.TITLE ^^LIBRARY#PROGRAM#_#4.2.1\\ .LEFT MARGIN 5 .RIGHT MARGIN 67 .CENTER ^^WESTERN MICHIGAN UNIVERSITY\\ .CENTER ^^COMPUTER CENTER\\ .SKIP 2 ^^LIBRARY#PROGRAM#_#4.2.1\\ .SKIP 2 ^^PROGRAMMED BY\\:#^RUSS#^BARR* .BREAK ^^CALLING#NAME:\\##^^FINANC\\ .BREAK ^^PREPARED#BY:\\ .BREAK ^^APPROVED#BY\\:###^JACK#^R.#^MEAGHER .BREAK ^^DATE:\\##^OCTOBER, 1976 .SKIP 2 .CENTER ^^INTEGRATED FINANCIAL PACKAGE\\ .SKIP 2 .FOOTNOTE 5 --------------- .BREAK *^TWO OPTIONS AND A SUBROUTINE WERE PUT INTO THIS PACKAGE BY ^BILL#^GRANET. ^WE ACKNOWLEDGE ^PROFESSORS#^EDWARDS, ^JOHNSON, ^BALIK AND ^MR.#^SNYDER FOR THEIR CONTRIBUTIONS RELATING TO FINANCIAL KNOWLEDGE. ! ^^TABLE#OF#CONTENTS\\ .BREAK ----------------- .SKIP 1 .LEFT MARGIN 10 1.0##^PURPOSE .BREAK 2.0##^SAMPLE#^TERMINAL#^RUN .BREAK 2.1##^BATCH#^SET-UP .BREAK 3.0##^REFERENCES .BREAK 4.0##^OPTIONS .SKIP 2 .LEFT MARGIN 5 ^^1.0##PURPOSE\\ .BREAK ------------ .SKIP 1 ^THIS PROGRAM COMBINES CAPABILITIES OF POCKET CALCULATORS AND ADDITIONAL OPTIONS TO CALCULATE SPECIFIC TYPES OF FINANCIAL ANALYSIS. ^THE SPECIFIC TYPES OF FINANCIAL ANALYSIS THAT CAN BE SOLVED THROUGH OPTIONS ARE DEPRECIATION (3 DIFFERENT WAYS), ^RULE#OF#78, MORTGAGES (ANNUITY), NET PRESENT VALUE, NET PRESENT RATE, NET FUTURE VALUE, AND NET FUTURE RATE. ^THROUGH THE DESK CALCULATOR CAPABILITIES, MUCH MORE CAN BE DONE. .SKIP 1 ^^2.0##SAMPLE#TERMINAL#RUN\\ .BREAK ------------------------ .SKIP 1 ^THE TERMINAL RUN ILLUSTRATES THE SOLUTION OF TWO PROBLEMS. ^UNDERLINED INFORMATION IS ENTERED BY THE USER. .SKIP 1 .LEFT MARGIN 15 .INDENT -5 A)###^ASSUME AN INITIAL COST OF $1100 AND A SALVAGE VALUE AFTER 10 YEARS OF $100. ^CALCULATE DEPRECIATION BY THE STRAIGHT LINE, DOUBLE DECLINING, AND SUM OF YEARS DIGITS METHODS. (^SEE REFERENCE 4 OF ^SECTION 3.0) .SKIP 1 .INDENT -5 B)###^FIND THE NOMINAL (ANNUAL) RATE COMPOUNDED SEMI-ANNUALLY AT WHICH $1500 WILL AMOUNT TO $2400 IN 9 YEARS. ^THIS LEADS TO 1500*(1+^R/2)**18 = 2400 WHICH IN TURN LEADS TO: ^R=2((8/5)**(1/18)-1). (^SEE REFERENCE 7.) .BREAK * MEANS MULTIPLICATION. .BREAK ** MEANS RAISING TO A POWER E.G. 10**2=100. .SKIP 1 .LEFT MARGIN 5 ^THIS FIRST PROBLEM USES THE ^D^E^P^R^E^C OPTION. ^THE SECOND PROBLEM USES THE NUMERICAL FORMULA AND ASSIGNMENT STATEMENT OPTIONS. ^THE ^^EXIT\\ OPTION IS THEN USED TO TERMINATE THE PROGRAM. ^ALL OF THESE ARE EXPLAINED IN ^SECTION 4.0. .SKIP 1 .NOFIL .LITERAL .R FINANC -------- WMU FINANCIAL CALCULATION PACKAGE TYPE "HELP" FOR HELP *DEPREC ------ ENTER DEPRECIABLE COST 1100 ---- ENTER ESTIMATED LIFE 10 -- ENTER SALVAGE VALUE 100 --- STRAIGHT LINE DOUBLE DECLINING SUM OF DIGITS YRS REM BAL NXT YR DEP REM BAL NXT YR DEP REM BAL NXT YR DEP 0 1000.00 100.00 1100.00 220.00 1000.00 181.82 1 900.00 100.00 880.00 176.00 818.18 163.64 2 800.00 100.00 704.00 140.80 654.55 145.45 3 700.00 100.00 563.20 112.64 509.09 127.27 4 600.00 100.00 450.56 90.11 381.82 109.09 5 500.00 100.00 360.45 72.09 