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CALCULATING FUTURE VALUES WITH EXCELInitial Deposit 100Interest Rate 6%Number of years, n 2
Account balance after n years 112.36
Year Future Value0 $100.001 $106.002 $112.363 $119.104 $126.255 $133.826 $141.857 $150.368 $159.389 $168.95
10 $179.0811 $189.8312 $201.2213 $213.2914 $226.0915 $239.6616 $254.0417 $269.2818 $285.4319 $302.5620 $320.71
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21$0.00
$50.00
$100.00
$150.00
$200.00
$250.00
$300.00
$350.00
Future Value of $100 at 6% Annual Interest
Fut
ure
Val
ue
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21$0.00
$50.00
$100.00
$150.00
$200.00
$250.00
$300.00
$350.00
Future Value of $100 at 6% Annual Interest
Fut
ure
Val
ue
Initial Deposit 100 100 100Interest Rate 0% 6% 12%
Year FV at 0% FV at 6% FV at 12%0 100 100.00 100.001 100 106.00 112.002 100 112.36 125.443 100 119.10 140.494 100 126.25 157.355 100 133.82 176.236 100 141.85 197.387 100 150.36 221.078 100 159.38 247.609 100 168.95 277.31
10 100 179.08 310.5811 100 189.83 347.8512 100 201.22 389.6013 100 213.29 436.3514 100 226.09 488.7115 100 239.66 547.3616 100 254.04 613.0417 100 269.28 686.6018 100 285.43 769.0019 100 302.56 861.2820 100 320.71 964.63
FUTURE VALUE OF A SINGLE DEPOSIT AT DIFFERENT INTEREST RATES
HOW $100 AT TIME 0 GROWS AT 0%, 6%, 12%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210
200
400
600
800
1000
1200
FV at 0%
FV at 6%
FV at 12%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210
200
400
600
800
1000
1200
FV at 0%
FV at 6%
FV at 12%
Interest 6%
Year
1 0 100.00 6 $ 106.00 2 106.00 100.00 12.36 $ 218.36 3 218.36 100.00 19.10 $ 337.46 4 337.46 100.00 26.25 $ 463.71 5 463.71 100.00 33.82 $ 597.53 6 597.53 100.00 41.85 $ 739.38 7 739.38 100.00 50.36 $ 889.75 8 889.75 100.00 59.38 $ 1,049.13 9 1049.13 100.00 68.95 $ 1,218.08
10 1218.08 100.00 79.08 $ 1,397.16
$1,397.16
FUTURE VALUE WITH ANNUAL DEPOSITS at the beginning of year
Account balance, beginning of year
Deposit at beginning of year
Interest earned during year
Total in account at end of year
Future Value using Excel's FV functions
Interest 6%
Year
1 0 100.00 0 $ 100.00 2 100.00 100.00 6.00 $ 206.00 3 206.00 100.00 12.36 $ 318.36 4 318.36 100.00 19.10 $ 437.46 5 437.46 100.00 26.25 $ 563.71 6 563.71 100.00 33.82 $ 697.53 7 697.53 100.00 41.85 $ 839.38 8 839.38 100.00 50.36 $ 989.75 9 989.75 100.00 59.38 $ 1,149.13
10 1149.13 100.00 68.95 $ 1,318.08
$1,318.08
FUTURE VALUE WITH ANNUAL DEPOSITS at the end of year
Account balance, end of year
Deposit at end of year
Interest earned during year
Total in account at end of year
Future Value using Excel's FV functions
Future Payment (X) 100Time of future payment (n) 3interest rate(,r) 6%
83.96193
Discount rate0% 100.001% 97.062% 94.233% 91.514% 88.905% 86.386% 83.967% 81.638% 79.389% 77.22
10% 75.1311% 73.1212% 71.1813% 69.3114% 67.5015% 65.7516% 64.0717% 62.4418% 60.8619% 59.3420% 57.8721% 56.4522% 55.0723% 53.7424% 52.4525% 51.2026% 49.9927% 48.8228% 47.6829% 46.5830% 45.5231% 44.4832% 43.4833% 42.5134% 41.56
