Lecture Managerial finance - Chapter 2 provides knowledge of time value of money. After studying this chapter, you will know: Future value, present value, rates of return, amortization. | Chapter 2 Time Value of Money Time Value Topics Future value Present value Rates of return Amortization 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 100 50 75 0 1 2 3 I% -50 FV of an initial $100 after 3 years (i = 10%) FV = ? 0 1 2 3 10% Finding FVs (moving to the right on a time line) is called compounding. 100 After 3 years FV3 = FV2(1+I)=PV(1 + I)2(1+I) = PV(1+I)3 = $100()3 = $ In general, FVN = PV(1 + I)N. One Way to Find FVs Use a financial calculator. 3 10 -100 0 N I/YR PV PMT FV Clearing automatically sets everything to 0, but for safety enter PMT = 0. Set: P/YR = 1, END. INPUTS OUTPUT Here’s the setup to find FV 10% . | Chapter 2 Time Value of Money Time Value Topics Future value Present value Rates of return Amortization 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 100 50 75 0 1 2 3 I% -50 FV of an initial $100 after 3 years (i = 10%) FV = ? 0 1 2 3 10% Finding FVs (moving to the right on a time line) is called compounding. 100 After 3 years FV3 = FV2(1+I)=PV(1 + I)2(1+I) = PV(1+I)3 = $100()3 = $ In general, FVN = PV(1 + I)N. One Way to Find FVs Use a financial calculator. 3 10 -100 0 N I/YR PV PMT FV Clearing automatically sets everything to 0, but for safety enter PMT = 0. Set: P/YR = 1, END. INPUTS OUTPUT Here’s the setup to find FV 10% What’s the PV of $100 due in 3 years if i = 10%? Finding PVs is discounting, and it’s the reverse of compounding. 100 0 1 2 3 PV = ? 3 10 0 100 N I/YR PV PMT FV Either PV or FV must be negative. Here PV = . Put in $ today, take out $100 after 3 years. INPUTS OUTPUT Financial Calculator Solution 20% 2 0 1 2 ? -1 FV = PV(1 + I)N Continued on next slide Finding the Time to Double 20 -1 0 2 N I/YR PV PMT FV INPUTS OUTPUT Financial Calculator Solution ?% 2 0 1 2 3 -1 Finding the Interest Rate 3 -1 0 2 N I/YR PV PMT FV INPUTS OUTPUT Financial Calculator Ordinary Annuity PMT PMT PMT 0 1 2 3 I% PMT PMT 0 1 2 3 I% PMT Annuity Due Ordinary Annuity vs. Annuity Due What’s the FV of a 3-year ordinary annuity of $100 at 10%? 100 100 100 0 1 2 3 10% 110 121 FV = 331 3 10 0 -100 N I/YR PV PMT FV Have payments but no lump sum PV, so enter 0 for present value. INPUTS OUTPUT Financial Calculator Solution What’s the PV of this ordinary .
