1 30477 1 42331 1 55133 1 E0940 1 0304E 199900 217109 2 35795 2 55004 2 77300 3 00404 3 25195 3 51700 3 0029E 410040 4 43545 4 70545 515970 5 55992 5 9074 E 4430E E 93099 7 5050 10 E045 10 1 104E2 1 21099 1 34392 1 40024 1 E2009 1 79005 196715 215092 2 3E73E 2 59374 2 03942 310505 3 39457 3 70722 4 0455E 4 41144 4 00E03 5 23304 5 E94E0 E 19174 E 72750 7 304E 7 92595 0 59443 9 31323 13 7050 11 1 115E7 124337 130423 153945 171034 109030 210605 2 331E4 2 50043 2 05312 31517E 3 47055 3 0350E 4 22E23 4 E5239 51172E 5 E2399 E 17593 E 77EE7 7 43000 01403 0 9117 9 74091 10 E571 11 E415 17 921E 12 1 12E03 12E024 14257E 1 E0103 17950E 2 01220 2 25219 2 51017 2 012EE 313043 3 49045 3 09590 4 33452 4 01790 5 35025 5 93E03 E 50007 7 20759 0 0E424 91E1 0497 10 0722 119912 13 2140 14 5519 23 2901 13 1 13009 1 293E1 1 4E053 1 EE507 1 005E5 213293 2 40905 2 719E2 3 0E500 3 45227 3 00320 4 3E349 4 09001 5 49241 E 15279 E 00579 7 E90E0 0 5994 59E4 1 E993 11 9102 13 2E41 14 7491 1E 30E3 101099 30 2075 14 1 14947 131940 151259 1731E0 197993 22E090 257053 293719 334173 379750 431044 400711 553475 E2E135 707571 790752 0075 101472 114190 120392 144210 1E 1022 101414 203191 22 7374 39 3730 15 1 1E097 1 34507 1 55797 1 00094 2 07093 2 39E5E 2 75903 317217 3 E4240 417725 4 70459 5 47357 E 25427 713794 01370E 9 2E55 10 5307 11 9737 13 5095 15 4070 17 4494 19 7423 22 3140 25195E 20 4217 51 1059 16 1 17250 137279 1 E0471 107290 210207 2 54035 2 9521E 3 42594 3 97031 4 59497 5 31009 E 13039 7 0E733 013725 9 357E2 10 7400 12 3303 141290 1E 1715 10 4004 21 1130 24 005E 27 44E2 31242E 35 5271 EE 5417 17 1 10430 1 40024 1 E5205 196790 2 29202 2 E9277 315002 3 70002 4 327E3 5 05447 5 09509 E 0EE04 7 90E00 9 27E4E 10 7E13 12 4E77 14 42E5 1E E722 19 2441 2210E1 25 5477 29 3044 33 7500 30 7400 44 4009 0E 5042 13 1 19E15 1 42025 1 70243 202502 2 40EE2 2 05434 3 37993 3 99E02 4 71712 5 55992 E 54355 7 E0997 9 02427 10 5752 12 3755 14 4E25 1E 0790 19 E733 22 9005 2E E233 30 9127 35 0490 41 5233 40 030E 55 5112 112 455 19 120011 145E01 175351 210E05 2 52E95 3 025E0 3 E1E53 4 31570 5141EE E 11591 7 2E334 0 E127E 101974 12 0557 14 2310 1E 77E5 19 7404 23 2144 27 251E 319400 37 4043 43 7350 510737 59 5E79 E9 3009 14E 192 20 1 22019 1 40595 1 00E11 219112 2 E5330 3 20714 3 0E9E0 4 EE09E 5 E0441 E 72750 0 0E231 9 E4E29 11 5231 13 7435 1E 3EE5 19 4E00 23105E 27 3930 32 4294 30 337E 45 2593 53 357E E2 020E 73 0E41 0E 73E2 190 050 21 1 23239 1 515E7 1 0E029 2 27077 2 7059E 3 3995E 41405E 5 03303 E 10001 7 40025 0 94917 10 0030 13 0211 15 EE7E 10 0215 22 5745 27 033E 32 3230 30 5910 4E 0051 54 7E37 E5 09E3 77 2E94 91 5915 100 420 247 0E5 22 124472 154590 191E10 2 3E992 2 9252E 3 E0354 4 43040 5 43E54 E E50E0 014027 9 93357 121003 14 7130 17 0E10 21 E447 2E 10E4 31 E293 301421 45 9233 55 20E1 EE 2E41 79 4175 95 0413 113 574 135 525 321 104 23 1 2571 E 1 57E90 1 97359 2 4E472 3 07152 3 01975 4 74053 5 0714E 7 25707 0 95430 11 02E3 13 5523 1E E2EE 20 3E1E 24 0915 30 37E2 37 00E2 45 007E 54 E407 EE 2474 001795 9E 0094 11E 901 140 031 1E9 407 417 539 24 1 2E973 1 E0044 203279 2 5E330 3 22510 4 04093 5 07237 E 34110 7 91100 9 04973 12 2392 15170E 10 7001 23 2122 20 E252 35 23E4 43 2973 531090 E5 0320 79 49E0 97 0172 110 205 143 700 174 E31 211 750 542 001 25 1 20243 1 E40E1 209370 2 EE504 3 30E35 4 29107 5 42743 E 04040 0 E2300 10 0347 13 5055 17 0001 21 2305 2E 4E19 32 9190 40 0742 50 E570 E2 EEOE 77 3001 95 39E2 117 391 144 210 17E 059 21 E 542 2E4 E90 705 E41 26 12952E 1 E7342 215E59 2 77247 3 555E7 4 54930 5 00735 7 39E35 9 3991E 119102 15 0799 19 0401 23 9905 301EEE 37 05E0 47 4141 59 2E97 73 9490 92 0910 114 475 142 043 175 93E 217 537 2E0 512 330 072 917 333 23 132129 174102 220793 299070 392013 5111E9 EE4004 0E2711 11 1E71 144210 105799 23 0039 30 E335 39 2045 50 0E5E E3 0004 01 1342 102 9E7 130 411 1E4 045 207 9E5 2E10E4 329112 4120E4 51E900 1550 29 30 134705 10113E 2 4272E 3 24340 4 32194 5 74349 7 E122E 10 0E27 13 2E77 17 4494 22 0923 29 9599 391159 50 9502 EE 2110 05 0499 1110E5 143 371 104 E75 237 37E 304 402 309 750 497 913 E34 020 007 794 2E20 00 32 137494 100454 2 57500 3 5000E 4 7E494 E 45339 0 71527 117371 15 7E33 21 1130 20 205E 37 5017 49 9471 EE 2140 07 5E51 115 520 152 03E 199 E29 2E1519 341022 445 79 0011E 753 292 97E 099 12E210 4427 79 34 1 40250 196060 2 73191 3 79432 5 25335 7 25103 9 97011 13 E901 10 7204 25 5477 34 7521 471425 E3 7774 0E 0520 115 005 155 443 200123 277 9E4 370 337 492 22 E52 E0 0E3 444 1139 EE 1500 05 197215 7402 97 36 143077 2 03909 2 09020 410393 5 79102 014725 114239 15 9E02 22 2512 30 9127 42 0101 59135E 014374 111034 153152 2091E4 204 099 307 037 524 434 700 00 955 59 120515 172419 2307 71 300149 12E4E 2 33 1 45953 212230 3 07470 4 43001 E 30540 915425 13 0793 10 E253 2E 43E7 37 4043 52 75E2 741797 103 907 145 340 202 543 201 452 309 990 530 91 42 E5 1 20 E7 1399 00 1912 02 2E00 52 3540 33 4014 02 213721 40 1 4000E 2 20004 3 2E204 4 00102 7 03999 10 2057 14 9745 21 7245 31 4094 45 2593 E5 0009 93 0510 132 702 100 004 2E7 0E4 370 721 533 07 7 0 30 1051 E7 14E9 77 2040 40 2047 04 394E 43 5455 91 75231E 3E110 9 50 1 E44E3 2 E9159 4 30391 710EEO 11 4E74 10 4202 29 4570 4E 901E 74 3575 117 ISingle Payment Present Value Factors with Discrete Compounding FSPJquot Here P SnFSpM S1 r39quot and FSPM is the Present Value of100 at the end of period n given r and n Use the Jture forecast value S to compute the value now P that must be invested for n time periods earning interest or a return of r per period in order to grow to S As shown this table assumes that payment in P and payment out 8 are made at the ends of periods 0 and h respectively Example At 7 interest per year 1 00 that you expect to receive at the end of4 years is worth 10010074 100 13108 100 X 0762893 7629 right now 1 6 Note FSPM is the inverse of FPS FSPM 1 FPS T Period the opport v cost of capital in per time period n 1 2 3 4 5 6 7 8 9 10 1 D 99818 D 98839 D 97887 El 9E154 D 95238 D 94348 D 93458 D 92593 D 91743 D 98989 2 D 98838 El 9E117 E 942EE E 9245E D 98783 El 89EEE D 87344 D 85734 El 841E8 E 82E45 3 897859 894232 891514 888988 E8E384 E839E2 E81E3E 879383 877218 875131 4 El 9EE98 D 92385 D 88849 D 85488 D 82278 D 79289 H 7629 D 73583 D 78843 8 E8381 5 D 95147 D 98573 El 8E2E1 D 82193 D 78353 El 7472E D 71299 8 E8858 8 E4993 8 E2892 6 D 94285 D 88797 D 83748 D 79831 El 74E22 E 7E49E E EEE34 8 E3817 8 59E27 E 5E447 7 D 93272 El 87E5E D 81389 D 75992 El 71EE8 E EE5EE 8 E2275 8 58349 D 54783 El 5131 E 3 D 92348 D 85349 D 78941 El 73EE9 E E7E84 8 E2741 D 58281 D 54827 D 58187 El 4EE51 9 D 91434 El 83E7E E 7EE42 D 78259 El E44E1 D 59198 D 54393 D 58825 El 4EE43 El 4241 El 10 D 98529 D 82835 D 74489 El E755E 8 E1391 8 55839 D 58835 El 4E319 D 42241 D 38554 11 El 89E32 E 8E42E D 72242 8 E4958 8 584E8 E 52E79 D 47589 D 42888 D 38753 D 35849 12 D 88745 D 78849 D 78138 El E24EE E 55E84 E 49E97 D 44481 D 39711 D 35553 El 318E3 13 El 878EE D 77383 8 E8895 8 E8857 D 53832 El 4E884 E 4149E E 3E77E E 32E18 E 289EE 14 El 8E99E D 75788 El EE112 D 57748 D 58587 D 44238 D 38782 El 34E4E D 29925 El 2E333 15 E8E135 E743E1 EE418E E5552E 848182 841727 E3E245 831524 827454 823939 16 885282 872845 EE2317 853391 845811 E393E5 833873 829189 825187 E217E3 17 884438 E7141E EEE5E2 E51337 E43E3E E3713E E31E57 827827 823187 819784 13 El 83EE2 E 7EE1E D 58739 El 493E3 D 41552 D 35834 El 2958E D 25825 D 21199 E1798E 19 D 82774 El E8E43 D 57829 El 474E4 