272.73 90.91 6 400.00 100.00 288.36 57.67 181.82 72.73 7 300.00 100.00 230.69 46.14 109.09 54.55 8 200.00 100.00 184.55 36.91 54.55 36.36 9 100.00 100.00 147.64 29.53 18.18 18.18 10 0.00 0.00 118.11 23.62 0.00 0.00 *2*((8/5)**(1/18)-1) ------------------- 5.2910388E-02 .END LITERAL .PAGE .LITERAL *EXIT ---- END OF EXECUTION CPU TIME: 0.65 ELAPSED TIME: 13.55 EXIT . .END LITERAL .FILL .SKIP 1 ^NOTE: 1.3^E-02 MEANS MOVING DECIMAL PLACE TWO PLACES TO THE LEFT, I.E. 1.3^E-02 EQUALS .013 AND 1.3^E+02 MEANS MOVING DECIMAL PLACE TWO PLACES TO THE RIGHT, I.E. 1.3^E+02 EQUALS 130. .SKIP 1 ^^2.1##BATCH#SET-UP\\ .BREAK ----------------- .SKIP 1 ^IN THE FOLLOWING ^^BATCH\\ JOB SET-UP, EACH LINE REPRESENTS ONE CARD, EACH CARD STARTING IN ^COLUMN 1. ^DO NOT INCLUDE THE COMMENTS ON THE RIGHT. ^SEE ^COMPUTER ^CENTER ^USERS ^GUIDE#_#7 OR THE ^D^E^CSYSTEM-10 ^USERS ^HANDBOOK FOR OTHER ^BATCH ^SYSTEM COMMANDS. .SKIP 1 ----------------------------------------------------------- .TAB STOP 32 .SKIP 1 $^^JOB\\#[_#,_#] ;_#,_# REPRESENTS THE USER'S .BREAK ;PROJECT-PROGRAMMER NUMBER. .BREAK $^^PASSWORD##_#\\ ;_# REPRESENTS THE USER'S .BREAK ;PASSWORD. .BREAK _.^^R#FINANC\\ ;RUN FINANCE .SKIP 1 ###[RESPONSES TO PROMPTINGS AS .BREAK ######EXPLAINED IN ^SECTION 4.0] .SKIP 1 (^^EOF\\) ;END-OF-FILE CARD .SKIP 1 ------------------------------------------------------------ .SKIP 1 ^^3.0##REFERENCES\\ .BREAK --------------- .SKIP 1 .LEFT MARGIN 9 .INDENT -4 1)##^PAUL#^M.#^HUMMEL AND ^CHARLES#^L.#^SEEBECK, "^MATHEMATICS OF ^FINANCE", ^MC^GRAW-^HILL ^BOOK ^CO., THIRD EDITION, (1971). .SKIP 1 .INDENT -4 2)##^B.^P.#^DZIELINSKI, "^A ^GUIDE TO ^FINANCIAL ^PLANNING ^TOOLS AND ^TECHNIQUES", ^I^B^M ^SYSTEM ^JOURNAL, 2, 126-144, (1973). .SKIP 1 .INDENT -4 3)##^JOHN#^H.#^MYERS, "^USEFUL ^FORMULAE FOR ^D^D^B AND ^S^Y^D ^DEPRECIATION", ^ACCOUNTING ^REVIEW, 33, 93-95, (1958). .SKIP 1 .INDENT -4 4)##^WESTON AND ^BRIGHAM, "^MANAGERIAL ^FINANCE", ^HOLT, ^RINEHART, AND ^WINSTON, FOURTH EDITION, 743-745, (1972). .SKIP 1 .INDENT -4 5)##^EDWARD#^A.#^DYL AND ^MICHAEL#^D.#^JOEHNK, "^PREPAYMENT ^PENALTIES ^INHERENT IN THE ^RULE#OF#78'S -- ^A ^TRUTH-IN-^LENDING ^ISSUE?", ^RESEARCH PAPER (1974), ^COLLEGE OF ^COMMERCE AND ^INDUSTRY, ^UNIVERSITY OF ^WYOMING, ^LARAMIE, ^WYOMING 82071. .SKIP 1 .INDENT -4 6)##^J.^F.#^TRAUB, "^ITERATIVE ^METHODS FOR THE ^SOLUTION OF ^EQUATIONS", ^PRENTICE-^HALL, 1964, PAGE 212. .SKIP 1 .INDENT -4 7)##^HEWLETT-^PACKARD, ^H^P-80 ^OWNER'S ^HANDBOOK. .SKIP 1 .INDENT -4 8)##"^ACCOUNTING ^REVIEW" V.33, 1958,PAGES 93-95. .SKIP 1 .INDENT -4 9)##"^FINANCIAL ^MANAGEMENT AND ^POLICY" BY ^J.#^C.