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07/9/2015     A picture is worth 1K words....Part 5 Final on Extended Yield Methods

                                                     "WILL THE REAL YIELD PLEASE STAND UP!"

At this date, it looks very much like the MISFM-Legacy may not survive expected changes in accounting rules now close to a decision. Be that as it may, The MISFM-Legacy remains a good example of what good discounted cash flow techniques should not be. We will continue to use it as a model of what not to do even if it survives. I will refer to the MISFM as MISF-Legacy to denote the issues surrounding its' continued use.

We can start by looking at the first picture, a picture of the MISF-Legacy  method's investment amortization schedule or proof of yield report. This is the report that shows the source of the rate used by FASB13 of 8.647% and all the related tables associated with computing that rate. We can call that Exhibit A-2.  It is conspicuously absent from Appendix E of FASB13. It is difficult to explain an issue if the foundational schedule supporting the computations is not presented.  FASB13 failed to present this schedule as best as we can tell after reviewing Appendix E. Along with the MISFM amortization schedule we are presenting the other two schedules PAMS-DCF produces on all cash flows, The IRR (XX-1)schedule and the SSFM (XX-3) schedule. So each different cash flow will always be analyzed 3 different ways. By doing this 3 way approach (A-1, A-2, A-3, etc.) we will have comparative analysis and we will be prompted to ask pertinent questions.

The first observation to be made is that the raw, un-extended or unmodified flows discount to a PV of zero at a rate of 9.257543% (IRR Schedule A-1), hence this rate can be added to a bucket of "Pick Your Rate" options  that discount to zero It is a mathematical  solution to a series of flows that discounts to a zero PV(present value) . This begins to  demonstrates that a rate can generally be found for any cash flow that will discount to zero mathematically  The flow does not meet the Sign test criteria of only one change in rolling flows. There are 3 changes. This should not stop us from using it since the MISFM-Legacy modified flow does not meet the sign test  either. That is the flow that gives rise to the 8.647% yield  that we are using to distribute income. So by any logical measure, the raw flow used in the IRR analysis and the modified flow used in the MISFM analysis should have equal standing before the court, at least as far as the sign test  for a unique rate or yield existing is concerned.

Let's look at the original FASB13 MISFM-Legacy schedule that was never presented in the publication. This is represented by  Exhibit A-2. It uses an algorithm or routine wherein it starts by picking a test rate,  Discounts the flows to the point where the inflows plus interest at the rate being tested recoup the initial investment and the interest computed. It then transfers to a fund the remaining cash flows or portions thereof until it encounters outflows that are then paid from the sinking fund( the transferred money) until the sinking fund is used up. Thereafter, any outflows encountered are deemed by the rules of the algorithm set somewhere in the universe to come from new investment or multiple investments with no cost or time value associated with them for prior years. So we have a scheme that uses a sinking fund created on the basis of some logic associated with positive and negative investment periods, (the negative investment period is when the investment is eradicated by the payback and the positive investment period is when the out flowing funds turn the  PV back to a negative number again on which interest is earned). Other terminology used in describing this somewhat convoluted reasoning includes asset and liability phases of the investment. The rate of 8.647% (Exhibit A-2) is the first rate iterative solution routines land on when following this algorithm. So let's add this rate to our bucket of potential rates as a possible solution. That makes two potential rates and counting,

Therefore the MISFM-Legacy  is a method that uses both the sinking fund concept and additional new investment as sources to cover outflows,  the sinking fund first and then thereafter, new investment as needed. The process of going outside the transaction for new investment can introduces sign change swings and begs the question of why are we using an extended method in the first place?  It allows and promotes more than one sign change to exist or remain in the flow series. Why not just use the first rate we landed on for the raw flows of 9.2575% (
IRR Exhibit A-1)if in fact we are going to allow the sign changes to remain at more than one (three in this case)? I do not have a logical answer to that question because there probably is none. Absent an amortization schedule to study  we can't begin to discern this. Again, no such schedule was apparently provided in FASB13?