D 39573 D 33851 El 27E51 D 23171 D 19449 E1E351 20 D 81954 8 E7297 8 553E8 E 45E39 E 37E89 D 31188 D 25842 D 21455 D 17843 E148E4 21 881143 EE5978 853755 843883 835894 E2941E E24151 E198EE E1E37E D 13513 22 D 88348 El E4E84 D 52189 El 4219E D 34185 D 27751 D 22571 D 18394 815818 8 12285 23 879544 EE341E E5EEE9 848573 832557 E2E18E 821895 817832 8 13778 E111E8 24 878757 EE2172 849193 839812 831887 E24E98 D 19715 815778 E12E4E 818153 25 D 77977 8 E8953 8 477E1 D 37512 D 29538 D 23388 D 18425 E14EE2 D 11597 D 89238 26 D 77285 D 59758 El 4E3E9 E 3EEE9 D 28124 D 21981 817228 813528 E1EE39 D 88391 23 El 75E84 D 57437 D 43788 D 33348 D 25589 E195E3 815848 8 11591 D 88955 El EE934 30 874192 855287 841199 838832 823138 8 17411 D 13137 889938 887537 885731 32 D 72738 El 53EE3 D 38834 El 285EE D 28987 El 1549E El 1147 D 88528 El EE344 E E473E 34 D 71297 D 51883 El 3EEE4 E 2E355 819835 8 13791 818822 D 87385 D 85339 D 83914 36 8 E9892 D 49822 D 34583 El 243E7 E172EE D 12274 D 88754 El EE2E2 D 84494 D 83235 33 8 E8515 8 47119 D 32523 D 22529 E15EE1 818924 8 E7E4 E E53E9 D 83783 El E2E73 40 El E71E5 D 45289 El 3EE5E D 28829 814285 D 89722 El EEE78 E E4EE3 D 83184 D 82289 50 8 E8884 8 37153 D 22811 814871 D 88728 D 85429 D 83395 D 82132 D 81345 D 88852 100 El 3E971 813883 D 85283 D 81988 El EE7EE D 88295 D 88115 D 88845 D 88818 El EEEE7 1quot 2 3 4 5 6 7 8 9 10 11117111 T 11 nannan 0811132 nuns 11 12 D 89285 D 79719 12 ins 12 13 n nn222 EVEIE 49 13 Sn 14 D 87719 2 EIErEIE 14 15 n unn92 E 5517 15 16 3 BED 16 17 17 18 D 84745 E SEVEIE 18 19 2 8E7 19 20 1 2EVEIE 20 n unnm 5 3EE9 21 22 3 rug 2 22 23 1 EIErEIB 23 24 n unnn2 4 5Er1 24 25 2 EIEr1EI 25 30 4 EIEr12 30 35 a 3Er14 35 Period mbuuuuunnnnnnnnaa 2222222 A 80 combmommasunaommqmmsunaomm mmPQN Note on PV X15 7 Dlscrete FactorTableS 8901712 26 E ual Pa ment Series Future Value or Annui Future Value Factors with Discrete Com oundin FRSJquot Here S RFRS Use the periodic r r an 95 Ist e uture a us 0 n en 0 peno payments 0 per peno given r R1 quot1 dFH39hF VI f df 39d f100 39d39 R mime value S in 39 39 J at the end of each ofn time periods eaming interest or a return of r per period 5quot Annuity Due or Annuity in Advance 3 Payments in at the beginning of each period 0 1 2 3 5 6 7 I1nr1l n RET RI R R R R R REI R OrdinaryAnnuityorAnnuityinArrearsPaymentsinattheendofeachperiod As shown this table assumes that all payment in R and payment out 8 are made at the ends of periods starting with the end ofperiod 1 007 100 X 443994 44399 at the end ofthe 4 h year R Example At 7 interest per year 100 that you pay in at the end of each year will be worth 100 X 10074 1 Note The Sinking Fund Factor FER is the inverse of F95 FERquot 1 F95 Also F95quot FRPMU rquot FRPMFPSM Finally if payments are made at the beginning ofeach period instead ofthe end Rb not RE Rb X 1 r R Use that value in computations Here with beginningof period payments the example becomes 100 X 1 007 X 443994 47507 the opportu of capital in per time period Period 1 5 6 7 A 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 30 35 4 n 1 00000 1 00000 1 00000 1 00000 1 00000 1 00000 1 00000 3000 2 07000 2 08000 2 09000 210000 211000 218000 318330 3 21490 3 24340 3 27810 3 31000 3 34210 3 37440 3 40390 3 43930 3 47250 3 50530 3 53890 3 57240 3 30310 3 34000 3 37410 3 70840 3 74290 3 77730 3 E1250 3 99000 417250 4 33000 5 21543 a 199999 199999 199999 199999 199999 199999 199999 29 495949 412151 437452 M3994 459511 457313 454199 479973 477933 494999 492114 499339 595559 514951 529125 535999 544555 552425 559377 559422 575553 519799 553299 719499 519191 529494 553799 575974 595559 599471 519519 522799 535295 549927 551919 574239 597714 791449 715 1 729559 744159 759925 773959 799253 994944 929793 994319 995439 199455 515292 539912 597532 715329 733593 752333 771551 791295 911519 932271 953552 975374 997749 929595 944197 9 939 99299 191939 194423 197979 199991 11 599 127559 144394 153239 721354 743429 939394 955492 992299 929943 949717 979327 199999 1 47 197395 119559 114139 117729 121415 125227 129159 133214 137395 141799 1 53 159735 175929 294919 239534 929557 959297 999747 192599 195355 119295 114359 119594 122997 127573 132329 137259 142491 147733 153279 159929 154991 171199 177523 194399 191229 199419 239577 295549 343947 935953 975453 119799 135795 154157 157959 175195 192947 199959 297999 225799 235599 247125 329159 395954 491525 149715 157935 155455 175593 195312 195514 295545 219143 239445 243493 257329 271999 297551 394935 321594 349913 359529 399399 492379 425551 554953 745957 997391 551191 599553 552597 729351 793395 951922 925594 199915 199597 157295 254739 395429 399957 339999 374592 413913 455992 593959 557497 517251 593941 759354 941497 934955 193749 115255 129117 142441 159495 175199 195994 219945 371519 539925 195479 459959 534351 599933 5 19 795439 911479 194593 129295 139297 159275 193591 211991 244497 292352 325237 377945 435951 593917 592539 573525 139945 293994 573714 95 2 5 154752 199535 259957 337992 442593 591925 757991 191379 134293 177999 235975 313452 415321 552993 734395 974952 129355 171549 399997 129393 455959 195495 27 93 315153 454972 555172 955494 135992 195373 299255 17E95 94E95 515497 5 100 179491 312232 597299 123752 93 553937 4945 10E15 100 1 7 1 2519 514227 137795 399 E03 79E95 17E97 39E97 95E97 19E99 41E B99 2 0E10 E3E11 31E13 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 30 35 40 buuuuuNNNNNNNNaaaaaaaaaa A oococaNooncamsunsommqmmsunso om mmbuk Note on PV X15 7 Discrete FactorTabieS 890171326 Egual Payment Series Present Value or Annuity Present Value Factors with Discrete Compounding FRPJquot Note For a Perpetuity n w and P Rr Here P RFRPM R1 rquot 1 r1 rquot and F95quot is the Present Value at time t ofn end of period payments of100 per period given r Compute the present value P that must be invested ifthe return is r per period and the desired periodic payment the annuity is R to be paid out at the end of each ofn periods R R R R R R R R R R Annuity Due or Annuity in Advance 3 Payments in at the beginning of each period 0 1 2 3 4 5 6 7 971 n I I P Ordinary Annuity or Annuity in Arrears Payments in at the end of each period As shown this table assumes that payment in P is made at the end of period 0 and all payments out the n R are made at the ends ofn periods therealter Example To fund 4 years of100 yearend payments with 7 interest per year invest 1 00 X 10074 1 00710074 100 X 338721 33872 now Note The Capital Recovem Factor F99 is the inverse of F99quot FPRM instead ofthe end Rb not RE Rb X 1 r R Use that value in computations Here with beginningof period payments the example becomes 100 X 1 007 X 338721 36243 F99 Also F95quot FRP 1 rquot FRPMFPSM Finally if payments are made at he beginning of each period Period the opportunitv cost of capital in per time period Period 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 30 35 40 n E El 9523E E 9434E E 9345E D 92593 D 91743 El E92EE E EE49E 71 El E547E E E474E E E4E34 E E3333 E E2E45 3E1 E EEE45 E EEEEE E 7E923 E 74E74 1 97E4E 1 9415B 1 91347 1 EEEE9 1 E5941 1 E3339 1 EEEE2 1 7E32E 1 75911 1 73554 1 71252 1 E9EE5 1 EEE1E 1 E4EEE 1 E2571 1 EE523 1 5E521 1 5E5E4 1 54E5E 1 5277E 1 5E94E 1 49153 1 47399 1 45EE2 1 44EEE 1 3EE95 1 2E944 1 22449 2 EE3EE 2 E2EE1 2 775E9 2 72325 2 E73E1 252432 2 5771E 2 53129 2 4EEE5 2 44371 2 4E1E3 2 3E115 2 321E3 2 2E323 2 245E9 2 2E95E 217427 213992 21EE4E 2 