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Bài giảng Chapter 2: Time Value of Money

Bài giảng Chapter 2: Time Value of Money provides about future value, present value, rates of return amortization. | Future value Present value Rates of return Amortization Chapter 2 Time Value of Money Time lines show timing of cash flows. CF0 CF1 CF3 CF2 0 1 2 3 i% Tick marks at ends of periods, so Time 0 is today; Time 1 is the end of Period 1; or the beginning of Period 2. Time line for a $100 lump sum due at the end of Year 2. 100 0 1 2 Year i% Time line for an ordinary annuity of $100 for 3 years. 100 100 100 0 1 2 3 i% Time line for uneven CFs: -$50 at t = 0 and $100, $75, and $50 at the end of Years 1 through 3. 100 50 75 0 1 2 3 i% -50 What’s the FV of an initial $100 after 3 years if i = 10%? FV = ? 0 1 2 3 10% Finding FVs (moving to the right on a time line) is called compounding. 100 After 1 year: FV1 = PV + INT1 = PV + PV (i) = PV(1 + i) = $100(1.10) = $110.00. After 2 years: FV2 = FV1(1+i) = PV(1 + i)(1+i) = PV(1+i)2 = $100(1.10)2 = $121.00. After 3 years: FV3 = FV2(1+i)=PV(1 + i)2(1+i) = PV(1+i)3 = $100(1.10)3 = $133.10. In general, FVn = PV(1 + i)n. Three Ways to Find FVs Solve the equation with a regular calculator. Use a financial calculator. Use a spreadsheet. Financial calculator: HP10BII Adjust display brightness: hold down ON and push + or -. Set number of decimal places to display: Orange Shift key, then DISP key (in orange), then desired decimal places (e.g., 3). To temporarily show all digits, hit Orange Shift key, then DISP, then = HP10BII (Continued) To permantly show all digits, hit ORANGE shift, then DISP, then . (period key) Set decimal mode: Hit ORANGE shift, then ./, key. Note: many non-US countries reverse the US use of decimals and commas when writing a number. HP10BII: Set Time Value Parameters To set END (for cash flows occuring at the end of the year), hit ORANGE shift key, then BEG/END. To set 1 payment per period, hit 1, then ORANGE shift key, then P/YR Financial calculators solve this equation: There are 4 variables. If 3 are known, the calculator will solve for the 4th. Financial Calculator Solution 3 10 -100 0 N I/YR PV PMT FV 133.10 . | Future value Present value Rates of return Amortization Chapter 2 Time Value of Money Time lines show timing of cash flows. CF0 CF1 CF3 CF2 0 1 2 3 i% Tick marks at ends of periods, so Time 0 is today; Time 1 is the end of Period 1; or the beginning of Period 2. Time line for a $100 lump sum due at the end of Year 2. 100 0 1 2 Year i% Time line for an ordinary annuity of $100 for 3 years. 100 100 100 0 1 2 3 i% Time line for uneven CFs: -$50 at t = 0 and $100, $75, and $50 at the end of Years 1 through 3. 100 50 75 0 1 2 3 i% -50 What’s the FV of an initial $100 after 3 years if i = 10%? FV = ? 0 1 2 3 10% Finding FVs (moving to the right on a time line) is called compounding. 100 After 1 year: FV1 = PV + INT1 = PV + PV (i) = PV(1 + i) = $100(1.10) = $110.00. After 2 years: FV2 = FV1(1+i) = PV(1 + i)(1+i) = PV(1+i)2 = $100(1.10)2 = $121.00. After 3 years: FV3 = FV2(1+i)=PV(1 + i)2(1+i) = PV(1+i)3 = $100(1.10)3 = $133.10. In general, FVn = PV(1 + i)n. Three Ways to Find FVs Solve the .