tmvmoney - TIME VALUE OF MONEY 1 2 3 4 5 6 7 8 9 10 11 12...

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TIME VALUE OF MONEY Page 1 FUTURE AND PRESENT VALUE FACTORS Interest rate 10% Present value 1,000 First of End of % of Year Year Initial Year Balance Interest Balance Investment 1 1,000 100 1,100 110% 2 1,100 110 1,210 121% 3 1,210 121 1,331 133% 4 1,331 133 1,464 146% % of Initial Investment ( Future Value Factor ) = ( 1 + Interest Rate ) ^ # of Years Present Value Factor = 1 / ( 1 + Interest Rate ) ^ # of Years A B C D E F G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
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TIME VALUE OF MONEY Page 2 AMORTIZATON TABLE The following amortization table shows the link between the present value (amount borrowed), cash flow (payment) and discount rate (interest rate) on a five-year loan. Interest rate 10% Payment 1,000 Amount borrowed 3,791 Beginning Plus Less Ending Year Balance Interest Payment Balance 1 3,791 379 (1,000) 3,170 2 3,170 317 (1,000) 2,487 3 2,487 249 (1,000) 1,736 4 1,736 174 (1,000) 909 5 909 91 (1,000) 0 A B C D E F G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
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TIME VALUE OF MONEY Page 3 PRESENT VALUE CALCULATION The following shows how to calculate the present value as the sum of the present values of the cash flows. Interest rate 10% Payment 1,000 Year 0 1 2 3 4 5 Payment 1,000 1,000 1,000 1,000 1,000 Present value factor 100% 91% 83% 75% 68% 62% PV of payment 909 826 751 683 621 PV of all payments 3,791 A B C D E F G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
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TIME VALUE OF MONEY Page 4 SPREADSHEET FUNCTIONS Given the number of periods (or number of payments), any two of the following determine the third: present value, cash flow, discount rate. Be careful about the signs! 1. The present value is computed as PV(interest rate, # of periods, cash flow). Discount rate 10% Number of periods 5 Cash flow 1,000 Present value (3,791) 2. The present value can also be computed as NPV(interest rate, series of cash flows). Year 0 1 2 3 4 5 Cash flow 1,000 1,000 1,000 1,000 1,000 PV of cash flows 3,791 3. The cash flow is computed as PMT(discount rate, # of periods, present value). Discount rate 10% Number of periods 5 Present value 3791 Cash flow (1,000) 4. The discount rate is computed as IRR(series of present value and cash flows). Year 0 1 2 3 4 5 Cash flow (3,791) 1,000 1,000 1,000 1,000 1,000 Internal rate of return 10% A B C D E F G H 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 26 27 28 29 30 31 32 33 34 35
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TIME VALUE OF MONEY Page 5 MONTHLY COMPOUNDING Annual interest rate 10% Monthly interest rate 0.83% ( Annual rate / 12 ) Future Beginning Ending Value Month Balance Interest Balance Factor 1 100.00 0.83 100.83 100.83% 2 100.83 0.84 101.67 101.67% 3 101.67 0.85 102.52 102.52% 4 102.52 0.85 103.38 103.38% 5 103.38 0.86 104.24 104.24% 6 104.24 0.87 105.11 105.11% 7 105.11 0.88 105.98 105.98% 8 105.98 0.88 106.86 106.86% 9 106.86 0.89 107.75 107.75% 10 107.75 0.90 108.65 108.65% 11 108.65 0.91 109.56 109.56% 12 109.56 0.91 110.47 110.47% Effective annual rate 10.47% Effective annual rate = FVF - 100% = ( 1 + Monthly Rate )^12 - 100% A B C D E F 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
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tmvmoney - TIME VALUE OF MONEY 1 2 3 4 5 6 7 8 9 10 11 12...

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