E7393 2 E4224 2 E1137 19E13E 1952EE 1E1E11 1E95EE 15EE92 3 15997 3 79979 3 59599 3 59479 5 79549 5 59143 5 41719 5 24214 5 97559 4 91732 4 75554 4 52299 4 49592 4 35525 4 23954 411141 3 99957 3 79449 3 59474 3 59919 3 49759 3 49979 3 32551 5 47199 5 23929 5 99295 5 79537 5 59239 5 39929 5 29537 5 93295 4 95942 4 71229 4 55375 4 42251 4 29939 415942 4 93957 3 92239 3 91153 3 79579 2 49354 2 95354 315592 3 99225 3 92947 2 95142 2 54275 2 39515 215797 3 41551 3 32794 3 24232 315114 2 99211 2 59752 2 25294 3 51927 3 79529 5 53492 5 33493 4 97757 5 99525 5 75992 4 39392 947139 999259 953929 911999 772173 735999 792359 571999 541755 514457 599923 555922 521512 591977 493323 455959 449499 433993 419247 392319 379927 359195 357959 399154 271594 241357 193575 979595 925252 975949 939541 799597 749957 713995 599519 549595 529552 593779 559594 545273 523371 592954 493541 455591 449559 432795 493549 399195 377559 355549 314734 275199 243925 112551 195753 995499 939597 995325 939394 794259 753599 715973 591359 549235 519437 591755 555929 542952 519711 499939 479322 451959 443922 412737 399524 395135 372512 319925 277917 245599 121337 113494 195359 999555 939357 995259 935755 799379 749599 719335 574997 542355 512191 594235 559315 534233 511929 499951 471471 453259 429277 495394 391239 379919 322329 279939 245959 139937 121952 112951 195531 999954 929499 974547 924424 779515 735559 599197 552917 539249 599297 572449 545753 522939 599995 499229 451957 443179 425455 419915 395159 392499 324957 291435 247759 545239 514217 594737 557545 532419 599159 497595 457547 449991 431522 415299 499129 395925 325921 292545 249393 155523 142919 131551 121557 112741 194773 975322 912154 954353 992155 754979 711953 572999 537295 594715 574979 547451 522233 499955 477453 457551 439977 421994 495911 249199 153993 149929 137535 125593 115995 199275 199591 937199 975553 929141 779152 724957 593991 545742 512797 591795 553395 527315 593333 491219 459795 441955 424312 497993 392794 339359 294425 249414 199579 179112 154159 149292 129212 117541 199355 199159 929224 954959 997597 755299 719155 559595 531245 597314 555475 539359 512577 499132 457495 447553 429155 412117 395311 331994 295191 249797 175599 159359 144511 131539 129415 119512 192997 944243 977154 917574 754455 715951 574294 535955 591133 559537 549999 514955 499943 459994 449922 439299 412999 397949 332295 295327 229232 195235 174131 155221 149939 127934 115535 195749 992259 997794 942174 794314 597293 545415 599799 575523 545591 519515 494759 472134 451393 432324 414742 399499 332951 295557 249944 722955 729299 732999 227952 291219 179759 159929 143752 139932 119259 199199 992997 915995 949995 799555 737157 599599 549955 511919 579311 549943 529591 495532 472939 451952 432794 415115 399791 332979 295599 249959 243154 212913 197541 155531 149991 134952 121371 119511 191151 939557 959152 799442 744129 595955 553351 515294 599995 559159 522299 495957 473991 452919 433452 415557 399225 333119 295559 249999 259977 223955 195994 172929 153725 137549 124999 112579 192737 942591 959379 995519 749555 799255 555599 517729 592939 551591 523455 497994 474527 453379 433999 415919 399595 333295 295579 249999 272595 234593 293999 179735 159927 149949 125455 114359 194952 952539 975959 911159 753939 793499 559953 519599 594355 552773 524393 499537 475122 453752 434295 415249 399593 333259 295595 249995 297927 244995 211319 194112 151929 143591 129549 115959 195179 959957 992932 915555 757179 795995 559919 529979 595499 553557 524995 499994 475451 454919 434491 415399 399797 333299 295794 249997 391975 254999 219323 199993 155459 145219 139352 117172 195119 957551 997959 919241 759795 797999 552314 522912 595171 554129 525312 499295 475592 454192 434539 415495 399979 333397 295799 249999 314947 254495 224925 193579 159579 149459 131935 119299 195999 973255 991959 922999 751933 799371 553375 522779 595727 554525 525597 499519 475959 454399 434515 415549 399917 333319 295711 249999 329347 273555 231149 197929 171591 159453 133317 119245 197574 995195 924379 753439 719594 554179 523359 597133 554915 525915 499559 475959 454395 434572 415599 399947 333324 295713 259999 OlbuuuuuNNNNNNNNaaaaaaaaaa oomoanNoonmornunaommummbunao om mmbukquot3 OlbuuuuuNNNNNNNNaaaaaaaaaa A coomoanNoonaxonsunsommqmmsunsomm wmbuk39 977995 1951 314235 257299 214922 192559 157519 139997 122335 199517 991491 994155 939459 757524 713255 555951 524525 599995 555414 525229 499945 475155 454524 434759 415559 399994 333333 295714 259999 1 539299 439994 315999 245959 199479 155175 142593 124943 111991 999927 999954 933323 759227 714294 555555 525999 599235 555555 525315 599999 475199 454545 434793 415557 499999 333333 295714 259999 10 mPerp 199999 599999 333333 259999 299999 155557 142957 125999 111111 199999 999991 933333 759231 714295 555557 525999 599235 555555 525315 599999 475199 454545 434793 415 57 499 99 333333 295714 259999 gt0 Perp 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 30 35 40 Note on PV X15 7 Discrete FactorTableS 890171426 Checking Examples Given Above Year x Interest Rate r A per year Single Values P at end of year 0 and 5 at end of year4 Equal Periodic Dollar Payments R Future quot 39 39 5 Pavoff quot J of Year 4 Factors 1 rquotquot 5 FV after initial investment of P R1r 5 FV after annual end of year payments of R3 R1rH 5 FV after annual beginning of year payments of Rh 1quot139R1quot139H Ordinary Annuity or Annuity in Arrears a Annuity Due or Annuity in Advance gt Present P Equivalent Values if Invested at End of Year 0 Factors 111139quot P PV equivalent to 5 R 1r P PV before annual end of year payments of R3 R 1rquot P PV before annual beginning of year payments of Rh 1rR 1rquot Ordinary Annuity or Annuity in Arrears gt Annuity Due or Annuity in Advance a PV FV 5ums in Each Year 5ums 0 1 2 3 4 7 7 7 7 7 100 100 100 100 100 100 13108 12250 11449 10700 10000 57507 131 88 122 58 11449 1E7 EIEI 1EE EIEI 443 99 131 88 12258 11449 18788 47587 3 3872 10000 0 9348 0 8734 0 8183 0 7829 7E 29 338 72 93 4E 87 34 81 E3 7E 29 3E2 43 188 EIEI 93 4E 87 34 81 E3 Note on PV X15 7 Discrete FactorTableS 890171526 Single Payment Investment Sin e Pa mentor Future Pa off Future Value Factors FPS n Present Value Factors Fsp n Note Discrete com pounding Note Discrete com pounding 39 r V V 09 minimMWWW WIIIH A WV 2 F V 2339 m V 07 Egm m m a 1 5 06 91v 39 V 39 V V mm Y AVM39A Vquot quot v quot39ampvv V AWL A V 39 A Aquot Aampquottquot2 quot 0392 25 1 70 01 quot13 0 13 Interest 32so N Interest 9 Rates r Rates r Note on PV MS 7 Discrete FactorTabieS 890171626 Eg ual Payment Series or Annuity E ual Pa ment Series or Annuit Discrete Future Value Factors FRSJn Discrete Present Value Factors FRPJn iii minim 140 t d 4 y v39 I i hi gunman iiwmm39 0 v v 39 L 39Lquot 39 9quot 39 V39Vv 39 vliv w quot o oe 090211quotng v A 59 5 FRSrn iiii nte rest Interest Rates r Rates r quot g quot Time Periods n Note Discrete compounding Time Periods n e39 Discrete compounding Comparing Annuity Factors FRPm for Different r amp n Values l2 0 Discrete Compounding Each line plots a different time period n FRPrn 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 Interest Rates r Note on PV MS 7 Discrete FactorTabieS 890171726 Egual Pavment Series or Annuitv Discrete Present Value Factors FRPJn 20 15 FRPrn 10 Q 3 s W s A O Q 0 s Q x Q Ngt 39 Interest 19 Rates r s h Perpetuity Time Note Discrete compounding Per39Ods n CapEx