The Hard Math of Discounted Income Streams or What Will Normal Interest Rates Do To Stocks?

This is just a reminder.
I know our readers know this in their fingertips but sometimes one gets caught up in the details and forgets the Junior High School stuff.

Friday, the U.S. 10-year yield closed at 2.8290 up 0.0740 after touching  2.8640 a print last seen on July 29, 2011.
On July 24, 2012 the 10-year set its intraday and closing all-time record lows, 1.394 and 1.40 percent, respectively. We've doubled off the bottom.
And as recently as June 6th the bond traded at 2.00%.
I blame Larry Summers.

From MarketWatch:

Fed tapering: The math investors need to know
Commentary: What ‘normal’ interest rates would do to stock valuation

In October, 2007, just before the crash, the stock market put on one last surge to new highs. Even though it was clear there were icebergs all around — and indeed several ships were already taking on water and listing heavily — the participants in the market decided to party One Last Time. 

My excellent friend Peter Bennett, a money manager in London who has called most of the big market moves over the past 15 years, sent a missive to his clients with a powerful one-word headline: “Farce.” 

Well, here we are again. I am not so bold as to predict what is going to happen over the next few months, but the situation on Wall Street brings that word to mind yet again.

In the past two months bonds have slumped, long-term interest rates have surged, and yet the Dow Jones Industrial Average and the Standard & Poor’s 500 have been hitting new highs.

Farce. 

I don't offer crystal-ball gazing, hocus-pocus or any other associated magic or marketing shtick. I can only offer some basic math, basic common sense (I hope) and the perspective of someone who’s first discipline was neither management nor science but history. 

In a nutshell: Federal Reserve “tapering” — the winding down of “quantitative easing,” and the normalization of interest rates — changes absolutely everything in the markets.

The bond markets already know this. The stock market doesn’t. Investors need to understand the math. Most of them don’t, and Wall Street isn’t going to tell them.

So let’s do the numbers, shall we? 

As recently as May, as a result of the policies of the Federal Reserve, the basic interest rate which underpins financial markets — the interest rate on the 10-year Treasury note — was as low as 1.6%. Today it’s already risen to 2.7%. Furthermore, history says the interest rate has typically fluctuated around 2% above inflation. Over time, that’s what people who’ve been willing to own ten-year Treasury bonds have expected as an average return on their money. As the bond market currently predicts inflation of about 2.5% over the next decade, we can estimate that when the Fed stops rigging interest rates and they go completely back to normal, the rate on the ten-year would probably be around 4.5%. 

Now let’s look at what that means for stocks.

When you buy shares in the stock market, you are purchasing the right to a stream of dividends stretching out into the far distant future (forever, at least in theory). You’re buying the right to all those lovely dividends from Exxon XOM -0.28%   and General Electric GE -0.21%   and Wal-Mart WMT -0.40%   and Coca-Cola KO -0.10%   and Procter & Gamble PG -0.72%   and so on. Although you won’t claim those dividends forever, because you aren't immortal, you can claim them for as long as you like. And when you no longer want any more you can sell the stock, with its claim on all the subsequent dividends, to someone else. And so on. 

Imagine a share of stock that will pay you $100 in dividends every year for the next, say, 100 years. How much is that worth in today’s money? How much would you pay for that stock? To know the value, you have to apply a relevant “discount rate” — in layman’s terms, and with some oversimplification, you have to know what interest rate you could get on the money if you didn’t buy the stock. 

In May, you knew you could earn 1.6% a year, at least for the next 10 years, if you left your money in ten-year Treasury notes. Applying a 1.6% discount rate to our stream of $100 dividends produces a value of $4,972. In other words, that’s how much that theoretical stock would be worth, in today’s money, if we use a discount rate of 1.6%. 

Hike that discount rate to 2.7% — the interest rate on the Treasury note today — and that value collapses by nearly a third, to $3,445. Hike the discount rate to 4.5% — a normal rate on the Treasury — and the value halves to $2,240....MORE

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