A short note I prepared for the former students of my Corporate Valuation class. Maybe people reading this thread might find this interesting as well (some subscripts/superscripts may not copy well from the original document).
Are you smarter than PIMCO Managing Director Bill Gross?
I don’t know whether you caught today’s exciting CNBC article where Bill Gross, the Managing Director of the bond giant PIMCO claims that “stocks are dead.”
Here is the gist of his fascinating argument:
For his part, Gross argues that the return of stocks above the rate of economic growth as measured by gross domestic product cannot be sustained.
"The 6.6 percent real return belied a commonsensical flaw much like that of a chain letter or yes — a Ponzi scheme," he says. "If wealth or real GDP was only being created at an annual rate of 3.5 percent over the same period of time, then somehow stockholders must be skimming 3 percent off the top each and every year.
"If an economy’s GDP could only provide 3.5 percent more goods and services per year, then how could one segment (stockholders) so consistently profit at the expense of the others (lenders, laborers and government)?"
Now, here is my “homework” for you. Without scrolling down, uncover the giant logical fallacy in Mr. Gross’ argument (after my Advanced course you are absolutely equipped to spot it). That is, I want you to be able to show that even in the economy where the GDP grows by 3.5%, the rates of appreciation on ANY investment (including equity) in excess of that number are completely rational, and not associated with “profiting at the expense of the others.”
AFTER you form your argument, scroll down…
The gist of the fallacy is this: In terms of valuation formulas, Mr. Gross in his argument inexplicably insinuates that rates of returns on investment have to be tied to the numerators (cash flows), while in reality they have everything to do with the denominators (that is, the discount rates investors use to discount the cash flows, to get the compensation for inflation, lost opportunities (reflected by the “real rate”), and the riskiness of investment).
If you click on the actual article:http://www.cnbc.com/id/48417337
(just in case, the same video should be here: http://www.cnbc.com/id/48423635
you’ll get the video of the interview with Prof. Siegel (whom Mr. Gross criticized). Prof. Siegel took Mr. Gross “to school” by pointing precisely the above argument. However, since he talked in pretty abstract terms, here is a simple math example to hammer the point down:
Consider an all-equity firm (so that there are no “poor bondholders” to be taken advantage of) that will pay you FCF=$100 next year. And, because we are in an “anemic economy”, the cash flows will grow by just 1% per year forever. However, shareholders feel their willingness to invest will be rightfully compensated only if they earn 11% per year (because of inflation, lost opportunities, and the riskiness of investment)
In that case, the Equity in the Company (E, incidentally equal to V, as D=0), will be equal to the PV of the growing perpetuity:
E0 = FCF1 / (r-g) = 100 / (0.11 – 0.01) = $1,000 today.
next year, the equity will be worth
E1 = FCF2 / (r-g )= 100*(1.01) / (0.11-0.01) = $1,010
two year from now, the equity will be worth
E2 = FCF3 / (r-g) = 100* (1.01)2 / (0.11-0.01) = $1,020.10
and so on.
Now, remember that the return on investment always equals
Rt = (Dt + Pt) / Pt-1 -1
In the context of our valuation, the “dividend” will be the FCF generated in the particular year, and the “price” will be the value of equity. So, for Year 1:
R1 = (FCF1 + E1)/E0 -1 = (100+1010)/100 -1 = 11%
For year 2:
R2 = (FCF2 + E2) /E1 -1 = (101 + 1020.1)/1010 -1 = 11%
and so on. That is, shareholders will earn 11% return EVERY year, even if the company’s cash flows grow by just 1% per year.
So, what should you take away from this?
1) It is NOT that the growth in economy does not matter. It very much does, as it influences the “starting” value of investments. In our example, if the FCF growth was, say, 6%, then the initial value of the Equity would be E = 100/(0.11-0.06) = $2,000 , not our original $1,000. Remember that the PERPETUAL growth rate we always used in most of our valuations perfectly reflects the growth in the US economy (that’s why we used the 6% = 3% for the “typical” inflation + 3% for the real growth of the economy).
2) At the same time, the growth in cash flows has very little to do with the RETURNS investors achieve on their investments. The returns are determined by the discount rates investors apply to computing PVs of FCFs. If investors use 11%, their investment return (in expected terms) will be 11%.
3) The negative returns on equity are not the evidence that the “stocks are dead.” Instead, they reflect the fact that both cash flows and the discount rates are revaluated on a daily basis. If the market expects cash flows to decline and/or discount rates to increase, stock prices must go down. BUT, at the end of every trading day, the prices of stocks reflect the base values from which the stock investments are expected to appreciate precisely by the required return. [I don’t want to make this example too long, but imagine that tomorrow we lean really bad news about the economy, causing you to revaluate FCF1 to $50, and growth to 0.5% in perpetuity. The stock will immediately drop to 50 / (0.11-0.005) = $476.19. A really bad news for those who held the stock between today and tomorrow. However, if nothing changes after that, the investment of equityholders will once again grow by 11% per year from the “new base” of $476.19. Try it…
4) You should expect that “bond people” will talk trash about stocks, but, apparently, sometimes their arguments are allowed to make no sense.
5) And, most importantly, if you got the gist of the argument, you are now smarter than the guy whose net worth is.. http://www.forbes.com/lists/2010/10/bil ... _3ESQ.html
Enjoy your summer!