S&P 2162: Understanding The 'Fed Model'

by: Philip Mause

As the market drifts higher and higher and more and more bears scratch their heads in disbelief, I begin to wonder when they will admit that interest rates may have some relevance to equity valuations. I am not dogmatic in this regard and I do not think that there is a "magic formula" for calculating stock indices based on interest rates. However, it is useful to examine the analysis that has been done on this issue because it will provide some useful information as to why we are where we are and where we are likely to be going. One very plausible theory of the connection between interest rates and stock valuations suggests that the S&P 500 could easily move up to 2162.

In the 1990's, a leading securities guru - I believe it was Ed Yardeni - coined the phrase "Fed Model" and calculated the earnings yield on the S&P 500 in comparison with the interest rate on the 10 year Treasury. The earnings yield is the inverse of the price earnings ratio (NYSE:PE); a 10 year Treasury interest rate of 8 would suggest an earnings yield of 8 and a PE of 12 1/2. The Model was presumably based on an "investor migration" theory under which investors would buy stocks and sell Treasuries until the earnings yield on stocks equaled the interest rate on 10 year Treasuries. Rates were coming down in the 1990's and stock prices were going up and people were looking for an explanation of what was going on in the stock market. I think that this model served as a kind of rationalization for what was happening without a sufficient explanation of the mechanism which would drive stock prices to the levels specified by the model. Of course, if you applied this approach to the current situation, it would suggest a PE of roughly 50 and an S&P 500 target of over 4300; most people reject this as implausible and this sometimes leads to a total rejection of the approach.

A much more interesting and well reasoned approach was set forth by Jan Timmer in his working paper - "Understanding the Fed Model, Capital Structure and Then Some". Timmer reasoned that the really relevant interest rates were the interest rates that the corporations themselves faced - not the interest rates paid by the federal government. His model is called "capital structure substitution" and it assumes that corporate executives will borrow money and repurchase stock as long as the effort increases earnings per share. Based on this premise (which I will analyze a bit below), he reasoned that earnings yields on stocks should be equal to the after tax cost of borrowing because a corporation will borrow and repurchase stock as long as earnings yields are higher than that cost.

Under Timmer's model, if the pre-tax borrowing cost is 6% and the tax rate is 33% so that the after-tax borrowing cost is 4%, then the earnings yield will be 4% and the PE will be 25. 6% is a relatively high borrowing cost for most large corporations and so it could be described as producing a "conservative" PE. At any rate, applied to S&P 500 earnings of $86.50, the model suggests that the index should trade at 2162.

Timmer's approach is more convincing than the Fed Model because it suggests how and why deviations from the result will be corrected. If money can be borrowed at an after-tax cost of 4%, corporate executives, anxious to report consistently higher earnings per share, will borrow and repurchase unless and until the PE gets to 25. One of my earlier articles took the analysis a step further by suggesting that acquisitions will be accretive to earnings as long as the target is acquired at an earnings yield below the after tax cost of the funds borrowed to finance the acquisition. This will also tend to drive earnings yields down by removing targets from the market and driving up the share prices of companies deemed to be future targets. Both cash for stock acquisitions and share repurchases also have the effect of reducing the quantity of stock in circulation, which would also have a tendency to drive share prices up.

Of course, some companies do not have to borrow a cent to perform share repurchases or to complete a cash for stock acquisition. They have hoards of balance sheet cash available. For these companies, the comparison should be with the after tax interest yield on the balance sheet cash. Unfortunately, this produces such a low number that it would suggest ridiculously high PEs. Many companies earn less than 1% pre-tax on balance sheet cash and after-tax returns can be in the 1/2% range, suggesting that share repurchases would increase earnings per share as long as the shares are repurchased at a PE below 200.

Timmer's approach also fails to specify the duration of the loan and would require the calculation of a PE specific to each individual company based on its borrowing costs. This is why I have been using 6% as a "conservative" metric because it represents a fairly high rate of interest for borrowing by an S&P 500 corporation- indeed, we are getting to the point where 6% is beginning to look like "high yield."

There are some important caveats to bear in mind. First of all, some companies are so leveraged that additional borrowing is out of the question and the model is simply inapplicable. Secondly, banks and other financial institutions have regulatory and other concerns which affect the decision to borrow and repurchase equity. Even if such action would increase earnings per share, it may be barred by regulation or rejected as too risky by executives mindful of the Panic of 2008. Thirdly, many companies face enormous capital expenditures which make share repurchases imprudent - in this regard, cash flow may be a better metric than earnings for applying the rule. Finally, there may be indirect costs associated with more borrowing. A company which borrows heavily enough to adversely affect its credit rating is incurring costs in addition to the interest rate on the marginal borrowing; it is likely to be incurring higher interest rates on future borrowing as well. When these indirect costs of additional borrowing are included, the after tax total cost may be considerably more than 4%. A couple of other points. Corporate managements - or at least some of them - may not maximize earnings per share but may maximize size instead. This would lead them to avoid share repurchases and use cash for acquisitions instead. Finally, if a company borrows extensively and becomes highly leveraged, this balance sheet change itself may affect the price earnings ratio the market is willing to give the company.

Nevertheless, for many, many companies the "Timmer Rule" may be useful. Companies with net balance sheet cash or with low borrowings and stable sources of income can likely expend cash or borrow large sums without any of the "indirect" effects described above. Indeed, corporate balance sheets are probably as strong as they have ever been. Many corporations have net balance sheet cash and many are able to borrow on very attractive terms. The market seems to be close to reaching a conclusion that a company like Microsoft (NASDAQ:MSFT) may actually be a better credit risk than the United State Treasury; after all, Congress can refuse to increase the debt ceiling and precipitate a default. If MSFT chooses to default, a lender can run into bankruptcy court and get his money out of their balance sheet cash. there is really no similar remedy for a United States Treasury default.

Where does this leave us? For many, many companies, the potential to increase per share earnings by buying back shares is enormous. There are also attractive opportunities for cash for stock acquisitions that will be immediately accretive to earnings. The path to higher multiples and a higher market will be through the door of financial engineering - share repurchases and acquisitions. It will affect different companies in different ways. But as long as earnings yields are substantially below after tax borrowing costs, the incentives for these measures will be very strong.

Timmer's model doesn't necessarily tell us where the S&P 500 will trade, but it does tell us what is likely to happen if it trades considerably below 2162. As long as earnings yields are below after- tax borrowing costs, we will be likely to see significant share repurchase activity and also acquisitions at earnings yields below after-tax borrowing costs. These trends will tend to give the market a powerful tailwind. They may be derided as "financial engineering" or Wall Street manipulation but, in reality, they simply reflect the efficient allocation of capital.

Companies with strong balance sheets are especially attractive because they have lower borrowing costs or can use balance sheet cash to fund repurchases. In this regard, Microsoft , Cisco (NASDAQ:CSCO), Apple (NASDAQ:AAPL), Johnson & Johnson (NYSE:JNJ) and Western Digital (NYSE:WDC) are particularly attractive. Dell Computer (NASDAQ:DELL) also has a very strong balance sheet, which may explain some of the motivation behind recent efforts to take it private. As noted above, there is no "magic formula", but investors who ignore the impact of interest rates on equity markets are missing what should be a very important factor in investment strategy.

Disclosure: I am long MSFT, AAPL, CSCO, JNJ, WDC, DELL. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.