How Much Is That in Present Dollars?

Investors hear lots of talk about compounding, the process used to find the future value of a cash flow, but much less about discounting, the process used to find the present value of a cash flow. Discounting and compounding are two sides of the time-value-of-money coin.

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By Richard McCaffery (TMF Gibson)
December 7, 2000

You don't see much talk about time value of money concepts in newspapers, but understanding a little about what money is and how it's valued can help make sense of financial transactions.

The handiest definition of money I've seen is in Martin Mayer's book, The Bankers: The Next Generation: "Money... is a medium of exchange, a unit of account, and a store of value." (These are old definitions but Mayer's book is where I found them.) This definition stopped me from thinking of money as something static, which makes it very hard to understand the time value of money. The reason money works so well as a store of value and medium of exchange is that it moves with the tides.

This flexibility brings us to the time value of money concept, one of the most important ideas in finance. All it means is that cash received at different times has different values. A dollar today is worth more than the same dollar tomorrow. How come? Today that dollar is yours to spend on something fun, or to invest at a good rate of return. Money represents opportunity.

Let's start with compounding, one side of the time-value coin. Compounding helps us understand the value of future cash flows. Say you're at a restaurant and about to plunk down $20 for a steak. There are two ways to think about this money -- its present value or its future value. Suppose instead of buying a steak you invest that $20 in an index fund that over the next 20 years grows an average of 11% annually. You just turned that steak into $161.25. There are plenty of institutions that will pay you an attractive interest rate for the use of your money, so learn to be your own money boss.

We hear a lot about compounding, but there's another side of the time-value coin: discounting. This is the process used to find the present value of a future stream of cash flows. It's the reverse of compounding.

Let's go back to the steak example. Say you're in a different kind of restaurant. In this case, you're the holder of a security -- a certificate of deposit, for example -- that will pay you $150 at the end of three years. It's a safe investment that pays 5% interest over three years. As long as you hold the security until maturity, the money is yours.  

But this is a different kind of restaurant. Here, you're going to get an offer for that security. How much would the waiter have to pay you in dollars today -- or in steak --  to talk you out of holding that investment? Remember, money today is more valuable than the same amount of money tomorrow, so we know the waiter will offer less than $150. Without an understanding of discounting you're up a creek on this kind of problem.

Fortunately, we have financial calculators that can crunch the numbers for you and keep you from scribbling on the tablecloth to get the right answer. In this case, if the waiter offered $129.58, you should be indifferent between holding the security and selling it. That's what I meant above when I said cash received at different times has different values. With this investment, $129.58 today is the same as $150 in three years (assuming you're happy with a 5% rate of return.) If the waiter offers more than $129.58 you should take it since you could invest it in the same security and end up with more than $150. If he offers less, go to a different restaurant.

Okay, I don't go to a lot of restaurants where waiters try to buy securities. But discounting is used all the time by investors trying to determine how much a given stock is worth, and businesses use it to value companies when considering mergers and acquisitions. Remember a stock is worth the sum of its future cash flows discounted back to present value at a certain rate for risk. Again, it's just like compounding except we're working in reverse.

Let's look at PepsiCo's (NYSE: PEP) acquisition of Quaker Oats (NYSE: OAT). Pepsi agreed to pay $13.4 billion, which comes out to roughly $12.8 billion in stock and $750 million in assumed debt. To arrive at this number Pepsi had to estimate how much cash Quaker is likely to generate in the future and how much it's worth in today's dollars. The discounting process is more complicated in this example since no one really knows how much cash Quaker will generate in the future and Pepsi has to pay a premium for Quaker's brand, but the concept is the same.

With an understanding of discounting (and a handy spreadsheet) we can plug in a few numbers to get an idea what kind of growth Pepsi is expecting. Considering that Quaker generated about $250 million in free cash flow over the last 12 months, Pepsi is expecting those cash flows to grow an average of about 10% annually over the next 10 years if those cash flows are discounted at an 8% rate. In my book that's perhaps aggressive considering Gatorade -- which is owned by Quaker, and coveted by Pepsi -- is really a niche product and Quaker is a food company. Pepsi wouldn't agree with this reasoning, of course, and clearly believes the two companies will be more valuable together than apart.

Also, many people would argue the cash flows should be discounted at a higher rate, or a lower rate depending on how they view the company. There's no precise answer. But an understanding of discounting and compounding -- two sides of the same time-value-of-money coin -- can help give investors an idea of what companies and the market are expecting.

Have a great day.