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.

Risk premiums

Ok, so by the above argument you would say that you ought to be happy enough taking $2.00 in the future instead of $1.00 today since it is all the same thing. Well, partly, but how many people really would take that deal? Wouldn't you rather have the dollar now and invest it yourself instead of enter into some sort of agreement where you have to wait ten years for your money? What if the party you were dealing with went broke? What if interest rates rose after you signed the deal and you could have missed out on extra profits? What if the other party ran off to Majorca and was never heard from again?

So in all probability you wouldn't take a future $2.00 payment for $1.00, but if you discounted even further it might be worth taking a bite. Would you pay 90c for $2.00 in the future? What about 50c? 10c? This question is impossible to answer without being able to assess the risk that you are taking. If the party you are entering into an agreement with is a trusted friend with ample money to cover the debt, and you were comfortable with the promise of a 7.2% return you might take something nearer one dollar. If the other party had bad credit and you think they may take a runner, you will take far less, in fact you might demand an exorbitant interest rate in order to justify taking the risk.

What sort of interest rate? Whatever you are comfortable with and whatever the other guy is willing to pay, it is an auction after all. If you would only lend this person 25c and expect $2.00 back in 10 years, this would be an interest rate of 23.1%. (The tenth root of 8 is 1.23114, which equates to a 23.1% per annum gain). In this case you would expect a 16% premium to the "risk free" rate of putting money with a blue chip bank, or alternatively a 75% discount to par value. This next step of wanting a higher return to justify a higher risk is called a risk premium, and this discount is how the market values something on the basis of risk, so speculative issues and junk bonds get sold down until they trade at such attractive yields that there will be enough takers to make a market for that issue.

Discounting by a risk premium is also a way to reduce risk with issues of better credit. The whole principle of value investing is about paying much less than par for an asset, so when you see the stock of a blue chip company with an impeccable record and flawless operating history, and little reason to believe that the future is any less rosy trading at a substantial discount to fair value, you know that a margin of safety has already been put into the share price. Even less esteemed stocks can become great buys if the risk premium is so great that you can feel comfortable that the company can rise up to meet and surpass the apparently low expectations the market has of it.