lnvestme Periodic Paymen Discount Rate Numb nt tAm un at Time t o per Period er ofPeriods PV Example An Ordinary Annuitv 1000000 150000 50 I NPV 7 CapEx RPRPM e1000000 150000r p m 150000 150000 150000 150000 150000 150000 150000 150000 150000 150000 0 t at 3t A at J 7 8 g m P Raw 150000PRP W 1 1000000 Time Period Years 0 1 2 3 4 5 8 7 8 9 CapEx investment 1 000000 Return for Each Period 150000 150000 150000 150000 150000 150000 150000 150000 150000 Cumulative Return 150000 300000 450000 800000 750000 900000 1050000 1200000 1350000 Cumulative Actual Cash Flow 1000000 850000 700000 550000 400000 250000 100000 50000 200000 350000 Current Dollars Discount Rate 5 Discount Factor 95 238 90 703 88 384 82 270 78 353 74 822 71 088 87 884 84 481 v of Returns 142857 138054 129578 123405 117529 111932 108802 101528 Pv of Cumulative Return 142857 278912 408487 531893 849422 781354 887958 989482 3510661720 Cumulative Pv Cash Flow 1000000 519857143 721088 591513 488107 350578 238848 132044 30518 88173 onstant Dollars t Net Present Value NPV 158280 7 CapEx 2Pv or Returns 158260 EXCEL NPV 7 Ca Ex 158280 7 CapEx RFRPM 7 1000000 150000F p 5wu lnternal Rate of Return lRR 8 14 Discount Rates 45 50 55 60 65 70 75 00 05 NPV 218834 188908 158280 130844 104013 78325 53537 29812 8512 15798 150000 1 500000 500000 61391 1158260 158260 90 37351 600000 7 400000 Cash Flows Actual amp PV Periodic amp Cumulative 200000 7 0 III is 200000 a 400000 0 600000 I 800000 a 39 39 39 i PV of Periodic CFS CorlSlarll at Tirne to 139ooo39ooo 39 I b Curnuialive Actual CF Current DollarS 1200000 I 0 Tirne to 1 2 3 4 Time Per ad Year 5 7 3 9 1quot 250000 Flndlnq the Pr0lect Internal Rate of Return lRR 200000 150000 g100000 2 50000 0 2 3 2 l 3 2 N 50000 oProlect NPV Constant Dollars at Time to 100000 00 10 20 30 40 Time pangs Year60 70 80 00 100 Nule Drl PV xis 7PV with Peiiudic CF 89017192E Cash Flows Actual g PV Periodic g Cumulative 600000 400000 200000 0 9 200000 3 o 0 400000 600000 Actua Periodic CFs Current Dollars 800000 D PV of Periodic CFs Constant at time zreo namp Cumulative Actual CF Current Dollars 1000000 0 Cumuative PV CF Constant at time zreo 1200000 0 1 2 3 4 5 6 7 8 9 10 Time Period Year Note on PVXIs Actual amp PV CF Plot 8901 2026 Findinq the Proiect Internal Rgte of Return IRR 250000 200000 150000 100000 Dollars 50000 0 I 50000 7 100000 00 10 20 30 40 50 60 70 80 90 100 Time Period Year Note on PVXls IRR Plot 8901 21 26 Problem 21 Martha Keough Leases a Caddy Consumer automobile lease Is this atrue lease or a disguised sale See KEATING SALES A SYSTEMS APPROACH at 3637 1998 Initial Used Caddy Value at Time t P 20000 Monthly Lease Payment R Rh 300 Option to Purchase at End of Lease S6quot 7000 50 n Lou39s NPV CapEx RFRPM SEDFSWD 20000 300FRP51U 7000F5p544m Discount Rate nominal compounded monthly ber of Payment Periods 60 300 300 300 300 300 300 300 4 4 4 4 4 4 4 Lou39s Perspective Lou39s NPV 2000000 2000 96345 5 45444 141789 141789 Martha39s NPV 1596345 5 45444 2141789 2141789 Martha39s Perspective plus 8 year old car 8 year old used car 0 1 2 3 4 5 6 58 59 60 300T 3001 3001 3001 300T 3001 3001 300 3001 7000 Notes Ignore questions ofhow much Lou paid for the car and his potential pro t 39om a sale now He is forgoing a 20000 sale now to lease this car Assume that all lease payments must be made at the beginning ofthe month due a R b Interest rate rM r 12 Total Interest Lou39s Perspective Martha39s Perspective Lou39s Initial Optional Current Rate per Present Cumulative Present Cumul I Payment Investment Lease inaI ayments Period Discount Value Present aIu Present XCEL Period Value Payments Purchase Each Period r 12 Factor for Period Value for Period Value Functions Raw Current 20000 18000 7000 5000 PV Totals Time 0 1 141789 2141789 0 20000 300 19700 000000 1000000 19700 19700 30000 30000 Lou39s NPV 1 300 300 041667 0995851 29876 19401 29876 59876 Time 0 2 300 300 041667 0991718 29752 19104 29752 89627 141789 3 300 300 041667 0987603 29628 18807 29628 119255 4 300 300 041667 0983506 29505 18512 29505 148760 Note on PV x5 7 Martha s Lease W 21 89017 2226 Note on PV X157 Martha s Lease w 21 89017 2326 041667 0979425 0975361 0971313 0967283 0963269 0959272 0955292 0951328 0947381 0943450 0939535 0935637 0931754 0927888 0924038 0920204 0916385 0912583 0908796 0905025 0901270 0897530 0893806 0890097 0886404 0882726 0879063 0875416 0871783 0868166 0864564 0860976 0857404 0853846 0850303 0846775 0843261 0839762 0836278 0832808 0829352 082591 1 0822484 0819071 0815672 0812288 0808917 0805561 0802218 0798890 0795575 0792274 0788986 0785712 0782452 29383 29261 291 39 29018 28898 28778 28659 28540 28421 28303 281 86 28069 27953 27837 27721 27606 27492 27377 27264 271 51 27038 26926 26814 26703 26592 26482 26372 26262 261 54 26045 25937 25829 25722 25615 25509 25403 25298 251 93 25088 24984 24881 24777 24675 24572 24470 24369 24268 241 67 24067 23967 23867 23768 23670 23571 23474 18219 29383 29261 29139 29018 28898 28778 28659 28540 28421 28303 28186 28069 27953 27837 27721 27606 27492 27377 27264 271 51 27038 26926 26814 26703 26592 26482 26372 26262 26154 26045 25937 25829 25722 25615 25509 25403 25298 25193 25088 24984 24881 24777 24675 24572 24470 24369 24268 24167 24067 23967 23867 23768 23670 23571 23474 1 781 43 207404 236543 265562 294460 1596345 Lou39s IRR 060821 or 7298 Nominal Compoundd Montth Martha39s Time 0 2141789 60 7000 7000 041667 0779205l 545444 1410 545444 2141789 Lou and Martha Automobile Lease Lou and Martha Automobile Lease Payment Sequence Present Value Graph 10000 10000 5000 5000 0 0 N L0 00 V l O 0 L0 07 N L0 00 V l O 0 L0 N N N N 0 0 0 V V V LO LO LO 2 5000 0 5000 0 e il 5 2 10 000 g10000 395 o 0 15000 15000 5 IPurchase Price of Car 20 000 Lease Payments 201000 IMonthly Lease Payments El la Ve Monthly IEnd of Term Option to Purchase 25000 25000 9 m9 8 88383 Period Months Period Months Note on PV Xlsi Martha s Lease w 21 89017 2426 Problem 231 Sam Miller Leases a Taurus and Defaults and Damages It l Consumer automobile lease What can Lou recover for Sam39s default and damage to the cal See KEATING SALES A SYSTEMS APPROACH at 336337 1998 Lou39s Recovery Lou39s Recovery UR PVOL PVML ID ES See KEATING SALES A SYSTEMS APPROACH at 330 1998 400 Lou39s Recovery UR PVOL PVNL ID ES 5 See KEATING SALES A SYSTEMS APPROACH at 330 1998 2000 Remaining payments in Original Lease 21 PV of remaining payments in Original Lease PVOL 806044 Monthly New Lease Paymen Remaining payments in replacement Market Lease 21 PV of rema ng payments in Market Lease PVNL Incidental Dama Expenses Saved or Bene ts to Lessor E5 240 Discount Rate nominal compounded monthly 50 Total Payment Periods in Original Lease 36 Residual Value Retumed 400 400 400 400 400 400 400 400 400 0 1 2 4 5 6 34 Lou39s Perspective Payments at P t 3993 Cadd End of Months Beginning of Months Lou39s Recovery UR 200000 200000 PVOL 4 3 M slowHM 192309 5000 50 4 24000 24000 Total 302511 373309 Note on PV gtltl5 7 Charlie s Lease w 231 89017 2526 Notes Athe following assumes that all lease payments must be made at the beginning ofthe month due a R Rb Interest rate rM r 12 Payment Unpiad Remaining Ne Interest a Lease ew Lease Present Value of Lease Lease Unpd Lease Lease Rate per Cumulative Present Cumulative Pament Differences Original Lease Rent Payments Pa m Period Discount Present Valu Present Per Period Cumulative New Leaase Paid for UR for PVOL for