On Sat, 29 Nov 2003 03:23:40 -0500, Michael Pollak wrote: >Had there been such a miracle, then some > though not all of the > > higher valuations would be justified; if the S&P 500 > Index is selling on > > 20 times earnings, and productivity growth undergoes > a secular and > > permanent increase of 1 percent per annum, without a > change in real > > interest rates, then the S&P 500 should start selling > on 25 times > > earnings (an earnings yield of 4 percent rather than > 5 percent.) > > Could somebody briefly explicate the math in that last > sentence? >
A somewhat garbled but not absolutely egregious use of the good old "Gordon Growth Model". Basically, if you're given the responsibility of valuing a series of cashflows which stretches off into perpetuity and grows over time (like a stylised version of common stock earnings), then the GG model is a reasonable way of going about it. Where D is today's earnings, R is the discount rate and G is the rate at which the cashflows grow, then the value of a growing series of dividends is given by V= D/(R-G). The derivation of the formula shouldn't be hard to find in a finance textbook or via Google, but I always contrive to screw it up in some way or other, so I'm not going to try here. Hence, if we say that, for a decent average of US companies, R might be 10% and G might be 5%, then V/D (the price/earnings ratio) would be 1/(10% - 5%) = 1/0.05 = 20. Bung an extra 1% onto the growth rate for "productivity miracles", and you get 1/0.04 = 25. All the above is of course dependent on the discount rate being a valid concept, average productivity growth being a valid concept across sectors, plus the growth rates being in the "right" sort of order of magnitude (as you can see, this model will blow up as R-G approaches zero). etc etc. But I'm pretty sure that's what they mean. dd > Michael
