The Aleph Blog » Blog Archive » Toward a New Theory of the Cost of Equity Capital, Part 2

Toward a New Theory of the Cost of Equity Capital, Part 2

When I write a piece, and entitle it “Toward…” it means that I don’t have all of the answers.  Typically I think I am getting somewhere, but the speed of progress is open to question.  That said, good questions and constructive criticism aid me on my way.

From Private Equity Beat at the WSJ: Toward a new theory of the cost of equity capital, on the Aleph Blog. We confess to not being entirely up on the benefits of Modern Portfolio Theory versus Modigliani-Miller irrelevance theorems, which is probably why we are journalists and not PE execs. But we nonetheless find this analysis of how to price equity interesting.

From Eddy Elfenbein at Crossing Wall Street: I like the logic, but my question is—what if a firm has little or no debt?

Good question.  The total volatility of a firm can be broken up into three pieces: financial leverage, operating leverage, and sales volatility.  Saturday’s piece dealt with financial leverage and its costs.  An unlevered firm in the financial sense still possesses operating leverage and volatility of sales.  Different unlevered firms have different costs of equity capital because they have different levels of sales volatility, and different degrees of operating leverage.

That will manifest itself in option implied volatility, which is a crude measure of what people would pay to gain and lose exposure to the equity of the company.  The cost of equity should be positively related to that.  More volatile companies should have a higher cost of equity.

Another way to look at it is to ask what is the effect on the firm if the company issues or buys back equity.  How much does the generation of free cash flow change relative to the price paid or received for equity?

Another question:

Doug Says:

October 19th, 20098:25 am

“As for common stocks, they should trade at an earnings or FCF yield greater than that of the highest after-tax yield on debts and other instruments.”

How do you account for the potential for earnings growth in this calculation? The debt investor trades seniority and (in some cases, collateral) for a fixed claim on cash flows. Common stock investors often (but not always) will earn rising “coupons” and get back value much greater than “par” at the end of his/her investment.

I realize that models such as gordon growth take this into account, but you don’t address it in your “debt plus a premium” calculation.

Doug, good point.  The FCF yield, unlike a dividend yield, as used by the Gordon and other DCF models, reflects the ability of the company to reinvest the FCF that is not paid out as dividends.  It reflects growth already in a crude way.  If the ability to grow via reinvestment is below the FCF yield, then the company may as well just sit around and buy back stock.  If the ability to grow earnings is higher (unusual), then the FCF yield will understate prospects.

That’s a crude way of phrasing it, but the FCF yield is a good place to start.

Finally, regarding my thoughts on M-M:  Take Falkenstein’s recent book — high yield tends to underperform with both debt and equity. Or consider that less levered companies tend to return better over the long haul (Megginson, Corporate Finance Theory, page 307.)

M-M, like the CAPM, does not survive the data. Low leverage is a positive factor for returns in both debt and equity, and a decent part of that is the high costs of financial stress for highly levered firms.


The idea here is to try to view the cost of equity capital as a businessman would, rather than an academic who has little exposure to the world as it operates.  Look to the degree of certainty in obtaining cashflows; the yields on various assets should rise as certainty declines.

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7 Responses to Toward a New Theory of the Cost of Equity Capital, Part 2

  1. JRH says:

    to the point above, basically just an IRR right?

  2. tom says:

    “That will manifest itself in option implied volatility, which is a crude measure of what people would pay to gain and lose exposure to the equity of the company.”

    This doesn’t make sense – it’s just another way of saying the market is efficient, and if that is the case, then why not just use CAPM?

  3. Chris says:

    Doesn’t MM assume an efficient market as an axiom?

    From my understanding the logic is:

    1) Companies can capitalize in different ways.
    2) Investors may find the capital structure suboptimal, so
    3) Investors can leverage or deleverage at the security level, so
    4) There is no benefit to companies cost of financing based on structure

    Of course in the real world not all investors can access financing; small investors may be able to buy stocks but lack the scale to buy bonds, and so on.

    If you don’t believe efficient markets to begin with, then there is no reason to believe MM.

