Pams logo

Saturday, June 27, 2015

Extended Yield methods:Part 4
Where's the Sunshine? 

To sum up, extended yield methods were designed to deal with complex cash flows (cash flows wherein the rolling sum of the flows change signs more than once). they go from negative to positive and back to negative then to positive again such that their rolling forward sums give rise to yield curves that cross the zero rate axis more than once. The intent was and is to eliminate the wild swings in cash flows so as to limit the sign changes to only one.  Doing so eliminates the potential for other positive rates existing in the modified flow.  Any method that does not eliminate the multiple yield potential from the cash flows is not doing its' job. It leaves us with a transaction that can't be represented by rate of return, as many or more than one rate may exist. To pick one rate ignores the rest.  It also facilitates  the manipulation of rate by making it easy to move cash flows around the term as long the total flows remain the same. Many yield rates can be sought and landed on for many different adjusted flows using the "Pick Your Rate" method. This makes the model entirely arbitrary and hence unacceptable. It is not logically computed and does not provide a unique computation of rate inherent to the flow. It is just one of many rates that performs a mathematical function of resolving the present value to zero and nothing more.

We have tried to relate in this discussion how and why rate analysis must adhere to the mathematical principles espoused by Descartes' rule of signs.  The genesis of extended yield methods was created for the sole purpose of making it possible to adhere  to Descartes rule of signs.

PAMS-DCF's yield engine checks for adherence to Descartes' rule of signs in both the initially presented unmodified flow and the modified flow, giving appropriate warnings when necessary. If someone wishes to use  a non-unique rate to distribute income over the transaction term,  then they can do so. It may be a misrepresentation of the return on the transaction, and it may give rise to violations of good accounting principles that call for using a distribution that matches costs against revenues, full disclosure, a non-arbitrary basis for computation, etc., but so be it. The Investment Tax Credit  (does anyone remember the ITC ?) was taken into income all in the year of acquisition and not amortized over the life of the asset as good accounting demanded. The accounting profession objected loudly but with little success.  Congress said it was OK. 

Similar to the MISFM (Legacy), the ITC accounting served as an immediate economic incentive resulting in increased earnings per share in the early years. Rules are broken all day long, and principals are violated over and over again, but one should be aware of the what and wherefore of these issues so that they are not misapplied to other situations. I repeat, the MISFM-Legacy had and may have a place, but not as representing a good example of yield analysis techniques.

We intend to demonstrate  that new investment is a non-starter in building cash flow models and using discounted cash flow analysis. We will be using examples of FASB13 in the next installment of this discussion on "Extended Yield Methods" because it is a well known example and easily available for study. It will clearly show that the modified cash flow generated by the MISFM-Legacy results in arbitrarily adjusted cash flows distribution of income and is not the only rate that , once given the freedom to introduce "new Capital",  that will discount other adjusted flows  to zero within the confines of the transactions net income.  We will then proceed to review one or two methods that do work to eliminate the multiple yield issue and what their impact is on the timing of profit recognition within the transaction. 

The entire purpose of this exercise is to demonstrate that Descartes  Rule of Signs must be adhered to and that "Extended Methods" were created to for the sole purpose of making this possible. To have created a method such as the MISFM-Legacy that only partially adheres to the " rule of signs" by providing for only the first few negative flow and ignoring  the remaining negative flows is at best obscuring the technically correct approach, demonstrating incorrect concepts and principals and causing confusion about the techniques used in DCF analysis. It is an example of  obfuscation at its' best. That is perhaps one reason it is being abandoned, except that the current thought is to abandon all after tax accounting recognition done using good DCF techniques or bad ones. On the positive side the MISFM-Legacy added incentive to do these transactions. I do not see why EPS has to be tied to good DCF techniques! Let the EPS issue be whatever the parties agree to, but the mathematical truisms should always be honored.

As an aside, FASB13 is a great publication and it broke new ground in accounting in many areas.  The concepts as noted in our book that accompanies PAMS-DCF, should not be discarded. They included the "Economic Reality" concept, and substance over form concepts that FASB13 dealt with. That FASB13 did not land on a proper method for use in distributing  leveraged lease income is a minor flaw in the overall achievement, and can be easily fixed by simply clarifying the need to adhere to Descartes Rule of Signs. Any method that results in an inherent unique yield should be acceptable to spread income with. Yes, changes can be made that will improve FASB13 in several areas, but discarding after tax analysis and reporting is not necessarily one of them.

