app3 - A3-1 1APPENDIX 3 TIME VALUE OF MONEY The simplest...

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Unformatted text preview: A3-1 1APPENDIX 3 TIME VALUE OF MONEY The simplest tools in finance are often the most powerful. Present valueis a concept that is intuitively appealing, simple to compute, and has a wide range of applications. It is useful in decision making ranging from simple personal decisions—buying a house, saving for a child’s education, and estimating income in retirement—to more complex corporate financial decisions—picking projects in which to invest as well as the right financing mix for these projects. Time Lines and Notation Dealing with cash flows that are at different points in time is made easier using a time line that shows both the timing and the amount of each cash flow in a stream. Thus a cash flow stream of $100 at the end of each of the next four years can be depicted on a time line like the one depicted in Figure A3.1. 1234$ 100$ 100$ 100$ 100Figure A3.1: A Time Line for Cash Flows: $ 100 in Cash Flows Received at the End of Each of Next 4 yearsCash FlowsYearIn the figure, 0refers to right now. A cash flow that occurs at time 0 is therefore already in present value terms and does not need to be adjusted for time value. A distinction must be made here between a periodof time and a pointin time. The portion of the time line between 0 and 1 refers to period 1, which in this example is the first year. The cash flow that occurs at the point in time 1 refers to the cash flow that occurs at the end of period 1. Finally, the discount rate, which is 10 percent in this example, is specified for each period on the time line and may be different for each period. Had the cash flows been at the beginning of each year instead of at the end of each year, the time line would have been redrawn as it appears in Figure A3.2. A3-2 21234$ 100$ 100$ 100$ 100Figure A3.2: A Time Line for Cash Flows: $ 100 in Cash Received at the Beginning of Each Year for Next 4 yearsCash FlowYearNote that in present value terms, a cash flow that occurs at the beginning of year two is the equivalent of a cash flow that occurs at the end of year one. Cash flows can be either positive or negative; positive cash flows are called cash inflows and negative cash flows are called cash outflows. For notational purposes, we will assume the following for the chapter that follows: Notation Stands For PV Present value FV Future value CFtCash flow at the end of period tA Annuity: constant cash flows over several periods r Discount rate g Expected growth rate in cash flows n Number of years over which cash flows are received or paid The Intuitive Basis for Present Value There are three reasons why a cash flow in the future is worth less than a similar cash flow today. 1. Individuals prefer present consumption to future consumption.People would have to be offered more in the future to give up present consumption. If the preference for current consumption is strong, individuals will have to be offered much more in terms of future consumption to give up current consumption, a trade-off that is captured by a...
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app3 - A3-1 1APPENDIX 3 TIME VALUE OF MONEY The simplest...

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