Chapter 2: Time Value of Money Calculator Preliminaries: C ALL clears all previous N, I/YR, PV, PMT, FV and CFj entires. Set P/YR to 1 Set DISP to 4 decimals I. Time Lines EX:
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II. Future Value: What is the FV in N years when PV is invested today at a specified interest rate. FV = PV * (1 + interest rate)N EX: What is the FV in 8 years of $550 invested today when the interest rate is 6%? Calculator: 8 N 6 I/YR -550 PV 0 PMT FV => 876.6164 Numerical: FV = 550(1.06)8 = 876.62 EX: What is FV in 2 years of $10 invested today when the interest rate is 8%? Numerical: FV = 10(1.08)2 = Calculator: 2, N 8, I/YR -10, PV 0, PMT FV => III. Present Value: What is the PV of a FV received in N years at a specified interest rate. PV = FV / (1+interest rate)N = FV*(1+interest rate)-N EX: What is $110 received in 5 years worth today if the interest rate is 5%? Calculator: 5 N 5 I/YR 0 PMT 110 FV PV =>
Chapter 2: Time Value of Money IV. Solving for time and interest rates Calculator: Given four of the five variables (N, I/Y, PV, PMT, FV) calculator will solve for the 5th. Numerical: laborious and complicated EX: How long will it take for $100 to accumulate to $1000 if the interest rate is 12%? Calculator: 12 I/YR -100 PV 0 PMT 1000FV N => EX: The PV of 15,000 received in 6 years is 11,500. What is the interest rate? Calculator: -11,500 PV 0 PMT 15,000 FV 6N I/Y = V. Future Value of an Annuity Annuity = Series of equal payments at fixed intervals for a specified number of periods.
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EX: $100 at the end of the year for 8 years. Ordinary (Deferred) Annuity = Annuity where payments occur at end of period EX: Time line
Annuity Due = Annuity where payments occur at the beginning of period EX: Time line
Chapter 2: Time Value of Money Future Value of N period Annuity: Calculator: N, I/YR, PV, PMT => FV EX: FV of 8 year annuity with $100 annual payments and a interest rate of 9% Time line:
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Calculator: 8 N 9 I/Y 0 PV -100 PMT FV => EX: FV of 8 year annuity with $100 annual payments and a interest rate of 10% 8N 10 I/Y 0 PV -100 PMT FV => What if interest rate is 9% 9 I/Y FV => 1,102.85
VI. Present Value of an Annuity PV of N period an annuity: Calculator: N, I/YR, PMT, FV => PV EX: Present Value of $100 at the end of the year for 12 years with an interest rate of 6% Time line:
Calculator: 12 N 6 I/Y -100 PMT 0 FV PV =>
Chapter 2: Time Value of Money VII. Uneven Cash Flow Streams Net PV = CF0 + CF1/(1+interest rate)1 +. . .+ CFN/(1+interest rate)N FV = CF0 * (1+interest rate)N + . . . + CFN EX: PV of 0 today, 100 in 1 year, -200 in 2 years and 300 in 3 years with an interest rate of 8% Timeline:
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Calculator: C ALL 0 CFj 100 CFj -200 CFj 300 CFj 8 I/YR NPV => VIII. Solving for the Internal Rate of Return (interest rate) with uneven cash flows EX: Spend 159.27 today and get 100 in 1 year, -200 in 2 years and 300 in 3 years what is the IRR? Calculator: C ALL -159.27 CFj 100 CFj -200 CFj 300 CFj IRR/YR => IX. Semi-annual and Other Compounding Periods Periodic rate = Nominal rate / number of periods per year (I/Y) Number of periods = number of years*number of periods per year (N) Effective annual rate = rate of interest actually being earned EFF = (1 + periodic rate)m -1 m = compounding periods per year Annual Percentage Rate = Periodic rate * number of compounding periods per year
Chapter 2: Time Value of Money EX: 10% nominal rate with semiannual compounding => 2 periods per year => Periodic rate = 0.05 = 5% EFF = (1 + 0.05)2 - 1 = 10.25% APR = 0.05* 2 = 0.1 = 10% EX: PV of 100 received in 5 years with semiannual compounding and a 10% nominal rate N I/Y 0 PMT 100 FV PV => X. SPREADSHEETS EX: See the Time Value of Money Spreadsheet on the homepage. Amortization Table = Shows the breakdown of interest and principal in each payment EX: See the Amortization Table Spreadsheet on the homepage. XI. Problems: 1, 2, 10a-d, 15a-c, 18, 23a-d, 30, 34, 37
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