How do interest rates relate to stock prices?

Question

I couldn't understand this passage from Alan Blinder's 2013 book After the Music Stopped: The Financial Crisis, the Response, and the Work Ahead, page 28.

I don't understand this bit about the time value of money, and how time value of money applies to the value of a stock.

Because the sentimental value is nil, the fundamental determinants of stock values are dividends, their expected growth rates, and interest rates. Period.
      Why interest rates? Because dividends and capital gains received in the future are worth less today when interest rates are higher and more when interest rates are lower. The reason is the time value of money: 1 dollar received later is worth less than 1 dollar received sooner because, if you can get your hands on money sooner, you can put it to work earning interest. When interest rates fall, this difference shrinks. The time value of money becomes less and less important. The reverse happens when interest rates rise.

Answer 1

This is because the same amount of money does not have the same value across time. \$100 today is not worth the same as \$100 tomorrow, which is not worth the same as \$100 in 2025.

There are several reasons for why money have different value across time. These reasons include inflation, people's impatience, peoples opportunity cost (of postponed consumption), and so on. Most of these factors are already expressed in interest rate you can earn on your saving which is compensation you get for postponing your consumption (see discussion in Mankiw Principles of Economics Ch 27 or this recent Economics.SE answer).

Next, stock fundamentally (now taking the ownership rights and other matters aside) represents a streams of cashflow.

If you purchase stock today and hold it for one year and then collect your dividend $D_1$ and then sell the stock for its price next year $P_1$ what you are purchasing is essentially a stream of cashflow $D_1+P_1$. For example, if the stock sells next year for \$200 and pays dividend of $\\\$10$, you are purchasing little more than a \$210 cash stream you receive next year (again now I am putting issues like ownership/voting rights which the stock entitles you to aside).

As a consequence, if you want to know what the value of the stock will be today (i.e. its price today $P_0$), you need to essentially discount the present value of the cashflow you are receiving for correcting the fact that money today has different value as money tomorrow (the same way as if scientists would decide to create new meter that is 2x our current meter all heights would have to be recalculated).

The time value of money formula is given by:

$$PV=\frac{FV}{1+r}$$

where $PV$ is present value, $FV$ future value and $r$ interest or more broadly some discount rate.

So continuing the example above if we want to know what a stocks current price is we would take the future stream of cashflow we will get from the stock and discount it:

$$P_0 = \frac{P_1+D_1}{1+r}$$

So with the $P_1=200$ and $D_1=10$ and assuming $r=0.06$ (or 6%), the stock that I can later sell for \$200 (after getting \$10 dividend) should sell for:

$$P_0 = \frac{200+10}{1+0.06} \approx 198.11$$

Now you should note the above is oversimplification as stocks are not just streams of cash, and of course in real life you cannot know what $P_1$ and $D_1$ will be next year with certainty, but the point is that value of stocks today necessarily depends on their discounted future value and value of dividends they earn you. More complex models try to take into account more factors but they still take this time value of money into account.

Answer 2

1muflon1's answer is correct, but here's a shorter simpler answer.

Your quotation is referring to the Federal Reserve's and other central banks' expansionary monetary policy. Central bankers can raise interest rates to counter inflation. How? Central banks must contract the money supply, or at least stop it from expanding further. Raising interest rates is contractionary, shall raise interest costs, and deter investment spending. Raising interest rates affects the stock market three inter-related ways.

1. Companies can borrow less to expand. Then their growth prospects lower.

2. As margin loan interest rises, some speculators can no longer afford margin, and borrow less to speculate.

3. Bonds become a relatively more attractive investment than stocks.