THE PRESENT VALUE OF $100 IN 3 YEARS in this example we vary the discount rate r
Present Value (X/(1+r)n)
Present Value
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 510.00
20.00
40.00
60.00
80.00
100.00
120.00
Present Value of $100 to be paid in 3 Years wen Discount Rate Varies
Discount Rate
Present Value
35% 40.6436% 39.7537% 38.8938% 38.0539% 37.2440% 36.4441% 35.6742% 34.9243% 34.2044% 33.4945% 32.8046% 32.1347% 31.4848% 30.8549% 30.2350% 29.63
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 510.00
20.00
40.00
60.00
80.00
100.00
120.00
Present Value of $100 to be paid in 3 Years wen Discount Rate Varies
Discount Rate
Present Value
CALCULATING PRESENT VALUES WITH EXCEL
Annual Payment 100r, interest rate 6%
Year1 100 94.339622642 100 88.9996443 100 83.96192834 100 79.209366325 100 74.72581729
Present value of all paymentsSumming the present value $421.24Using Excel's PV function $421.24
Using Excel's NPV function $421.24
Payment at end of
year
Present value of payment
CALCULATING NET PRESENT VALUE (NPV) WITH EXCELr, interest rate 6%
Year1 100 $94.342 200 $178.003 300 $251.894 400 $316.845 500 $373.63
Present value of all paymentsSumming the present values $1,214.69Using Excel's NPV function $1,214.69
Payment at end of year
Prsent value
CALCULATING NET PRESENT VALUE (NPV) WITH EXCELr, interest rate 5%
Year Payment Present Value0 -800 -800.001 100 95.242 150 136.053 200 172.774 250 205.685 300 235.06
NPVSumming the present values $44.79Using Excel's NPV function $44.79
Discount Rate NPV0% 200.001% 165.862% 133.363% 102.414% 72.925% 44.796% 17.967% -7.658% -32.119% -55.48
10% -77.8311% -99.2112% -119.6713% -139.2614% -158.0415% -176.0316% -193.28
0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16%
-250.00
-200.00
-150.00
-100.00
-50.00
0.00
50.00
100.00
150.00
200.00
250.00
NPV and the Discount Rate
Discount Rate
NPV
0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16%
-250.00
-200.00
-150.00
-100.00
-50.00
0.00
50.00
100.00
150.00
200.00
250.00
NPV and the Discount Rate
Discount Rate
NPV
USING NPV TO CHOOSE BETWEEN INVESTMENTS
Discount Rate 15%
Year Investment A Investment B0 -800 -8001 250 6002 500 2003 200 1004 250 5005 300 300
NPV 219.06 373.75
CALCULATING THE IRR WITH EXCELr, interest rate 6.6965%
Year Payment0 -8001 1002 1503 2004 2505 300
NPV 0.00IRR 6.6965%
Discount Rate NPV0% 200.001% 165.862% 133.363% 102.414% 72.925% 44.796% 17.967% -7.658% -32.119% -55.48
10% -77.8311% -99.2112% -119.6713% -139.2614% -158.0415% -176.0316% -193.28
0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16%
-250.00
-200.00
-150.00
-100.00
-50.00
0.00
50.00
100.00
150.00
200.00
250.00
NPV and the Discount Rate
Discount Rate
NPV
0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16%
-250.00
-200.00
-150.00
-100.00
-50.00
0.00
50.00
100.00
150.00
200.00
250.00
NPV and the Discount Rate
Discount Rate
NPV
0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16%
-250.00
-200.00
-150.00
-100.00
-50.00
0.00
50.00
100.00
150.00
200.00
250.00
NPV and the Discount Rate
Discount Rate
NPV
HELPING MARIO SAVE FOR A CAR