An argument can be made that leveraged leases are less needed in today's tax environment as companies are paying much lower effective tax rates than in the past, but that can change quickly. Further, leveraged lease accounting may be more trouble than it is worth from some peoples perspective, however, it was the segue into areas of finance that accounting types such as myself never had cause to look at. Perhaps it is simply to complex to deal with from a practical standpoint. The economic analysis of a leveraged lease or a leveraged real estate transaction, or business acquisitions, etc..will always require good DCF understanding and techniques regardless of what happens to FASB13.

   Congress would not allow accounting firms to write an exception when ITC was taken in year one. I don't know of any firms that did. The Financial Accounting Standards Board may not allow pretax income to be distributed on an after tax proportional basis as conceived of when the deal is done, but that does not change the reality of why it was done and how it will be earning real cash. It is a step backwards for the accounting profession to throw it all out ( in my humble opinion).

(to be continued using examples as Part 5 " A Picture is Worth 1,000 Words")

Sunday, June 21, 2015

Extended Yield Methods: Part 3 Smoke and Mirrors

Extended Yield Methods: 
Part 3  Smoke and Mirrors

Let's look at the second source of funds into which we lumped loans and new investment.  Let's discuss loans first as they are less problematic than new investment.  In order to make the transaction logically supportable, with all loose ends sewed up, a loan commitment along with interest rates would have to be put in place.  The loan proceeds would be used to zero the negative flows and thereby avoid a sign change situation. The payback of the loan plus interest would come from subsequent positive inflows. This approach is the only approach where the prior flows are not adequate to meet subsequent outflows or set up a sinking fund of adequate size, unless you resort to the "new investment assumption".

The new investment or multiple investment assumption has many issues that are inherent in it.  Unlike a loan, it is not assumed to be paid back by the end of the transaction. Neither is there a cost introduced to the deal to cover its availability and use as in a loan. A loan has a commitment fee and interest for the use as part of the transaction costs. A commitment from investors could be gotten and put in place similar to a loan commitment.  With or without a commitment,  new investment is being introduced at a later date.  Even if early flows are adequate to meet  future outflows, they must be set aside in a sinking fund and not left in the transaction to enhance yield by relying on new expense free investment  to cover outflows. The question becomes how do you cost the new investment such that it factors into the computations of the return on the original investment which is often years earlier? Simply put, the answer is you can't. The new investment destroys the present value computations on the original investment, and effectively starts a new deal. Hence, multiple rates arise.  It is a non-starter and a red herring to include new investment in a model if it changes the rolling total of flows sign. There can't be any significant outflows such that they cause the sign of the rolling forward sum of the flows to change without creating a meaningless yield that will resolve to zero mathematically. That is the primary issue with the use of cost free new investment . You have to ignore the sign change requirement of Descartes rule of signs.

What happens if you ignore the single sign change requirement?  What would govern the amount of capital you would need?  The simple answer is very little would constrain the amount of capital that could be introduced to meet negative flows. In fact, scenarios or modifications could be easily formulated for pushing positive flows anywhere in the flow stream and making up for them with new investment in other years within the flow steam so that they total to the same overall income.  You could call that method the PYR method or "Pick Your Rate" method. There are only limited constraining requirements to the modifications. Consider also that it would not be possible to assure an investor that the return on investment presented is the only positive return that would discount the flows to zero. The rate can be easily manipulated over a wide spectrum of rates, each giving rise to a different earnings curve. This makes the periodic earnings arbitrary at best.

The above noted situation will be demonstrated later on in this series by using many examples of the FASB13  leveraged lease model in which the modified flows do not meet the single yield rule test. Again, the unmodified flows fail to meet the single yield requirement and the modified flows also fail! The early year's flows can be enhanced by some arbitrary amount, and future negative investment can be increased to offset the early enhancement resulting in a new rate of earnings curve amortizing the same total income. You could as the MISFM-Legacy does, just set up a sinking fund to cover the first few negative flows and ignore the rest of the negative flows saying new investment will cover them. You could say the MISFM is a mix of a Sinking Fund Method and the PYR method since it does both. The MISFM-Legacy kind of introduces the sinking fund idea but does not execute it across the term of the deal.  As long as you accept the notion that you can introduce expense free capital at any time during the transaction life cycle you have an infinite number of potential rates you can orchestrate. The rates do not reflect any meaningful solution.  The rates are simply mathematical solutions to the new flow series you have created. The example in FASB13 of a  leveraged lease (using MISFM-Legacy) is a very poor example of the use of discounted cash flow analysis as it demonstrates the improper use of techniques and promulgates an arbitrary answer. This can only lead to confusion and distrust.

