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Discounted Cash Flow Analysis
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What are Extended Yield Analysis Methods ?
Introduction Part 1:
One of PAMS-DCF's goals was to introduce a new way of learning about Discounted Cash Flow Analysis that provided a hands on approach using sophisticated yield analysis software that here- to- fore was available only to the big guys on the block. This forum will discuss definitions and issues of various topics, many of which are covered by the glossary contained in our book. I'd like to start by discussing the mathematical principals that are required in the use of DCF. We intend to keep the discussion in strictly laymen's terms. Our first goal is to explain the geniuses of "Extended Yield Methods" and why they are needed.
DCF (discounted cash flow ) analysis uses various formulas in computing Present Values and Future Values , payment amounts and terms depending on the given information. Some of theses formulas in mathematics' jargon are generally referred to as Polynomials. They are equations that have certain attributes common to all in their class and they behave in a fixed and determinable way across their entire spectrum. There are certain rules that should always be tested for when dealing with this class of equations known as or called Polynomials. We don't really care what the attributes are or what most of the rules are for theses equations, but (and there is always a "but") there is one rule that does effect DCF analysis that we must learn to deal with in order to avoid making some very serious miscalculations. We don't have to learn the proof of this rule, or why it is always true. The appendix of our book covers a proof and extended discussion, but you had better be a mathematician of sorts to follow it. We simply have to learn how to test for cash flows that have the potential of breaking this rule and do something to reestablish the rule's principal in the flows we are examining.
Some of you are already familiar with the name Descartes. He was a great mathematician of the 18th century. He demonstrated that when dealing with equations in the class of "polynomials" in general, (here as they are applied to cash flows), certain conditions arise that allow us to have multiple positive rates that will discount to zero (NPV=0). Obviously, Descartes was not doing DCF problems when he formulated this principle. It applies to all polynomials including those representing cash flows. The rule he discovered was that if there is more than one sign change in the polynomial's terms (which in DCF are determined by the flows which starts out negative, otherwise there is no investment), then there is a potential for, but not necessarily always, more than one positive solution that will resolve the polynomial equation to zero. Putting this statement differently, if there is only one sign change in the rolling total, then there is only one rate that will resolve to a zero NPV. This rate is unique or it can be said to be "inherent" in the cash flows.
So who cares? If we have five different sign changes in the rolling total of the flows and potentially five different positive rates that will resolve to a zero present value, then let's just pick one that we like and use it to distribute the income over the term of the deal on that rate basis (interest basis). After all the total earnings remains the same (total interest income) at the end of the day, only the timing of income changes as the rate changes.
(to be continued)
June 12, 2015...
Discussion ....Extended Yield Methods
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