Continuing the examination of the logic surrounding the MISFM -Legacy algorithm, we can ask if new investment is allowed into the transaction towards the end of the deal to pay the negative flows, then why not allow the introduction of new money via  loans or new investment in the beginning of the deal that can be  paid back towards the end or retained?  New investment that is paid back can be viewed as loans and visa versa. Let's look at how early new inflows or indirectly, early existing inflows that are allowed to stay when they should be set aside in a sinking fund for future outflows (exactly what the MISFM -Legacy is doing)impact yield and earnings per share.
Exhibit B-2shows that by introducing a loan of $200,000 into the deal in year 4 (can be viewed as temporary equity) and paying it back in year 15th we have increased the reported yield to 10.585% This is exactly the same impact as leaving money that should be put into the sinking fund( but instead is left to enhance early year flows), has on yield and EPS. Again, the unmodified flows continue to have more than one sign change in the rolling forward total flows as does the modified flows for this scenario. Same question, why bother changing the flows or modifying or extending the flows if they do not eliminate the multiple yield issue? So we now have a third yield of 10.585% for the MISFM to throw into the bucket  of possible rates to use.  Oh yes, there is no apparent reason to disqualify the IRR rate under Exhibit B-1 as yet another potential rate to use. It is given as 21.4273%. That make two more rates we can add to the bucket or a total of 4 and counting. After all, these rates are only being used to distribute the same total income over the term, only using different mix of proportions by year.

As long as we can introduce new capital and thereby leave existing flows to enhance yield early on or introduce new money via loans early on to be paid back late in the deal, or return the capital investment later in the deal, then we have a large scenario of rates we can orchestrate. It is all about timing of flows....the time element which we are trying to eliminate when doing DCF. Yes. we will consistently get the same unique yield using the MISFM-Legacy on the first iterative pass (remember other rates may exist if the yield engine continues searching per Descartes Rule of signs). The first yield landed on has absolutely no basis in reason. It is a consistently arrived at wrong and illogical answer.  It is no more logical to leave money that should be set aside in a sinking fund for future payments and then rely on expense free new investment  to meet the payment than it is to lend new money in via cost free loans early on and pay it back towards the end. New money from investment or loans destroys the integrity of the rate analysis by allowing the continuation of the multiple rate potential, and distorting the original cash flow using an endless number of arbitrarily arrived at cash flow solutions.

We could recode the yield engine so as to keep searching for potential rates that discount to zero. This would be an academic exercise of little value. Descartes rule states that not in all cases will there be multiple yields so if you use the MISFM-Legacy it may be a unique rate. Is that any way to roll? We do not think so nor do the people that invented the extended yield methods. They would not have gone to such lengths to avoid multiple sign changes if they felt they could work with a "may be". Can you tell an investor that the rate he thinks he is earning may not be the only rate existing for his investment?

There  are complex cash flows wherein the modifications under the MISFM -Legacy result in the same adjusted cash flow as the SSFM adjusted cash flow, thereby giving the same rate answer and being correct in that they both meet the single sign change test. Most of the time the MISFM-Legacy will give a different answer from the SSFM.  Only on rare occasions will the nature of the flows produce this same result. We have examples of this among our 65 examples supplied with PAMS-DCF software.

Enough said about the MISFM-Legacy and its' issues. As far as PAMS-DCF and good DCF techniques is  concerned, the MISFM-Legacy  is a non-starter in the vast majority of cash flows. That is why we test every adjusted flow for Descartes rule. We have demonstrated how arbitrary and illogical the MISFM-Legacy's algorithm is , and how easily it can be manipulated once you accept the logic of ADDING NEW MONEY .

