Question about value of the firm from the presentation

[wrongsaidfred]

Hi David,

At one point you state that the perfect markets view says value of the firm depends on the systematic risk, but then (in the Stulz worksheet) you show that even if Beta changes the PV of the firm stays the same because of discounting.

Maybe I am just getting some of the terminology screwed up but it seems like these two statements contradict each other.

Is there something that I am interpreting incorrectly?

Thanks,
Mike

 

[David Harper CFA FRM]

Hi Mike,

That's a good point. I hope you'll forgive that these statements are based on Stulz' Chapters 2 & 3 which have been in the FRM for several years and, to my knowledge, have been variously interpreted. (I have my own views but clearly these two chapters do not summarize with total consensus). One of the issues is that Stulz is using a really simplified model (CAPM) yet somehow complicates it in a way that few authors seem to achieve (!); another is that arguably he employs circular logic. In any case, my view on this is:

The perfect markets view says diversification is easily achieved and therefore idiosyncratic risk (non systemic risk) should not be beared; since elimination of it is free, reduction of it is worthless. As the CAPM simplifies risk into only two pieces, systemic and idiosyncratic, the relevant risk is only the systemic risk. Finally: if current value is a function of expected return, and expected return (under CAPM) is only a function of systemic risk, current firm value is only a function of beta (systemic risk) and nothing else. In this view, all other things being equal (i.e., firm's cash flows), higher beta lowers current firm value and lower beta increases current firm value. For example, you will pay less (lower firm value) for a firm with a high beta because you deserve/expect the higher expected returns implied by a lower price.

The second, apparently contradicted idea, is that modification of the beta has no impact on firm value. What?? All he means is something very specific: for a given firm beta, reduction of the beta by hedging (as in the spreadsheet) as a sort of "next step" cannot really change things. It only transfers the portion of the systematic risk either to shareholders (internally) or investors (externally). So, for example, if a beta of 1.5 implies a firm value of $X, the firm can reduce the "net beta" to 1.2 but, here is the key, Stulz is saying that in this case, ALL OTHER THINGS ARE NOT EQUAL. Unlike reducing idiosyncratic risk, the firm must incur a cost roughly equal to the benefit. If they keep it internally, the cost to reduce is a reduction in the cash flow (numerator) offset by the benefit of a lower discount rate (denominator). So, the spreadsheet is meant to illustrates Stulz' idea that, in this case to paraphrase, the firm's "natural" 1.5 beta cannot be hedged to alter the firm's value. Precisely because it is systemic risk; systemic risk here is like energy or matter: it can only be transferred but it must be conserved.

I hope that helps, although i am sure it's not the best reconciliation! Maybe keep in mind Stulz is, in a way, just piling on a bunch of interpretation to the CAPM, itself much simpler than his interpretation, namely: current firm value = expected cash flows discounted by a CAPM-determined rate, and the CAPM discount rate is only a function of beta.

Thanks, David