Here’s a conundrum: the S&P; 500 is trading roughly at its June 2007 level, before the first cracks in the dam were visible. Earnings per share are also the same ($94.12 in the fourth quarter of 2012, compared to $96.24 in the second quarter of 2007). Has the world simply reset the clock and forgotten the financial crash and the Great Recession? Spoiler alert: the big difference is the price of leverage, and the private equity takeover of Heinz last week is a case in point.

Exhibit 1: Back to 2006 – or are we?

That seems most unlikely. The world has changed, and for the worse. Expectations are much gloomier than they were in 2007. US economic growth is crawling along in the 1%-2% range, and was negative during the fourth quarter of 2012.

Exhibit 2: Real GDP growth, year on year

After a sharp post-crash recovery, S&P; operating profits have been stuck in a range for the past three quarters, and fell slightly from the third to fourth quarters of 2012. It’s hard to imagine that investors expect a surge in profits in the present economic environment.

Exhibit 3: S&P; 500 Operating profits per share)) Source: S&P;

Even worse, there is nothing in particular to get investors excited – no next new thing, no entrepreneurial hat trick no market leader. A year ago, social media and gadgets were supposed to be the future of the American economy, and Facebook and Apple were the poster children. But an investor who bought Facebook and Apple in May 2012 would have lost nearly 20% as of last Friday, while an investor in an S&P; index fund would have gained 20% (including dividends).

Exhibit 4: Apple and Facebook versus the S&P; 500

Source: Yahoo Finance

Something else has changed beside growth expectations, and that is the price of long-term leverage. That’s sometimes called the discount rate on equities. The standard finance models state that we discount expected future earnings by the time value of money, whatever that might be. We could think of that as the yield on fixed-interest investments which compete with equities, or – more realistically – as the borrowing cost to buy corporate cash flows.

That has come down to the lowest level in history, thanks to the Federal Reserve. It costs junk-rated single-B borrowers only 6% on average to issue new 10-year debt. It’s hard to compare the yield on single-B securities with prospective earning s on stocks. Single-B borrowers are likely to default. The time value of money argument becomes confusing because the future default rate is unknown.

But if you are a private equity fund buying a traded company, as Brazil’s 3G Capital and Warren Buffett bought Heinz last week, the likelihood of default has a totally different meaning: that’s the likelihood that you will default to people who lent money to you. As much as it hurts to default, it hurts a lot more to be on the receiving end of a default. As one industry giant told me years ago: “High yield bonds are there to be sold, not bought.”

Exhibit 5: Junk bonds at lowest yields on record

Why are junk bond yields at all-time lows? There are two big reasons. The first is that the economy has been more cartelized, less entrepreneurial and less risky. The bad news is always someone’s good news. During the 1990s, disruptive new technologies turned a lot of stable franchises to junk – literally, in the case of some telephone company bonds. The Facebook misfire and Apple’s fall from grace point up the sclerotic character of the economy. No-one need worry about entrepreneurial challengers. They have nothing to do with the price of ketchup.

And the second is that the Federal Reserve has vacuumed up a vast amount of risk into its own portfolio (by purchasing longer-term Treasuries and mortgage-backed securities), leaving the market chronically short of yield.

Private equity firms can borrow at the lowest yields on record and lever up the earnings of stable corporations like Heinz, extracting the difference between the cost of financing and the levered earnings yield. That makes the equity of predictable companies like Heinz valuable.

Exhibit 6: Federal Reserve purchases of long-term treasuries and mortgage-backed securities reduce price of risk in bond market

We can show the sensitivities of the equity market to expected growth and the cost of financing, respectively, through a simple numerical example using a variant of the old-fashioned dividend discount model. The dividend discount model in its various guises states simply that the price of a stock is equal to expected cash flow adjusted for the cost of financing.

In the following example, P (the price of a stock) is equal to earnings (E) divided by the discount rate (K) multiplied by expected growth (G) divided by the discount rate (K), plus dividends (D) divided by the discount rate (K).

We use the average yield for long-term debt of S&P; 500 companies, the long-term Baa bond yield, as the discount rate (K). That is a known variable. Earnings are also a known variable (operating earnings per share as reported by S&P;). The price P is simply the price of the S&P; 500. There is one unknown in the equation, namely the expected growth rate (G). Because we know the other variables in the equation, we can back out the value of G.

Exhibit 7: S&P; 500 – What’s the right discount rate on earnings?

A fairly simple dividend discount model (sum of perpetuities method) lends itself to intuitive sensitivity analyst on equity prices. The S&P; 500 is close to where it was in June 2007, and operating earnings per share are roughly the same (annualized at $96.24 for the 2nd quarter of 2006, and at $94.12 for the fourth quarter of 2012).

Dividends are considerably higher, at $35.74 per share (annualized) in December 2012 versus $26.77 in June 2007. For the market portfolio, the best approximation of a risk-adjusted discount rate is the long-term borrowing rate for the average company, roughly equal to the Moody’s long-term Baa bond yield. That stood at 6.34% in the middle of 2007 and has fallen to $4.73 at present.

Using the sum of perpetuities method, we plug in the above values, and back out the expected growth rate of earnings that gives us the observed value for the S&P; 500 in mid-2007 and today. As shown in Exhibit 2, the backed-out expected growth rate was 4.514% in June 2007 but has fallen to 1.594% today.

In summary, the expected growth rate backed out from the model is quite modest, far below the consensus of analysts’ expectations, but consistent with the stagnation of earnings during the past six quarters.

There are two takeaways from this simple exercise.

The good news is that the stock market is not particularly sensitive to earnings disappointments. The expected growth rate embedded in equity prices is extremely low as it is. That helps explain why the market rallied through a very mediocre earnings season.

The bad news is that the stock market may be extremely sensitive to an increase in the risk-adjusted discount rate. A 50-basis-point rise in the discount rate would cost about 200 points on the S&P; 500, according to the simple model. The so-called “great rotation” out of fixed income into equities, according to this line of reasoning, is a myth: the price of equities depends on the cost of leverage.

The “great rotation” is a contradiction in terms, because stocks are the new bonds. It’s not quite true that stocks are the new bonds. Only some stocks are the new bonds. The implied volatility of General Motors stands at 25%, for example, while the implied volatility of Heinz falls around 9%, which means barely moving. It makes eminent sense to cut high yield debt (in this case preferred stock) out of stable cash flows. The attractiveness of Heinz was not valuation (Buffett and the Brazilians bought at a forward P/E of 18, at double the Jan. 2006 price for the stock. It was stability.

So much for opportunities in the BRICs. If the best a Brazilian billionaire can do is buy into an American ketchup company, it’s hard to get excited about the growth prospects of Brazil. In fact, it’s hard to get excited about Heinz at a pre-acquisition P/E of 18. What is the upside of a stodgy food processor whose equity price had already run from $35 to $60 between January 2002 and the present? The acquirers are not looking for a capital gain, but for the capacity to apply cheap leverage to bond-like cash flows. The advantage of private equity is access to cheap non-resource leverage.

America has devolved from a creative-destruction, entrepreneurial model to a cartelized, sclerotic model where equity cash flow (or at least a large portion of equity cash flows) are boring and predictable. They are sufficiently predictable that Warren Buffett and his Brazilian partners can apply cheap leverage (courtesy of the Federal Reserve’s balance sheet expansion) to generate high earnings. That’s good news for Warren Buffett (who financed part of the Heinz deal by purchasing preferred stock with a 9% coupon), but bad news for the American economy.