#^VAN^HORNE, ^PRENTICE-^HALL, 1974, THIRD EDITION. .LEFT MARGIN 5 .SKIP 1 ^^4.0##OPTIONS\\ .BREAK ------------ .SKIP 1 ^THE FIRST PROMPTING GIVEN BY THIS PROGRAM IS *. ^AN EXPECTED RESPONSE IS EITHER A WORD FROM A LIST OF WORDS THAT IS GIVEN BELOW, A NUMERICAL FORMULA WHOSE VALUE WILL BE PRINTED IMMEDIATELY, OR AN ASSIGNMENT STATEMENT. ^EXPLANATIONS ARE GIVEN IN ^SECTIONS 4.1 AND 4.2. .SKIP 1 ^^4.1##NUMERICAL#FORMULAS#AND#ASSIGNMENT#STATEMENTS\\ .BREAK ------------------------------------------------- .SKIP 1 .NOFIL ^AVAILABLE FUNCTIONS .BREAK ------------------- .SKIP 1 ^^ATAN\\ - ARCTANGENT ^^TANH\\ - HYPERBOLIC TANGENT ^^COSH\\ - HYPERBOLIC COSINE ^^SINH\\ - HYPERBOLIC SINE ^^COS\\ - COSINE ^^SIN\\ - SINE ^^SQRT\\ - SQUARE ROOT ^^ALOG10\\ - LOG TO THE BASE 10 ^^ALOG\\ - NATURAL LOG I.E., LOG TO THE BASE E ^^EXP\\ - EXPONENTIAL I.E., E TO THE POWER OF THE ARGUMENT ^^ACOS\\ - ARC COSINE ^^ASIN\\ - ARC SINE ^^ABS\\ - ABSOLUTE VALUE .FILL .SKIP 1 ^THE ABOVE FUNCTION NAMES MUST BE FOLLOWED BY A LEFT AND RIGHT PARENTHESIS WITH A NUMBER OR A NAME IN BETWEEN (E.G., ^E^X^P(15)). .SKIP 1 ^NAMES IN A NUMERICAL FORMULA MAY HAVE UP TO TEN CHARACTERS WHERE THE CHARACTERS MAY BE ANY COMBINATION OF LETTERS AND DIGITS. ^WITH THE EXCEPTION OF ALLOWABLE NAMES, A NUMERICAL FORMULA IS DEFINED THE WAY IT IS IN THE ^^FORTRAN\\ LANGUAGE. .SKIP 1 ^IF NO EQUAL SIGN IS USED, THEN AFTER THE CARRIAGE RETURN IS ENTERED THE ANSWER WILL PRINT. ^CARRIAGE RETURN IS INDICATED BY <^C^R>. ^IF AN EQUAL SIGN IS USED, THEN AFTER THE CARRIAGE RETURN IS ENTERED THE VALUE OF THE NUMERICAL FORMULA TO THE RIGHT OF THE EQUAL SIGN IS ASSIGNED TO THE NAME ON THE LEFT OF THE EQUAL SIGN. ^THIS IS CALLED AN ASSIGNMENT STATEMENT. .SKIP 1 ^SOME ALLOWABLE NUMERICAL FORMULAS ARE: ^E^X^P(2.3)*(-17.2/^B), -100.17/2.36, ^A^L^O^G(119)/(^A+^B). ^NOTE THAT BEFORE THE FIRST AND THIRD FORMULAS CAN BE USED, ^A AND ^B MUST HAVE BEEN PREVIOUSLY USED IN AN ASSIGNMENT STATEMENT. ^SOME ALLOWABLE ASSIGNMENT STATEMENTS ARE: ^^SUM=A+B-19.06, B=ALOG(C)*11.8, D=100.9.\\ ^NOTE THAT BEFORE THE FIRST AND SECOND ASSIGNMENT STATEMENTS CAN BE USED, ^A,^B, AND ^C MUST HAVE BEEN PREVIOUSLY USED IN AN ASSIGNMENT STATEMENT. .SKIP 1 ^^4.2#LIST#OF#WORDS#WHICH#ARE#PROPER#RESPONSES#AND#EXPLANATIONS\\ .BREAK ------------------------------------------------------------ .SKIP 1 .NOFIL ^^HELP PRINT TYPE INFORMAT DUMP EXIT FREE FINISH RULE78 NETPVALU NETPRATE NETFVALU NETFRATE DEPREC ANNUIT\\ .SKIP 1 .FILL ^EXPLANATIONS#OF#THESE#WORDS .BREAK --------------------------- .SKIP 1 .LEFT MARGIN 16 .INDENT-11 ^^HELP\\#####-#^THE ABOVE LIST WILL PRINT. .SKIP 1 .INDENT -11 ^^PRINT\\####-#^CAUSES THE PRINTING ON THE LINE PRINTER OF ALL OUTPUT GENERATED BY SUCCEEDING OPTIONS. ^THIS ASSUMES THAT THE USER EVENTUALLY ENTERS EITHER THE ^^EXIT, FINISH\\, OR ^^TYPE\\ OPTION. .SKIP 1 .INDENT -11 ^^TYPE\\#####-#^IF THE ^^PRINT\\ OPTION HAD BEEN USED PREVIOUSLY, THIS OPTION WILL CAUSE SUCCEEDING OUTPUT TO BE PRINTED ON THE TELETYPE. ^IF NEITHER ^^PRINT\\ NOR ^^TYPE\\ OPTIONS ARE USED, PROGRAM OUTPUT WILL GO TO THE TELETYPE. .SKIP 1 .INDENT-11 ^^INFORMAT\\#-#^INFORMATION ON ONE OR MORE OF THE ABOVE WORDS CAN BE PRINTED. .SKIP 1 .INDENT-11 ^^EXIT\\#####-#^THIS