Presentation on theme: "Future value Present value Rates of return Amortization CHAPTER 2 Time Value of Money."— Presentation transcript:
Future value Present value Rates of return Amortization CHAPTER 2 Time Value of Money
Introduction In fact, of all the concepts used in finance, none is more important than the time value of money, which is also called discounted cash flow (DCF) analysis. PV : present value, or beginning amount, in your account i : interest rate INT : dollars of interest you earn FV : future value n : number of periods involved in the analysis
Time lines show timing of cash flows. CF 0 CF 1 CF 3 CF 2 0123 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. 100 012 Year i%
Time line for an ordinary annuity of $100 for 3 years. 100 0123 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 0123 i% -50
What’s the FV of an initial $100 after 3 years if i = 10%? FV = ? 0123 10% Finding FVs (moving to the right on a time line) is called compounding. 100
Excel Function for Annuities Due Change the formula to: =PV(10%,3,-100,0,1) The fourth term, 0, tells the function there are no other cash flows. The fifth term tells the function that it is an annuity due. A similar function gives the future value of an annuity due: =FV(10%,3,-100,0,1)
HOME WORK Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1; a. $400 per year for 10 years at 10 percent. b. $200 per year for 5 years at 5 percent. c. $400 per year for 5 years at 0 percent. d. Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.
HOME WORK Find the present value of the following ordinary annuities: a. $400 per year for 10 years at 10 percent. b. $200 per year for 5 years at 5 percent. c. $400 per year for 5 years at 0 percent. d. Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.
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