  4. The empirical evidence seems to suggest that debt and equity markets are not efficient with respect to default risk. It tends to be underpriced most of the time. In situations where default is near, the cost of all types of capital goes up rapidly.

  5. gaffer says:

    When I was an undergraduate (after already having been in business for a long time), I realized that M-M was erroneous, because of all the things they CP’d (ceteris paribus) away. For my own consumption, I went a long way to demonstrating that quantitatively, but children, work and family intervened, and who was I to argue with Nobel winners.

    But time, experience and events convince me that I was right then and you are right now. As you’ve noted the market does not price risk well. In large part this is due to a fundamental misunderstanding of value. The professional appraisal community has a far better handle on this, exemplified by drawing the formal distinction between “fair market value as a going concern”, “investment value”, “fair market value in a orderly liquidation”, “fair market value in a forced liquidation” and so on. One corollary to the foregoing is one of those lessons that stick from sit-down education, that “Book Value” is not a standard of value but rather a mathematical identity.

    Without going into a long involved academic tome, the cost of capital (and from which results the mathematical determination of value per the income approach) has a shape more approaching that of a an asymmetric parabola (if one graphs return on the y axis and equity debt weight on the x.).

    If I was coming up with a new theorem, risk would be an independent variable. So for example:

    WAAC = wgt avg cost of equity + wgt avg cost of debt + risk premium

    You’ll note the difference that in standard WAAC formulation risk is a component of the both the equity and debt variable – and practically impossible to consistently and logically quantify. Yes, one can look to Ibbottson for historical risk premia, or leave one to the individual decision making of lenders, butt it complicates and obscures the analysis.

    In the formulation above, cost of equity and cost of debt are very straightforward and can be drawn from readily available market metrics. But what does risk look like? Again if you plot risk as a % cost of capital on the y axis and on the x axis the increasing debt weight, on a absolute basis risk is lowest @ 100% equity. From there is upwards slopes. However, risk however is not linear, but rather follows a power law.

    The reason risk follows a power law is that while equity is prepared to lose 100%, debt is not. Also, debt weight increases IRR to equity (in the real world) contrary to MM. Again, debt is never priced well, because issuers don’t understand orderly and forced liquidation, whereby in “orderly”, e.g. say Chapter 11,recoveries may be 80 cents on the dollar, and forced, e.g., Chapter 7, 10 cents on the dollar. One really doesn’t begin to understand the foregoing until you’ve been through it more than a few times.

    So in the real world, as debt increases, equity is far more easily “playing with house money.” A recent poster child for this phenomena is the Simmons Mattress story. In the most recent go round equity was pulling cash out (playing with house money) and the bankers were either (depending on one’s POV) incredibly stupid for letting equity do so, or incredibly smart, because they got their fees and left someone else holding the bag. I’m seen some commentators say that ‘Oh it was OK because rates were so low, the debt service (the I component only) was manageable.’ Poppycock; sometime it’s the dollar value and sometimes it’s the percentage weight and sometimes it is both.

    But you’ve already said that: “company specific risk is significant and varies a great deal.” I would also add that – or amplify – that in any appraisal assignment the first thing that must be set is the appraisal date. Everything drives off that and what is ‘known or knowable’ at the time.

  6. Sajal says:

    David, Sajal from Fundamental Insights. Pension assets are also a source of leverage and should be included while calculating the cost of equity capital. Thanks,


David Merkel is an investment professional, and like every investment professional, he makes mistakes. David encourages you to do your own independent "due diligence" on any idea that he talks about, because he could be wrong. Nothing written here, at RealMoney, Wall Street All-Stars, or anywhere else David may write is an invitation to buy or sell any particular security; at most, David is handing out educated guesses as to what the markets may do. David is fond of saying, "The markets always find a new way to make a fool out of you," and so he encourages caution in investing. Risk control wins the game in the long run, not bold moves. Even the best strategies of the past fail, sometimes spectacularly, when you least expect it. David is not immune to that, so please understand that any past success of his will be probably be followed by failures.

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