Articles and Papers

Note on Determining the Fair Value of a Variable Rate Callable Loan

A paper by Stan Feldman and Ryan Tang describing the process of valuing a variable rate callable loan. 

It is well accepted that the value of a callable variable rate debt security is equal to is value without the call feature. Although bonds and loans are debt securities there are notable differences. Loans are generally senior to bonds in the cap stack, have coupons that are typically variable, often with LIBOR floors, and loans are callable at any time over their life while bonds typically have a fixed time frame within which the issuer can call the security, e.g. anytime within the first two years after issuance. While in both the callable bond and loan cases the investors face prepayment risk, this risk is generally greater for the investor in the loan than in the callable bond. This note addresses the valuation of variable rate callable loans and specifically focuses on the value of the call embedded in these loans.

Building Wealth: Purchasing a Home or Building an Equity Portfolio?

A paper by Stan Feldman and John Roberts looking at whether it is better to buy a home or invest in equities to build wealth. 

The paper shows that wealth building should not start with owning a home. It should start with owning assets that produce sustainable income because as this income grows the value of the owned assets will increase. At some point, a percentage of the assets owned can be sold and the proceeds can then be used to purchase a home.

Understanding the Firm Specific Risk Premium

A paper by Stan Feldman and Todd Feldman determining whether a firm specific risk premium (FSRP) exists for private firms. 

The paper seeks to determine whether a firm specific risk premium (FSRP) exists for private firms. It shows that private equity investors price firm specific risk as part of establishing the expected rate of return hurdle rate. The research is based on survey data constructed by the Private Capital Markets Project. It decomposes the rate of return into its component parts- market risk premium, size premium, liquidity premium and firm specific risk premium (FSRP). It finds that on average PE FSRP varies between zero and six percent. These findings indicate that the cost of capital buildup used in valuing private firms should include a premium for firm specific risk unless facts and circumstances suggest otherwise. 

The Musk Brand Has Contributed to the Massive Decline in Tesla’s Equity Value but the Tesla Brand is Still as Valuable as Ever

An article by Stan Feldman and John Roberts examining the influence of the Elon Musk Brand on the share price of Tesla since Musk’s acquisition of Twitter. 

Several financial analysts, have noted that Musk’s actions have reduced Tesla’s brand equity. This is not quite accurate because the Tesla brand is separate from the Musk mystique (the Technoking), although both impact the share price but are driven by different determinants. To understand this separation, we need to appeal to purchase price accounting and finance principles.

When a firm is acquired, its purchase price is allocated to the fair value of acquired tangible assets- plant and equipment and current assets- and identified intangible assets- patents, brand names, trademarks, and customer relationships. In effect, accounting principles require the reconstruction of the acquired firm’s balance sheet from an accounting balance sheet based on historical values to an economic or market-based balance sheet reflecting fair values. Because of accounting rules, most intangible assets do not appear on the historical balance sheet and only show up when there is a change in control, which is the case when a firm is acquired. This means, for example, the Tesla brand is not an asset on Tesla’s accounting balance sheet nor is the value of Tesla goodwill which in part is driven by the Musk brand. Keep in mind that the Musk brand is not owned by Tesla but belongs to Elon Musk, but its impact shows up in its effect on the value of Tesla’s goodwill- the value that remains after allocating fair value to all identified assets. Hence, the Tesla brand and the Musk brand are separate identifiable intangible assets, and each has a separate impact on Tesla’s equity value,

Does Improving a Firm’s Environmental Management System Result in a Higher Stock Price

From the Journal of Investing (Winter 1997), this article, submitted by Stan Feldman, Peter Soyka, and Paul Ameer, examines whether initiatives to improve the environmental performance of corporations, either compliance-driven or voluntary, have consistent impacts on the financial performace of these firms. 

The traditional view holds that expenditures on environmental improvement represent costs that (generally) confer no corresponding benefits on the firm in terms of improved product quality, productivity, ease of manufacturing, distribution, or use, of other desirable attributes. If this is true then rational management behavior would be to minimize and delay environmental costs as much as possible, so as to reduce their impact on the bottom line.