Deposit, X 8903.133Interest rate 8.00%
Year
0 0 8903.133 8903.133 $9,615.38 1 $9,615.38 8903.133 $18,518.52 $20,000.00 2 $20,000.00 -20000 ($0.00) ($0.00)
0.00
Deposit, X 8903.13Interest rate 8.00%
Year
0 0 8903.13 8903.1339 $9,615.38 1 $9,615.38 8903.13 $18,518.52 $20,000.00 2 $20,000.00 -20000 $0.00 $0.00
0.00
Goal $20,000.00When to reach the goal? 5Interest rate 6.00%Deposit, X $3,347.10
In bank, before deposit
Deposit or
withdrawl
Total at beginning
of year
End of year with interest
NPV of all deposits and payments
HELPING MARIO SAVE FOR A CAR USING AN EXCEL FUNCTION GOAL SEEK
In bank, before deposit
Deposit or
withdrawl
Total at beginning
of year
End of year with interest
NPV of all deposits and payments
HELPING MARIO SAVE FOR A CAR using Excel's PV function
SAVING FOR COLLEGE
Interest rate 8.00%Annual deposit $4,000.000Annual cost of deposit $20,000.00
Birthday Total10 0 $4,000.00 4,000.00 11 $4,320.00 $4,000.00 8,320.00 12 $8,985.60 $4,000.00 12,985.60 13 $14,024.45 $4,000.00 18,024.45 14 $19,466.40 $4,000.00 23,466.40 15 $25,343.72 $4,000.00 29,343.72 16 $31,691.21 $4,000.00 35,691.21 17 $38,546.51 $4,000.00 42,546.51 18 $45,950.23 -$20,000.00 25,950.23 19 $28,026.25 -$20,000.00 8,026.25 20 $8,668.35 -$20,000.00 (11,331.65)21 ($12,238.18) -$20,000.00 (32,238.18)
NPV of all payments -$13,826.40
SAVING FOR COLLEGE USING TRIAL AND ERROR
Interest rate 8.00%Annual deposit $6,227.78Annual cost of deposit -$20,000.00
Birthday Total10 0 $6,227.78 6,227.78 11 $6,726.00 $6,227.78 12,953.77 12 $13,990.07 $6,227.78 20,217.85 13 $21,835.28 $6,227.78 28,063.05 14 $30,308.10 $6,227.78 36,535.87 15 $39,458.74 $6,227.78 45,686.52 16 $49,341.44 $6,227.78 55,569.21 17 $60,014.75 $6,227.78 66,242.52 18 $71,541.93 -$20,000.00 51,541.93 19 $55,665.28 -$20,000.00 35,665.28 20 $38,518.50 -$20,000.00 18,518.50 21 $19,999.98 -$20,000.00 (0.02)
In bank on birthday, before
deposit/withdrawl
Deposit or withdrawl at
beginning of year
In bank on birthday, before
deposit/withdrawl
Deposit or withdrawl at
beginning of year
NPV of all payments -$0.01
Interest rate 8.00%Annual deposit $6,227.78Annual cost of deposit -$20,000.00
Birthday Total10 0 $6,227.78 6,227.78 11 $6,726.00 $6,227.78 12,953.77 12 $13,990.08 $6,227.78 20,217.85 13 $21,835.28 $6,227.78 28,063.06 14 $30,308.10 $6,227.78 36,535.88 15 $39,458.75 $6,227.78 45,686.52 16 $49,341.45 $6,227.78 55,569.22 17 $60,014.76 $6,227.78 66,242.54 18 $71,541.94 -$20,000.00 51,541.94 19 $55,665.29 -$20,000.00 35,665.29 20 $38,518.52 -$20,000.00 18,518.52 21 $20,000.00 -$20,000.00 -
NPV of all payments $0.00
SAVING FOR COLLEGE USING EXCEL FORMUALS ONLYLinda's age when plan started 10Linda's age at last deposit 17Number of deposits 8Number of withdrawls 4Annual cost of college $20,000.00Interest rate 8.00%
Annual deposit $6,227.78
Linda's age today0 $1,768.811 $1,962.732 $2,184.473 $2,439.68
SAVING FOR COLLEGE USING GOAL SEEK
In bank on birthday, before
deposit/withdrawl
Deposit or withdrawl at
beginning of year
Annual amount deposited
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16$0
