| Appendix to Chapter 16: Present Discounted Value
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Use these documents and activities to introduce yourself to concepts and topics from this chapter.

Appendix to Chapter 16: Present Discounted Value

  1. The concept of discounting is based on the simple notion that a dollar in the future is worth less than a dollar today. Imagine the following situation. Your economics professor offers you (because you are the best student in the class) $100 today or $100 a year from now. With total honesty, which would you choose? People generally have what economists call a positive time preference—you will pick the $100 now. Instead of waiting, you could purchase things and derive utility from them now or you could invest the money and earn interest. But what if the offer is $100 now or $110 a year from now? Here, waiting provides a benefit of $10. You may still opt for the $100. However, if your professor continued to increase the future payoff, it would eventually reach a point where you would wait.

    This could be described another way. Suppose the offer was $90 now or $100 a year from now. Again there is a benefit from waiting. You may still feel that $90 today is worth more than the future payment of $100. But the present value could be lowered until you did not know which one to take—both would be equally desirable to you.

  2. The formula for finding the present discounted value (PDV) of a future amount (F) received one year from now is PDV = F/(1 + r). This formula can be expanded to determine the present discounted value for future amounts received over many future years as well. Regardless of the length of the chain, it is important to see the role played by the interest rate or the discount rate (r) found in the denominator. What rate should you choose? Well, it depends on many things, including what rate you could have made on your next best investment alternative—your opportunity cost. Furthermore, you should note that as the discount rate rises, the discounted present value falls. This is to say, as the interest rate rises, the value of the future falls.



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