TERMINATES THE PROGRAM AND RETURNS THE USER TO MONITOR. ^^FINISH\\ ACCOMPLISHES THE SAME JOB. .SKIP 1 .INDENT-11 ^^FINISH\\###-#^THIS TERMINATES THE PROGRAM AND RETURNS THE USER TO MONITOR. ^^EXIT\\ PERFORMS THE SAME JOB. .SKIP 1 .INDENT-11 ^^FREE\\#####-#^THIS CAUSES NAMES TO WHICH VALUES HAVE BEEN ASSIGNED, AS EXPLAINED IN ^SECTION 4.1, TO BE DELETED FROM MEMORY. .SKIP 1 .INDENT-11 ^^DUMP\\#####-#^THIS CAUSES THE LISTING OF ALL NAMES AND THEIR ASSIGNED VALUES. ^THE SPECIAL NAME, ^^ANSWER\\, WHICH IS ASSIGNED THE VALUE OF THE LAST NUMERICAL FORMULA ENTERED BY THE USER, IS ALSO PRINTED. .LEFT MARGIN 5 .SKIP 1 ^INFORMATION RELATING TO THE NUMBERS OF ROWS AND COLUMNS SHOULD BE IGNORED FOR THE PRESENT. .SKIP 1 ^TERMINAL#^EXAMPLES#AND#^EXPLANATIONS .BREAK ---------------------------------- .SKIP 1 ^UNDERLINED INFORMATION AND INPUT DATA ARE ENTERED BY THE USER. .SKIP 1 ^IT IS UNDERSTOOD THAT ONE ENTERS THE ^^RETURN\\ AT THE END OF EACH LINE OF INPUT. <^C^R> INDICATES CARRIAGE RETURN WHEN NEEDED FOR CLARITY. .SKIP 1 ^SOME ANSWERS ARE GIVEN WITH MANY MORE DECIMAL PLACES THAN NECESSARY BECAUSE THESE NUMBERS COULD BE USED AS INPUT TO OTHER CALCULATIONS. .SKIP 1 ^^NETPVALU#AND#NETPRATE\\ .BREAK --------------------- .SKIP 1 ^^(NETPRATE\\ IS ALSO KNOWN AS ^INTERNAL ^RATE OF ^RETURN) .SKIP 1 ^^NETPVALU\\ IS AN ABBREVIATION FOR NET PRESENT VALUE WHICH IS THE DIFFERENCE BETWEEN THE TOTAL OF THE DISCOUNTED INCOME (RETURNS OR SAVINGS) AND THE TOTAL OF THE DISCOUNTED EXPENSES (CAPITAL EXPENDITURES, INVESTMENT COST) AS ILLUSTRATED IN THE FOLLOWING FORMULA: (^SEE REFERENCES 2 AND 9) .SKIP 1 .NOFIL ######################################2######################N .BREAK ^P^V=(^R(1)-^C(1))/(1+I)+(^R(2)-^C(2))/(1+I)#+...+(^R(N)-^C(N))/(1+I) .SKIP 1 ^WHERE: .SKIP 1 N####= ^LIFE OF THE INVESTMENT PROJECT (IN TIME PERIODS) I####= ^DISCOUNT RATE ^R(T)#=#^REVENUE OF TIME PERIOD T ^C(T)#=#^INVESTMENT COST (EXPENSES) OF TIME PERIOD T ^P^V###=#^PRESENT VALUE .SKIP 1 .FILL ^WITH THIS OPTION, ^R(T)#-#^C(T) ARE ENTERED. ^IF ^R(T) AND ^C(T) ARE AVAILABLE AND ^R(T)#-#^C(T) ARE NOT, THEN ONE MAY USE THE NUMERICAL OPTIONS OF THIS PROGRAM TO CALCULATE ^R(T)#-#^C(T). .SKIP 1 ^THE PROFITABILITY INDEX DEFINED BY PRESENT VALUE OF RETURNS DIVIDED BY PRESENT VALUE OF COSTS CAN BE OBTAINED AS FOLLOWS: .SKIP 1 ^USE ^^NETPVALU\\ OPTION ENTERING ONLY RETURNS (I.E. ^R(T) AND NOT ^R(T)#-#^C(T)) TO OBTAIN PRESENT VALUE OF RETURNS. ^THEN USE ^^NETPVALU\\ OPTION AGAIN ENTERING ONLY COSTS ^C(T) TO OBTAIN PRESENT VALUE OF COSTS. ^FINALLY USE THE DESK CALCULATOR CAPABILITY (NUMERICAL FORMULA OPTION) TO OBTAIN THE PROFITABILITY INDEX AS FOLLOWS: ENTER THE PRESENT VALUE OF RETURNS, DIVISION SYMBOL, PRESENT VALUE OF COSTS, AND <^C^R> (CARRIAGE RETURN). .SKIP 1 ^PROBLEM: ^GIVEN FIFTEEN ^R(T)#-#^C(T) FOR FIFTEEN TIME PERIODS AND A DISCOUNT RATE OF 76.94 PER CENT, FIND THE NET PRESENT VALUE. .SKIP 1 ^TERMINAL#^DIALOGUE: .BREAK ------------------ .SKIP 1 .NOFIL ^^*NETPVALU\\ (ANSWER IS ALWAYS IN DOLLARS, I.E. NOT PERCENT) #-------- .SKIP 1 ^^NUMBER OF PERIODS = 15 ####################-- .SKIP 1 ENTER PAYMENTS (1 PER LINE) .SKIP 1 -756 294 -398 1048 2124 2375 2340 2341 2326 2308 2406 2372 2303 2269 2267 <^C^R> ENTER RATE AS A PERCENT (I.E. 5.04) 76.94 #####################################----- .SKIP 1 PRESENT VALUE = 0.22730216E-01\\ .SKIP 1 * .SKIP 1 .FILL ^NOTE: ^THESE PAYMENTS WERE ORIGINALLY USED IN AN INTERNAL RATE OF RETURN ^^(NETPRATE)\\ PROBLEM WHERE A NET PRESENT VALUE OF 0 WAS ENTERED. ^THE CALCULATED NET PRESENT RATE THEN IS 76.942163. ^IF THIS RATE IS USED IN A NET PRESENT VALUE PROBLEM, THEN THE CALCULATED NET PRESENT VALUE, ROUNDED TO TWO DECIMAL PLACES IS 0.00. ^THIS KIND OF CONSIDERATION IS THE REASON MORE THAN TWO DECIMAL PLACES ARE GIVEN FOR SOME ANSWERS. .SKIP 1 ^WHENEVER EITHER THE ^^NETPVALU, NETPRATE, NETFVALU, AND NETFRATE\\ OPTIONS ARE IMMEDIATELY FOLLOWED BY ONE OF THE SAME FOUR OPTIONS, THE FOLLOWING PROMPTING WILL PRINT. .SKIP 1 ^^DO#YOU#WISH#TO#USE#THE#SAME#PAYMENTS#AS#LAST#TIME?(YES#OR#NO)\\ .SKIP 1 ^^NETPRATE\\ IS AN ABBREVIATION FOR NET PRESENT RATE. ^THIS OPTION SOLVES THE ^^NETPVALU\\ FORMULA GIVEN ABOVE FOR THE DISCOUNT RATE WHEN THE USER SUPPLIES THE PAYMENTS, THE NUMBER OF TIME PERIODS, AND THE NET PRESENT VALUE. .SKIP 1 ^THE ^^NETPVALU, NETPRATE, NETFVALU\\, AND ^^NETFRATE\\ OPTIONS ALLOW THE USER TO SOLVE PROBLEMS WHERE ONE PAYMENT COVERS A FRACTION OF THE PERIOD OF TIME. ^THIS IS DONE BY ENTERING ON THE LAST TWO LINES OF INPUT THE PAYMENT AND THE FRACTIONAL PERIOD OF TIME RESPECTIVELY. ^AFTER THE FRACTIONAL PERIOD OF TIME IS ENTERED, THIS PROGRAM AUTOMATICALLY GIVES THE NEXT PROMPTING. .SKIP 1 ^^NETFVALU\\#AND#^^NETFRATE\\ .BREAK --------------------- .SKIP 1 ^THESE TWO WORDS ARE ABBREVIATIONS FOR NET FUTURE VALUE (NET COMPOUNDED VALUE) AND NET FUTURE RATE (NET COMPOUNDED RATE) RESPECTIVELY. ^THE DETERMINING FORMULA IS: (^SEE REFERENCE 1.) .SKIP 1 .NOFIL N N-1 ^R#(1+I)#+^R#(1+I)###+...+^R#(1+I)#=#^^NETFVALU\\ 1 2 N .SKIP 1 ^WHERE: .SKIP 1 N = ^NUMBER OF PAYMENTS I = ^INTEREST RATE ^R#= ^PERIODIC PAYMENTS #J .SKIP 1 .FILL ^PROBLEM: ^DEPOSITS OF $100 AT THE END OF EACH QUARTER IN A SAVINGS ACCOUNT HAVE BEEN MADE FOR THE PAST 10 YEARS. ^IF THE NOMINAL INTEREST RATE IS 1.47% WHAT DOES THE FUND HAVE NOW? (^SEE REFERENCE 1 PAGES 68 _& 246, EXERCISE 17, PROBLEM 3) .SKIP 1 ^^COMPUTER SOLUTION:\\ .BREAK ------------------ .BREAK ^SINCE THE LAST PAYMENT OF $100 DID NOT EARN INTEREST, WE ADD $100 TO THE ^^NETFVALU\\ COMPUTED BY THIS PROGRAM. ^THE QUARTERLY INTEREST IS 0.3675. .SKIP 1 ^TERMINAL#^DIALOGUE: .BREAK ------------------ .NOFIL .SKIP 1 ^^*NETFVALU -------- NUMBER OF PAYMENTS\\ =-39########(^SEE NOTE BELOW FOR ####################---#############EXPLANATION OF (-) SIGN.) .SKIP 1 ^^ENTER#PAYMENTS###(1#PER#LINE) 100 --- <^C^R> ---- ^^ENTER#RATE#AS#A#PERCENT#(I.E.