Simtel MSDOS 1992 June

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.mb5 .mt1 Thσ ideß oµ presen⌠ valuσ i≤ illustrateΣ iε thσ followinτ ì short example: WhicΦ woulΣ yo⌡ rathe≥ have¼ $10░ ß yea≥ fo≥ threσ year≤ o≥ ì $248.6╣ righ⌠ now┐ Iµ yo⌡ assumσ aε interes⌠ ratσ oµ 10%¼ yo⌡ ì shoulΣ bσ indifferent« Iε othe≥ words¼ thσ presen⌠ valuσ oµ $10░ ì pe≥ yea≥ fo≥ │ year≤ i≤ onl∙ $248.69. Alternative 1 -- put $248.69 in the bank at 10% interest: year balance ááááá░ 248.69 ááááá▒ 248.6╣ ½ 24.8╖ ╜ 273.56 ááááá▓ 273.5╢ ½ 27.3╢ ╜ 300.92 ááááá│ 300.9▓ ½ 30.0╣ ╜ 331.01 Alternativσ ▓ -- receivσ $10░ pe≥ yea≥ fo≥ │ years║ ááyear balance ááááá░ 0 ááááá▒ 100 ááááá▓ 10░ ½ 10░ ½ 1░ ╜ 210 ááááá│ 10░ ½ 21░ ½ 2▒ ╜ 331 Eithe≥ way¼ yo⌡ havσ $33▒ iε you≥ accoun⌠ a⌠ thσ enΣ oµ thσ thirΣ ì year (allowing for roundoff error). Wha⌠ woulΣ happeε t∩ thi≤ examplσ iµ thσ interes⌠ ratσ werσ ì changed to zero? What would happen if it were changed to 20% .pa è Herσ arσ summarie≤ oµ thσ format≤ oµ thσ function≤ wσ havσ ì seen« Notσ tha⌠ ╔ havσ useΣ space≤ fo≥ legibility¼ bu⌠ the∙ ì shoulΣ no⌠ bσ useΣ iε 123. @SUM (<range to be added>) @AVG (<range to be averaged>) @MIN (<range to search for smallest value>) @STD (<range to compute standard deviation over>) @I╞ (<conditiona∞ expression>¼ <formulß iµ true>¼ <formulß iµ false>) @IRR (<formula with guess>, <income stream range>) @NPV (<interest rate formula>, <income stream range>) @VLOOKU╨ (<argumen⌠ formula>¼ <tablσ range>¼ <formulß witΦ the offse⌠ ì oµ the returneΣ value>) @DAVG (<data table range>, <offset formula>, <criterion range> .pa è This example illustrates a few functions. Numbers: Functions: 2 110 total 4 11 average 6 2 smallest 8 5.744562 standard deviation 10 12 14 16 18 20 Try changing the numbers in A5 through A15, then check the formulii in C5 through C8. ----- This example illustrates conditional evaluation using the IF function. Try changing the numbers in cells A27 and A28. Can you figure out what is happening to A30, when you do that? Look at A30 to see how it was done. 22 44 44 ----- This example calculates the internal rate of return of a ten-year investment. $1,000.00 investment amount $250.00 annual payout 21.4% internal rate of return ($1,000.00) $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 .pa è This example calculates the present value of a ten-year income stream. $250.00 annual income 10.0% interest rate $1,536.14 present value $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 ----- This example calculates the present value of a ten-year investment. $1,000.00 investment amount $250.00 annual payout 10.0% interest rate $487.40 present value ($1,000.00) $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 .pa è This example uses both @NPV and @IRR and a more complex example of the @IF function. $1,000.0░ investmen⌠ amoun⌠ -1.4E-1│ p.v« a⌠ A10╖ percent $250.00 annual payout 21.4% internal rate of return 0 better looking ($1,000.00) $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 $250.00 ----- This example illustrates a table lookup function. Income: 25000 Rate: 10% Tax Rate Table Income Rate $0.00 0% $10,000.00 5% $20,000.00 10% $30,000.00 15% $40,000.00 20% $50,000.00 25% $60,000.00 30% $70,000.00 35% $80,000.00 40% $90,000.00 45% $100,000.00 50% .pa è This function is more complex. Try changing the "sex" in F145 and see what happens to the average "amount." NAME SEX AMOUNT SEX John Press m 12 m Roberto Lastrico m 22 Natalia Lastrico f 30 Samantha Press f 100 Carla Lastrico f 200 Thomas Lasorda m 12 Evelyn Ashford f 300 Mary Decker f 400 Carl Lewis m 21 Edwin Moses m 18 William Banks m 11 average 16 .pa è A1: 'This example illustrates a few functions. A3: "Numbers: C3: 