$5,000
$10,000
$15,000
$20,000
$25,000
Annual Deposit Required to Fun 4 Years of $20,000
When Linda is 18
Linda's age at start of plan
4 $2,735.615 $3,081.726 $3,490.657 $3,979.618 $4,572.699 $5,304.68
10 $6,227.7811 $7,423.9612 $9,029.8813 $11,291.4714 $14,700.6015 $20,404.92
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16$0
$5,000
$10,000
$15,000
$20,000
$25,000
Annual Deposit Required to Fun 4 Years of $20,000
When Linda is 18
Linda's age at start of plan
SAVING FOR COLLEGE SAVING FOR COLLEGE
Interest rate 9.00%Annual deposit $75,000.000Annual cost of deposit $30,000.00
Birthday Total$4,320.00 1 0 $75,000.00 75,000.00 $81,750.00 $8,985.60 2 $81,750.00 81,750.00 $97,127.18
$14,024.45 3 $97,127.18 97,127.18 $115,396.80 $19,466.40 4 $115,396.80 115,396.80 $137,102.93 $25,343.72 5 $137,102.93 137,102.93 $162,892.00 $31,691.21 6 $162,892.00 162,892.00 $193,531.98 $38,546.51 7 $193,531.98 -$30,000.00 163,531.98 $194,292.35 $45,950.23 8 $194,292.35 -$30,000.00 164,292.35 $195,195.74 $28,026.25 9 $195,195.74 -$30,000.00 165,195.74 $196,269.05
$8,668.35 10 $196,269.05 -$30,000.00 166,269.05 $197,544.26 ($12,238.18)($34,817.24)
NPV of all pa -$22,191.60
SAVING FOR COLLEGE USING TRIAL AND ERROR
$6,726.00 $13,990.07 $21,835.28 $30,308.10 $39,458.74 $49,341.44 $60,014.75 $71,541.93 $55,665.28 $38,518.50 $19,999.98
($0.02)
End of year with interest
In bank on birthday,
before deposit/withd
rawl
Deposit or withdrawl
at beginning of year
End of year with
interest
End of year with interest
$6,726.00 $13,990.08 $21,835.28 $30,308.10 $39,458.75 $49,341.45 $60,014.76 $71,541.94 $55,665.29 $38,518.52 $20,000.00
$0.00
SAVING FOR COLLEGE USING EXCEL FORMUALS ONLY
End of year with interest
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16$0
$5,000
$10,000
$15,000
$20,000
$25,000
Annual Deposit Required to Fun 4 Years of $20,000
When Linda is 18
Linda's age at start of plan
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16$0
$5,000
$10,000
$15,000
$20,000
$25,000
Annual Deposit Required to Fun 4 Years of $20,000
When Linda is 18
Linda's age at start of plan
89107.597127.17
105868.62115396.79
125782.5104402.93
81099.1955698.12
SAVING FOR RETIREMENT
Joe's age today 20Joe's age at last deposit 64Number of deposits 45Number of withdrawls 20Annual withdrawal from age 65 $ 100,000.00 Interest rate 8.00%
Annual deposit $ 2,540.23
Joe's age today Annual amount deposited20 2,540.2321 2,750.5722 2,978.9623 3,227.0724 3,496.7325 3,789.9626 4,109.0227 4,456.3928 4,834.8529 5,247.4830 5,697.7331 6,189.4732 6,727.0333 7,315.3234 7,959.8535 8,666.9036 9,443.6237 10,298.1638 11,239.9139 12,279.6840 13,430.0341 14,705.5842 16,123.5343 17,704.1544 19,471.6045 21,454.8246 23,688.8647 26,216.5148 29,090.6149 32,377.1850 36,159.7951 40,545.8652 45,675.7953 51,736.7454 58,983.8455 67,774.17
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 642,000.00
22,000.00
42,000.00
62,000.00
82,000.00
102,000.00
122,000.00
142,000.00
162,000.00
182,000.00
202,000.00
222,000.00
242,000.00
262,000.00
282,000.00
302,000.00
322,000.00