#5.04):#.3675 #####################################----- NET#FUTURE#VALUE#=#4200.4593\\ .SKIP 1 * .FILL .SKIP 1 ^NOTE: THE NEGATIVE SIGN IN FRONT OF NUMBER OF PERIODS (39) INDICATES TO THIS PROGRAM THAT THE PAYMENTS ARE EQUAL. ^IF ALL THE PAYMENTS ARE NOT EQUAL, THEN NO MINUS SIGN IS TO BE ENTERED IN FRONT OF THE NUMBER OF PERIODS AND EACH PAYMENT MUST BE ENTERED ONE PER LINE. ^IN OTHER WORDS WHEN PAYMENTS ARE EQUAL, ONLY ONE VALUE HAS TO BE ENTERED. .SKIP 1 ^THE ^^NETFRATE\\ OPTION USES THE SAME FORMULA AND SOLVES THE PROBLEM WHERE N, ^R#, AND ^^NETFVALU\\ ARE GIVEN AND ONE WISHES TO FIND I.############J .SKIP 1 ^^DEPREC\\ - ^THIS WILL PRINT A TABLE GIVING THE ANSWER TO A DEPRECIATION PROBLEM BY THREE DIFFERENT METHODS. ^THEY ARE STRAIGHT-LINE, DOUBLE DECLINING AND SUM OF DIGITS. ^WITH EACH OF THE THREE METHODS THE REMAINING BALANCE AND NEXT YEARS DEPRECIATION ARE GIVEN. .LEFT MARGIN 9 .SKIP 1 .INDENT-4 1)##^IN THE STRAIGHT-LINE METHOD, IF ^C IS THE INITIAL COST OF THE ASSET (BOOK VALUE) AND ^S IS THE SALVAGE (TRADE-IN) VALUE AT THE END OF AN EXPECTED LIFE OF ^N YEARS, THEN THE YEARLY DEPRECIATION IS TAKEN AS: ^^(C-S)/N\\#. (^SEE REFERENCE 1) .SKIP 1 .INDENT-4 2)##^IN THE DOUBLE DECLINING METHOD A UNIFORM RATE OF DEPRECIATION EQUAL TO TWICE THE STRAIGHT-LINE RATE IS APPLIED, WITH NO ADJUSTMENT FOR SALVAGE VALUE, TO THE UNDEPRECIATED BALANCE OF THE ASSET. .SKIP 1 ^IF ^C IS THE COST AT A CERTAIN TIME, ^M IS THE NUMBER OF YEARS SINCE THE PURCHASE AT COST ^C, AND ^N IS THE EXPECTED LIFE, THEN: .LEFT MARGIN 15 .SKIP 1 .INDENT-4 A)##^THE DEPRECIATION IS GIVEN BY: (2/^N)^B WHERE ^B IS THE UNDEPRECIATED BALANCE OF THE COST. .SKIP 1 .INDENT-4 B)##^THE UNDEPRECIATED BALANCE OF THE COST IS GIVEN BY: ^C(1-(2/^N))**^M#. (^SEE REFERENCE 8.) .LEFT MARGIN 9 .SKIP 1 .INDENT-4 3)##^IN THE SUM OF DIGITS METHOD THE DEPRECIATION RATE FOR ANY YEAR IS A FRACTION, THE NUMERATOR OF WHICH IS THE REMAINING NUMBER OF YEARS OF THE EXPECTED LIFE AND THE DENOMINATOR OF WHICH IS THE SUM OF THE INTEGERS FROM 1 TO ^N, ^N BEING THE EXPECTED LIFE. .SKIP 1 ^FOR EXAMPLE, IF THE EXPECTED LIFE IS 5 YEARS, THE DEPRECIATION RATE WOULD BE: .SKIP 1 .NF.NJ ####5########5### ---------#=#--##=##0.333 FOR THE FIRST YEAR 1+2+3+4+5###15 .SKIP 1 #############4 ##########=#--##=##0.267 FOR THE SECOND YEAR ############15 .SKIP 1 #############3 ##########=#--##=##0.200 FOR THE THIRD YEAR ############15 .SKIP 1 #############2 ##########=#--##=##0.133 FOR THE FOURTH YEAR ############15 .SKIP 1 #############1 ##########=#--##=##0.067 FOR THE FIFTH YEAR ############15 .SKIP 1 .LEFT MARGIN 5 .SKIP 1 .F.J ^THEREFORE, IF THE INITIAL COST IS 1500 DOLLARS, AND SALVAGE VALUE IS 100 DOLLARS THEN THE FIRST YEAR'S DEPRECIATION IS (5/15)*1400, THE SECOND YEAR'S DEPRECIATION IS (4/15)*1400, ETC. .SKIP 1 .NOFIL ^^RULE\\#78 ------- .FILL ^THIS IS AN APPLICATION OF THE SUM OF DIGITS