#### Discounting

The topic of discounting frequently causes all sorts of trouble for university finance students, but I'll try to explain it here as simply as possible, leading on to more involved models and mathematical formulae in the next couple of articles.

First of all, to explain the effect of interest rates on valuations...

By the "rule of 72", which you'll find mentioned in an article in the "time value of money" section of the FAQ, you can see that at an interest rate of 7.2%, you can double your money every 10 years.

This means that one dollar received today is worth two dollars in ten years, or alternatively that an IOU promising one dollar in ten years would only be worth 50c today. At 7.2%, one dollar in ten years is worth 50 cents.

What if interest rates were higher? What if interest rates were 10%? Well \$1.00 today will be worth \$2.59 in ten years at that rate, which is the same thing as saying \$1.00 in ten years time is worth 39 cents today.

Likewise, if interest rates were lower, at 4%, in ten years a dollar grows to \$1.48, or 68 cents grows to a dollar.

Where is all this going? Well that amount you receive in the future could be the earnings of a company. A stock is worth to you only what it will pay you in terms of dividends and capital gains, and all things being equal a company that doesn't pay out a dividend should compensate for that by holding onto that money and hence increasing the share price. In a simplistic analysis they amount to the same thing, though there is a bit more mentioned on dividend policy in other parts of the shares FAQ.

If interest rates are 7.2%, you "discount" the money you will receive in the future back at the same rate. The company's earnings in ten years get discounted by half, and you do the same thing with the earnings for other years as well.

The intrinsic value of a stock by the discounting method is next year's earnings, discounted by 7.2% over one year, plus the next year's earnings discounted by 1.072^2 plus the third year discounted by a factor of 1.072^3, the fourth year at 1.072^4 etc etc, right off into the future.

This is a simplistic model, of course you don't know that interest rates are going to be fixed at 7.2% indefinitely, (you know it won't), but market expectations of what interest rates are going to do over the next few decades shape the actual discount rates built into stock prices.

So see how interest rate changes will affect stock markets by looking at the discount rate. As interest rates rise you discount future values heavily, stock prices fall. As interest rates fall the discounting factor decreases, stocks go up. If you've ever wondered why the stock market rises when they anticipate interest rate cuts and falls when they raise them, now you know why.

The next few articles will talk about this in greater detail and give proper formulae, but it will suffice for anyone who doesn't want to go on that the effect of interest rates on stock prices is a "time value of money problem", as well as any other changes in the costs of doing business related to company debt.