I can’t remember where I ran into it, but I found this article on a blog that I had not run into before on Calculating [the] Cost of Equity for Value Investors. ?I think it gets close to the right answer, and I would like to sharpen it here.

My answer to a lot of economic questions is: what’s the alternative? ?Many people look at the shiny formulas in investing but don’t ask what they really mean. ?(More people just don’t look at the formulas… which has its pluses and minuses. ?The math reveals, but it also conceals hidden assumptions.)

After wisely dismissing how to calculate the cost of equity from Modern Portfolio Theory [beta] and the Gordon model, he considers cost of equity based off of return on equity, and begins to get tied up in problems. ?Let me try.

The cost of equity is important for a number?of reasons:

• It helps answer the question, “When should a company issue?or buy back?stock?”
• It provides a measure for the alternative use of equity capital on competing unlevered projects/investments of equivalent riskiness.

Note the each of the reasons is structured as a series of comparisons. ?I’ll use a discounted cash flow [DCF] analysis as an example. ?Imagine a simple project requiring an investment of equity capital. ?There is a certain cost, and the risk is enough that you can’t borrow money for financing — it must be funded by equity. ?There are expected after-tax cash flows from the project that you think are a best estimate of returns. ?When would you invest in the project?

I would compare investments versus other similar investments, and look at as many similar projects from a riskiness perspective, and see which investment yielded the best return. ?The second place project as returns go is the alternative project for investment by which the winning project is judged, and surprise, the winning project?has a positive net present value evaluated at the rate of the alternative project.

(An aside: it just hit me that I am recreating part of the learning process that I went through back when I was a TA at UC-Davis 31 years ago, helping teach Corporate Financial Management [CFM], while taking quadratic programming [QP] course at the same time — I ended up doing my QP paper on using QP to choose investments to maximize returns without explicitly calculating internal rates of return, thus quietly solving a problem that the undergrad CFM textbook said could not be done. ?FWIW, which isn’t much.)

Now, I’m waving my hands at what I mean by risk, but to me it is the best estimate of the probability distribution of outcomes, thus giving you estimates of what the likelihood and severity of adverse outcomes could be. ?The thing is, in real life we know these figures poorly at best, but the framework is still useful because the investor making the decision needs to choose the project of a class of projects with roughly the same risk profile. ?Though my initial example included only equity-financed projects, this could be expanded to consider all projects, where the amount of debt on projects affects their risk, and the tax-affected?debt cash flows are?a deduction from returns.

The process would remain the same:?look at as many similar projects from a riskiness perspective, and see which investment yielded the best return on the equity. ?The second place project as returns on the equity go is the alternative project for investment by which the winning project is judged.

Back to Stocks

Where does that leave us as stock investors? ?I subscribe to the “pecking order” theory of the cost of capital, which says that firms use the cheapest form(s) of capital to fund their incremental financing needs, which means they should rarely issue equity.?The exception would be if?they are undertaking a project so large that it would make the company significantly more risky if they were to issue only debt for financing.

We do see companies engaging in buyback activity when they can’t find better uses for slack capital. ?In many cases, there are few large projects begging for the attention of management. ?Buying back stock earns the earnings yield for?the firm. ?Managements buying back stock make the statement that there are no more incremental projects of equivalent risk that would have an unlevered return on equity greater than the earnings yield for the firm.

Now maybe shareholders may have a bigger set of investment choices than the firm does, so perhaps dividends could be a better choice for shareholders, but it will have to be a lot better, because?dividends are taxable.

In general, we want to see management teams be careful users of equity capital, taking note of its cost for the benefit of shareholders. ?Every good management team should have their schedule of possible projects for investment, but always recognize there is the alternative of buying back stock as a last resort. ?In that limited sense, the earnings yield is the cost of equity for the firm, unless big profitable projects beckon.

There’s more to say here, but maybe this is a good start. ?Thoughts?