342,000.00
362,000.00
382,000.00
402,000.00
422,000.00
442,000.00
462,000.00
482,000.00
502,000.00
522,000.00
542,000.00
562,000.00
582,000.00
602,000.00
622,000.00
642,000.00
662,000.00
682,000.00
702,000.00
722,000.00
742,000.00
762,000.00
782,000.00
802,000.00
822,000.00
842,000.00
862,000.00
882,000.00
902,000.00
922,000.00
942,000.00
962,000.00
982,000.00
Annual Deposit Required to Fund 20 Years of $100,000When Joe is 65
Joe's age at start of plan
56 78,623.4457 92,305.0858 110,034.3459 133,836.4660 167,356.6661 217,885.1262 302,431.8463 472,026.3264 981,814.74
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 642,000.00
22,000.00
42,000.00
62,000.00
82,000.00
102,000.00
122,000.00
142,000.00
162,000.00
182,000.00
202,000.00
222,000.00
242,000.00
262,000.00
282,000.00
302,000.00
322,000.00
342,000.00
362,000.00
382,000.00
402,000.00
422,000.00
442,000.00
462,000.00
482,000.00
502,000.00
522,000.00
542,000.00
562,000.00
582,000.00
602,000.00
622,000.00
642,000.00
662,000.00
682,000.00
702,000.00
722,000.00
742,000.00
762,000.00
782,000.00
802,000.00
822,000.00
842,000.00
862,000.00
882,000.00
902,000.00
922,000.00
942,000.00
962,000.00
982,000.00
Annual Deposit Required to Fund 20 Years of $100,000When Joe is 65
Joe's age at start of plan
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 642,000.00
22,000.00
42,000.00
62,000.00
82,000.00
102,000.00
122,000.00
142,000.00
162,000.00
182,000.00
202,000.00
222,000.00
242,000.00
262,000.00
282,000.00
302,000.00
322,000.00
342,000.00
362,000.00
382,000.00
402,000.00
422,000.00
442,000.00
462,000.00
482,000.00
502,000.00
522,000.00
542,000.00
562,000.00
582,000.00
602,000.00
622,000.00
642,000.00
662,000.00
682,000.00
702,000.00
722,000.00
742,000.00
762,000.00
782,000.00
802,000.00
822,000.00
842,000.00
862,000.00
882,000.00
902,000.00
922,000.00
942,000.00
962,000.00
982,000.00
Annual Deposit Required to Fund 20 Years of $100,000When Joe is 65
Joe's age at start of plan
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 642,000.00
22,000.00
42,000.00
62,000.00
82,000.00
102,000.00
122,000.00
142,000.00
162,000.00
182,000.00
202,000.00
222,000.00
242,000.00
262,000.00
282,000.00
302,000.00
322,000.00
342,000.00
362,000.00
382,000.00
402,000.00
422,000.00
442,000.00
462,000.00
482,000.00
502,000.00
522,000.00
542,000.00
562,000.00
582,000.00
602,000.00
622,000.00
642,000.00
662,000.00
682,000.00
702,000.00
722,000.00
742,000.00
762,000.00
782,000.00
802,000.00
822,000.00
842,000.00
862,000.00
882,000.00
902,000.00
922,000.00
942,000.00
962,000.00
982,000.00
Annual Deposit Required to Fund 20 Years of $100,000When Joe is 65
Joe's age at start of plan
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 642,000.00
22,000.00
42,000.00
62,000.00
82,000.00
102,000.00
122,000.00
142,000.00
162,000.00
182,000.00
202,000.00
222,000.00
242,000.00
262,000.00
282,000.00
302,000.00
322,000.00
342,000.00
362,000.00
382,000.00
402,000.00
422,000.00
442,000.00
462,000.00
482,000.00
502,000.00
522,000.00
542,000.00
562,000.00
582,000.00
602,000.00
622,000.00
642,000.00