Lets discuss the 3rd method that  PAMS_DCF's  yield engine uses, the Standard Sinking Fund Method or  the SSFM. Sometimes this method is referred to as the "Traditional sinking fund Method".  See Exhibit A-3, B-3 and C-3. All Exhibit C schedules begin with the SSFM cash flow as modified by its' algorithm which results in a modified flow that does pass the single sign change test and then we modify it again to include new capital or debt by adding a $ 200,000 flow to year 4 and a negative offsetting flow to year 15 for the payback or removal of the equity. We did this as one of many efforts to manipulate the rate using this method. As you can see from
Exhibit C-1 and C-2, the rate is manipulated upwards, but does not change in Exhibit C-3 In fact if you look at all three Exhibits, A, B and C you will note that the SSFM(X-3) has remained the same at 5.367%. We tested many other scenarios and the same result was found to hold true.  At most, a relatively small change in rate will result (under 10 basis points as compared to the hundreds of basis point changes in the MISFM-Legacy). You may also notice that the interest earnings in the first 5 years is substantially lower under the SSFM than under the MISFM-Legacy by about 80%, hence EPS are 80% lower in the first 5 years.  Is this good Economic Incentive enhancement ?  "Not so much" as compared to the MISFM-Legacy. Exhibit C-1 and C-2 produce two more different rates we can throw into the bucket, making 6 and counting. We could go on making an infinite number of cash flow scenario's all returning a net income of $116,600 over the same term or years.  The IRR is 14.285% and the MISFM  is 10.4887%. They both  fail the sign change test  in unmodified (IRR) or modified (MISFM) cash flows. This method with the $200,000 added to the SSFM modified flow is just another Pick Your Rate method. We can call this method the Enhanced Standard Sinking Fund Method.  It is  useless  other than to demonstrate that different rate scenarios can be orchestrated to amortize the same amount of income for an infinite number of cases. The only method that consistently returns a rate that is guaranteed unique and is always or nearly always (varying only slightly if at all) the same for the flows presented even when enhanced or modified by manipulation in timing and/or introduction of new flows from capital or loans seems to be the SSFM ( Traditional Sinking Fund Method). A manual or computer driven adjustment to cash flows that results in only one sign change will result in one unique rate and can be a qualifying method, whatever name we give it!

As an aside, adding a realistic sinking fund rate to earn interest on the sinking fund results in a whole new set of rates and considerations.  As an example, a sinking fund rate of 6.5% will increase the SSFM return yield to 8.4155% nearing the same rate as the MISFM-Legacy with a zero SFR assumed.  Another words if the company owning the leveraged lease had a means of investing the sinking fund at 6.5% doing the SSFM would return nearly the same rate as the MISFM-Legacy since the method creating the larger sinking fund (SSFM)will tend to catch up on earnings with the MISFM-Legacy all other things being equal... Ignoring Sinking Fund Earnings opens up a whole new can of worms best left for future discussion.

We have tried to explain what "Extended Yield Methods" are and what their purpose is. In trying to do so we covered some mathematical  territory driving home the importance of Descartes Rule of Signs and its' impact on cash flow analysis. We have examined just two of many potential extended yield methods or concepts that can be created.  The MISFM-Legacy which provides for future flows partly from a sinking fund (created for a short period early in the transaction), but mostly through reliance on new investment , and the SSFM which generally relies solely on earlier flows from within the transaction with which it creates a sinking fund to cover all the subsequent out flows. It was our intention to present the fundamental reasons for doing extended yield analysis and providing you with the necessary understanding to help you develop your own scenarios in addition to the two extended methods PAMS uses. We have computer power at our disposal that was not available to Joe Blow at the time the MISFM-Legacy was conceived.

Doing DCF analysis without access to a computerized system is impossible given our life spans. The use of a capable, versatile, easily and quickly manipulated computerized system is absolutely necessary. PAMS-DCF is just such a system thanks in part to the choice of EXCEL as its database,  which most people have and are familiar with. Excel, when coupled to the front-end input software and powerful yield analysis engine make an unprecedented combination for dealing with DCF analysis.

PAMS-DCF is a tool that is affordable and easily learned and should be as basic to the tool box of every financial industry person and financial educator as a hammer is to a carpenter. We at PAMS-DCF Inc. intend to see to it that everyone can afford to have access to this tool and the knowledge to use it,

                                                                                that is our Mission.                                                     (examples are sub folders to this page in the navigation dropdown)

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