Any cash flow analysis system worth its salt must have a test for multiple sign changes and clearly report on that test. Whether the cash flow is modified by hand or using a computerized algorithm, the system should test and report on the modified flows as well. Modifications and testing has to be done until the multiple yield issue is eliminated. If the modifications can't be done and still provide a viable transaction investment, then the transaction may have to be abandoned. The key point is that there can be only one real yield, the one that discounts the flows to zero with the knowledge that no other positive rates will do the same. To find that rate, the flow must show only one sign change over the term. This is the only purpose of using extended methods. Telling an investor that he is earning at a rate that may not be inherent in the transaction is at best misleading.

It does not matter what the nature of the investment is, real estate construction and sales, business projections, leveraged leases etc. , the same principals will apply. A polynomial is still a polynomial, a cash flow is still a cash flow, that will not change. 

(to be continued) . . . parts 1, 2 and 3 are now completed

Saturday, June 20, 2015

Extended Yield Methods: Part 2 Sources of Funds

Page 2 of the Discussion Page at


The answer to the question "who cares" is " everyone should care".  Firstly, if a flow fails Descartes' rule of signs test it will be because contained in the flows are negative outflows after the first initial investment outflow. That is what causes the sign changes of the rolling forward totals. The first question that should come to mind is "Where will these negative subsequent flows come from? " The second question is what cost, if any, should be introduced to the analysis and how will it be introduced.

Let's try to answer the first question and watch what happens. Where is the money going to come from? There are two main sources of the money, one would be from within the transaction, and the other would be from outside the initial transaction, such as a loan or additional investment.  Let's look at the source from within the transaction flows first. In many instances the cash flows we are examining will have sufficient prior inflows to adequately meet the subsequent required outflows. In those cases we could set aside some of the inflowing money in sufficient amounts to meet the subsequent required outflows. The transaction will be fully self-supporting and all outflows, after the initial investment, will be expensed to the transaction by being part of the net flows. The set-aside money needed to pay out the negative periods is conceptually provided for by putting the money in an account called a sinking fund. A physical fund may not be set up. The savings may be viewed as being held by the parent company. In that case it is valued at the parent's marginal cost of borrowing (or some other agreed rate). The earnings on the fund, real or conceptual, would be the interest rate paid by the institution holding the money. If it is in a bank, then it is at some bank savings rate, if used by the parent, then it should be the parent's marginal cost of funds. The fund money can be viewed as an offset to existing debt until returned to the transaction by the parent company. The governing limits of the sinking fund are usually to put aside just enough money to meet the negative flows. Taking more money than minimally needed and placing it in a savings account will usually be detrimental to the profitability of the transaction since the transaction is presumed to be earning more than can be earned at the sinking fund institution, all other things being equal. If this is done precisely, it will have the effect of smoothing out the cash flow's swings from positive to negative and eliminate the multiple sign change issue introducing zero cash flows in some of the periods that were formerly negative. More importantly, the transaction model is now pictured and set up as a logical flow of cash that defines all of the sources of the flows, income and expenses associated with the model. Since all of the funds are from within the transaction after the initial investment, the profitability (or lack thereof), as measured by the rate of return within the flows, is all-inclusive recognizing all costs and income associated with transaction. By addressing the issue of "where does the money come from" we have solved three issues: where is it from, what is the cost, and is the rate so determined reliable and unique.  For the case where the money comes from within we have solved it all. Voila! In case anyone hasn't noticed, we also explained what an "Extended Yield Analysis Method " is and why it is needed. Simply put, it is needed to present a logical, all inclusive, verifiable and complete flow model and develop a unique and implicit rate from an otherwise incomplete, illogical arbitrary multiple rate potential flow scenario.

(to be continued)

Thursday, June 18, 2015

Extended Yield Methods: Introduction

                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.

It is noted that in the leasing arena much is changing, however, whatever the outcome, the financial analysis of the transaction's economics will always require a comprehensive understanding of Discounted Cash Flow Analysis. That being said, when reference is made to FASB 13, it should be understood that it may be a legacy document in many respects going forward, particularly in the lessor leveraged lease area. As PAMS-DCF uses an extended yield method called MISFM which should never have been adopted in the first place, and will have no good reason to remain other than to do review type work with,  it will be referred to as "MISFM Legacy". 

(to be continued)

(Completed through page 2)

Wednesday, June 17, 2015

Saying Hello

Hello everyone in the accounting and finance world:

We hope to use this blog to mirror posts that will appear on my web site "Discussion" pages at WWW.PAMSDCF.COM. It will also serve to archive the web site postings and make it easy for readers to comment on topics.

We will also comment from time to time on current tax and financial issues.

I look forward to hearing from you.

Phil T.