The results of this study suggest that firms that improve both their environmental management system and environmental performance can increase their stock price by as much as 5%. For a firm wit a capitalization of $a billion, this represents an increase in stockholder wealth of as much as $50 million

The Banality of Trust: Why Financial Market Bubbles and Crashes Happen

Financial crises occur when market participants realize that asset prices have reached levels that are far in excess of their fundamental or intrinsic values. Intrinsic values are based on “reasonable assessments” of the fundamentals that drive asset values- informed market participants’ assessments of future cash flows and current rates of return required by informed investors

When asked how investor managements assured themselves that the reported values were correct, more than half said they communicated with managers and felt “comfortable” that the values were correct. Moreover, respondents reported that they did very little relevant analytical due diligence to ensure reported values are correct and their auditors appeared to be “comfortable” with their due diligence practices. It seems almost incomprehensible, considering Madoff stealing hundreds of millions of dollars, the rating agencies not doing proper due diligence on many of securities rated, that fiduciaries responsible for billions of dollars would be so trusting. Yet they are..

The End of History or a New Beginning?

Valuations of public and private firms have and will continue to decline as inflation accelerates and interest rates increase. But these developments are not symptoms of a traditional economic cycle but rather reflect serious cracks in the global economic infrastructure and that have significant negative secular implications for the global economy going forward. 

We have arrived at a third inflection point- a New Beginning, for lack of a better term, that is a break with the optimism of Fukuyama’s world. This new world has already unleashed negative forces that will be with us for a long time. The pandemic underscored the interdependency of the global economy and how an unexpected development could negatively impact the global supply chain.  While my original thought was that we would be living with supply chain disconnects for the medium term- two years post pandemic- it has become clear that the supply chain detachments are more serious than I expected. The Ukraine war has added to the severity of the supply chain disconnects, and the result is that global capacity to produce has been significantly reduced. .

Do Tax Pass Through Entities Have a Valuation Premium Relative to C Corporations of Equivalent Risk? OF COURSE THEY DO!

Modigliani and Miller (M&M) have shown that shielding income from taxes has a value. The Internal Revenue Service (IRS) has argued that TPTE should not be tax effected denying the M&M view that tax benefits have value. Rate of return data used to develop the cost of capital comes from guideline public companies that are predominately C-Corps. Therefore, this information cannot be used directly to value a TPTE.

The COVID-19 Pandemic Signals the Suspension of the Fair Market Value Standard for Npw

Several of our clients are in the middle of a capital raise. The values established are fair market value at year end and well before the collapse of the financial markets related to both the pandemic- a black swan event- and the crash in oil prices-a systematic and predictable event. Our advice to them is that while year-end values would ordinarily be within the fair market value range, these values no longer meet the fair market value standard.

Risk Building in the Financial Markets is Not Being Priced Properly

The focus on Fed policy and whether short rates are higher than long rates as an indicator of future recession is overdone. The real key to understanding movements in the financial markets is being able to evaluate changes in financial risk and whether these changes are priced into asset valuations. Axiom’s analysis of both the public and private equity markets indicate that there is a growing financial risk that has not been priced by market participants.

Identifying Weak Points in Valuing an Enterprise in Chapter 11

The presentation examines the keys to evaluating whether an enterprise valuation is bullet proof in cases where the enterprise is in Chapter 11. It explores different types of errors in valuing an enterprise and presents case studies to illustrate the errors.

The Role of Valuation When Oversight Agencies Increase the Scrutiny Threshold

Even without the latest outcries of the system being rigged and the rich not paying their fair share of taxes, the IRS has been spending more time trying to uncover what it views as tax avoidance strategies and puts enormous pressure on those identified to demonstrate that there are real economic benefits to the claims they make.

