This article shows how you can value any security - if you know how much it will pay, when it will pay it and the return you want to make.
Time value of money
The principle is known as the 'time value of money' and we can flesh it out with an example. We'll assume that all money earns interest at 8% a year and costs the same to borrow. On that basis, if I have $100 now, what will it be worth in 10 years' time?
The answer is: 100 x 1.0810 = $215.89. Now, if someone offered you $215.89 in 10 years' time, how much would you pay them now for it? The answer goes like this. The money you pay now is either money that won't be earning interest for you at 8% a year for the next 10 years, or it's money that you've borrowed and on which you must pay interest at 8% for the next 10 years. Either way, paying out money now costs you 8% a year until you get it back. So, to buy a cash flow of $215.89 in 10 years' time, you'd pay up to $100 because, if you'd kept the $100 (or not borrowed it), you'd have turned it into $215.89 over 10 years (or saved yourself that amount).
So the $215.89 in 10 years' time has a value of $100. If you paid more than that then you'd make a loss; if you paid less, then you'd make a profit; and if you paid a lot less, then you'd make a really good profit. That's value investing.
Why 8%, though? Good question. It was nothing more than a stab in the dark really. People will argue until the cows come home about the right figure to use. Essentially, it should represent the 'opportunity cost of capital'. So you'd come up with a different figure depending on what you might otherwise plan on doing with the money. If you would otherwise have put it into a term deposit paying 5%, you'd use 5%. If you might otherwise have put it to work in an exciting business venture on which you expected to make 15% a year, then you might use that figure (although anticipating a return of more than 10% is pretty optimistic by most standards).
Of course most securities have more than one cash flow to consider, which means that to get the total value you have to work out the value of each individual cash flow and then tot them all up. How much would you pay for a bond that promised to pay $7.50 at the end of each of the next nine years, and then $107.50 at the end of the tenth, assuming you wanted to make 6% a year? Looking at things from the other direction, what would be your annual return if you paid $106.73 for the bond?
Principle always the same
Doing all the sums is beyond the scope of this article (but the answers are $111.04 and 6.56% in case you want to check your working and, if you're hungry for more, take a look at the Investor's College articles of issue 110/Aug 02 and issue 163/Oct 04). But the principle is always the same: all cash flows have a value according to when they are going to be received and the 'opportunity cost' (otherwise known as the 'discount rate') you ascribe to them. To get the value of a set of cash flows, you just tot up the values of the individual components.
When you get a cash flow that repeats every year, forever, something really handy happens: the sum of all the individual cash flows simplifies down to just one cash flow divided by the discount rate. So if you have a security paying 10 cents a year, forever, and you decide you want a return of 8% a year, then the security's value is 10 cents divided by 8%, which is 125 cents.
And the sums even have the decency to remain pretty simple if you assume growing cash flows - at least if you assume that they grow at the same rate each year. In this case, you just divide the first cash flow by the difference between the discount rate and the growth rate (the growth effectively offsets part of the discount rate). So if you have a security paying 10 cents this year, growing forever at 4% per year, and you decide that you want a return of 8% per year, then the security is worth 10 cents divided by 4% (that is, the difference between 8% and 4%), which is 250 cents.
Paradox
So if you're aiming to make 8% a year, then an annual payment of 10 cents growing at 4% a year is worth exactly double the value of a flat 10 cents a year. A payment growing forever at 6% would be worth four times (250 cents) as much and, somewhat paradoxically, a payment growing at 8% or more would be worth an infinite amount.
This curious result is arrived at because you've assumed an opportunity cost below the growth you expect from your investment, even though that investment is itself an opportunity.
Paradoxes aside, this is hopefully beginning to sound rather like companies paying dividends - precisely because it is rather like companies paying dividends. But companies introduce problems because the cash they pay out is neither predictable nor grows steadily. And some companies don't pay out dividends at all.