PVNL r 12 Factor Value for Period Value PVOL PVNL PVOL PVNL Raw Current 4400 2000 8000 6300 Total PV Time 0 769236 576927 192309 0 400 1 400 2 400 3 400 4 400 5 400 6 400 7 400 8 400 9 400 10 400 11 400 12 400 13 400 14 400 15 400 16 0 400 300 000000 1000000 40000 40000 30000 30000 10000 10000 17 1 400 300 041667 0995851 39834 79834 29876 59876 9959 19959 18 2 400 300 041667 0991718 39669 119503 29752 89627 9917 29876 19 3 400 300 041667 0987603 39504 159007 29628 119255 9876 39752 20 4 400 300 041667 0983506 39340 198347 29505 148760 9835 49587 21 5 400 300 041667 0979425 39177 237524 29383 178143 9794 59381 22 6 400 300 041667 0975361 39014 276539 29261 207404 9754 69135 23 7 400 300 041667 0971313 38853 315391 29139 236543 9713 78848 24 8 400 300 041667 0967283 38691 354082 29018 265562 9673 88521 25 9 400 300 041667 0963269 38531 392613 28898 294460 9633 98153 26 10 400 300 041667 0959272 38371 430984 28778 323238 9593 107746 27 11 400 300 041667 0955292 38212 469196 28659 351897 9553 117299 28 12 400 300 041667 0951328 38053 507249 28540 380437 9513 126812 29 13 400 300 041667 0947381 37895 545144 28421 408858 9474 136286 30 14 400 300 041667 0943450 37738 582882 28303 437162 9434 145721 31 15 400 300 041667 0939535 37581 620464 28186 465348 9395 155116 32 16 400 300 041667 0935637 37425 657889 28069 493417 9356 164472 33 17 400 300 041667 0931754 37270 695159 27953 521369 9318 173790 34 18 400 300 041667 0927888 37116 732275 27837 549206 9279 183069 35 19 400 36962 769236 27721 576927 9240 192309 36 20 0 920204 Omitted 27606 604533 21 0916385 Extra 27492 632025 22 0912583 in NeW 27377 659402 23 300 041667 0908796 Lease 27264 686666 24 041667 0905025 Note on PV gtltl5 7 Charlie s Lease w 231 89017 2626 CHEE 6369 INTRODUCTION TO CASE STUDY amp ANALYSIS INTRODUCTION The engineering student exposed to cases for the rst time is usually confounded at the very least or overwhelmed at the very most All of his or her academic training has been directed toward solving speci c and reasonably well de ned problems which usually require only a single numerical answer Even when confronted with complex engineering problems the student has been taught to break down the problem into smaller elements which are then independently solved The independent or stepwise solutions are then combined to produce a single or simple solution to the overall complex problem Essentially the technique is one based on quantitative analysis using either wellestablished mathematical techniques and equations or new equations derived speci cally for solving the problem In essence it is an objective exercise and the engineering student has been trained to minimize or eliminate subjective functions in solving engineering problems Even assumptions that are made are based on a quantitative analysis of the problem in order to aid in the mathematical solution Presented with a case for study the student is now faced with a problem that is not easily solved by the techniques usually applied to solving engineering problems At a minimum the case differs from the typical engineering problem in several signi cant ways The case is of greater length and requires much more reading A case is made up of facts opinions estimates and simply pure guesses not easily lending themselves to experimental veri cation A case may be far more qualitative than quantitative a situation that is the reverse of the typical engineering problem A case is inherently associated with a people factor and is therefore subjective in nature virtually all engineering problems are devoid of people or at least the effect of people can be quanti ed to maintain a high degree of objectivity A signi cant difference between the case and an engineering problem is the dif culty with which one can de ne what it is that has to be done For case analysis the most dif cult part of the procedure is to discover Case Study Introdoc Page 1 0f 17 Last Saved 21200 INTRODUCTION TO ChEE 6369 CASE STUDY amp ANALYSIS de ne and nally answer the critical questions which form the basic structure of the case In analyzing engineering problems the questions are almost always de ned and the solution requires the most effort in the analysis The end goal of the case analysis is to prepare a set of recommendations to company management for future policy or strategy which will hopefully lead to an improved economic position for the company The end goal of an engineering problem analysis is to arrive at a speci c answer for a speci c set of conditions to accomplish a predetermined objective PURPOSE OF CASE STUDY The major reason for the use of case study in this course is to expose you to a real life a real world situation in which you will ultimately function Not only is a knowledge of basic engineering subject required but one must acquire an ability to couple this knowledge with economic principles in order to make decisions in the business world The rst purpose of case study is to help you develop skills in de ning and delivering the vital questions which ought to be answered then to learn how to go about answering such questions These skills are needed since in the ordinary course of business you may nd yourself compelled to take action before you can get all the facts which you would like to have in deciding what is the right course of action to take It is vitally important to develop the ability to ask the key questions The question not asked is not answered and in many instances represents the critical problem which was not solved with a resultant loss of pro t In business the ability to spot key issues and to ask good probing problem solving questions frequently requires greater insight than that needed for nding the answer VALUE OF CASE ANALYSIS Case analysis will prove to be helpful to you in many ways Initially you may feel completely lost in carrying out a case analysis This usually is the result of your Case Study Introdoc Page 2 0f 17 Last Saved 21200 INTRODUCTION TO ChEE 6369 CASE STUDY amp ANALYSIS previous engineering training plus lack of industrial experience The absence of de nite objectives positive and authoritative answers and the requirement to make decisions which neither you nor anyone else even this instructor can absolutely demonstrate as wrong may initially be the cause for great concern Sometimes as in contrast to the solution of engineering problems you feel no sense of solid accomplishment At least at rst with no benchmarks it is dif cult to detect forward motion Generally an addition to one s power to act is not as noticeable as additions to one s store of facts It is harder to be aware of an increase in the ability to make intelligent decisions than to show a notebook of lecture notes After the initial shock of case analysis you will acquire more con dence in your ability to face the unknown Indeed there may be times when you will fall victim to brazen overcon dence But you will be learning in the same manner as does the real world business person that of evaluating risks and contending with uncertainty You will acquire a great deal of factual knowledge about the case with which you are dealing and appreciate the unpredictabilities of business and economic problems as contrasted with engineering problems Ultimately you will learn the value of constant experimentation constant reappraisal of results goals and methods constant dissatisfaction with