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Unformatted text preview: "We shall not cease from exploration And the end of all exploring Will be to arrive where we started And know the place for the first time." T. S. Eliot, 1943 9. Time Value 9.1 Current and Present Value Calculation In the previous chapter, we modeled a firm that applied a given technology to produce a desired output. We started the models under the assumption that the initial input quantities, and therefore the level of output, were too low. Then, we let input quantities and output adjust to yield the profit maximum. Such problems of profit- maximizing firms are typically solved in economics as static problems, but we pretended that adjustments took place over time. Let us now explicitly introduce time into decision making by the firm. With the following models we try to answer the questions of how firms can compare profits that occur at different periods of time. Having a dollar today is surely different from having a dollar next year. In order to compare profits that accrue at different time periods, we may calculate their present value rather than their current value. In later chapters we take up the issue of present versus current value in more detail and provide the tools necessary to assess, for example, optimal resource use by firms over time. Typically firms value higher those profits that occur in the present or nearby future than profits in the distant future. There are many reasons for valuing profits differently based on their occurrence. For example, the timing and amount of profits may be more uncertain for the more distant future. Furthermore, if profits accrue today, they may be reinvested to generate even higher profits in the future. Therefore, lower weights are assigned to future profits when firms evaluate a stream of profits over time. 112 The value of a fixed profit from today’s perspective is the lower the further in the future that profit is earned. The percentage rate at which the present value of the profits, PVP, declines into the future is called the discount rate . It captures risk, uncertainty, and alternative investment possibilities. For practical purposes we may choose a fixed interest rate, I , as the discount rate. In the first diagram, the stock of PVP is drawn down by a given interest of 3%. The stock contains an initial value of $200. The outflow present value of profit rate, PVPR, deceases PVP over time. The outflow depends on the remaining stock and the interest rate. Because both PVP and the interest rate, I, influence the size of the outflow PVPR over time, both are connected to that outflow with information arrows. PVP PVPR I The model shows the present value of $200 at various times, t , in the future. Running the model at a DT = 0.25, you can see from the graph, for example, that the value of $200 for the decision maker in the present is only approximately $110, 20 years into the future. Conversely, if the firm had invested $110 today at the given interest rate, it would own $200 in 20 years from now....
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This note was uploaded on 07/23/2010 for the course ECON 203 taught by Professor Petry during the Spring '08 term at University of Illinois at Urbana–Champaign.
- Spring '08