Toward a New Theory of the Cost of Equity Capital

I have never liked using MPT [Modern Portfolio Theory] for calculating the cost of equity capital for two reasons:

  • Beta is not a stable parameter; also, it does not measure risk well.
  • Company-specific risk is significant, and varies a great deal.  The effects on a company with a large amount of debt financing is significant.

What did they do in the old days?  They added a few percent on to where the company’s long debt traded, less for financially stable companies, more for those that took significant risks.  If less scientific, it was probably more accurate than MPT.  Science is often ill-applied to what may be an art.  Neoclassical economics is a beautiful shining edifice of mathematical complexity and practical uselessness.

I’ve also never been a fan of the Modigliani-Miller irrelevance theorems.  They are true in fair weather, but not in foul weather.  The costs of getting in financial stress are high, much less when a firm is teetering on the edge of insolvency.  The cost of financing assets goes up dramatically when a company needs financing in bad times.

But the fair weather use of the M-M theorems is still useful, in my opinion.  The cost of the combination of debt, equity and other instruments used to finance depends on the assets involved, and not the composition of the financing.  If one finances with equity only, the equityholders will demand less of a return, because the stock is less risky.  If there is a significant, but not prohibitively large slug of debt, the equity will be more risky, and will sell at a higher prospective return, or, a lower P/E or P/Free Cash Flow.

Securitization is another example of this.  I will use a securitization of commercial mortgages [CMBS], to serve as my example here.  There are often tranches rated AAA, AA+, AA, AA-, A+, A, A-, BBB+, BBB, BBB-, and junk-rated tranches, before ending with the residual tranche, which has the equity interest.

That is what the equity interest is – the party that gets the leftovers after all of the more senior capital interests get paid.  In many securitizations, that equity tranche is small, because the underlying assets are high quality.  The smaller the equity tranche, the greater percentage reward for success, and the greater possibility of a total wipeout if things go wrong.  That is the same calculus that lies behind highly levered corporations, and private equity.

All of this follows the contingent claims model that Merton posited regarding how debt should be priced, since the equityholders have the put option of giving the debtholders the firm if things go bad, but the equityholders have all of the upside if things go well.

So, using the M-M model, Merton’s model, and securitization, which are really all the same model, I can potentially develop estimates for where equities and debts should trade.  But for average investors, what does that mean?  How does that instruct us in how to value stock and bonds of the same company against each other?

There is a hierarchy of yields across the instruments that finance a corporation.  The driving rule should be that riskier instruments deserve higher yields.  Senior bonds trade with low yields, junior bonds at higher yields, and preferred stock at higher yields yet.  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.

Thus, and application of contingent claims theory to the firm, much as Merton did it, should serve as a replacement for MPT in order to estimate the cost of capital for a firm, and for the equity itself.  Now, there are quantitative debt raters like Egan-Jones and the quantitative side of Moody’s – the part that bought KMV).  If they are not doing this already, this is another use for the model, to be able to consult with corporations over the cost of capital for a firm, and for the equity itself.  This can replace the use of beta in calculations of the cost of equity, and lead to a more sane measure of the weighted average cost of capital.

Values could then be used by private equity for a more accurate measurement of the cost of capital, and estimates of where a portfolio company could do and IPO.  The answer varies with the assets financed, and the degree of leverage already employed.  Beyond that, CFOs could use the data to see whether Wall Street was giving them fair financing options, and take advantage of finance when it is favorable.

I’ve wanted to write this for a while.  Though this is an outline of how to replace MPT in estimating the cost of capital, it has broader ramifications, and could become a much larger business, much like the rating agencies started with a simple business, and branched out from there.

Maybe someone is doing this already.  If you are aware of that, let me know in the comments.


PS — Sorry that I have been gone for the last few days.  Church business took me away. I’m back now, and will be posting on Monday.


  • tom says:

    Or, you can calculate the IRR instead. While cost of equity is a good concept, we don’t know if it can be measured – do we know for sure that it can be calculated? Perhaps it can’t be done.

  • matt says:

    How does one calculate the cost of equity, ex post facto? It would be interesting to see a regression of the CAPM cost of equity on the real discount.

  • Doug says:

    “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.

  • ed says:

    It’s silly to say you’re “not a fan” of Modigliani-Miller theorems. Before we can figure out what makes capital structure important, it is crucial to remove our fuzzy incorrect ideas about it. MM shows that capital structure matters precisely because of things like taxes, costs of financial distress, etc., and not simply because of fuzzy ideas about “risk.”

    • ed — I may not have tipped all of my hand, but it is far from silly. Take Falkenstein’s recent book — high yield tends to underperform. Or consider that less levered companies tend to return better over the long haul (will need to dig up the reference, but it came from a standard textbook used by the Society of Actuaries for their syllabus).

      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.

  • Anonymous says:

    David: You’re absolutely right about the silliness of M-M and “optimum” capital structures. That the cost of equity capital goes up after some debt/equity threshold is surpassed is obvious but non-trivial. What that threshold might be is entirely context relative to the economic climate, competitive advantage of the firm, and secular trends of the industry at the time. Importantly, the relationship of higher debt levels that lead to higher cost of equity is likely non-linear.
    Another less appreciated aspect is that managements generally prefer to finance with debt because it’s cheaper and they don’t have to worry about shareholder votes particularly for M&A.
    As Martin Whitman noted, it’s rare for any company in the US to go for five years without some sort of transaction. Hence, most five year DCFs have to account for changing capital structures and what effect that would have on the cost of equity capital.
    But how many analysts actually model that?

  • Anon — few if any analysts model it. Analysts are not portfolio managers, and they are certainly not corporate managers.