results and constant striving for improving your problemsolving skills METHOD OF ANALYSIS General Consideration Case analysis is a system of learning You are given real problems for analysis and discussion for solution and decision Like a member of middle management of a company or as an outside consultant called in by a company you must defend them both orally and in written form to higher management Since the essence of good case analysis is to ask good questions some of the questions to be asked would be such as the following What if anything should be done Why How would you get it done What facts would you like before you decide what to do Will it be worth your while to get them Can you afford to wait Ifyou decide now Case Study Introdoc Page 3 0f 17 Last Saved 21200 INTRODUCTION TO ChEE 6369 CASE STUDY amp ANALYSIS what are your calculated risks What is your ou or fallback position in the event you are wrong or conditions change Case analysis does not necessarily create or enhance intelligence so much as it gives one the opportunity to exercise it Whereas the knowledge of engineering basics is absolutely required for an engineer to succeed in his or her work the business executive succeeds not so much by what he or she knows as by what he or she does In business knowledge divorced from action is sterile Ability and willingness to take action or make decisions soon enough is frequently more important than being 100 right when it is too late Indecision or inaction frequently constitutes action of the wrong kind An analysis of a given case may lead one or a group to a certain recommendation whereas another individual or group may arrive at an entirely different recommendation for future company policy There are frequently several good answers all partly valid and none completely and demonstrably accurate Such a situation presents problems to an engineering student who has been trained to determine the correct answer for any problem that is confronted In case analysis the results or answer should be evaluated on the basis of the logical process employed whereby questions are raised and answers presented particularly the balance judgment and awareness shown concerning the intricacies of the case Case Analysis Principles The first step in case analysis consists of recognizing and identifying the existence of a problems and determining the underlying significant issues and factors with which management must deal For any company the f1rm s strategies and policies are derived from its basic purposes and objectives which in turn are in uenced by the various constraints of the company s internal and external environments An analytical study of the case facts is required to determine why and when the problem arose who is concerned and how critical the situation is In addition the adequacy of company resources and the probable impact on organizational performance capability must be properly evaluated Case Study Introdoc Page 4 0f 17 Last Saved 21200 INTRODUCTION TO ChEE 6369 CASE STUDY amp ANALYSIS One method of case diagnosis to identify the major problems is to l accumulate the Signi cant facts and opinions 2 review or evaluate them and 3 generate a diagnosis which pinpoints the problems and how it is they are in uenced by all the diverse aspects of the situation as for example new opportunities for or potential threats to the company s future well being It is not unusual to nd that problems can be ranked as to importance in terms of their in uence or bearing upon the company s existing situation Problems will usually be seen to exist in the form of higher level or lower level depending on the ability to de ne and discover their in uence on the context of the case Lower level problems are usually wellde ned and as a result are most likely to be interrelated which leads to the possibility of combining a group of them to form a single higher level problems By the process of combining the more numerous lower level problems into fewer higher level problems it is possible to analyze and diagnose the causes of some or all of the major problems in the case For example consider a set of lower level problems such as excessive inventory rising sales costs and declining cash ow These are essentially interrelated and may be combined into a higher level problem namely product obsolescence or inferior product Or on the other hand the same set of lower level problems may be combined to illustrate a higher level problem which may be marketing effectiveness To discover the problems of a case requires one to accumulate study and analyze the supporting data of the case The information given in a case is usually both qualitative and quantitative in nature Some generalizations may be made as follows 0 Quantitative Information I Adequacy Although conclusive and precise as possible gures on such items as cost data and market statistics are desired rough estimates and approximations may need to be used if they are the only gures available and are signi cant in terms of developing the decision making process In many cases intelligent analysis calls for the need for recognition and identi cation of assumptions Case Study Introdoc Page 5 0f 17 Last Saved 21200 INTRODUCTION TO ChEE 6369 CASE STUDY amp ANALYSIS Accurate Usage Generally there will be several methods of calculation available for a given set of gures Care should be exercised in applying textbook techniques mechanically ie cookbook fashion without establishing their value and application in the speci c case 0 Qualitative Information Case Study Introdoc Adeguacy The particular decision or position taken is usually based on a persuasive analysis which provides an accumulation of evidence to support the position A particularly dangerous weakness in this area is the excessive reliance on generalizations and principles which are not really applicable to the speci c case under consideration Balance Subjective analysis may tend to become overly unbalanced or one sided An analysis which consistently recognizes only evidence or information favorable to its own conclusions leaves the impression that the analyst did not see the other side and cannot have properly considered its merits Validity Some of the information in a case is established fact Other information is in the form of statements opinions estimates feelings guesses and the like The validity of such evidence must be examined to determine its value Reasonableness of Interpretations In analyzing a case it is necessary to take the facts through a series of interpretations before arriving at a judgment as to their effect upon the main issues of the case The process involves the analyst s applying hisher own judgments supported by case information andor general knowledge Objectivity Caution is advised in case analysis to maintain objectivity In some instances there are analysts who omit arguments other than those favoring a given position In others there are interpretations which are based on prejudices or preconceptions of the individual analyst which blinds herhim to other potential or possible interpretations These types of case Page 6 of 17 Last Saved 21200 INTRODUCTION TO ChEE 6369 CASE STUDY amp ANALYSIS analyses usually result from strong generalizations of the analyst rather than sufficient consideration of the specific case information I Thoroughness of Reasoning The degree of completeness