662,000.00
682,000.00
702,000.00
722,000.00
742,000.00
762,000.00
782,000.00
802,000.00
822,000.00
842,000.00
862,000.00
882,000.00
902,000.00
922,000.00
942,000.00
962,000.00
982,000.00
Annual Deposit Required to Fund 20 Years of $100,000When Joe is 65
Joe's age at start of plan
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 642,000.00
22,000.00
42,000.00
62,000.00
82,000.00
102,000.00
122,000.00
142,000.00
162,000.00
182,000.00
202,000.00
222,000.00
242,000.00
262,000.00
282,000.00
302,000.00
322,000.00
342,000.00
362,000.00
382,000.00
402,000.00
422,000.00
442,000.00
462,000.00
482,000.00
502,000.00
522,000.00
542,000.00
562,000.00
582,000.00
602,000.00
622,000.00
642,000.00
662,000.00
682,000.00
702,000.00
722,000.00
742,000.00
762,000.00
782,000.00
802,000.00
822,000.00
842,000.00
862,000.00
882,000.00
902,000.00
922,000.00
942,000.00
962,000.00
982,000.00
Annual Deposit Required to Fund 20 Years of $100,000When Joe is 65
Joe's age at start of plan
LOAN PAYMENT
Loan Principal 100,000.00Loan Interest 10.00%Years to pay off loan 10Annual payment $16,274.54
$16,274.54
Year1 100,000.00 $16,274.54 $10,000.00 $6,274.54 2 $93,725.46 $16,274.54 $9,372.55 $6,901.99 3 $86,823.47 $16,274.54 $8,682.35 $7,592.19 4 $79,231.27 $16,274.54 $7,923.13 $8,351.41 5 $70,879.86 $16,274.54 $7,087.99 $9,186.55 6 $61,693.31 $16,274.54 $6,169.33 $10,105.21 7 $51,588.10 $16,274.54 $5,158.81 $11,115.73 8 $40,472.37 $16,274.54 $4,047.24 $12,227.30 9 $28,245.07 $16,274.54 $2,824.51 $13,450.03
10 $14,795.04 $16,274.54 $1,479.50 $14,795.04
HOW LONG TO PAY OFF THIS LOAN?
Loan amount $1,000.00Interest rate 10.00%Annual payment $250.00
Year Interest1 $1,000.00 $250.00 $100.00 $150.002 $850.00 $250.00 $85.00 $165.003 $685.00 $250.00 $68.50 $181.504 $503.50 $250.00 $50.35 $199.655 $303.85 $250.00 $30.39 $219.626 $84.24 $250.00 $8.42 $241.58
Principal at beginning of
yearPrincipal at end of year
Part of payment that
is interest
Part of payment that is principal
Principal at beginning of
yearPayment at end of year
Return of principal
MERCK & CO. 1991-2000
Year Dividends
1991 893 184 481992 1,064 863 521993 1,174 371 831994 1,434 705 1391995 1,540 1,571 2641996 1,729 2,493 4421997 2,040 2,573 4131998 2,253 3,626 4901999 2,590 3,582 3232000 2,798 3,545 641
Purchase of
Treasury stock
Proceeds from
exercise of stock options
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 20010
500
1,000
1,500
2,000
2,500
3,000
Merck Dividends, 1991-2000
Year
Div
iden
ds
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 20010
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
Merck Treasury Stock and Option Exercise
Purchase of Treasury stockProceeds from exercise of stock options
Years
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 20010
500
1,000
1,500
2,000
2,500
3,000
Merck Dividends, 1991-2000
Year
Div
iden
ds
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 20010
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
Merck Treasury Stock and Option Exercise
Purchase of Treasury stockProceeds from exercise of stock options
Years
