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