or thoroughness required for each point reached should be determined by asking such questions as How important is this point How controversial is it and How deep must I go to be convincing A complete case analysis process will lead to logical conclusions which are usually in the form of alternate policies or strategies that can potentially be recommended to the company These are the alternatives of action the company take to solve the previously identi ed problems Some alternatives can be discarded at once All others must be formally evaluated This requires a determination of yardsticks by which their feasibility Utility and risk can be evaluated It is not enough that a given action would reduce costs there may be other offsetting disadvantages Human factors are always important and must be considered Likewise a lack of capital might prohibit certain courses of action Final conclusions and recommendations in the form of decisions should follow directly from the analysis The final results should not come as a surprise either because they are inconsistent with or not related to the analysis Ifthey do come as a surprise the effect is to weaken the discussion of the case analysis that has been developed It is important to avoid generalities in arriving at the final recommendations For example it is better to detail the actual steps that a company s management should take as l 2 3 4 etc rather than to simply state that the company should get better staff help Final recommendations should be based upon logical reasoning and evaluations which have narrowed the several feasible alternatives to the one or two with the least risk andor greatest potential reward and these should be the ones adopted The recommended course of action must solve the problem faced tend to optimize profits and costs and be feasible in terms of the people factor the company s organizational and functional configuration and the total resources available to the company A final decision is not complete unless the recommendation also contains operational plans for its Case Study Introdoc Page 7 0f 17 Last Saved 21200 INTRODUCTION TO ChEE 6369 CASE STUDY amp ANALYSIS implementation For example an effective date for initiation of action if any must be stipulated This must be related to a consideration of market factors and business cycles in terms of a favorable or otherwise unfavorable climate for initiating action The necessary resources must be obtained and the recommendation should address the meals of achieving this state of readiness Finally all individuals involved in carrying out the recommended course of action must be sold on its timeliness and validity DETAILS OF CASE ANALYSIS AND METHODOLOGY As a general rule a case analysis will take the form of the following steps 1 Read each case a minimum of three times 1 general idea 2 detail 3 notes 2 Analyze the company and product slate and determine major strengths and weaknesses I trends 2 developments 3 Prepare a statement of the major and minor problems facing the company outline form 4 Determine the feasible alternatives available to the company and analyze the pros and cons of adopting each alternative 5 Arrive at a course of action for the company Specifically and in more detail case analysis consists of the following methodology 1 Read through the case quickly to determine its general nature Then reread and begin to sort out facts During subsequent readings it will probably be desirable to outline and rearrange the material in the case or Case Study Introdoc Page 8 0f 17 Last Saved 21200 INTRODUCTION TO CASE STUDY amp ANALYSIS Case Study Introdoc ChEE 6369 to prepare tabulations and charts that permit the more ready comparisons of available data After you have mastered the facts and other information in the case isolate the major problems to be solved Then determine the major topics around which the analysis commonly encountered in problem analysis are l The market and its in uence on problem and decision 1 Present 2 Potential 3 Size andor characteristics of 4 Buying habits and motives of The product raw material and byproducts and their in uence on problem and decision 1 Characteristics of 2 Classi cation of Channels of distribution andor outlets and in uence on problem and decision Reaction of intermediaries customers or others if not included in A above and in uence on problem and decision Reaction of sales people andor other company personnel and in uence on problem and decision Competitiontypes of reaction of probable future action of and in uence on problem and decision Effectiveness of retaliation of competition intermediaries personnel others and effect on problem and decision Importance of good will and effect on problem and decision Position of the company in the industry and effect of this on problem and decision if not included in F above Financial position of the company and effect of problem and decision Page 9 of 17 Last Saved 21200 INTRODUCTION TO CASE STUDY amp ANALYSIS ChEE 6369 11 Importance of price elasticity of demand and effect on problem and decision 12 Effect on other product lines and or affiliated companies 13 Organizational and managerial effectiveness 14 J 39 quotquot39 andquot quot quot ofr 39 1 Work force 2 Management 3 Sales 15 Compatibility between personal and corporate objectives 16 Appropriateness and effectiveness of control policies and procedures 17 Technical capabilities of plant and equipment 18 Seriousness of the problem degree of urgency time and funds available before action must be taken and the effect or in uence of these factors on the decision 19 Legal implications if any and their in uence on the problem and decision 20 Economic conditions within and without the industry and effect on problem and decision 21 Effect on volume cost and profit and the in uence of these factors on problem and decision 1 Immediate 2 Short run 3 Long run 22 Probable profit commensurate with the risk involved 4 The foregoing list is not intended to be allinclusive or necessarily in order of importance Not all points will require consideration in each case and some cases will involve areas of analysis not listed above 5 Proceed with the analysis of the major points or areas Case Study Introdoc Page 10 of 17 Last Saved 21200 INTRODUCTION TO CASE STUDY amp ANALYSIS Case Study Introdoc ChEE 6369 The analysis consists of studying the problem from many different aspects and attempting to foretell the probable effect upon or reaction of the many factors which in uence the success or failure of a certain course of action 1 As the analysis proceeds alternative courses of action or possible solutions to the problem will come to mind These must be examined also and their feasibility appraised in much the same way as the original problem In fact as the analysis progresses it may be discovered that the problem as originally stated requires modification or that the whole approach to the case needs to be changed To be complete the analysis must take into consideration not only the strong points of each argument presented but the weaknesses of each as well The analysis of one set of factors will indicate one course of action The analysis of others may indicate a different solution It is important to recognize the alternative solutions Occasionally some assumptions must be made These should be logical and set forth clearly Do not make