tailieunhanh - Lecture Fundamentals of financial management - Chapter 6: Time value of money

Lecture Fundamentals of financial management - Chapter 6: Time value of money. This chapter presents the following content: Future value, present value, annuities, rates of return, amortization. | CHAPTER 6 Time Value of Money Future value Present value Annuities Rates of return Amortization Time lines Show the timing of cash flows. Tick marks occur at the end of periods, so Time 0 is today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period. CF0 CF1 CF3 CF2 0 1 2 3 i% Drawing time lines: $100 lump sum due in 2 years; 3-year $100 ordinary annuity 100 100 100 0 1 2 3 i% 3 year $100 ordinary annuity 100 0 1 2 i% $100 lump sum due in 2 years Drawing time lines: Uneven cash flow stream; CF0 = -$50, CF1 = $100, CF2 = $75, and CF3 = $50 100 50 75 0 1 2 3 i% -50 Uneven cash flow stream What is the future value (FV) of an initial $100 after 3 years, if I/YR = 10%? Finding the FV of a cash flow or series of cash flows when compound interest is applied is called compounding. FV can be solved by using the arithmetic, financial calculator, and spreadsheet methods. FV = ? 0 1 2 3 10% 100 Solving for FV: The arithmetic method After 1 year: FV1 = PV ( 1 + i ) = $100 () = $ After 2 years: FV2 = PV ( 1 + i )2 = $100 ()2 =$ After 3 years: FV3 = PV ( 1 + i )3 = $100 ()3 =$ After n years (general case): FVn = PV ( 1 + i )n Solving for FV: The calculator method Solves the general FV equation. Requires 4 inputs into calculator, and will solve for the fifth. (Set to P/YR = 1 and END mode.) INPUTS OUTPUT N I/YR PMT PV FV 3 10 0 -100 PV = ? 100 What is the present value (PV) of $100 due in 3 years, if I/YR = 10%? Finding the PV of a cash flow or series of cash flows when compound interest is applied is called discounting (the reverse of compounding). The PV shows the value of cash flows in terms of today’s purchasing power. 0 1 2 3 10% Solving for PV: The arithmetic method Solve the general FV equation for PV: PV = FVn / ( 1 + i )n PV = FV3 / ( 1 + i )3 = $100 / ( )3 = $ Solving for PV: The calculator method Solves the general FV equation for PV. Exactly like solving for FV, except we . | CHAPTER 6 Time Value of Money Future value Present value Annuities Rates of return Amortization Time lines Show the timing of cash flows. Tick marks occur at the end of periods, so Time 0 is today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period. CF0 CF1 CF3 CF2 0 1 2 3 i% Drawing time lines: $100 lump sum due in 2 years; 3-year $100 ordinary annuity 100 100 100 0 1 2 3 i% 3 year $100 ordinary annuity 100 0 1 2 i% $100 lump sum due in 2 years Drawing time lines: Uneven cash flow stream; CF0 = -$50, CF1 = $100, CF2 = $75, and CF3 = $50 100 50 75 0 1 2 3 i% -50 Uneven cash flow stream What is the future value (FV) of an initial $100 after 3 years, if I/YR = 10%? Finding the FV of a cash flow or series of cash flows when compound interest is applied is called compounding. FV can be solved by using the arithmetic, financial calculator, and spreadsheet methods. FV = ? 0 1 2 3 10% 100 Solving for FV: The arithmetic method After 1 year: FV1 =