METHOD EXPLAINED WITH THE ^^DEPREC\\ OPTION. (^SEE REFERENCE 5.) .SKIP 1 ^PROBLEM:##^LET THERE BE GIVEN $1000 WITH A FINANCE CHARGE OF $180.00. ^IT IS BEING REPAID AT $39.33 PER MONTH FOR 30 MONTHS. ^PRINT A TABLE GIVING UNEARNED INTEREST AND REMAINING PRINCIPAL EACH MONTH. (^SEE PP.43-44 OF REFERENCE 7) .SKIP 1 ^COMPUTER#^SOLUTION: .BREAK ------------------ .SKIP 1 I(1000)2.5=180 GIVES THE ANNUAL INTEREST RATE OF 7.2%. ^USING THE ^RULE#OF#78, WE HAVE 1+2+...+30=465. ^THEREFORE, (30/465)180 IS THE AMOUNT PAID OFF AFTER THE FIRST MONTH, (29/465)180 IS THE AMOUNT PAID OFF AFTER THE SECOND MONTH, ETC. .SKIP 1 180(5+4+3+2+1)/465=$5.81 IS THE UNEARNED INTEREST AFTER THE 25TH PAYMENT AND (5)(39.33)-5.81=$190.84 IS THE PRINCIPAL REMAINING AFTER THE 25TH PAYMENT. .LEFT MARGIN 5 .SKIP 1 ^TERMINAL#^DIALOGUE: .BREAK ----------------- .SKIP 1 .NOFIL .LITERAL *RULE78 ------ ENTER TOTAL FINANCE CHARGE OR IF NOT KNOWN 180 --- ENTER PRINCIPAL 1000 ---- ENTER TOTAL TERM OF LOAN IN MONTHS 30 -- ENTER NO. OF MONTHS REQUIRED TO REPAY, FOR TABLE .END LITERAL <^C^R> .BREAK ---- .LITERAL BEGINNING PRINCIPAL UNEARNED PERIOD OUTSTANDING INTEREST INTEREST 1 1000.00 11.61 168.39 2 972.28 11.23 157.16 3 944.17 10.84 146.32 4 915.68 10.45 135.87 5 886.80 10.06 125.81 6 857.53 9.68 116.13 7 827.87 9.29 106.84 8 797.83 8.90 97.94 9 767.40 8.52 89.42 10 736.58 8.13 81.29 11 705.38 7.74 73.55 12 673.78 7.35 66.19 13 641.81 6.97 59.23 14 609.44 6.58 52.65 15 576.69 6.19 46.45 16 543.55 5.81 40.65 17 510.02 5.42 35.23 18 476.11 5.03 30.19 19 441.81 4.65 25.55 20 407.12 4.26 21.29 21 372.04 3.87 17.42 22 336.58 3.48 13.94 23 300.73 3.10 10.84 24 264.49 2.71 8.13 25 227.87 2.32 5.81 26 190.86 1.94 3.87 27 153.46 1.55 2.32 28 115.68 1.16 1.16 29 77.51 0.77 0.39 30 38.95 0.39 0.00 .END LITERAL .SKIP 1 .FILL ^IF A USER WANTED ONLY THE UNEARNED INTEREST AND REMAINING PRINCIPAL AFTER THE 25TH PAYMENT, THEN IN RESPONSE TO ^^ENTER NO. OF MONTHS REQUIRED TO REPAY, <^C^R> FOR TABLE\\ ENTER 25 <^C^R>. .SKIP 1 ^IF A USER KNOWS THE INTEREST RATE BUT NOT THE FINANCE CHARGE, THEN IN RESPONSE TO ^^ENTER TOTAL FINANCE CHARGE OR <^C^R> IF NOT KNOWN,\\ ENTER <^C^R> AND LATER A PROMPTING WILL ASK FOR ANNUAL INTEREST RATE. .SKIP 1 .LEFT MARGIN 15 .INDENT-10 ^^ANNUIT\\##-#^THIS OPTION SOLVES ANNUITY (RENT, LIFE INSURANCE PREMIUMS, MORTGAGE PAYMENTS, AND INSTALLMENT PAYMENTS) PROBLEMS. .SKIP 1 ^THESE PROBLEMS INVOLVE INTEREST RATE, LIFE OF THE ANNUITY, AMOUNT BORROWED (INVESTED), AND PERIODIC PAYMENTS. ^IF ONE ENTERS ANY 3 OF THE FOUR ITEMS, THEN THIS OPTION PRINTS THE FOURTH ITEM. .SKIP 1 .NOFIL ^THE BASIC FORMULA IS: .SKIP 1 ##############-N############################N ^^AM=PER(1-(1+R)##)/R=PER[1/(1+R)+....