unnecessary assumptions or assumptions which are contrary to facts already given in the case In many instances more data may be desirable Use should then be made of the secondary sources available in magazines the library or elsewhere Based on the analysis arrive at one or more possible decisions as to the proper course of action to be taken in order to solve the problem facing the firm If as is customary more than one solution seems reasonable choose the one which all factors considered seems to contain the greatest strength and the fewest disadvantages Be sure that the arguments are based upon the facts Page 11 of 17 Last Saved 21200 INTRODUCTION TO ChEE 6369 CASE STUDY amp ANALYSIS in the case upon logical and clearcut reasoning and upon such assumptions as are made The framework around which the case analysis is made is composed of the several factors in uencing the company s economic viability at present and in the future In order to develop the framework for analysis several factors have to be developed and identified The following is a table of such factors applicable to any case and should be considered in carrying out the case analysis 1 What are the Fundamental Objectives of the Company in Terms of l Profitability 2 Market position 3 Ownership 1 Family 2 One or more outsiders 3 Partnership 4 Corporate structure 4 What the company wants to become 1 Specialist in one line 2 Diversified producer of related types of products 3 Diversified into unrelated lines 4 Size 2 What are the Major Strengths and Weaknesses of the Company 1 Present market position 1 Market share 2 Reputation 1 Overall 2 In different market segments 2 Product line 1 Quality 2 Extent of line 3 Relationship to market demand pattern Case Study Introdoc Page 12 0f 17 Last Saved 21200 INTRODUCTION TO CASE STUDY amp ANALYSIS Case Study Introdoc ChEE 6369 Nature of the market 1 Rate of growth of market for general type of products produced 2 Rate of growth for speci c products or types of products 3 Prospects for future growth 4 Nature and extent of competition 1 Strategies being followed by competing rms 2 Strengths and weaknesses of actual and potential competitors Financial capability 1 Availability of internal funds 2 Borrowing capability 3 Earnings potential 4 Ability to attract outside capital Production potential 1 Costs compared to those of competitors 2 Production potential 1 Quality levels 2 Flexibility of product mix 3 Availability of production capacity 3 Facility location 1 Ability to expand 2 Access to markets Marketing capability 1 Advertising and sales promotion 2 Sales force 1 Technical skills 2 Size 3 Number of personal customers Management capabilities Page 13 of 17 Last Saved 21200 INTRODUCTION TO CASE STUDY amp ANALYSIS 4 Case Study Introdoc ChEE 6369 1 Depth 1 Will loss of one individual affect the company s ability to compete 2 Are capable people available 1 To replace present members of management if necessary 2 For meeting needs caused by growth of business 2 Managerial ability of present management team 1 Ability to handle present job 2 Ability to handle future responsibilities in light of growth prospects for rm Personnel 1 Availability of capable technical people 2 Labor relations 3 Skill level of labor force 4 Size of labor force Identify Overall Strategies Available to Organization 1 Purpose of strategy formulate overall plan of action enabling company to attain its goals Identify Requirements for Implementing Alternative Strategies 1 Required resources for each strategy 1 Production capacity 1 Facilities 2 Capacity Additions or deletions to present product lineraw material position Marketing capabilities Management 1 Skills Page 14 of 17 Last Saved 21200 INTRODUCTION TO ChEE 6369 CASE STUDY amp ANALYSIS 2 Numbers 5 Technical personnel 6 Labor 1 Numbers 2 Skills 7 Money 2 Timing and strategy execution 1 Time when each type of resource is required 2 Amount of resources required at that time 3 Probable results of strategy 1 Time of expected results 2 Time at which or over which results are expected 3 Size of results expected 5 Bases for Evaluation of Alternative Strategies 1 Intemal consistency 1 Are the policies and goals outlined in formulating the strategy consistent with one another and with company objectives 2 Consistency with the economic environment 1 Does the strategy make sense in light of present market and competitive conditions 2 Does it make sense in light of expected changes in the economic environment for example changes in the demand pattern for various types of products 3 Consistency of resource requirements and resource availability 1 Must balance goals against the availability of needed resources 2 Do requirements leave margin of error with respect to needs 1 To meet unexpected business downturns Case Study Introdoc Page 15 0f 17 Last Saved 21200 INTRODUCTION TO CASE STUDY amp ANALYSIS ChEE 6369 To cover requirements in case strategy does not yield expected results 1 may be more successful than anticipated 2 may be less successful than anticipated 4 Does the strategy have an anticipated degree of risk 1 How much risk is management willing to take 2 How much risk does the strategy involve 3 Aspects of risk 1 Amount of resources whose value or continued existence is not assured 1 skills 2 specialized facilities 2 Time period of commitment 1 length of time required to recover capital investment 2 salability or usefulness elsewhere in company of committed resources if strategy is abandoned 3 rapidity with which economic environment changes 4 Proportion of company s resources committed to a particular strategy 6 If a particular strategy meets all these tests then it is an appropriate one to follow A final written case analysis should be based as closely as possible on the following format A case Case Study Introdoc Statement of the Problem 7 What is the central issues in the Page 16 of 17 Last Saved 21200 INTRODUCTION TO ChEE 6369 CASE STUDY amp ANALYSIS 3 Case Study Introdoc Solution or Decision 7 State the nal conclusion or decision The conclusion should be stated in sentence form Analysis 7 This section is the heart of the report It involves selection of factors or pertinent areas that must be considered to solve the problem as well as analysis of those factors or areas It involves gathering information and evaluating the significance of that information Also it requires determination of the relative importance of the various factors 1 Analytical Presentation 1 Make the report consist of analysis rather than mere restatement of the facts Show specifically how a particular factor affects the problem Do not present just the arguments that support the decision The purpose of the analysis is to find the best decision possible hence all phases of the problem must be brought out regardless of the decision they suggest In some instances incorporate into the analysis sound suggestions or alternatives to the decision Conclusions 7 This section should represent a summary of the conclusions reached concerning each of the major elements in the case It should not be a listing of all the arguments presented in the analysis Implementation 7 A detailed statement of a plan for implementing the recommendations including steps to be taken their timing and resources required to implement each step Page 17 of 17 Last Saved 21200

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