Line versus XY Chartsx y0 136 228 31
15 -822 1497 6
0 6 8 15 22 97
-10
-5
0
5
10
15
20
25
30
35
y
y
0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96
-10
-5
0
5
10
15
20
25
30
35
x
0 6 8 15 22 97
-10
-5
0
5
10
15
20
25
30
35
y
y
0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96
-10
-5
0
5
10
15
20
25
30
35
x
AVERAGE MONTHLY MAXIMUM AND MINIMUM TEMPERATURES--NEW YORK CITYJan Feb Mar Apr May Jun Jul Aug Sep
38 40 50 61 72 80 85 84 76
25 27 35 44 54 63 68 67 60
Avg max temp (F)
Avg min temp (F)
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0
102030405060708090
NYC Temprature
Avg max temp (F)Avg min temp (F)
Months
AVERAGE MONTHLY MAXIMUM AND MINIMUM TEMPERATURES--NEW YORK CITYOct Nov Dec
65 54 43
50 41 31
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0
102030405060708090
NYC Temprature
Avg max temp (F)Avg min temp (F)
Months
GRAPHS TITLES THAT UPDATE AUTOMATICALLYGrowth 15%
Year Cash flow1 1002 115.003 132.254 152.095 174.906 201.147 231.31
Cash Flow Graph When Growth = 15.0%
1 2 3 4 5 6 70
50
100
150
200
250
Cash Flow Graph When Growth = 15.0%
1 2 3 4 5 6 70
50
100
150
200
250
Cash Flow Graph When Growth = 15.0%
EXERCISE 1Future Value, FV
Deposit $ 600.00 Interest rate, r 15%Number of years, n 10Future Value, FV $2,427.33
YEAR FUTURE VALUE1 $690.00 2 $793.50 3 $912.52 4 $1,049.40 5 $1,206.81 6 $1,387.84 7 $1,596.01 8 $1,835.41 9 $2,110.73
10 $2,427.33
EXERCISE 2
Interest rate 8.00%
Year Gift
0 10000 $21,589.25 1 10000 $19,990.05 2 10000 $18,509.30 3 10000 $17,138.24 4 10000 $15,868.74 5 10000 $14,693.28 6 10000 $13,604.89 7 10000 $12,597.12 8 10000 $11,664.00 9 10000 $10,800.00
TOTAL $156,454.87 Future value in year 10 $156,454.87
EXERCISE 3
Interest rate 7.00%
Year Gift
Future value in year 10
Future value in year 10
1 2 3 4 5 6 7 8 9 10$0.00
$250.00 $500.00 $750.00
$1,000.00 $1,250.00 $1,500.00 $1,750.00 $2,000.00 $2,250.00 $2,500.00
FUTURE VALUE, FV
YEARS
FUTU
RE V
ALUE
0 10000 $7,628.95 1 10000 $8,162.98 2 10000 $8,734.39 3 10000 $9,345.79
TOTAL $33,872.11 Present Value of as of today $33,872.11
EXERCISE 4
Interest rate 14.00%
Year Gift
1 1000 $592.08 2 1000 $674.97 3 1000 $769.47 4 1000 $877.19
TOTAL $2,913.71 Present Value of as of today $2,913.71
EXERCISE 5
Year Payment0 -10001 1502 1503 1504 1505 1506 1507 1508 1509 150
10 15011 15012 15013 15014 15015 150
USING IRR EXCEL FUNCTION 12%USING RATE EXCEL FUNCTION 12%
Future value in year 10
EXERCISE 6
Year Payment0 -10001 1002 2003 3004 4005 5006 6007 7008 8009 900
10 1000
USING IRR EXCEL FUNCTION 32%
EXERCISE 7
BOND FACE VALUE $ 1,000.00 NUMBER OF PAYMENTS 6PAYMENTS $ 120.00 INTEREST RATE 7.00%PV $ 1,238.33
SAVING FOR THE FUTUREYour age today 35Retirement age 65Number of deposits 30Planned age of demise 85Number of withdrawls 20Annual desired pension payout 100,000Annual payment 10,733 Interest rate 8%
Your age55 10,733 10,733 56575859
Account balance, beginning of year
Deposit orwithdrawalbeginning of
year
Interest earned
during year
60616263646566676869707172737475767778798081828384
SAVING FOR THE FUTURE
Total in account
end of year