Financial Mathematics Text

Wednesday, February 20, 2013

Einhorn and AAPL's preferred shares

So there's a lot of fuss regarding David Einhorn's proposal that Apple (AAPL) issue preferred shares in order to "unlock value".  To be clear, I like Einhorn and even liked his book, Fooling Some of the People All of the Time (in spite of the fact that it was excruciatingly detailed oriented).

But I concur with Prof Damodaran that this doesn't really create value; it simply changes capital structure. Granted, as Damodaran points out this might unlock price (I suspect it would since the market sometimes overprices leveraged situations. The fact that many analyses of Einhorn's strategy assumes that PE ratios will stay the same in spite of the leverage is evidence of this fact. They make the mistake that one wouldn't make if one understood the ideas in this post.)

But it does enhance value in at least one sense. Cash distributed now is worth more than cash sitting in an account earning next to nothing in interest. 

But I'm more interested in this question: is 4% the correct price for the preferred shares?

In my post, Yield-Duration Curve, I noted that there appears to be a linear relationship between yield and duration. While I still have no theoretical reason for why this need to be the case, we can (assuming the relationship is valid) use this idea to extrapolate yields for a perpetuity.

Now one thing we should consider here. Preferred shares are lower on the pecking order than bonds are. So while they are less risky than common stock, they are still more risky than bonds. So I'm not sure that bond yields are the best comparison. But it's at least a place to start.

The duration of a perpetuity is the inverse of the yield. If Y is the yield and D is the duration then:

$$D = \frac{1}{Y}$$

Now the idea that there is a linear relationship between states:

$$Y = \alpha + \beta D$$

We can then substitute the duration of the perpetuity and solve for Y to obtain:

$$Y = \frac{\alpha + \sqrt{\alpha^2+4\beta}}{2}$$

We can use the coefficients I obtained in the Vanguard graph to estimate the appropriate yield for a perpetuity of similar quality:

$$Y = \frac{(0.96\%) + \sqrt{(0.96\%)^2+4(0.25\%)}}{2} = 5.5\%$$

So based on this model, 4% seems like too low of a number for AAPL preferred shares.

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