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September 16, 2008

Chandan Sengupta**Physician's Money Digest**, July15 2004, Volume 11, Issue 13

Chandan Sengupta

Opinions vary, so it's generally risky to callanything "the most important." But it's relativelysafe to call "time value of money"the most important concept in modernfinancial theory. In one way or another, it becomes thebasis for most other important financial theories andconcepts. We invoke it, knowingly or otherwise, inmaking almost all financial decisions such as choosinga mortgage or estimating a stock or bond'sworth. Fortunately for busy physician-investors,it's a simple concept, althoughapplying it in practice can be very difficult. Firstthing's first; let's go over what the concept involves.

**Overall Concept**

The time value of money concept says that a dollaryou will get in the future is worth less than a dollartoday, or equivalently, a dollar today is worthmore than a dollar in the future. It's easier to understandwhy the second is true, and if so, then the firsthas to be true as well.

The point:

A dollar today is worth more because you caninvest it and expect to have more than a dollar in thefuture. Note that I said, "expect to have," becausedepending on what you invest it in (eg, stocks), youmay end up having less than the dollar in the future. A rational person will only invest that dollarin something that is expected to provide a positivereturn. Therefore, to all of us, a dollar today is worthmore than a dollar in the future.

Consider a simple example, which will also lead toa few more important related concepts. Suppose youhave $100 today and you invest it in a bank CD for 1year at an interest rate of 4%. A year from now, youwill have $104. That $104 is called the future value oftoday's $100 a year from now.

We can invert this example and also say that $104a year from now is worth only $100 today. In thiscontext, the $100 today is called the present value of$104 a year from now. The process of getting to thefuture value of $104 from the $100 today by incorporatingthe investment return is called "compounding."The reverse process of calculating how much$104 a year from now is worth today is called"discounting." The 4% rate of return iscalled the discount rate.

Another related financial concept is cash flow. Itmeans just what it sounds like—the in- or outflow ofmoney. Generally, money coming to you is called"positive cash flow" and money that you pay out iscalled "negative cash flow."

**Two Key Factors**

To calculate the present or future value of cashflow, you need to know two things in addition to theamount of the cash flow. The first is its timing (ie,when we will receive or pay out the money), and thesecond is the appropriate discount rate.

The timing issue is simpler, although not entirelysimple. If you definitely know when a cash flow of aspecific amount will take place, then it's easy. Butwhat if you don't know that for sure? If you invest insomething that you expect will generate cash flows foryou in the future (eg, dividends on a stock) but youdon't know for sure when and how much, you willhave to estimate them.

The discount rate you have to use for compoundingor discounting is often very difficult to estimatebecause it will depend on the timing and the risk of acash flow you want to discount. Here's why:

When you invest in that 1-year CD at a 4% interestrate, the discount rate is 4%. If instead you investin a stock with an expected 1-year return of 10%, thenthe appropriate discount rate is 10%. The expectedreturn on the stocks is higher because, as risk-averseinvestors, we demand a higher expected return to takea higher risk. But it's difficult to decide how muchhigher the expected return on a risky investment willhave to be relative to that of a safe investment.

The implication of the different possible discountrates is that $100 today doesn't have the same futurevalue for everyone, or even for you under differentcircumstances. It depends on the risk you decide totake with the money. Similarly, all $100 cash flowsyou expect to receive in the future don't have the samepresent value. The appropriate discount rates, andtherefore, the present values, depend on the risks ofthe different cash flows.

Now you can see why these concepts are so important.The value of any investment (eg, a stock) canonly be equal to the sum of the present values of all itsexpected future cash flows—primarily dividends. Thisis the fundamental method for valuing any investment,although applying it is far from easy.

**Chandan Sengupta,** author of The Only ProvenRoad to Investment Success (John Wiley; 2001)and Financial Modeling Using Excel and VBA(John Wiley; 2004), currently teaches finance atthe Fordham University Graduate School ofBusiness and consults with individuals on financialplanning and investment management. He welcomesquestions or comments at chandansen@aol.com.

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