+1/(1+R)#)]\\ .BREAK .FILL .SKIP 1 (^SEE REFERENCE 1 PAGE 50.) ^WHERE: .SKIP 1 ^A^M##=#^AMOUNT BORROWED OR INVESTED .BREAK ^P^E^R#=#^PERIODIC PAYMENT .BREAK ^R###=#^THE RATE OF INTEREST FOR THE PERIOD OF TIME .BREAK N###=#^THE NUMBER OF PERIODS .SKIP 1 .INDENT-10 ^PROBLEM:##^A PERSON BORROWS $2344.63 AND IS TO REPAY THE LOAN IN 36 EQUAL MONTHLY PAYMENTS OF $76.76. ^WHAT WILL BE THE ANNUAL INTEREST RATE? .PAGE .LEFT MARGIN 5 ^TERMINAL#^DIALOGUE: .BREAK ------------------ .SKIP 1 .NOFIL .LITERAL *ANNUIT ------ ENTER : TO FIND: 1 RATE 2 LIFE 3 AMOUNT BORROWED 4 PERIODIC PAYMENT 1 - ENTER NUMBER OF PERIODS TO LIFE OF ANNUITY 36 -- ENTER AMOUNT OF ANNUITY 2344.63 ------- ENTER AMOUNT OF A PAYMENT 76.76 ----- ENTER RANGE OF TABLE IN PERIODS(E.G. 1,10) .END LITERAL <^C^R> .BREAK ---- .LITERAL NOMINAL RATE= 10.9998% LIFE OF ANNUITY= 36 PERIODS AMOUNT OF ANNUITY= 2344.6300 PAYMENTS= 76.760000 TOTAL INTEREST= 418.73 .END LITERAL .PAGE .LITERAL ANNUITY TABLE BEGINNING PRINCIPAL PRINCIPAL PERIOD OUTSTANDING INTEREST REPAYMENT 1 2344.63 21.49 55.27 2 2289.36 20.99 55.77 3 2233.59 20.47 56.29 4 2177.30 19.96 56.80 5 2120.50 19.44 57.32 6 2063.18 18.91 57.85 7 2005.33 18.38 58.38 8 1946.95 17.85 58.91 9 1888.04 17.31 59.45 10 1828.59 16.76 60.00 11 1768.59 16.21 60.55 12 1708.04 15.66 61.10 13 1646.94 15.10 61.66 14 1585.28 14.53 62.23 15 1523.05 13.96 62.80 16 1460.25 13.39 63.37 17 1396.88 12.80 63.96 18 1332.92 12.22 64.54 19 1268.38 11.63 65.13 20 1203.25 11.03 65.73 21 1137.52 10.43 66.33 22 1071.19 9.82 66.94 23 1004.25 9.21 67.55 24 936.70 8.59 68.17 25 868.53 7.96 68.80 26 799.73 7.33 69.43 27 730.30 6.69 70.07 28 660.23 6.05 70.71 29 589.52 5.40 71.36 30 518.16 4.75 72.01 31 446.15 4.09 72.67 32 373.48 3.42 73.34 33 300.14 2.75 74.01 34 226.13 2.07 74.69 35 151.44 1.39 75.37 36 76.12 0.64 76.12 * .END LITERAL .FILL .SKIP 1 ^EXPLANATIONS FOR ^^ENTER RANGE OF TABLE IN PERIODS(E.G. 1,10):\\ .SKIP 1 ^THE ENTIRE TABLE FOR EVERY PERIOD OF THE LIFE OF THE ANNUITY IS OBTAINABLE IN THREE WAYS. ^THE FIRST WAY IS SHOWN ABOVE I.E., BY THE ENTERING OF CARRIAGE RETURN ON THE LINE FOLLOWING THE PROMPTING. ^IN THE SECOND WAY, ONE ENTERS EITHER 1,^N,1 OR 1,^N WHERE ^N IS THE NUMBER OF PERIODS OF THE ANNUITY. .SKIP 1 ^ONE CAN SPECIFY THAT LESS THAN THE ENTIRE TABLE BE PRINTED BY ENTERING ^N1,^N2,^N3 WHERE ^N1 IS THE FIRST LINE, ^N2 IS THE LAST LINE, AND ^N3 IS THE INCREMENT. ^FOR EXAMPLE, IF 12,36,12 IS ENTERED, THEN THE 12TH, 24TH, AND 36TH LINES WILL BE PRINTED. .SKIP 1 ^IN THE THIRD WAY, ONE ENTERS ANY NON-NUMERIC CHARACTER (E.G. ^A,^B,=,ETC.). ^WITH THIS WAY YOU OBTAIN ALL THE PERIODIC PAYMENTS GROUPED BY YEARS WHERE YEARLY TOTALS ARE GIVEN. .SKIP 1 ^TO FULFILL THE REQUIREMENTS OF THE TRUTH IN LENDING LAW, THE LAST PERIODIC PAYMENT WILL ALWAYS BE LESS THAN OR EQUAL TO ALL THE PREVIOUS PAYMENTS. .SKIP 1 ^ON ACCOUNT OF ROUND OFF ERROR THE TOTAL FOR ^^PRINCIPAL REPAYMENT\\ MAY NOT BE EXACTLY 2344.63 AND THE TOTAL FOR THE ^^INTEREST COLUMN\\ MAY NOT BE EXACTLY 418.73. ^HOWEVER, FOR EACH MONTH ^^INTEREST + PRINCIPAL REPAYMENT\\ IS EXACTLY 76.76, WHICH IS THE MONTHLY PAYMENT.