'Functions: A5: U 2 C5: @SUM(A5..A14) D5: 'total A6: U 4 C6: @AVG(A5..A14) D6: 'average A7: U 6 C7: @MIN(A5..A14) D7: 'smallest A8: U 8 C8: @STD(A5..A14) D8: 'standard deviation A9: U 10 A10: U 12 A11: U 14 A12: U 16 A13: U 18 A14: U 20 A16: 'Try changing the numbers in A5 through A15, A17: 'then check the formulii in C5 through C8. ----- A21: ' This example illustrates conditional evaluation A22: 'using the IF function. Try changing the numbers in A23: 'cells A27 and A28. Can you figure out what is A24: 'happening to A30, when you do that? Look at A30 to A25: 'see how it was done. A27: U 22 A28: U 44 A30: @IF(A27>A28,A27,A28) A41: 'This example calculates the internal rate of return of a ten-year A42: 'investment. A44: (C2) U 1000 B44: ' investment amount A45: (C2) U 250 B45: ' annual payout A47: (P1) @IRR(0.1,A50..A60) B47: ' internal rate of return A50: (C2) -A44 A51: (C2) +$A$45 A52: (C2) +$A$45 A53: (C2) +$A$45 A54: (C2) +$A$45 A55: (C2) +$A$45 A56: (C2) +$A$45 A57: (C2) +$A$45 A58: (C2) +$A$45 A59: (C2) +$A$45 A60: (C2) +$A$45 .pa è A61: 'This example calculates the present value of a ten-year income stream. A64: (C2) U 250 B64: ' annual income A65: (P1) U 0.1 B65: ' interest rate A67: (C2) @NPV(A65,A71..A80) B67: ' present value A71: (C2) +$A$64 A72: (C2) +$A$64 A73: (C2) +$A$64 A74: (C2) +$A$64 A75: (C2) +$A$64 A76: (C2) +$A$64 A77: (C2) +$A$64 A78: (C2) +$A$64 A79: (C2) +$A$64 A80: (C2) +$A$64 ----- A81: 'This example calculates the present value of a ten-year investment. A83: (C2) U 1000 B83: ' investment amount A84: (C2) U 250 B84: ' annual payout A85: (P1) U 0.1 B85: ' interest rate A87: (C2) @NPV(A85,A90..A100) B87: ' present value A90: (C2) -A83 A91: (C2) +$A$84 A92: (C2) +$A$84 A93: (C2) +$A$84 A94: (C2) +$A$84 A95: (C2) +$A$84 A96: (C2) +$A$84 A97: (C2) +$A$84 A98: (C2) +$A$84 A99: (C2) +$A$84 A100: (C2) +$A$84 .pa è A101: ' This example uses both @NPV and @IRR and a more complex A102: 'example of the @IF function. A105: (C2) U 1000 B105: ' investment amount E105: @NPV(A107,A110..A120) F105: 'p.v. at A107 percent A106: (C2) U 250 B106: ' annual payout A107: (P1) @IRR(0.1,A110..A120) B107: ' internal rate of return E107: @IF(@ABS(@NPV(A107,A110..A120))<0.001,0,@NPV(A107,A110..A120)) F107: 'better looking A110: (C2) -A105 A111: (C2) +$A$106 A112: (C2) +$A$106 A113: (C2) +$A$106 A114: (C2) +$A$106 A115: (C2) +$A$106 A116: (C2) +$A$106 A117: (C2) +$A$106 A118: (C2) +$A$106 A119: (C2) +$A$106 A120: (C2) +$A$106 ------ A121: 'This example illustrates a table lookup function. A123: 'Income: B123: (G) U 25000 A124: 'Rate: B124: (P0) @VLOOKUP(B123,A130..B140,1) A126: ' Tax Rate Table A128: ' Income B128: "Rate A130: (C2) 0 B130: (P0) 0 A131: (C2) 10000 B131: (P0) 0.05 A132: (C2) 20000 B132: (P0) 0.1 A133: (C2) 30000 B133: (P0) 0.15 A134: (C2) 40000 B134: (P0) 0.2 A135: (C2) 50000 B135: (P0) 0.25 A136: (C2) 60000 B136: (P0) 0.3 A137: (C2) 70000 B137: (P0) 0.35 A138: (C2) 80000 B138: (P0) 0.4 A139: (C2) 90000 B139: (P0) 0.45 A140: (C2) 100000 B140: (P0) 0.5 .pa è A141: ' This function is more complex. Try changing the "sex" in A142: 'F145 and see what happens to the average "amount." A144: 'NAME C144: ^SEX D144: "AMOUNT F144: 'SEX A145: 'John Press C145: ^m D145: U 12 F145: U 'm A146: 'Roberto Lastrico C146: ^m D146: U 22 A147: 'Natalia Lastrico C147: ^f D147: U 30 A148: 'Samantha Press C148: ^f D148: U 100 A149: 'Carla Lastrico C149: ^f D149: U 200 A150: 'Thomas Lasorda C150: ^m D150: U 12 A151: 'Evelyn Ashford C151: ^f D151: U 300 A152: 'Mary Decker C152: ^f D152: U 400 A153: 'Carl Lewis C153: ^m D153: U 21 A154: 'Edwin Moses C154: ^m D154: U 18 A155: 'William Banks C155: ^m D155: U 11 A157: 'average D157: @DAVG(A144..D155,3,F144..F145)