Some Inconvenient Truths about Income Inequality in America

Reducing income inequality is the cornerstone of the democratic party’s economic platform. According to Senator Warren rising income inequality occurs because the system is “rigged” in favor of the rich. Democratic politicians have beat the rising income inequality drum to death and as a result its existence has become an accepted fact. But like most facts of this sort, it needs to be explored to determine whether the income inequality outcry not only has a basis, but the policy proposals that emanate from this concern have been shown to achieve their stated objectives.

Is the New York Stock Market High Telling Us the Congressional Budget Office’s Warning About the Evils of the Trump Tax Law are Simply Wrong? So, is Seems!

Our research is in response to clients telling us that they are concerned that the liquidly event window is narrowing because the runup in Federal debt due to the tax law will trigger large increases in interest rates accompanied by lower transaction multiples. All of this means lower valuations for firms looking to sell and a higher cost of capital for firms raising additional financing to fund expansion investment. Our analysis indicates that the incremental Federal debt that the tax law is expected to generate will not result in any deterioration in credit market conditions. Indeed, credit market conditions are likely to improve.

Predicting Market Prices of Fixed Income Instruments Using Axiom Credit Rating and Fair Value Pricing Platform

In the current regulatory environment a necessary but not a sufficient condition for establishing a non-traded asset’s fair value price is to demonstrate that the system used to produce it yields an unbiased estimate of a transaction price at the measurement date. This developing standard is being applied by oversight organizations as well as audit firms. For example, the Securities and Exchange Commission’s Aberrational Performance Initiative is designed to uncover misreporting of fair values of underlying assets of hedge and private equity funds. While many hedge funds only invest in financial securities that trade, many fixed income funds as well as CLOs and CDOs invest in debt instruments that do not trade on a regular basis and for which there is no dealer quote. In cases where dealer bid-asked quotes are available, they often do not accurately reflect the range with which the transaction would take place. In this case, a dealer quote does not meet the fair value financial reporting standard. Since a significant percentage of fixed income securities do not trade on a regular basis and are not routinely priced as a result, other means need to be employed that properly mimic transaction market activity in order to establish a non-traded asset’s fair value. This paper is the first of several papers that Axiom Valuation Solutions (“Axiom”) will produce, to address this critical issue.

The research design employed by Axiom is divided into three distinct phases. In the first phase, one tests whether the system can accurately reproduce prices of traded securities. The second phase identifies factors that determine the illiquidity associated with non-traded securities. The third phase combines the results of the first two phases and tests how accurately the system reproduces reported prices at which illiquid securities have been exchanged. This paper reports phase one research results. These results indicate that Axiom’s Credit Rating and Fair Value Pricing Platform produces unbiased estimates of market prices.

Determining the Fair Value of Debt When the Issuer May Not Be A Going Concern: When is Liquidation Value Fair Value?

Default risk is the uncertainty surrounding a firm’s ability to service its debts and obligations. The Debt holders of a firm near bankruptcy face significant default risk. If the firm is a going concern at the measurement date but loses this status at some point at or prior to maturity, the traditional YTM approach to calculating fair value will always overvalue the debt obligation. To ensure this does not happen, Axiom Valuation Solutions (“Axiom”) first compares the firm’s enterprise value with its book value of debt. If there is insufficient coverage, we then employ Merton’s contingent claims framework and the underlying Binomial Lattice Model to determine the likelihood that coverage will exceed unity. If the probability is either zero or very low that the coverage ratio will exceed unity at maturity, the fair value of debt is equal to the present value of the liquidation proceeds of assets available at the expected recovery date.

Axiom Brochure

Revisiting the Liquidity Discount Controversy: Establishing a Plausible Range

Six Myths of Transacting a Private Business

Valuing a Highly Leveraged ESOP

by Dr. Stanley Jay Feldman

Using Option-Pricing Models to Estimate the Value of Control

Dividend Plan Will Increase Value Firms

by Dr. Stanley Jay Feldman Guest Editorial in Boston Business Journal (2004)

A Primer on Calculating Goodwill Impairment

by Dr. Stanley Jay Feldman, revised

Dr. Stanley Jay Feldman, Chairman of Axiom Valuation Solutions and Associate Professor of Finance, has authored a working paper describing key uncertainties and challenges to business valuation analysts created by recent accounting rule changes by the Financial Accounting Standards Board (FASB).

04.28.2004 – This is a revised version of an earlier paper dated May 2002. This version is essentially equivalent to the earlier paper, although the examples used were amended to improve clarity and understanding of what is a difficult and complex subject.


Financial Accounting Standard (FAS) 142 requires that goodwill emerging from acquisitions be tested to determine whether it has been impaired. Prior to FAS 142, goodwill was amortized over as many as forty years with the amortized amount deducted from net income. FAS 142 requires firms to effectively undertake a market test to see if goodwill has been impaired. This test is completed in two steps. The first simply requires a revaluing of the reporting unit. If this value is equal to or greater than the unit’s carrying value then goodwill has not been impaired. On the other hand, if the calculated value is less than the unit’s carrying value, then step 2 must be undertaken. The purpose of step 2 is to assign the value of the reporting unit to its identified and recognized assets and liabilities. These assets are valued as standalone entities. The sum of recognized asset values less the market value of liabilities is the fair market value of net assets. The difference between the fair market value of the reporting unit and the fair market value of net assets is the implied fair market value of goodwill. If this value is less than the carrying value of goodwill, then the difference is equal to the value of goodwill impairment loss.

The purpose of FAS 141R and FAS 142 is to provide investors with better financial information as to the success of past acquisitions. In the process of doing this, the FASB has forced firms to deal with a number of thorny and, in some cases, unresolved valuation issues. These issues include:

  • Valuing the reporting unit from the perspective of hypothetical new buyer or from the perspective of the acquiring firm implementing its strategy for deploying the acquired assets.
  • Applying a marketability discount to the value of a reporting unit when the unit no longer has equity trading in a liquid market.
  • Estimating the proper cost of capital when the discounted cash flow approach is used to value the reporting unit.

Using Regression Models to Predict the Marketability Discount

by Dr. Stanley Jay Feldman Published in Business Valuation Review, September 2002

In the September 2002 issue of the Business Valuation Review published by the American Society of Appraisers, Dr. Stanley Jay Feldman, Chairman of Axiom Valuation Solutions, and Associate Professor of Finance, Bentley University, has authored a paper reviewing regression analysis results used in evaluating the size of the marketability discount for privately held firms. The paper that this article was based upon is available here.


Academic research suggests that the size of the marketability discount is in the neighborhood of 13.5% and more recent work has suggested it may be as low as 7.23%. The regression models of Silber, and Hertzel and Smith have provided both the intellectual and empirical basis for these conclusions. These models were initially developed to study the determinants of the marketability discount. It has been suggested that they should now be used as a basis for forecasting the marketability discount. This paper demonstrates that these models should not be used for this purpose because the forecast errors are likely to be large. Moreover, based on the structure of these models and their prediction errors, it is not possible to state with any certainty that a 13.5% marketability discount is statistically different than a discount of say 25%.

The Five Myths of Valuing a Private Business

by Dr. Stanley Jay Feldman SCORE Guest Feature Article

Financial Service Needs of Established Business Owners

Dr. Stanley Jay Feldman and Roger M. Winsby, revised

A Note on Determining the Fair Value of a Variable Rate Callable Loan

A Note to Investment Committees: Are You Prepared for the Next Bernie Madoff?

A Research Note on the Value and Under Pricing of Life Policies

Is Investing in an Equity Tranche of a CLO Too Risky?

Maximizing Shareholder Wealth Using The Value-Based Manager Model

Maximizing the Rate of Return on Your Next Acquisition: Why the Allocation of Purchase Price Should be Done Before the Deal Closes

New Opportunities for Business Borrowers: The Bank Monopoly is Ending

The Benefits of Offshoring Intellectual Property: Minimizing Taxes and More

The Cost of Illiquidity in the Syndicated Loan Market

Valuing a Startup as an Exercise in Quantum Physics

Valuing Intellectual Property of an Early Stage Company

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